New Wave Maths - Teachers Guides: Level A - Ages 5-6

RIC–1084 11.7/586

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New Wave Maths Teachers Guide – A Published by R.I.C Publications® PO Box 332, Greenwood Western Australia 6924

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Robert Dayman 2003

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RIC-1084 ISBN 978-1-86311-705-0 Copyright Notice No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system without written permission from the publisher.

Foreword The New Wave Maths Teachers Guide has been written to both supplement and support the New Wave Maths Workbook series based on the Western Australian Mathematics Student Outcome Statements.The New Wave Maths Teachers Guide provides a summary of three documents that are at the forefront of mathematical teaching and learning:

• Curriculum Frameworks;

• Student Outcome Statements; and

• National Outcome Statements.

Between the New Wave Maths Teachers Guide and the New Wave Maths Workbook, there is a comprehensive coverage of activities to assist the development of the students' mathematical concepts. However, student progress is very much in the hands of the teacher, his or her style of teaching and the provision made for each individual to ensure complete mastery of concepts is gained.

r o e t s Bo r e p ok u S This series caters for:

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Assessment followed in this series is consistent with the approach outlined within the appropriate section in the Curriculum Framework document.

• sharing ideas through discussion;

• school–home partnerships through parent information sheets;

• mixed ability groups through the use of challenge activities; and

• the use of concrete materials where required by teachers and students.

R.I.C. Publications has a recommended range of blackline masters that, together with New Wave Maths, will ensure a thorough coverage of the mathematics outcomes and further develop the students' mathematical competency at this level.

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The author and publisher wish to acknowledge the Education Department of Western Australia for its permission to reproduce selected information contained within this document.

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References Learning Mathematics Handbook: Pre-primary to Stage Seven Mathematics Syllabus, Curriculum Programs Branch, Ministry of Education, Perth, WA – 1989 Learning Mathematics Pre-Primary to Stage Seven, Curriculum Programs Branch, Ministry of Education, Perth, WA – 1989 Curriculum Framework, Curriculum Council of Western Australia, Perth, WA – 1998 A National Statement in Mathematics for Australian Schools, The Australian Education Council and Curriculum Corporation, Australian Education Council, Carlton, Vic. – 1991 Mathematics – Student Outcome Statements, Education Department of Western Australia, 1998

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New Wave Maths Book A – Teachers Guide • i •

Contents Introduction..........................................................................................................................................................1 Appreciating Mathematics............................................................................................................................2 Learning Environment.....................................................................................................................................3 Language and Mathematics..........................................................................................................................4 Mixed Abilities.....................................................................................................................................................4 General Content Outline.................................................................................................................... 5 – 9 Technology......................................................................................................................................................... 10 Assessment........................................................................................................................................................ 11 Cross-curriculum Linkages........................................................................................................................ 12 How to Use the Teachers Notes.......................................................................................................... 14 Materials List...................................................................................................................................................... 15 Overview of Activities Term One—Units 1 – 10..................................................................................................................... 16 Term Two—Units 11 – 20................................................................................................................... 17 Term Three—Units 21 – 30................................................................................................................ 18 Term Four—Units 31 – 40.................................................................................................................. 19 Lesson Notes­, Consolidation and Answers Term One—Units 1 – 10..........................................................................................................20 – 59 Term Two—Units 11 – 20........................................................................................................60 – 99 Term Three—Units 21 – 30...............................................................................................100 – 139 Term Four—Units 31 – 40.................................................................................................140 – 179

r o e t s Bo r e p ok u S Additional Activities

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Teachers Notes and Answers

Space Activities...............................................................................................................................182 – 183 Measurement Activities............................................................................................................................ 184 Number Activities....................................................................................................................................... 185

Assessment

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Grid Paper.........................................................................................................................................196 – 199 Number Charts and Cards......................................................................................................200 – 204 Spinners..............................................................................................................................................205 – 206 2-D Shapes........................................................................................................................................207 – 209 Classification Chart.................................................................................................................................... 210 Sorting Circles.................................................................................................................................211 – 212 Sorting Activity – Zoo.............................................................................................................................. 213 Sorting Activity – Farm............................................................................................................................. 214 Attribute Labels..............................................................................................................................215 – 217 Venn Diagram..........................................................................................................................................................................218 Carroll Diagram.....................................................................................................................................................................219 Line or Bar Graph....................................................................................................................................... 220 Picture Talk....................................................................................................................................................... 221 Coins................................................................................................................................................................... 222 Clocks – Blank................................................................................................................................................ 223 School Map..................................................................................................................................................... 224

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Reference to Student Outcomes....................................................................................................... 188 Record Sheets – Blank.................................................................................................................189 – 193 Proforma – Blank.......................................................................................................................................... 194

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Expectations of Knowledge of Basic Facts.................................................................................... 226 Primary School Mathematics................................................................................................................ 227 Developing Mathematical Awareness.............................................................................................. 228 Concrete to Mental................................................................................................................................... 229 Mathematical Learning Areas................................................................................................................ 230.

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Introduction Mathematics provides methods of representing patterns, relationships and logic and developing mathematical knowledge. Students should be encouraged to speculate, observe and investigate, to explore and solve problems in mathematics in real-life situations.

Mathematics is important to people in providing tools which can be used at the personal, civic and vocational level. A National Statement on Mathematics for Australian Schools, 1990 (pages 11 – 14) lists the following goals for school mathematics: 1. Students should develop confidence and competence in dealing with commonly occurring situations.

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2. Students should develop positive attitudes towards their involvement in mathematics.

3. Students should develop their capacity to use mathematics in solving problems individually and collaboratively.

5. Students should learn techniques and tools which reflect modern mathematics.

6. Students should exercise the processes through which mathematics develops.

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4. Students should learn to communicate mathematically.

A National Statement in Mathematics for Australian Schools, 1990 (page 15) continues in goal identification by determining that, as a result of learning mathematics in school, all students should: 1. realise that mathematics is relevant to them personally and to their community; 2. gain pleasure from mathematics and appreciate its fascination and power; 3. realise that mathematics is an activity requiring the observation, representation and application of patterns;

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(a) conduct everyday affairs such as money exchanges, planning and organising events, and measuring;

(b) make individual and collaborative decisions at the personal, civic and vocational levels; and

(c) engage in the mathematical study needed for fur ther education and employment.

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4. acquire the mathematical knowledge, ways of thinking and confidence to use mathematics to:

5. develop skills in presenting and interpreting mathematical arguments; 6. possess sufficient command of mathematical expressions, representations and technology to:

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(a) interpret information (for example, from a court case or media report) in which mathematics is used;

(b) continue to learn mathematics independently and collaboratively; and

(c) communicate mathematically to a range of audiences.

7. appreciate:

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(a) that mathematics is a dynamic field with its roots in many cultures; and

(b) its relationship to social and technological changes.

New Wave Maths Book A – Teachers Guide • 1 •

Appreciating Mathematics The following attitudes are seen as fundamental to the acquisition of processes and content and should be the focus of mathematical development. The attitudes are listed in Learning Mathematics Pre-Primary to Stage Seven Mathematics Syllabus Handbook (pages 6 – 7) as: 1. an awareness of the relevance of mathematics to life; 2. an ability to enjoy mathematical games and pursuits; 3. having pride in their skills and abilities; 4. being confident of their ability to experiment and solve problems; and 5. a willingness to express ideas and hypotheses.

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1. Show a disposition to use mathematics to assist with understanding new situations, solving problems and making decisions, showing initiative, flexibility and persistence when working mathematically and a positive attitude to their own continued involvement in learning and doing mathematics.

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These are summarised as part of the Appreciating Mathematics substrand found in The Curriculum Framework 1998 (page 180):

The development of positive attitudes towards mathematics is an important goal. This may be done by: 1. providing mathematical experiences relevant to the students' world;

2. providing students with mathematical opportunities to gain personal enjoyment and satisfaction; 3. providing activities which construct conceptual understanding through manipulation of materials and time to reflect on the activities;

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5. providing mathematical activities which are appropriate to the students' levels of development; 6. recognising that students require differing amounts of time to complete tasks as they explore problems and ideas in a variety of ways; 7. assessment that reflects the teaching methods used; and

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8. modelling positive attitudes towards mathematics.

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Learning Environment Much has been learnt about how students learn mathematics and the classroom conditions required to support that learning.

The teaching of mathematics requires a suppor tive, stimulating, varied and rich mathematical learning environment that reflects the diversity of Australian society.There should be a wide range of resources that includes collected and commercial products.

The classroom learning environment should encourage practical activity, the use of appropriate technology and discussion. Mathematics lessons should extend beyond a ‘chalk and talk’ or ‘textbook, pencil and paper’ subject.

The Curriculum Framework, 1998 (pages 206 – 209) highlights the following perspectives on learning mathematics:

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• Opportunity to learn

Learning experiences should enable students to engage with, observe and practise the actual ideas, processes, products and values which are expected of them.

• Connection and challenge

Learning experiences should connect with students' existing knowledge, skills and values while extending and challenging their current ways of thinking and acting.

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• Action and reflection

Learning experiences should be meaningful and encourage both action and reflection on the part of the learner.

• Motivation and purpose

Learning experiences should be motivating and their purpose clear to the student.

• Inclusivity and difference

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Learning experiences should respect and accommodate differences between learners.

• Independence and collaboration

Learning experiences should encourage students to learn both from, and with, others as well as independently.

The school and classroom setting should be safe and conducive to effective learning.

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• Supportive environment

These perspectives have several implications for teaching. They are listed as:

• a supportive environment for learning;

• appropriate mathematical challenge is provided; and

• fostering processes which enhance learning.

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The teaching of mathematics is not definitive in approach or style but rather is influenced by the mathematical concept being taught, and the abilities, experiences and attitudes of the students. Enhanced mathematical learning is likely to occur when activities are provided which build upon and respect students’ experiences, and which the learner regards as purposeful and interesting. Feedback is critical to enhanced learning. Students need to believe that mathematics makes sense; therefore, clear and logical feedback on errors or inconsistencies is required.

Students should be encouraged to take risks in a challenging environment to extend their knowledge. Challenges need to be achievable as success is critical in building positive attitudes towards mathematics. Success on easy or rote tasks does not enhance mathematical learning.

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New Wave Maths Book A – Teachers Guide • 3 •

Language and Mathematics Developing appropriate language is important to the growth of a student’s conceptual understanding. Teachers need to be aware of the natural language used by students and respond appropriately to it. To assist in developing an understanding of mathematical ideas, students need to represent their knowledge in spoken and written words, with concrete material and with pictures, diagrams and graphs, and symbols.

The use and development of appropriate language should also enhance mathematical learning. The use of appropriate language helps in working through and clarifying ideas.

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Mathematical ideas are more likely to be developed when they are clearly labelled when discussed by students. Regular, clear and explicit use of mathematical expressions by the teacher is essential. Students should be encouraged to develop their knowledge and understanding of mathematical expressions by being encouraged to describe orally or in writing the situations in which they are involved.

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Teachers need to be aware of the individual differences of all students and provide learning experiences which develop a level of success and independence for each student.

To do this, teachers plan lessons that build on current knowledge and allow progress and success at the students' own rate. New concepts should be introduced in simple form leading to the complex by using concrete materials and relevant examples. Where possible, use group work to allow for content language and ability differences. Keep parents well informed of their child’s progress and work with them to aid students in reaching their potential. Above all, provide a positive, receptive learning environment, acknowledging various differences.

Students with special needs can be catered for by ensuring that fundamental concepts are understood before proceeding with dependent concepts. The identification of the initial point of difficulty must be made and the concept then developed from this stage. Instructions need to be given slowly, simply and clearly and then checked for understanding.

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New Wave Maths allows individuals to achieve at their own rate by providing a number of similar activities. The series may also be used at differing stages of students' development so the workbook chosen is level-appropriate rather than Year-level specific, because each book is sequentially developmental with both the previous and following book.

By allowing students to work to their capacity on activities, teachers are also able to provide the learning opportunities for individual students to perform at their optimum level.

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General Content Outline Goals and Guidelines Students learn at different rates and in different ways and bring to school a diverse range of attitudes and experiences from living within different cultural and geographic settings. Because of this we require uncommon curricula to achieve common outcomes.

Young students develop strong mathematical values if activities reflect the mathematics inherent in home activities. Activities should use a wide variety of materials and be presented in a problem-solving format that has meaning to the child.

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The student relies on visual perceptions of concrete materials and needs to manipulate these materials extensively to begin developing concepts. Conservation of number and measurement is not yet developed. However, some awareness of size, shape, position and movement has developed.

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Mathematical thinking will reflect, in most instances, the students' family as this is the centre of their personal world. Many cultural beliefs will reinforce the values shown by students at this age. Strengths in spatial knowledge and number should be utilised as starting points for the development of mathematical ideas.

In all activities the development of mathematical language should be a key focus.

Students should be encouraged to question mathematical aspects of their world and seek to answer such questions themselves, or in collaboration with their peers.

Students should be encouraged to persist with problems and ask questions. They are also more able to think of concepts as mathematical objects in their own right. With teaching emphasising the investigation of mathematical ideas and relationships, students should also be learning to make speculations and to test them.

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The teaching of processes is necessary to develop independent problem-solvers.

Therefore, for students to acquire concepts, skills and factual knowledge, opportunities need to be provided in settings that foster positive attitudes to mathematics. The Curriculum Programs Branch, Ministr y of Education, 1989, publication Learning Mathematics: Pre-Primary to Stage Seven Mathematics Syllabus Handbook (page 4) lists the following processes as part of the learning of mathematics. These processes are not tied to one particular aspect of content but are used across a range of areas: 1. comprehension of mathematical information given in oral and/or written forms; 2. selection of appropriate strategies; 3. purposeful use of materials;

4. selection of appropriate operations to solve problems;

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6. expression of mathematical ideas in words, pictures and symbols; 7. construction of lists, tables and graphs;

8. estimation of number and measurement activities; 9. identification of patterns and relationships; 10. classification, ordering and comparing;

11. analysis and interpretation of information; 12. formulation of hypotheses; and 13. justification of conclusions and inferences.

Understanding, skills and knowledge relationships make up the content that builds up conceptual structures.

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New Wave Maths Book A – Teachers Guide • 5 •

In the New Wave Maths series the following areas of mathematical content are included:

1. Working Mathematically – develops mathematical thinking processes through conceptualising, investigating, applying and verifying and reasoning mathematically.

2. Space – describes and analyses the features of objects, environments and movements through location, shape, transformations and geometric reasoning.

3. Measurement – using direct and indirect measurement and estimation skills in length, area, mass, volume and capacity and time.

4. Chance and Data – using knowledge of chance and data processes to collect and organise data, summarise and represent data, interpret data and understand chance.

5. Number – using operations, number concepts and relationships in the number system to calculate, reason about number patterns and understand numbers and operations.

r o e t s Bo r e p ok u S Appreciating Mathematics

Students appreciate mathematics through using it to assist with understanding new situations, solving problems and decision making, and show a positive attitude in learning and doing mathematics. They should also recognise mathematical origins from a range of cultures, its significance in reflecting social and historical contents and understand its significance in explaining and influencing aspects of our lives.

Working Mathematically

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The Curriculum Framework, 1998 (pages 183 – 193) identifies seven clusters of outcomes, some of these being:

Students should not wait to be told but rather be actively involved in calling on a range of problem-solving techniques, personal and collaborative management strategies and appropriate technology to find solutions to practical problems. To do this students need to choose mathematical ideas and tools to fit the constraints of a practical situation.

They need to interpret and make sense of the results within the content then evaluate the work done to determine the appropriateness of the methods used. Much of the work done will involve investigation, generalisation and reasoning about patterns in number, space and data and justification of conclusions reached.

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Problems in the New Wave Maths series relate to the students' immediate physical and social world. Problems are aimed at attracting and involving children so they develop an ownership over them and their solutions. Children should be encouraged to persist with problems and checking their mathematical work. Children are encouraged to make speculations and test them under a range of circumstances.

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The classroom teacher has an important role in the development of processes used in problem-solving. Through guidance, discussion and experimentation, students are able to adopt different strategies to solve problems and appreciate that there is more than one approach to a solution. The following broad strategies may be of assistance in helping students solve non-routine problems: 1. Understand the problem – rewording, breaking into smaller parts may assist.

2. Prepare a plan to solve the problem – working from the known to the unknown, draw diagrams, tables, charts to assist.

3. Carry out the plan – using different strategies as appropriate.

4. Review final solution to check and discuss its reliability and validity.

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By asking questions of the student, providing hints (without providing answers), having students suggest strategies, guiding discussion and comparison of strategies used and providing extension to the original problem, the teacher helps the students develop processes which allow generalisation to a variety of other situations. It is the teacher’s responsibility to provide experiences which contribute to the construction of each student’s mathematical understanding. Each student is an individual with different experiences and knowledge. The teacher should recognise that because of this the student may interpret the teaching in a different way.

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Students move through a number of phases as they develop understanding. Students manipulate the materials and work through activities guided by open-ended questioning and discussion. The activities are explored by the students using the processes as listed in Learning Mathematics Pre-Primary to Stage Seven Mathematics Syllabus Handbook, 1989 (pages 16 – 18): 1. observing and identifying; 2. comparing, ordering and classifying; 3. making patterns and arrangements;

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In accepting the individuality of each student, teachers should also accept that students will interpret teaching in different ways and need new content to be presented by easily understood, believable methods and for that content to be seen as more useful than knowledge already held. Knowledge that students already hold is important to later learning and should be used as the basis for subsequent teaching through learning activities which are relevant to the students' environment. Encouragement of discussion within the class allows for reflection on experiences and understanding. Where students lack the skills required to complete a task satisfactorily, more effective alternative methods that nurture their understanding need to be used.

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5. estimating and measuring; ir workings by: 1. discussing findings and interpretations; 2. identifying patterns and relationships; 3. using symbols and words;

4. drawing pictures, diagrams and graphs; 6. translating between relationships;

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7. making lists and tables; 8. drawing conclusions; 9. interpreting results; and

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5. constructing models;

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10. communicating findings.

Then follows a period of consolidation of understanding through further activities that embody the mathematical idea. Students should apply and extend their understanding through work in familiar, and then more novel, contexts.

New Wave Maths Book A – Teachers Guide • 7 •

Number Students should be able to count in one-to-one correspondence situations, develop cardinal and ordinal concepts to 10, as well as be able to combine and separate small sets of objects in informal settings.

The New Wave Maths series focuses heavily on these activities and on developing the use of number sequence to determine the number of items in the set. There are also extensive activities requiring the combinations and partitioning of numbers to assist the development of the value of a number as a composition of other numbers.

Students at this stage need a lot of varied experiences using concrete materials involving estimating, counting, ordering, classifying, sorting and comparing. By the end of Year 1, students should be able to use verbal, pictorial and symbolic representation of number to 10.

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Recommended Progression for Algorithms

• Use concrete materials to manipulate and arrange objects with either oral or written answer in addition and subtraction.

• Counting equivalent sets by two, threes, fours and fives up to 20.

• Sharing objects in practical situations.

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Year 1

Year 2

• Using basic facts to 9 + 9 = 18 and adding three numbers each less than 6. It is recommended that concrete materials are used.

• Symbol 'x' is introduced to assist with grouping. Use of language to support activities – 'lots of', 'sets of' or 'groups of' to 20 or 30.

• Division experience is through sorting, sharing and grouping activities using concrete materials.

• Introduction to open number sentences. For example:

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3+2=

4–1=

3 lots of 4 =

Measurement

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Initially, students will make judgments of more or less, bigger or smaller, equal to or not equal to when applying measurement to objects. Students will need to be guided to an awareness of the attributes of length, area, mass, capacity and time in order to make appropriate comparisons. A wide and continuous range of activities is an integral component of the program.

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Development of the language of mathematics will take time but is an essential part of the learning process. Language is developed as part of the direct comparison of objects.

Encouragement in estimation and checking will assist in developing children's preparedness to make educated guesses and develop the habit of checking for accuracy.

Chance and Data

Students will be involved in investigations that develop the use and understanding of the language of chance and, from this, make a statement about the likelihood that an event will occur.

A range of activities in classifying objects will help develop classification skills. Results may be represented in graph form – concrete or pictorial. Comparisons of records may then be made.

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Space

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Space activities should relate to the students' environment and the objects within it.

Making models of familiar parts of the environment using a variety of objects helps in developing spatial awareness and recognising the interrelation between component parts. Movement of components or parts thereof develops a knowledge of the understanding of transformation.

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New Wave Maths Book A – Teachers Guide • 9 •

Technology Calculators are an important technological resource in the teaching and learning of mathematics. The calculator should be used as both an instructional aid and as a computational tool.

With the advent of cheaper and more sophisticated calculators there comes a natural de-emphasis on written calculations. There is, as a consequence, a reduction in the complexity of written computation work but a clear emphasis on the use of concrete material to improve understanding of concepts to be developed through the New Wave Maths series. Greater emphasis is placed on quick and accurate mental computation. Students' expected level of written computational skill is to a two-digit by two-digit multiplication, addition or subtraction sum, and a single divisor into a two-digit number for division.

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Mental calculations and calculator use need to be developed as these form the basis of most computational needs of adults in real-life situations. It is strongly recommended that all students use calculators at all Year levels (K–12). The Learning Mathematics Handbook Pre-Primary to Stage Seven Mathematics Syllabus, 1989 (pages 30 – 31) details where calculators can be used as an instructional aid to:

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An emphasis on knowledge of basic addition and multiplication facts and relationships, place value understanding, estimation, checking of results and confidence in applying appropriate calculations is essential.

• assist in the development of mathematical content and processes; for example, place value, multiplication as repeated addition and the learning of basic facts;

• provide immediate feedback on a student’s own calculation so errors and misunderstandings can be remedied; and

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• improve attitudes towards mathematics through its effective use.

As a computational aid, the calculator can:

• enable attention to focus on mathematical processes by allowing calculations to be done swiftly and accurately by all children; for example, in problem-solving or investigative activities;

• enable rules or patterns to be discovered and investigated, by generating many examples in a short time;

• encourage students to employ a wider range of strategies to solve problems; and

• allow students to use data drawn from real life, rather than artificial numbers chosen to make the computation easier; for example, in exploring distances or costs of shopping.

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Computers also have their place in the mathematical learning environment and should be accorded appropriate time. Computers may be used for ‘number crunching’ and data analysis; as a simulation device; for graphics and symbol manipulation; and for running spreadsheets.

Teachers need to select software which is sufficiently flexible and open-ended to allow children to develop their own ideas and use their initiative.

The computer can be used in problem-solving, investigations, modelling, strategy games, refining ideas, concept development, skill development and gaining factual knowledge.

There is still a place for textbooks in the teaching and learning of mathematics. However, emphasis must be placed on the need to use a variety of print materials. No single text is likely to cater for the interests of all students or cover the mathematics curriculum in full. The New Wave Maths series provides a solid foundation and allows teachers the opportunity to add their own ideas and activities to suit their individual class and students.

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Assessment Assessment is a critical component of the teaching program and is outlined in The Curriculum Framework, 1998 (pages 210 – 212) by these points:

• Valid

Assessment should provide valid information on the actual ideas, processes, products and values which are expected of students.

• Educative

Assessment should make a positive contribution to students' learning.

• Explicit

Assessment criteria should be explicit so that the basis for judgments is clear and public.

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• Fair

Assessment should be demonstrably fair to all students and not discriminate on grounds that are irrelevant to the achievement of the outcome.

• Comprehensive

Judgments on student progress should be based on multiple kinds and sources of evidence.

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Assessment is a crucial aspect of the mathematics learning process. Assessment provides feedback on individual development to the student, teachers and parents. It provides the information for future teaching. All the outcomes of the school mathematics curriculum should be reflected in the assessment process. All assessments should be demonstrably fair, valid and reliable.

The fairness of mathematical testing is brought into question by the practice of using one form of test only. Individual students respond to different environments in different ways; therefore the use of a single assessment tool, such as a pencil and paper test, may be valid and reliable but not fair, as the individual may respond better to short-answer questions, extended response questions or other forms of assessment. Hence, using nonrepresentative sampling of the mathematics curriculum outcomes or narrow sampling methods of assessment may be unfair to many students.

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It is clearly understood now that conventional forms of tests (pencil and paper) cannot address all areas of the mathematics curriculum; therefore, additional, not alternative, methods of assessment must be developed. Such methods include: teacher observation and questioning; structured interviews with students; paper and pencil tests; oral tests; practical skill tests; work- or project-based assessment; collected samples of students’ independent work; individual homework assignments; group reports; anecdotal records; self-assessment; and peer assessment.

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It is recommended that students' mathematics be assessed using the Student Outcome Statements. Commercially prepared assessment packages are available from R.I.C. Publications as follows: Maths Assessment Level 1 (RIC-0028) Maths Assessment Level 2 (RIC-0029) Maths Assessment Level 3 (RIC-0030) Maths Assessment Level 4 (RIC-0087) Where possible, links to these pages have been included in the teachers notes, pages 20 – 179.

New Wave Maths is not a stand-alone assessment document. Activities may be assessed based on Student Outcome Statements. Teachers will need to be familiar with these to make the appropriate assessments. All activities may be assessed in this way. It is suggested that a random sample of activities only is assessed using Student Outcome Statements to determine progress.

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New Wave Maths Book A – Teachers Guide • 11 •

Cross-curriculum Linkages The learning and application of mathematics occurs across all curriculum areas. Literacy skills are developed in the English learning area where language foundations are provided that are essential for the learning of mathematics. Mathematics also provides for the development of language skills.Together, English and mathematics provide the information skills used in activities such as reading the newspaper, information text such as a telephone directory, and preparing and presenting reports.

Spatial and measurement tasks are interwoven in many art activities which may in themselves provide alternative stimulus for the learning of mathematical skills.

Data collection and interpretation skills as well as measuring activities are a part of both The Society and Environment and Health and Physical Education areas.

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Science provides for a variety of measurement activities with particular emphasis on the measurement component.

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Design activities and spatial knowledge development are a practical component of the Technology and Enterprise learning area. Activities in this learning area provide a wider diversity of learning opportunities than those provided from the basic mathematics syllabus.

The cultural significance of mathematics, its origins and different developments may be explored in the Languages Other than English and Society and Environment learning areas.

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• 12 • New Wave Maths Book A – Teachers Guide

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Teachers Notes and Answers

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How to Use the Teachers Notes.......................................................................................................... 14 Materials List...................................................................................................................................................... 15 Overview of Activities

Term One—Units 1 – 10.......................................................................................................................... 16 Term Two—Units 11 – 20......................................................................................................................... 17 Term Three—Units 21 – 30..................................................................................................................... 18 Term Four—Units 31 – 40....................................................................................................................... 19 Lesson Notes­, Consolidation and Answers Term One—Units 1 – 10...............................................................................................................20 – 59 Term Two—Units 11 – 20..............................................................................................................60 – 99 Term Three—Units 21 – 30....................................................................................................100 – 139 Term Four—Units 31 – 40......................................................................................................140 – 179

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New Wave Maths Book A – Teachers Guide • 13 •

How to Use the Teachers Notes Indicators from the Student Outcome Statements have been included as a quick guide.

These are directly related to the main activity only.

Unit and student page shown here as a quick reference to the equivalent page in the student workbook.

Resources have been listed to aid organisation before the lesson.

Outcomes relevant to all activities on the student workbook page have been listed as a ready reference.

A space for you to record notes relevant to the lesson has been provided. This space could be used for any purpose. Some suggestions: • record any improvements you made to the lesson; • record any problems you or your students experienced during the lesson; • record individual student's progress or development; • add any ideas for extension or remediation of the lesson; or • include any interesting facts or ideas you came across which were relevant to the lesson.

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Skills relevant to the main activity have been listed.

Language terms relevant to the workbook page have been listed here. It is preferred these words be introduced before beginning the activity to ensure students have a clear understanding of the terminology used in the activities.

The great thing is that once this information is recorded, when you come to teach the lesson again, these notes will refresh your memory and enhance the smooth running of the lesson.

The student workbook page is broken into distinct sections. These are each discussed in detail in this section of the teachers notes.

The section is stated, followed by the relevant outcome in brackets. Then bullet points are used to guide you through the activity.

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This section is a guide only and you are more than welcome to take from it what you choose, modify it or add your own touches.

Answers have been provided to assist teachers in marking students' work. Some answers do require a teacher check as they are dependent on the classroom environment and the students in your class. Where possible, all answers are given.

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Where possible, links to a relevant assessment activity in the R.I.C. Publications Maths Assessment Level 1 document have been provided. Note: Page numbers will vary according to the edition.

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Suggested activities for consolidation of the main activity on the workbook page have been provided as a guide only. Feel free to use, modify, extend or disregard these as you feel necessary.

• 14 • New Wave Maths Book A – Teachers Guide

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Materials List The following list of suggested materials is a guide only. It is not suggested that they must be purchased or are the only items that may be used. If compiling a set of materials that will both supplement and compliment the teaching program, the following items will assist. Some items are required to complete the workbook activities. These are listed in more detail on the relevant page in the teachers notes.

• Denotes items produced in New Wave Maths Teachers Guide as a blackline master which are available on pages 196 to 224. Teachers may photocopy and use them with their class(es). adhesive tape

environment

overhead transparencies

analog clock/watch

fabrics

paper – coloured and plain – A4

attribute blocks

felt-tip pens

balance

and A3

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paper strips

fraction cake

pattern blocks

fraction chart

pegboards

fraction grid

pipe-cleaners

fruit

plastic animals

geoboards

plastic polygons

blocks

geometric blocks

playground

boxes – various shapes and sizes

grain

polystyrene

building blocks

glue

popsticks

butcher paper

heavy card – coloured or plain – A4

sand

balls – assorted Base 10 MAB beads

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bead frame

blackboard ruler

buttons

and A3

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fishing line

school buildings and grounds

calculator

hoops

school map • page 224

cardboard strips

interlocking cubes

scissors

cardboard tubes

jigsaw puzzles

shapes – 2-D

centicubes

kaleidoscope

shapes – 3-D

classmates

lead pencil

small squares

classroom

lids

Smarties™ or similar

light card – coloured and plain – A4

spinners • pages 205 and 206

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classroom furniture clocks • page 223

and A3

student stationery

coloured counters

magazines

streamers – paper

coloured pencils

marbles

street directory or town plan

mirror/mira

string

modelling clay

tape measure

money (coins/notes)

tiles

newspapers

washers

number strips • pages 201 – 202

water

number chart 1 – 100 • page 203

wool

number chart 0 – 99 • page 204

1-cm cubes

dice – six-sided

number cards • page 200

1-cm dot grid paper • page 198

digital clock/watch

objects for counting activities

1-cm grid paper • page 196

dominoes

objects for measuring activities

1-cm triangle grid paper • page 199

duster

objects for weighing activities

2-cm cubes

eggtimer

overhead pens

2-cm grid paper • page 197

elastic bands

overhead projector

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local area map

coloured rods

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containers – large and small counting rhymes crayons cutting tools for clay days of the week chart

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clock stamp

straws

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New Wave Maths Book A – Teachers Guide • 15 •

Term One Week Unit

Outcomes

1

S1.1—Follow guidelines to colour scribble patterns.

1

N1.1, S1.1—Identify the ordinal and positional location of pictures in sequence.

2

M1.1—Understand the comparative language of length to identify specific objects.

3

2

N1.1—Identify the ordinal position of objects. Recognise 2-D shapes.

4

C&D1.3—Collect, record and interpret data.

5

N1.1—Identify the order of cardinal numbers.

6

3

S1.1—Follow and choose paths on a given map.

7

N1.1—Identify the order of cardinal numbers.

8

M1.1—Understand the comparative language of length to identify specific objects.

9

4

WM1.2—Work mathematically to compare the mass of different shapes.

10

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2

3

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C&D1.1, C&D1.3—Investigate, record and explain results of chance activities.

N1.1,N1.2—Count and combine collections less than 10.

5

S1.4—Identify 2-D shapes.

5

12

13

N1.1, N1.2—Count and combine collections less than 10.

M1.1, M1.2—Use the comparative language of length and area. Compare the area of two objects.

6

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N1.1, N1.2—Count and combine collections less than 10.

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C.Publ i cat i ons N1.1, N1.2—Count and combine collections less than 10.

S1.4—Identify i •f o2-D rshapes. r ev ew pur posesonl y• C&D1.2, C&D1.3—Record and interpret data.

N1.1, N1.2—Count and combine collections less than 10.

15

16 17 18

19 20

M1.2, C&D1.3—Use informal units to measure the capacity of containers.

Collect, record and analyse data ions less than 10.

21

8

N1.1, N1.2—Count and add on to collections less than 10

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N1.1, N1.2—Recognise and write number names.

N1.1, N1.2—Count and add on to collections less than 10.

9

S1.4,—Identify and match similar 2-D shapes.

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22 23 24 25

N1.1, N1.2—Count and add on to collections less than 10.

26

M1.1, M1.3—Use the comparative language of mass. Use hefting to compare the mass of two objects.

27

10 10

N1.1, N1.2—Count and combine collections of up to 14.

28

C&D1.3, S1.1, S1.4—Find a pathway through a maze. Identify 2-D shapes.

Record data.

29

N1.1, N1.2—Count and sort collections less than 10.

30

• 16 • New Wave Maths Book A – Teachers Guide

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Term Two Outcomes

1 11

S1.2—Draw a picture using 2-D shapes.

31

N1.1, N1.2—Count and take away from collections less than 10.

32

M1.2—Use informal units to measure the length of objects.

33

2 12

N1.1, N1.2—Count and combine collections less than 10.

34

C&D1.3—Sort and record data.

35

N1.1, N1.2—Count and combine collections less than 10.

36

3 13

S1.2—Identify 2-D shapes in a pattern.

37

WM1.1, WM1.2—Work mathematically to discuss shapes used for particular purposes.

38

M1.2, C&D1.3—Use informal units to measure the capacity of containers. Collect, record and analyse data.

39

4 14

N1.1, N1.2—Count and combine collections less than 10.

40

C&D1.3—Interpret information on a graph.

N1.1, N1.2—Count and add on to collections less than 10.

5 15

S1.2—Convey spatial features in drawings.

N1.1, N1.2—Count, add on to and take away from collections less than 10.

44

M1.1, WM1.1—Recognise the hourly time on analog clocks. Relate that time to an activity.

45

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Week Unit

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C.Publ i cat i ons N1.1, N1.2—Count and take away from collections of 10 and less.

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6 16

N1.1, N1.2—Count and take away from collections of 10 and less.

C&D1.3—Interpret information on a graph.

41 42 43

46 47 48 49 50

M2.2, WM1.1—Draw personal activities relevant to each day of the week.

51

8 18

N1.1, N1.2—Count and take away from collections of 10 and less.

C&D1.3—Interpret information on a graph.

N1.1, N1.2—Count and take away from collections of 10 and less.

9 19

S1.4—Identify and match similar 2-D shapes.

N1.1, N1.2—Count and take away from collections of 10 and less.

56

M1.1, M1.2—Use the comparative language of length. Use informal units to measure the length of lines.

57

10 20

N1.1, N1.2—Count and take away from collections of 10 and less.

58

C&D1.2, C&D1.3—Collect, record and interpret data.

59

N1.1, N1.2—Count and add on to collections less than 10.

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N1.1, N1.2—Count and take away from collections of 10 and less.

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New Wave Maths Book A – Teachers Guide • 17 •

Term Three Outcomes

1 21

S1.1—Find a pathway through a maze.

61

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

62

M1.2, WM1.2—Find a solution to compare the area of two objects.

63

2 22

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

64

C&D1.2—Classify objects according to criteria.

65

N.1.1, N1.2—Count and add on to/take away from collections of up to 10.

66

3 23

WM1.2, N1.2—Find a solution to a mathematical problem.

67

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

68

S1.2, S1.3, WM1.2—Manipulate shapes to create new shapes.

69

4 24

N1.1, N1.2—Count and combine collections less than 10.

70

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C&D1.2, WM1.2, N1.1—Count collections. Suggest ways to find a solution to a mathematical problem.

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

5 25

S1.2, S1.4, WM1.1—Identify shapes in the environment.

N1.1, N1.2—Count and combine collections less than 10.

M1.2—Use informal units to measure the length of objects.

6 26

N1.1, N1.2—Count and combine collections less than 10.

C&D1.2, C&D1.3—Count, categorise and order data.

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Week Unit

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WM1.2, WM1.4—Find av solution a mathematical problem. e •f orr e i etow pur p os sonl y•

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79 80

M1.2—Use informal units to measure the length of objects.

81

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WM1.1, WM1.2—Recognise and explain ways numbers are used for particular purposes in real-life situations.

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N1.1, N1.2—Count and group collections less than 10.

82

C&D1.2, C&D1.3—Collect, count and pictorially record data.

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

9 29

S1.1, S1.2—Use the language of position and orientation to draw a specific picture. 85

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

86

M1.2, WM1.2—Estimate then measure the amount of informal units needed to cover shapes.

87

10 30

N1.1, N1.2—Count and group collections up to 10.

88

C&D1.2, C&D1.3—Collect, count and record data.

89

N1.1, N1.2, N1.3—Count and group collections up to 10. Count in a number sequence. 90

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• 18 • New Wave Maths Book A – Teachers Guide

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Term Four Outcomes

1 31

S1.1—Find pathways through a maze.

91

N1.1, N1.2—Count and group collections up to 10.

92

M1.1, M1.2, WM1.1—Draw personal activities relevant during a school day.

93

2 32

N1.3, C&D1.2, C&D1.3—Counting in twos. Collect, count, pictorially record and then interpret data.

94

C&D1.1, C&D1.2, C&D1.3—Investigate and record chance activities with dice.

95

N1.1, N1.2—Count and combine/group collections less than 10.

96

3 33

N1.4, S1.4—Solve pictorial number patterns. Identify 2-D shapes.

97

N1.1, N1.4—Count like denominations of money. Colour and copy pictorial patterns. 98

S1.2, S1.3—Distinguish 2-D shapes in a pattern and colour according to guidelines. 99

4 34

N1.1, N1.2, M1.2—Share numbers into equal groups. Use informal units to measure the length of objects.

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Week Unit

100

WM1.2—Work mathematically to explain the best approach to solve a problem. 101

N1.1, N1.2—Count and group collections up to 10.

5 35

C&D1.2, C&D1.3—Count and record data on a graph.

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C.Publ i cat i ons M1.2, C&D1.3—Use informal units to measure capacity and record results on af graph.

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N1.1, N1.2, WM1.1—Share coins into equal amounts. Count and group collections up to 10.

102 103 104 105

N1.1, N1.2—Count and group/add on to collections less than 10.

106

C&D1.2, C&D1.3—Collect and record information in a Carroll diagram.

107

N1.1, N1.2—Count and add on to/take away from collections of up to 10.

108

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7 37

S1.1—Follow paths on a given map.

N1.1, WM1.1—Recognise coin values.

S1.2, S1.3—Distinguish shapes in a tessellating pattern and colour according to guidelines.

111

N1.1, N1.2, WM1.1—Recognise coin values and identify coins needed for a given amount.

112

C&D1.2, C&D1.3—Record data in a table.

113

N1.1, WM1.1—Recognise coin values and count amounts of money.

114

9 39

S1.1—Follow paths on a given map.

115

N1.1, WM1.1—Recognise coin values; count and share amounts of money.

116

M1.2, WM1.2—Compare and discuss the area of two shapes.

117

10 40

N1.4, WM1.2—Create and describe pictorial number patterns.

118

C&D1.2, C&D1.3—Collect, record and interpret information on a graph.

119

N1.4, WM1.2—Identify errors in a repeating pictorial number pattern.

120

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New Wave Maths Book A – Teachers Guide • 19 •

Unit 1–1

Student page 1

Outcomes

Indicators

N1.1, S1.1

The student is able to: • draw pictures or make things which illustrate the meaning of words relating to position and orientation.

Skills • drawing • colouring • following instructions • recognising colours

Number (N1.1)

Resources • red, blue, green, yellow pencils/ crayons • A4 paper • pencils/crayons

Language • one • shape • red, blue, green, orange, yellow • patter • boundaries

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Notes

Main Activity (S1.1) Warm up

• Provide students with a sheet of blank paper and ask them to watch the blackboard/ whiteboard while you demonstrate making a scribble pattern. Emphasise limited number of lines and large spaces. Choose your own colours to colour the pattern.

• Circulate and encourage designs and colouring. Ask students to name the colours they use.

What to do

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• The focus for this unit is identification of one object and the number 1.

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• Direct students to their workbook to complete colouring the patterns drawn in the book.

• Identify the colours to be used and ensure all students are able to recognise the colours.

• Display some or all of the finished patterns for all to appreciate.

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• 20 • New Wave Maths Book A – Teachers Guide

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Unit 1–2

Student page 2

Outcomes

Indicators The student is able to: • understand the use of ‘first’, ‘second’, ‘third’ etc. to indicate position in a sequence.

• respond appropriately to the language of position and orientation.

N1.1, S1.1

Skills • counting ordinal numbers

Number (N1.1)

Resources

Language

• green pencil/crayon • pencil • plastic animals • shapes

• two • shapes • green • order • first, last • between • second, fourth

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Notes

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• The focus for this unit is identification of two objects and the number 2.

Main Activity (N1.1, S1.1) Warm up

• Provide groups of students with plastic animals, shapes or other materials.

• Allow students time for free play with their material.

• Direct students to make an ordered arrangement with three, then up to six, of the objects.

• Ask students to discuss their arrangements within the group. Describe which is first, last, second, behind, in front of, and between.

• Allow time for several arrangements and interactions.

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• Introduce the activity in the workbook, working through each question with the whole class.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 28 – 29.

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New Wave Maths Book A – Teachers Guide • 21 •

Unit 1–3

Student page 3

Outcomes N1.1, M1.1

Skills

Indicators

Resources

The student is able to: • respond appropriately to and use for himself/herself, comparative language of length.

• blue pencil/crayon • Base 10 MAB longs • variety of objects • pencils

• comparing • recording • analysing

Number (N1.1)

Language • three • shapes • blue • Base 10 MAB long • shorter, longer • tallest

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Main Activity (M1.1) Warm up

• Arrange the class into groups. Provide each group with a variety of different objects, including Base 10 MAB longs.

• Allow students free-play time with the materials.

What to do

• Direct students to find objects that are longer or shorter than others. Ask students how they determined which were longer or shorter. Share explanations with the class. Repeat this many times.

• Ask students to choose a Base 10 MAB long then find three things shorter than the long and two things longer than it.

• Share findings with all groups.

• Ask students to circle the tallest of the drawings as shown in their workbook. Ask for explanations as to why the choice was made. Share the answers with the whole class.

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• The focus for this unit is identification of three objects and the number 3.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 72 – 73.

• 22 • New Wave Maths Book A – Teachers Guide

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Unit 1—Answers

Student pages 1 – 3 Unit 1–2

Unit 1–1 Number 1. Teacher check Main Activity 2. (a) giraffe (b) elephant (c) zebra (d) monkey (e) zebra

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Number 1. Teacher check Main Activity 2. Teacher check 3. Teacher check

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C.Publ i cat i ons Consolidation 1–1 Unit •f orr evi e w1–3pu r posesonl y•

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• Students draw a free pattern and identify shapes to make objects or animals, then colour the pattern. Alternatively, after drawing the pattern, set a scene—sea, desert etc.—and use appropriate colours and/or add details to the design to make creatures found at that scene.

Number 1. Teacher check Main Activity 2. Teacher check 3. The flag is the tallest object.

• Use six students to stand in a line as in a race and identify first, third, who is in between certain students etc.

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Consolidation 1–3

• Select four to six students and decide who is the tallest by ‘eye’ and how to verify this. (Stand back-to-back etc.)

New Wave Maths Book A – Teachers Guide • 23 •

Unit 2–1

Student page 4

Outcomes N1.1, S1.4

Skills • colouring • writing • understanding ordinal numbers

Number (N1.1)

Indicators

Resources

The student is able to: • understand and use ‘first’, ‘second’, ‘third’ etc. to indicate position in a sequence.

• recognise shapes which are rectangles, squares, triangles and circles.

• yellow, red and blue pencils/crayons • shapes • counters • interlocking cubes • variety of objects • 2-D shapes

Language • four • shapes • yellow, red, blue • colour • third, fifth, second, fourth • age

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Notes

Main Activity (N1.1, S1.4) Warm up

• Arrange the class into small groups.

• Provide each group with a range of materials to manipulate.

• Provide time for free play.

• Ask individuals to explain to their group what they have been doing.

What to do

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• The focus for this unit is identification of four objects and the number 4.

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• Direct the groups to make patterns with their materials. Suggest that other group members might copy the patterns made.

• Ask group members to describe their patterns. Ask what comes before, after, first, third, fifth etc.

• Direct students to complete the activities in the workbook under teacher direction. Work through each activity with the class as a whole.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 8 – 9, 28 – 29.

• 24 • New Wave Maths Book A – Teachers Guide

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Unit 2–2

Student page 5

Outcomes

Indicators The student is able to: • display, in one-to-one correspondence, pictures or objects which represent themselves.

• summarise information by counting.

N1.1, C&D1.3

Skills • reading graphs • collecting information • recording information • completing graphs • colouring

Number (N1.1)

Resources

Language

• red pencil/crayon • coloured pencils/ crayons • pencil

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• five • shapes • red • chart • most • least • how many • blonde, brown, black, • boxes • coloured • graph

Notes

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• The focus for this activity is the identification of five objects and the number 5.

Main Activity (C&D1.3) Warm up

• Explain to the class that there are times when we need to compare information that has been collected in the form of a picture known as a graph.

• Use the students to demonstrate the collection and presentation of information by asking the girls to stand in one line and the boys to stand in another.

• Ask the boys and girls to line up beside each other to see which line is the longer.

• Explain that this is a form of a graph and it allows us to see which group has the most or least.

• Repeat with three groups wearing shorts, skirts or other clothing. Check the size of the groups.

• Repeat using the type of footwear—shoes, sandals etc. Check the size of the groups by direct comparison and then by counting.

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• When students are ready, work with them with the graph at the top of the workbook to count the stars after each player’s name, and decide who has the most and who has the least. Comparison may be made directly.

• Ask the students in the class to line up according to whether they like red, blue, green or yellow the best. (Students will need to take their workbook and pencils with them.)

• Count how many in each line. As each student is counted, colour one box in the column above that colour. Students will require help to do this. Pair weaker students with those who understand to assist with completing the graph.

• When completed, explain to the class that they have made their own graph showing the number of students in their class who like red, yellow, green or blue the best.

• Students may be asked to say which colour has the most students in its column and which has the least.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

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New Wave Maths Book A – Teachers Guide • 25 •

Unit 2–3

Student page 6

Outcomes N1.1

Skills • counting • writing • ordering

Number (N1.1)

Indicators

Resources

The student is able to: • match oral names to written numbers into the teens and write recognisable versions of them.

• say the number names in order into the teens and respect the order when counting.

• pencil • number chart/line (see pages 201 – 204) • green pencil/crayon

Language • six • shapes • green • number • before, after • order • smallest, largest

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Main Activity (N1.1) Warm up

• Ask students to count together to 10, then to 20.

• Using a number chart/line, ask students to identify numbers as you point to them.

• Using the number chart/line, ask students to identify what number comes before and after the numbers as you point to them.

• Give many opportunities with both of these activities.

What to do

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• The focus for this unit is identification of six objects and the number 6.

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• Ask students to write the numbers that come before and after the numbers in their workbook. Use the number chart/line to help.

• Using the number chart/line arrange the sets of numbers in order, starting with the smallest and working to the largest.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 30 – 31.

• 26 • New Wave Maths Book A – Teachers Guide

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Unit 2—Answers

Student pages 4 – 6 Unit 2–2

Unit 2–1 Number 1. Teacher check Main Activity 2. (a) Jill (b) Ben 3. Teacher check 4. Teacher check

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Number 1. Teacher check Main Activity 2. circle and triangle are red 3. circle 4. square 5. Teacher check 6. Teacher check

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• In pairs—one student arranges a number of objects and asks the other to point to the fifth, what colour is the fourth? etc. Students swap.

Number 1. Teacher check Main Activity 2.

• Sort and count groups of students who walked, rode, came by bus or came by car to school. Create a graph to show the results.

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• Play a ‘Guess my Number’ game with a partner and a 1 – 20 number chart or line. One student says ‘I am the number before twenty’, for example, and the other guesses and points.

3. 5, 6, 8, 9, 10, 11, 12, 13, 17 4. 1, 2, 3, 4, 7, 9, 12, 14, 15

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New Wave Maths Book A – Teachers Guide • 27 •

Unit 3–1

Student page 7

Outcomes N1.1, S1.1

Skills • drawing pathways • reading labels • following directions

Number (N1.1)

Indicators

Resources

The student is able to: • use some of the language of position and orientation for himself/ herself.

• respond appropriately to the language of movement.

• blue pencil/crayon • coloured pencils/ crayon

Language • seven • shapes • blue • draw • pathway • path • grid • shortest

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Notes

Main Activity (S1.1) Warm up

• Play a game of follow the leader—inside or outside. Change the leader frequently, but allow a fairly free rein on where the leader goes.

• Direct the leader to follow a path using given directions—go from the class to the library.

Change leader—go to the office. Change leader—go to the Year 7 class. Change leader— go to the oval. Use your own choice of destinations.

• Explain to the class that they are following a path each time they move from one place to another.

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• Paths may be drawn on a map to show where a person has moved. In the workbook, as the students to point to them, mark the classroom door, the library, the drinking fountain and the office in turn with a different coloured pencil or crayon. Use a cross, tick or dot to mark each location.

• Check to see that all locations have been identified.

• Ask students to select a coloured pencil or crayon and place it on the classroom mark.

Draw a line to show the path they would follow to arrive at the library. Check paths.

Continue from the library to the drinking fountain. Check paths. Continue to the office.

Check paths. Return to class. Check paths.

• Discuss with the class the choice of paths (these may differ for different students). Explain that all choices are correct.

• Ask students to find the start point on the grid. The task is to draw a path moving from one grid square to a neighbouring one to reach the end. The path may not pass through any coloured squares.

• Ask students if they can find a shorter path. Check results.

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• The focus for this unit is the identification of seven objects and the number 7.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 6 – 7.

• 28 • New Wave Maths Book A – Teachers Guide

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Unit 3–2

Student page 8

Outcomes N1.1

Skills • counting • writing • sorting

Number (N1.1)

Indicators

Resources

Language

The student is able to: • match oral names to written numbers into the teens and write recognisable versions of them.

• say the number names in order into the teens and respect the order when counting.

• yellow pencil/crayon • pencil • number line/chart – see pages 201 – 204

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• eight, three • number • shapes • yellow • between • number lines • sort • groups • order

Notes

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• The focus for this unit is identification of eight objects and the number 8.

Main Activity (N1.1) Warm up

• Ask students to count together to 10, to 20.

• Using a number chart/line, ask students to identify numbers as you point to them.

• Using the number chart/line, ask students to identify the number between the two numbers you point to on the chart/line.

• Provide many opportunities with this activity.

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What to do

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• Ask students to write the number that comes between the numbers in the workbook.

Use the number chart/line to help.

• Use the number chart/line to complete the number lines.

• Use the number chart/line to find groups of three consecutive numbers. Draw a circle around the groups of three. Ask students to read out the groups of three in order before they circle them.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 30 – 31.

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New Wave Maths Book A – Teachers Guide • 29 •

Unit 3–3

Student page 9

Outcomes N1.1, M1.1

Skills • comparing • recording • analysing • describing • understanding ordinal numbers

Number (N1.1)

Indicators

Resources

The student is able to: • respond appropriately to, and use for himself/herself, comparative language of length.

• red pencil/crayon • pencil • variety of objects— 2-D and 3-D

Language • nine • shapes, shape • red • second, fourth • tallest, shortest, largest, smallest, widest • most • number • edges

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Main Activity (M1.1) Warm up

• Arrange the class into groups. Provide each group with a variety of different objects, 2-D and 3-D. • Allow students time for free play with the materials. Encourage building of structures.

• Direct students to find objects that are taller or shorter than others. Ask students how they determined which were taller or shorter. Share explanations with the class. Repeat this many times.

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• Ask students to determine which of three shapes in the workbook is the shortest or tallest and to describe the first object orally. Elicit explanations of student discussions.

• Ask students to describe the first object. Discuss responses. Students may need assistance to write their description.

• Ask students to determine the largest, smallest, tallest and widest of the shapes in Exercise 3. Students should be encouraged to give full explanations of their decisions.

• As a class, count the edges of each shape. Which shape has the most edges?

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• The focus for this unit is identification of nine objects and the number 9.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 72 – 73.

• 30 • New Wave Maths Book A – Teachers Guide

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Unit 3—Answers

Student pages 7 – 9 Unit 3–2

Unit 3–1 Number 1. Teacher check Main Activity 2.

Number 1. Teacher check Main Activity 2. Teacher check 3. Teacher check

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• Use the map to follow a new pathway made up by the teacher or a student. Use a different coloured pencil.

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Number 1. Teacher check Main Activity 2. (a) no (b) shortest = shape 1 tallest = shape 3 (c) Teacher check 3. (a) no (b) smallest = shape 1 tallest = shape widest = shape 3 (c) 5

• Complete similar activities to Exercise 4, sorting numbers to 20 in groups of two or four in order.

Consolidation 3–3

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• Sort selections of recycled boxes into shortest, widest, tallest etc.

New Wave Maths Book A – Teachers Guide • 31 •

Unit 4–1

Student page 10

Outcomes WM1.2

Skills • estimating mass • problem-solving • discussing • explaining

Main Activity (WM1.2)

Resources

Language

The student is able to: • offer questions when prompted by the teacher.

• ask ‘why’ or ‘how’ mathematical questions of other children.

• manipulate objects mentioned in a problem to find a solution.

• pencil • four playdough shapes as pictured in the workbook (one set, or several if working in groups)

• more, less • bigger, smaller • shape • cylinder, ball, sphere, cube • flat • height • width

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• The aim of the activity is to introduce the concept of the conservation of mass. Each of the shapes pictured has been made with the same amount of playdough.

• At this stage of their development, most students will not understand this concept if the shapes are different. To them, one shape will appear to have more playdough in it. It could be the squashed flat shape as it seems to cover a greater area, the cylinder because it is the longest, and so on.

• Show students the playdough shapes. Ask them questions about the shape, size, width and height of each. Words and phrases can be written on the blackboard/whiteboard.

• Direct students to look at the playdough shapes in their workbook.

• Ask them to circle the shape they think has the most playdough.

• For Exercise 3, students’ answers may need to be scribed.

• Discuss the various answers with the class.

Notes

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Indicators

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• 32 • New Wave Maths Book A – Teachers Guide

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Unit 4–2

Student page 11

Outcomes

Indicators The student is able to: • recognise and take into account the possibility of different results for repetitions of the same simple action.

• summarise information by counting.

N1.1, C&D1.1, C&D1.3

Skills • throwing a die • recording • discussing

Number (N1.1)

Resources

Language

• red pencil/crayon • dice • pencil

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• first, second, third, fourth, fifth, sixth • shape • red • die • six • record • results • number

Notes

Main Activity (C&D1.1, C&D1.3) Warm up

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• The focus for this unit is the identification of place (cardinal number), first.

• Organise the class into groups of six. Provide each group with a die.

• Allow each group to throw the die randomly. Encourage discussion of the results. Who was first to throw a six? Who was first to throw the same number twice in a row? etc.

What to do

• Direct the group members to take turns to throw the die. Record the result of the first throw in the workbook. Continue until the sixth throw.

• Check the numbers thrown—ask students if they think they will throw the same six numbers with another six throws.

• Check the numbers thrown—ask students if they think they will throw the same six numbers with another six throws. Encourage discussion of their answers.

• Repeat the six throws, recording the results.

• If students are able, they may write or copy a response into their workbooks. (This may also by scribed.) Oral discussions of the results, comparing both sets of throws, should be held. These may be repeated a number of times.

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New Wave Maths Book A – Teachers Guide • 33 •

Unit 4–3

Student page 12

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many there are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• use objects to represent a number story and manipulate objects to find a solution.

• green pencil/crayon • pencil • concrete materials

Language • second • shape • green • how many • altogether • add

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Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to small groups. Allow free play with the materials.

• Ask students to take one object. Ask, ‘How many objects do you have?’ Take another object and ask, ‘How many objects do you have altogether?’

• Repeat this many times, starting with one object and adding on several, or starting with several and adding on one. Encourage students to count all objects or count on from the larger group if they know the total of the larger group. Encourage verb statements of the sum.

What to do

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• The focus for this unit is the identification of second place.

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• Use the activities in the workbook to complete written records of the above activities.

Concrete materials may be placed over the pictures to assist. Encourage whole-class participation in reaching the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 34 • New Wave Maths Book A – Teachers Guide

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Unit 4—Answers

Student pages 10 – 12 Unit 4–2

Unit 4–1 Number 1. Teacher check Main Activity 2. Teacher check 3. Teacher check 4. Teacher check

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Main Activity 1. – 3. Teacher check (Refer to comments in Teachers Notes on page 32.)

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• To assist students in developing the concept of conservation of mass, provide opportunities to make different shapes from the same amount of playdough. Share experiences with the class.

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• Repeat the activity as a class over a number of days and add to a tally displayed on the board.

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Consolidation 4–3

• Complete written records of the sums made with the concrete materials in the warm up. (Compile as a class.)

New Wave Maths Book A – Teachers Guide • 35 •

Unit 5–1

Student page 13

Outcomes N1.1, S1.4

Skills

Indicators

Resources

The student is able to: • recognise shapes which are rectangles, triangles, squares and circles.

• blue pencil/crayon • red and green pencils/crayons • variety of 2-D shapes

• recognising shapes • colouring

Number (N1.1)

Language • third • blue, red, green • shape • squares, circles • rectangle

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Notes

Main Activity (S1.4) Warm up

• Hold up a large square, ask the class to describe what they see. Encourage as much information as possible from the class.

• Repeat for a rectangle and a circle.

• Ask class to describe similarities and differences among the three shapes.

• Ask the class to identify the shapes as you hold them up. Allow the class to play with a variety of 2-D shapes.

What to do

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• The focus for this activity is the identification of third place.

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• Ask students to identify by pointing to a square, rectangle and circle in turn, in the pictures in the workbook.

• Ask students to colour the squares red; then when completed, the circles green; and finally, the rectangles blue.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 8 – 9.

• 36 • New Wave Maths Book A – Teachers Guide

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Unit 5–2

Student page 14

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• yellow pencil/crayon • variety of concrete materials • pencil

• fourth • shape • yellow • how many • altogether

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Notes

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• The focus for this unit is the identification of fourth place.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to small groups. Allow free play with the material.

• Ask students to take one object. Ask, ‘How many objects do you have?’Take another object and ask, ‘How many objects do you have altogether?’

• Repeat this many times, starting with one object and adding on several, or starting with several and adding on one. Encourage students to count all objects or count on from the larger group if they know the total of the larger group. Encourage verb statements of the sum.

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• Use the activities in the workbook to complete written records of the above activities.

Concrete materials may be placed over the pictures to assist. Encourage whole-class participation in reaching the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 37 •

Unit 5–3

Student page 15

Outcomes

Indicators The student is able to: • respond appropriately to, and use for himself/herself, comparative language of length.

• select something longer than/ shorter than/same length as another thing by matching.

N1.1, M1.1, M1.2

Skills • comparing • tracing • analysing

Number (N1.1)

Resources • red pencil/crayon • pencil • variety of shapes

Language • fifth • shape • red • bigger • trace • longer

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Main Activity (M1.1, M1.2) Warm up

• Arrange the class into small groups and provide them with a variety of shapes to play with.

• Encourage the students to discuss shapes and to compare them. Gradually direct thinking to comparing the size of a pair of shapes, discussing which is bigger. Encourage discussion of the ideas the students put forward.

What to do

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• The focus for this unit is the identification of fifth place.

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• Turn to the workbook and look at the hand. Ask if individual students can tell whether their hand is bigger than the one on the page. Trace around students’ hands with them placed on top of the drawing. Does this help to decide which is bigger? Why/Why not?

• Repeat for the foot. Draw attention to how students decide which is bigger in helping answer the question—does bigger always mean longer?

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 78 – 79.

• 38 • New Wave Maths Book A – Teachers Guide

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Unit 5—Answers

Student pages 13 – 15 Unit 5–2

Unit 5–1 Number 1. Teacher check Main Activity 2. (a) 1 (b) 4 (c) 1 + 4 = 5 3. (a) 1 (b) 5 (c) 1 + 5 = 6 4. (a) 1 (b) 6 (c) 1 + 6 = 7

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Number 1. Teacher check Main Activity 2. Teacher check 3. Teacher check

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• Identify square, circular and rectangular shapes in the classroom.

Number 1. Teacher check Main Activity 2. Teacher check 3. Teacher check

• Complete written records of the sums made with the concrete materials in the warm up. (Compile as a class.)

Consolidation 5–3

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• Compare similar size objects; e.g. two books. Guess which is bigger before placing one over another to check.

New Wave Maths Book A – Teachers Guide • 39 •

Unit 6–1

Student page 16

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• green pencil/crayon • variety of concrete materials • pencils

Language • sixth • shape • green • how many • altogether

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Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to small groups. Allow free play with the material.

• Ask students to take one object. Ask, ‘How many objects do you have?’Take another object and ask, ‘How many objects do you have altogether?’

• Repeat this many times, starting with one or two objects and adding on several, or starting with several and adding on one. Encourage students to count all objects or count on from the larger group if they know the total of the larger group. Encourage verb statements of the sum.

What to do

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• The focus for this unit is the identification of sixth place.

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• Use the activities in the workbook to complete written records of the above activities.

Concrete materials may be placed over the pictures to assist. Encourage whole-class participation in reaching the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 40 • New Wave Maths Book A – Teachers Guide

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Unit 6–2

Student page 17

Outcomes

Indicators The student is able to: • suggest how he/she can answer questions about his/her collections.

• summarise information by counting.

N1.1, C&D1.2, C&D1.3

Skills • counting • tallying • analysing • recording

Number (N1.1)

Resources

Language

• blue pencil/crayon • assorted concrete materials • pencil

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• seventh • shape • tally • how many • items • graph • total • most, least • altogether

• blue

Notes

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• The focus for this unit is the identification of seventh place.

Main Activity (C&D1.2, C&D1.3) Warm up

• Provide groups of students with a range of concrete materials. Allow time for free play.

• Ask each group to take a handful of objects then sort them into two groups. Ask for an explanation of how the material was sorted.

• Repeat, sorting into three or four groups. Ask for reasons for sorting. Suggest the same materials be sorted into different groupings.

• As students count, make tally marks for each item on the blackboard/whiteboard. Explain to the class that each stroke represents one item. At this stage it may be easier to use five downstrokes and a gap between groupings of five unless the class shows an understanding of the process. If this is the case, explain the cross stroke for every five items so tallying of larger numbers is easier.

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What to do

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• Ask students to make their own tally using the page in their workbook. Work through with the whole class.

• Answer the questions as a whole-class activity.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 94 – 95.

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New Wave Maths Book A – Teachers Guide • 41 •

Unit 6–3

Student page 18

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• yellow pencil/crayon • assorted concrete materials • pencil

Language • eighth • shape • yellow • how many • altogether

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Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to small groups. Allow free play with the materials.

• Ask students to take a small number of items. Sort these into two groups. Ask, ‘How many in each group? How many altogether?’

• Repeat this activity many times. Students will begin to see that one group and the other group provide a total—that is they add, rather than count on.

What to do

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• The focus for this unit is the identification of eighth place.

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• Use the activities in the workbook to complete written records of the above activities.

Concrete materials may be placed over the pictures to assist. Encourage whole-class participation in reaching the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 42 • New Wave Maths Book A – Teachers Guide

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Unit 6—Answers

Student pages 16 – 18 Unit 6–2

Unit 6–1 Number 1. Teacher check Main Activity 2.

Number 1. Teacher check Main Activity 2. (a) 1 (b) 7 (c) 1 + 7 = 8 3. (a) 1 (b) 6 (c) 1 + 6 = 7 4. (a) 2 (b) 6 (c) 2 + 6 = 8

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3. most items = plants and toys fewest items = animals total items = 13

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• Continue counting activities where students add on from one object or add on one from several.

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Number 1. Teacher check Main Activity 2. (a) 2 (b) 2 (c) 2 + 2 = 4 3. (a) 3 (b) 3 (c) 3 + 3 = 6 4. (a) 5 (b) 4 (c) 5 + 4 = 9

• Practise tallying objects or amounts up to nine.

Consolidation 6–3

• Complete counting activities with two groups of objects with no more than five in each group.

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New Wave Maths Book A – Teachers Guide • 43 •

Unit 7–1

Student page 19

Outcomes

Indicators The student is able to: • recognise shapes which are rectangles, squares, triangles and circles.

N1.1, S1.4

Skills • recognising shapes • sorting shapes • colouring

Number (N1.1)

Resources • red pencil/crayon • 2-D shapes • coloured pencils/ crayons

Language • ninth • shape • rectangles, circles, triangles • red • sort • three • groups • colour • different

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Notes

Main Activity (S1.4) Warm up

• Distribute a number of 2-D shapes for groups to handle and play freely with. Encourage discussion about the shapes.

• Display a number of large 2-D shapes and ask students to describe the shapes. Ask what is the same, what is different about the shapes.

• Ask the students to sort their shapes into two different groups. Describe the groups.

• Re-sort into three/four groups. Describe the groups each time.

What to do

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• The focus for this unit is the identification of ninth place.

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• Using three different colours to show three different groups, sort the shapes shown in the workbook. Ask students to describe their groupings. How many circles are there?

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 8 – 9.

• 44 • New Wave Maths Book A – Teachers Guide

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Unit 7–2

Student page 20

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• green pencil/crayon • pencil • assorted concrete material

• tenth • shape • green • how many • altogether

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Notes

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• The focus for this unit is the identification of tenth place.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to small groups. Allow free play with the materials.

• Ask students to take a small number of items. Sort these into two groups. Ask, ‘How many in each group? How many altogether?’

• Repeat this activity many times. Students will begin to see that one group and the other group provide a total—that is, they add rather than count on.

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What to do

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• Use the activities in the workbook to complete written records of the above activities.

Concrete materials may be placed over the pictures to assist. Encourage whole-class participation in reaching the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

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New Wave Maths Book A – Teachers Guide • 45 •

Unit 7–3

Student page 21

Outcomes N1.1, M1.2, C&D1.3

Skills • measuring • recording • graphing • analysing

Number (N1.1)

Indicators

Resources

The student is able to: • count informal units of capacity to say how many will fill the container.

• summarise information by counting.

• blue pencil/crayon • pencil • containers (cups, jars, cans) • ice-cream containers • sand • coloured pencils/ crayons

Language • eleven, three • shapes • blue • different sized • containers • fill • graph • number • most, least

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Main Activity (M1.2, C&D1.3) Warm up

• Collect a variety of containers of different sizes and aerosol lids. Take these and the class to the sandpit.

• Allow free play with containers and sand.

• Ask students to pour sand from one container to another. Ask if all containers hold the same amount of sand. ‘How do you know they hold different amounts?’

• Direct students to use an aerosol lid to fill containers.

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• Select three different containers and the lid. Use the lid to fill each container in turn.

Count the number of lids required to fill each container. Colour one space on the workbook graph for each lid.

• When all three containers have been filled, check to see which container holds the most and which the least sand.

• Count the number of lids used to fill each container and record the totals in the workbook.

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What to do

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• The focus for this unit is the identification of eleven objects and the number 11.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 76 – 77.

• 46 • New Wave Maths Book A – Teachers Guide

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Unit 7—Answers

Student pages 19 – 21 Unit 7–2

Unit 7–1 Number 1. Teacher check Main Activity 2. (a) 2 (b) 2 (c) 4 (d) 3 (e) 1 (f) 2 (g) 2 (h) 4 (i) 6 (j) 5 (k) 3

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Number 1. Teacher check Main Activity 2. Answers will vary—the most obvious grouping is circles, triangles, quadrilaterals. number of circles = 3

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• In pairs, sort a variety of objects into specified numbers of groups—but of their own choice.

Number 1. Teacher check Main Activity 2. Teacher check 3. Teacher check

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Consolidation 7–2 • Continue counting activities, sorting objects into groups with no more than five in each group, then adding the two groups.

Consolidation 7–3

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• Repeat the activity using a smaller or larger container to fill the same three containers. Compare the results.

New Wave Maths Book A – Teachers Guide • 47 •

Unit 8–1

Student page 22

Outcomes N1.1, N1.2

Skills • counting • drawing • adding

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• yellow pencil/crayon • pencil • concrete materials

• shapes • yellow • one, two, three, four, five, six, twelve • stars, squares, triangles, circles, lines, ovals • how many

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Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow free play.

• Ask students to take one object out, then take one more. Ask, ‘How many altogether?

‘Repeat this, starting with one object and adding different numbers to it. Find the total each time.

What to do

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• The focus for this unit is the identification of twelve objects and the number 12.

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• Direct students to their workbook and work through each activity with the whole class.

Draw the extra objects. Find and record the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 48 • New Wave Maths Book A – Teachers Guide

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Unit 8–2

Student page 23

Outcomes

Indicators The student is able to: • match oral names to written numbers into the teens and write recognisable versions of them.

• say the number names in order, into the teens and respect the order when counting.

N1.1

Skills • read number words • write number words

Number (N1.1)

Resources

Language

• red crayon/ pencil • pencil • number line • counting rhymes

• thirteen • shapes • red • before, after • number

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Notes

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• The focus for this unit is the identification of thirteen objects and the number 13.

Main Activity (N1.1) Warm up

• Sing, chant a range of counting-based rhymes; e.g. ‘One, two buckle my shoe’.

• Write the number names to ten on the blackboard/whiteboard. Read these with the class.

What to do

• Read the rhyme in the workbook, asking students to provide the missing numbers.Working with the class, identify the written number required for the space from those on the blackboard/whiteboard. Ask students to copy each in turn.

• Use a number line to identify the numbers that came before and after the numbers in the workbook. Write the missing numbers, copying from the blackboard/whiteboard to complete the lists.

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New Wave Maths Book A – Teachers Guide • 49 •

Unit 8–3

Student page 24

Outcomes N1.1, N1.2

Skills • counting • adding • drawing

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• green pencil/crayon • pencil • concrete materials

Language • two, three, four, eight, seven, fourteen • shapes • green • more • circles, triangles • how many • ovals, squares, stars • lines

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Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow free play.

• Ask students to take a small number of objects. Ask, ‘How many do you have? Take some more. How many did you take this time? How many objects are there altogether?’ Repeat this many times.

• Direct students to take a given number of objects. Count to ensure the correct number have been taken. Take another given amount. Check this number by counting. How many objects have been taken altogether? Repeat this many times.

What to do

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• The focus for this unit is the identification of fourteen objects and the number 14.

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• Use the workbook to obtain written records of this process by completing the set tasks.

Read instructions to the students and have them verbalise the answers before writing the correct number in the space provided.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 50 • New Wave Maths Book A – Teachers Guide

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Unit 8—Answers

Student pages 22 – 24 Unit 8–2

Unit 8–1 Number 1. Teacher check Main Activity 2. one, two, the shoe is blue, three, four, lock the door, five, six, little chicks, seven, eight, cakes on plates, nine, ten, catch the hen.

2. one two three four five six eight nine ten three four five six seven eight two three four five six seven seven eight nine

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Number 1. Teacher check Main Activity 2. 2 3. 3 4. 4 5. 5 6. 6 7. 7

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Consolidation 8–2

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• Repeat the activity using different groups of students as the ‘objects’. One student stands at the front of the class, another comes out. How many students are there now? Repeat with different numbers of students joining the single student.

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Number 1. Teacher check Main Activity 2. 5 3. 8 4. 9 5. 6 6. 10 7. 6

• Match number names to sets of objects.

Consolidation 8–3

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• Continue similar activities as described in the warm up. Create written records of the activities on the blackboard/whiteboard with students’ participation.

New Wave Maths Book A – Teachers Guide • 51 •

Unit 9–1

Student page 25

Outcomes

Indicators The student is able to: • recognise shapes which are rectangles, squares, triangles and circles etc.

N1.1, S1.4

Skills • recognising shapes • matching

Number (N1.1)

Resources • blue crayon/pencil • coloured pencils/ crayons • variety of 2-D shapes • attribute blocks

Language • fifteen • shapes • blue • large, small, same • square, circle, triangle, pentagon, hexagon • thick, thin

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Notes

Main Activity (S1.4) Warm up

• Distribute 2-D shapes or sets of attribute blocks to groups of students. Allow time for free play.

• Direct students to examine the shapes, find those that are the same and put them together.

Ask why these shapes have been identified as being the same.

• Use attribute blocks to identify large, small, thick and thin examples of the same shapes.

Ask students to describe the similarities and differences of these groups of shapes.

What to do

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• The focus for this unit is the identification of fifteen objects and the number 15.

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• Use the workbook to draw a line joining a large shape with its corresponding small shape.

Use a different colour for each new line for ease of identification of joined pairs.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 8 – 9.

• 52 • New Wave Maths Book A – Teachers Guide

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Unit 9–2

Student page 26

Outcomes N1.1, N1.2

Skills • counting • adding • drawing

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• yellow crayon/pencil • pencil • concrete materials

• one, two, three, four, five, seven, sixteen • shapes • yellow • how many

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Notes

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• The focus for this unit is the identification of sixteen objects and the number 16.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow free play.

• Ask students to take a small number of objects. Ask, ‘How many do you have? Take some more. How many did you take this time? How many objects do you have altogether?

‘Repeat this many times.

• Direct students to take a given number of objects. Count to ensure the correct number have been taken. Take another given amount. Check this number by counting. How many objects did they take altogether? Repeat this many times.

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What to do

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• Use the workbook to obtain written records of this process by completing the set tasks.

Read instructions to the students and have them verbalise the answers before writing the correct number in the space provided.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

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New Wave Maths Book A – Teachers Guide • 53 •

Unit 9–3

Student page 27

Outcomes

Indicators The student is able to: • respond appropriately to, and use for himself/herself, comparative language.

• find objects clearly heavier than, lighter than or about the same as a given object by hefting.

N1.1, M1.1, M1.3

Skills • hefting • comparing • weighing • recording • analysing

Number (N1.1)

Resources • red crayon/pencil • pencil • basketballs • soccerballs • footballs • softballs • T-balls • tennis balls

Language • seventeen • shapes • red • heaviest, lightest • pairs • weighing • different

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Main Activity (M1.1, M1.3) Warm up

• Distribute the balls to the groups of students, instructing them that they are not to be kicked or thrown. Play with the balls, discovering what you can about them. Encourage students to talk about the balls, and what they find.

• Ask students to pick up one ball each, or take turns to do so, and place it on one hand.

Change the ball for another. Which felt heavier? Place a different ball in each hand. Which feels heavier? Use the same two balls, but swap hands. Which feels heavier now?

• Ask students to weigh pairs of balls several times, discussing what they find with their group.

What to do

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• The focus for this unit is the identification of seventeen objects and the number 17.

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• Direct students to use the pairs of balls as set out in the workbook, weigh each pair and record the results by marking the box next to the heaviest ball.

• Ask students to find the heaviest and the lightest of the balls by weighing using their hands.

• Which ball has a different shape from the others?

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• 54 • New Wave Maths Book A – Teachers Guide

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Unit 9—Answers

Student pages 25 – 27 Unit 9–2

Unit 9–1 Number 1. Teacher check Main Activity 2. 8 3. 7 4. 4 5. 9 6. 5 7. 10

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Number 1. Teacher check Main Activity 2.

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• Identify different sized 2-D or 3-D objects in the classroom; e.g. a sheet of paper and a book have rectangular shapes.

Number 1. Teacher check Main Activity 2. Teacher check

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Consolidation 9–2 • Continue similar activities as described in the warm up. Create written records of the activities on the blackboard/whiteboard with students’ participation.

Consolidation 9–3

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• Participate in further hefting activities with groups of objects such as toys, fruit or desk items.

New Wave Maths Book A – Teachers Guide • 55 •

Unit 10–1

Student page 28

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• green pencil/crayon • pencil • concrete materials

Language • eighteen • shapes • green • how many • altogether

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Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to small groups. Allow free play with the materials.

• Ask students to take a small number of items. Sort these into two groups. How many in each group? How many altogether?

• Repeat this activity many times. Students will begin to see that one group and the other group provide a total—that is, they add rather than count on.

What to do

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• The focus for this unit is the identification of eighteen objects and the number 18.

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• Use the activities in the workbook to complete written records of the above activities.

Concrete materials may be placed over the pictures to assist. Encourage whole-class participation in reaching the total.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 56 • New Wave Maths Book A – Teachers Guide

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Unit 10–2

Student page 29

Outcomes N1.1, C&D1.3, S1.1, S1.4

Skills • recording • tallying

Number (N1.1)

Indicators

Resources

The student is able to: • summarise information by counting.

• talk about what he/she has found from the data collection and display.

• respond appropriately to the language of movement.

• recognise shapes which are rectangles, squares, triangles and circles.

• blue pencil/crayon • pencil

Language

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• nineteen • shapes • squares, circles, triangles • blue • size • tally • count • number • total

Notes

Main Activity (C&D1.3, S1.1, S1.4) Warm up

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• The focus for this unit is the identification of nineteen objects and the number 19.

• Screen a maze on an overhead or use a computer program which focuses on mazes.

Work with the class to find the way through the maze. Remind students that solid lines can not be crossed.

What to do

• Work with the class as a whole to find the way through the maze in the workbook (make an overhead transparency of the page and work from the overhead with the class).

• As each object is crossed, make a tally mark to represent it on the table. Remind students how to make tally marks.

• When the maze has been negotiated, count the total of each shape crossed and record the shape crossed most often.

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New Wave Maths Book A – Teachers Guide • 57 •

Unit 10–3

Student page 30

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• yellow pencil/crayon • pencil • concrete materials • coloured pencils • crayon

Language • two, twenty • shapes • yellow • how many • altogether • squares, triangles • sort • sets • different

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Main Activity (N1.1, N1.2) Warm up

• Distribute a variety of concrete materials to groups of students. Allow students time for free play.

• Direct students to sort selection of materials into two sets or groups. Ask students to count how many in each set and how many there are altogether. Repeat this many times.

• Ask students to select two different types of objects only and sort these into two groups.

How many in each group? How many altogether?

• Repeat this many times.

What to do

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• The focus for this unit is the identification of twenty objects and the number 20.

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• Written records of these activities may be made completing the workbook page using the same instructions and/or placing concrete materials over the different items in each set.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 38 – 39.

• 58 • New Wave Maths Book A – Teachers Guide

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Unit 10—Answers

Student pages 28 – 30 Unit 10–2

Unit 10–1 Number 1. Teacher check Main Activity 2.

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Number 1. Teacher check Main Activity 2. (a) 2 (b) 8 (c) 4 (d) 2 (e) 5 (f) 3 (g) 6 (h) 4 (i) 4 (j) 8 (k) 8 (l) 14

3. Circle

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• Continue counting activities, sorting objects into groups with no more than nine in each group, then adding the two groups.

Consolidation 10–2

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Number 1. Teacher check Main Activity 2. (a) 7 (b) 5 (c) 2 3. (a) 7 (b) 1 (c) 5 4. seahorses and seastars 5. circles and rectangles

• Complete maze activities independently. Practise tallying collections up to nine.

Consolidation 10–3

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• Sort selections of objects or pictures into two or three subsets.

New Wave Maths Book A – Teachers Guide • 59 •

Unit 11–1

Student page 31

Outcomes

Indicators The student is able to: • convey the essential spatial features of common mathematical figures in his/her drawings.

N1.1, S1.2

Skills • drawing • recognising shapes • counting

Number (N1.1)

Resources • coloured pencils/ crayons • 2-D shapes • pencil

Main Activity (S1.2) Warm up

• Provide groups of students with a variety of 2-D shapes and allow a period of free play.

• Ask students to make designs with the shapes. Experiment with different designs, discuss each design with the group.

• Ask students to select three shapes and make different designs. Discuss each design within the group.

Notes

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• match • larger • count • draw • shapes • square, triangle, circle

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

Language

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• Ask students to choose one or more squares, one or more triangles, and one or more circles. Use these three shapes to make a house on the page of the workbook. Each shape may be used a number of times in the design. Trace around each shape in the completed house design.

• Share house designs within the group.

• Display for class to see.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 4 – 5.

• 60 • New Wave Maths Book A – Teachers Guide

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Unit 11–2

Student page 32

Outcomes N1.1, N1.2

Skills • counting • colouring

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • variety of concrete materials

Language

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• match • larger • count • circles • one, two, three, four • how many • left • outside

Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

• Ask students to select a few items. Count them. Ask, ‘How many do you have?’ Take one item from the group. ‘How many are left?’

• Repeat this activity many times, taking away one, two or three items. Direct students to select a given number of items then take away a given number. Ask students to say how many they started with, how many were taken away and how many are left each time.

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• Written records of these activities can be made using the workbook. Concrete items may be placed over each drawing and the given number taken away to show how many are left if this helps student understanding.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 38 – 39.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 61 •

Unit 11–3

Student page 33

Outcomes

Indicators The student is able to: • use indirect methods to arrange by length objects which can’t be directly compared.

N1.1, M1.2

Skills • measuring • recording • comparing

Number (N1.1)

Resources • coloured pencils/ crayons • 1-cm cubes • variety of objects between 5 and 15 cm long (pencil, book etc.)

Main Activity (M1.2) Warm up

• Ask students to find several objects between the length of their middle finger and a new pencil. Place these objects with a number of 1-cm cubes.

Allow students time for free play.

• Ask students to demonstrate how they could measure the length of their pencil using 1-cm cubes. Have all of them try. Discuss what they did.

• Students may now use the cubes to measure the length of a variety of objects. Discuss findings and length within groups or with the whole class.

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• match • larger • measure • height • tallest • length

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

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• Use the 1-cm cubes to find the length of the toothbrushes and snakes on the workbook page. Discuss findings with the whole class.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 78 – 79.

• 62 • New Wave Maths Book A – Teachers Guide

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Unit 11—Answers

Student pages 31 – 33 Unit 11–2

Unit 11–1 Number 1. Set A has more.

Main Activity 2. 6 3. 6 4. 6 5. 5

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Number 1. Set A has more.

Main Activity 2. Teacher check

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• Draw pictures of objects such as robots, sheds or trees using 2-D shapes.

Number 1. Set A has more.

Main Activity 2. D is the tallest.

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Consolidation 11–3

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• Use 1-cm cubes to measure pencils and crayons of different lengths.

New Wave Maths Book A – Teachers Guide • 63 •

Unit 12–1

Student page 34

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials • pencil

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete material to groups of students and allow time for free play.

• Ask students to take out a small number of items. Count them.Take another small number of items. Count them. How many altogether?

• Repeat this many times.

• Direct students to take a set number of items and another set number of items. How many do they have altogether? Repeat this many times.

Notes

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• match • larger • number stories • two, three, four, five • and • equal • add

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

Language

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• Written records of this activity may be made using the workbook. Concrete materials may be placed over the drawings if this helps students.

• Focus on the use of the required vocabulary (four plus/add two equals six etc.).

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 64 • New Wave Maths Book A – Teachers Guide

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Unit 12–2

Student page 35

Outcomes N1.1, C&D1.3

Skills • counting • graphing • recording

Number (N1.1)

Indicators

Resources

The student is able to: • summarise information by counting.

• talk about what he/she has found from the data collection and display.

• coloured pencils/ crayons • concrete materials

Language • match • larger • how many • graph • altogether

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Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

Main Activity (C&D1.3) Warm up

• Provide small groups with a variety of concrete materials. Allow time for free play.

• Ask each group, or individual, to take out a number of items. Ask students to sort these items into two or three groups. Ask students to describe their sorting.

• Ask students to arrange items in rows for each group in the sort. Ask, ‘How many items in each group? Which group has the most? How many items altogether?’

• Repeat several times with new selections of materials.

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• Direct students to count the frogs in the picture in their workbook and colour one space above the word ‘Frogs’ for each frog counted.

• Do the same for tadpoles and insects.

• Ask, ‘How many of each creature? How many creatures altogether?’

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 65 •

Unit 12–3

Student page 36

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials

Main Activity (N1.1, N1.2) Warm up

• Provide concrete materials for groups of students. Allow free time to play with materials.

• Ask students to take out a small number of items. Count them.Take another small number of items. Count them. How many do they have altogether?

• Repeat this many times.

• Direct students to take a set number of items and another set number of items. How many do they have altogether? Repeat this many times.

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• match • larger • how many • total • equals

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

Language

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• Written records of this activity may be made using the workbook. Concrete materials may be placed over the drawings if this helps students.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 66 • New Wave Maths Book A – Teachers Guide

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Unit 12—Answers

Student pages 34 – 36 Unit 12–2

Unit 12–1 Number 1. Set B has more.

Main Activity 2. Frogs = 2 Tadpoles = 7 Insects = 3

Number 1. Set B has more.

Main Activity 2. (a) 4 + 2 = 6 (b) 5 + 4 = 9 (c) 3 + 2 = 5 (d) 4 + 4 = 8

Total = 12

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• Complete similar activities with concrete materials and make written records. Make sums equal to less than 10.

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Number 1. Set A has more.

Main Activity 2. 3 cats, 4 dogs, total = 7 3. 4 rabbits, 5 mice, total = 9 4. 4 birds, 4 fish, total = 8

• Graph selections of materials used in the warm up.

Consolidation 12–3

• Complete similar activities with concrete materials and make written records. Make sums equal to less than 10.

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New Wave Maths Book A – Teachers Guide • 67 •

Unit 13–1

Student page 37

Outcomes

Indicators The student is able to: • convey the essential spatial features of common mathematical figures in his/her drawings.

N1.1, S1.2

Skills

Resources • coloured pencils/ crayons

• colouring • recognising shapes

Number (N1.1)

• match • larger • pattern • green, blue, red • shapes

Main Activity (S1.2) Warm up

• Use a ‘feely’ bag with 2-D shapes to identify. Make the blue shape in the workbook from cardboard and add that too. Ask students to describe that shape before looking at it.

What to do

• Ask students to select a green, blue and red pencil or crayon.

• Open workbooks and discuss the three shapes shown on the page.

• Ask students to point to a shape in the pattern they will colour green. When satisfied that their identification is correct, ask students to colour that shape.

• If required, continue to identify shapes to be coloured green and colour all those shapes appropriately.

• Repeat for blue shapes until completed.

• Repeat for red shapes until completed.

• Count the green shapes individually then check with the whole class.Write the total number of green shapes in the space provided.

Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

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Language

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 4 – 5.

• 68 • New Wave Maths Book A – Teachers Guide

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Unit 13–2

Student page 38

Outcomes

Indicators The student is able to: • give some examples of shapes being used for particular purposes.

• offer questions when prompted by their teacher.

• ask ‘why’ or ‘how’ mathematical questions of other children.

WM1.1, WM1.2

Skills • working mathematically • exploring shape • discussing • explaining • observing

Resources

Language

• pencil • signs in the environment with shapes • photographs or pictures of signs from magazines etc. (optional)

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• sign • symbol • shape • size • colour • cross • square, rectangle, octagon, circle

Notes

Main Activity (WM1.1, WM1.2)

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What to do

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• The aim of the activity is for students to identify and discuss how and why particular shapes and colours are used for signs and symbols in their environment.

• Direct students to look at each sign in their workbook. Ask questions about the shape, size, picture and wording on each. Ask students if they would be able to work out what each sign meant if there was no wording. Discuss the meaning of each sign.

• Brainstorm other signs that include a shape. A walk around the school could add to the list. Signs could be drawn on the blackboard/whiteboard for students to refer to. If photographs or pictures are available, these could also be shown and discussed.

• Students draw two more signs in their workbook. Discuss with a partner and share with the class.

Note: • The colour red is used on signs to indicate danger or a warning, in the identification and location of firefighting equipment and in signs involving traffic regulations.

• Yellow is used in traffic advisory signs.

• Green is used on first aid and emergency escape routes. (This is why ambulances are now identified by a green checkerboard pattern.)

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New Wave Maths Book A – Teachers Guide • 69 •

Unit 13–3

Student page 39

Outcomes

Indicators The student is able to: • count informal units of capacity to say how many will fill the container.

• draw a picture as a record of his/ her results.

• summarise information by counting.

N1.1, M1.2, C&D1.3

Skills • measuring • recording • comparing • graphing

Number (N1.1)

Resources • coloured pencils/ crayons • cups • can • shoe • glass jar • hat • sand

• match • larger • small • fill • how many • most • graph

Main Activity (M1.2, C&D1.3) Warm up

• Ask groups of students to collect a cup, can, shoe, glass jar, hat and take them to the sandpit.

• Allow students time to play freely with the materials in the sand.

What to do

• Ask students to select one of the items and use the cup to fill it with sand. Count the number of cups required to fill the container.

• Record the answer in the workbook next to the container in the space provided.

• Repeat for the other three containers.

• Which container holds the most sand?

• Complete the graph by drawing a dot or a cup for each cupful of sand used to fill each container.

• Students may need close supervision and guidance to complete the graph. Explain to them that the dots or cups need to be the same size if possible.

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

Teac he r

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Unit 13—Answers

Student pages 37 – 39 Unit 13–2

Unit 13–1

Main Activity 1. The pictured signs are fairly self-explanatory.

Note: • The green cross is actually from a first aid kit.

• The LADIES and GENTS are on toilet doors.

• The FIRE EXTINGUISHER is on a wall above the actual extinguisher.

• The wheelchair access sign is on a toilet door and can also be used to indicate ramps and car parking.

• Students may notice that a stop sign is octagonal which, along with the red colour, helps it to stand out.

• The traffic light sign is situated some distance before a set of lights to notify drivers etc.

2. Teacher check

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Number 1. Set A has more.

Main Activity 2. Teacher check; 16

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• Count the number of blue and red shapes in the pattern.

Complete similar colouring activities with patterns.

Number 1. Set B has more.

Main Activity 2. Teacher check 3. Teacher check

• Students create a display, or a class book of shape signs in their environment. Direct students to look for signs going to and from school, visiting shopping centres or community centres etc.

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Consolidation 13–3

• Use different objects to fill with cups of sand or a different sized container to fill the objects listed on the worksheet.

Graph and compare.

New Wave Maths Book A – Teachers Guide • 71 •

Unit 14–1

Student page 40

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials • pencil

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete material to groups of students and allow time for free play.

• Ask students to take out a small number of items. Count them.Take another small number of items. Count them. How many do they have altogether?

• Repeat this many times.

• Direct students to take a set number of items and another set number of items. How many do they have altogether? Repeat this many times.

Notes

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• match • larger • number stories • two, three, four, five • and • equal • add

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

Language

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• Written records of this activity may be made using the workbook. Concrete materials may be placed over the drawings if this helps students.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 72 • New Wave Maths Book A – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 14–2

Student page 41

Outcomes

Indicators The student is able to: • summarise information by counting.

N1.1, C&D1.3

Skills • counting • graphing • recording

Number (N1.1)

Resources

Language

• coloured pencils/ crayons • pencil • fairytales – Snow White, Pinocchio, Jack and the Beanstalk

• match • larger • how many • graph • altogether • most, least • survey

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Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

Main Activity (C&D1.3) Warm up

• Read Snow White, Pinocchio and/or Jack and the Beanstalk. Discuss all three fairytales even if not read. Ask students what they liked about the tales.

• Ask the class to decide for themselves which of the three fairytales they liked the best.

Count hands for each selection and record on blackboard/whiteboard for future reference.

• Ask students to open their workbook and look at the graph showing preferences for liking each of the three fairytales. Explain that one dot represents one child.

• Count the dots for each fairytale. Which fairytale has the most dots? This is the fairytale that most children shown on the graph preferred.

• Which fairytale has the least dots? This is the fairytale least liked by the children in this survey.

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• Work through the questions with the class as a whole. Read the questions, guide students’ discussion and direct answers to be written.

• Use the results that were previously boarded to answer the class survey questions. Work with the class as a whole to complete the answers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 73 •

Unit 14–3

Student page 42

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials

Main Activity (N1.1, N1.2) Warm up

• Provide concrete materials for groups of students. Allow free time to play with materials.

• Ask students to take out a small number of items. Count them.Take another small number of items. Count them. How many do they have altogether?

• Repeat this many times.

• Direct students to take a set number of items and another set number of items. How many do they have altogether? Repeat this many times.

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• match • larger • how many • total • equals

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

Language

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• Written records of this activity may be made using the workbook. Concrete materials may be placed over the drawings if this helps students.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 74 • New Wave Maths Book A – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 14—Answers

Student pages 40 – 42 Unit 14–2

Unit 14–1 Number 1. Set B has more.

Main Activity 2. (a) Snow White (b) 3 (c) 4 (d) Jack and the Beanstalk (e) 2 (f) 9 (g) 3 + 2 = 5

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Number 1. Set B has more.

Main Activity 2. cats 4, dogs 2, total 6 3. 5c coins 7, 10c coins 3, total 10 coins 4. rabbits 4, mice 3, total 7

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• Complete similar activities with concrete materials and make written records. Make sums equal 10 or less.

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Main Activity 2. 5 3. 5 4. 8 5. 5 6. 5

• Choose groups of nine students and ask their favourite fairytale from the three given. Construct graphs with the class to compare answers to the same questions.

Consolidation 14–3

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• Use attribute blocks to complete similar activities and make written records. Make sums equal 10 or less.

New Wave Maths Book A – Teachers Guide • 75 •

Unit 15–1

Student page 43

Outcomes

Indicators The student is able to: • remember the shape of objects and component parts of objects.

• convey the spatial features of common mathematical figures in their drawings.

N1.1, S1.2

Skills • identifying shapes

Number (N1.1)

Resources • coloured pencils/ crayons • 2-D shapes • pencils

• match • larger • shape • top • flat • hoop • triangle • wide

Main Activity (S1.2) Warm up

• Distribute a number of 2-D shapes to groups of students. Allow free play with the shapes ,encouraging students to speak about the shapes and/ or what they are doing with them.

What to do

• Direct students to identify given shapes—square, triangle, circle, rectangle, oval etc.

• Ask students to identify attributes of shapes—flat, three-sided, wide, long, narrow, four corners etc.

• Ask students to open their workbooks and work with them to complete the activities on the page. Discuss each drawing as it is completed—focus on the shape and attributes specified in the instructions.

Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 4 – 5.

• 76 • New Wave Maths Book A – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 15–2

Student page 44

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials • pencil

Language

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• match • larger • triangle • squares • total • two, three, five, six, seven • how many • around • outside

Notes

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Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow free play.

What to do

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

• Direct students to select a given number of items; e.g. 2 or 5. Count to check total.

• Ask students to make the total to 6 or 8 etc. Count to check total.

• Repeat this many times.

• Ask students to select a given number of items up to 10. Ask students to remove a given number of items from the original group. How many items are left?

• Repeat this activity many times.

• Written records of both types of activity may be made in the workbook. Concrete materials may be placed on the drawings if this assists students.Work through the examples with the class as a whole if need be.

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New Wave Maths Book A – Teachers Guide • 77 •

Unit 15–3

Student page 45

Outcomes N1.1, M1.1, WM1.1

Skills • telling time

Number (N1.1)

Indicators

Resources

The student is able to: • refer to familiar recurring events when describing time.

• understand that clocks are used to tell the time of day and link specific times on a clock to recurring daily phenomena.

• coloured pencils/ crayons • large analog clock face

Main Activity (M1.1, WM1.1) Warm up

• Use a large analog clock face to assist students to learn to read time. Set hands to show hour times—6 o’clock, 12 o’clock, 3 o’clock and so on. Ask students what they might be doing at that time of the day (or night).

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• match • larger • clock face • time

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

What to do

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• Remind students that the small hand shows the hour time. The large hand always points to the twelve on the hour. The large hand is the minute hand—it tells how many minutes of the hour have gone.

• If sufficient clocks are available, allow groups of students to set hour times and read the time from the clocks.

• Ask students to turn to their workbook and read the times shown on each clock face in turn. Do this as a whole-class activity. Record times shown.

• Students draw pictures of something they would do at that time (day or night).

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Unit 15—Answers

Student pages 43 – 45 Unit 15–2

Unit 15–1 Number 1. Set B has more.

Main Activity 2. Teacher check 3. Teacher check 4. 8 apples, 6 left 5. 5 strawberries, 3 left 6. 6 bananas, 1 left

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Number 1. Set B has more.

Main Activity 2. Teacher check 3. Teacher check 4. Teacher check 5. Teacher check 6. Teacher check

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Consolidation 15–2

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Number 1. Set B has more.

Main Activity 2. (a) 8 o’clock (b) 2 o’clock (c) 10 o’clock

• Complete similar activities with concrete materials, adding on and subtracting amounts up to 10.

Consolidation 15–3

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• In turns, one student asks another to make an hour time on a clock face. Students can also describe something they might do at that time.

New Wave Maths Book A – Teachers Guide • 79 •

Unit 16–1

Student page 46

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials • pencil

• match • larger • one, two, three, four, five, six • how many • triangle, square, circle

Teac he r

• The focus for this unit is one-to-one correspondence or counting to determine the larger amount.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow time for free play.

What to do

• Ask students to select a given number of items. Count to check quantity is correct. Ask students to remove a given number of items. Count these to check that the correct number have been removed. How many items are left? Count to check.

• Repeat this activity using different numbers of items and removed items each time.

• Written records of this activity may be made using the workbook. Concrete materials may be placed over individual drawings to assist students. Activities may be completed with the class as a whole or individually.

Notes

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• 80 • New Wave Maths Book A – Teachers Guide

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Unit 16–2

Student page 47

Outcomes N1.1, C&D1.3

Indicators

Resources

The student is able to: • summarise information by counting.

• coloured pencils/ crayons • concrete materials • pencil

Skills • counting • sorting

Number (N1.1)

Language

r o e t s Bo r e p ok u S

• match • larger • graph • how many • altogether • same number • more than • least • amount

Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the larger amount.

Main Activity (C&D1.3) Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Ask students to take a handful or two of items then, within the group, sort them into three or four different categories. How many items are in each group? Why were the items sorted in this way? Can the items be sorted in a different way? Repeat the activity with a different sort.

• This activity may be done with different collections of items.

• Ask students to view the graph in the workbook. Explain that each shoe represents one shoe of that colour.

• Work with the class as a whole to answer the questions.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

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New Wave Maths Book A – Teachers Guide • 81 •

Unit 16–3

Student page 48

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials • pencil

• match • larger • how many • circle • two, three, four, five, six

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow time for free play.

What to do

• Ask students to select a given number of items. Count to check that the quantity is correct. Ask students to remove a given number of items. Count these to check that the correct number have been removed. How many items are left? Count to check.

• Repeat this activity using different numbers of items and removed items each time.

• Written records of this activity may be made using the workbook. Concrete materials may be placed over individual drawings to assist students. Activities may be completed with the class as a whole or individually.

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

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Unit 16—Answers

Student pages 46 – 48 Unit 16–2

Unit 16–1

Number 1. Set B has more.

Main Activity 2. Teacher check 3. (a) blue = 1, black = 3, red = 2, yellow = 1 (b) 7 (c) blue and yellow (d) no (e) no (f) blue and yellow

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Number 1. Set A has more.

Main Activity 2. 5 3. 3 4. 3 5. 1 6. 2 7. 9

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• Complete similar activities with concrete materials, subtracting amounts from up to 10 objects and making written records.

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Number 1. Set B has more.

Main Activity 2. 1 3. 6 4. 4 5. 4 6. 2 7. 5

• Make a graph using up to 10 objects over the range of the four colours in the workbook. Answer questions as for Exercise 3.

Consolidation 16–3

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• Complete similar activities with concrete materials, subtracting amounts from up to 10 objects and making written records.

New Wave Maths Book A – Teachers Guide • 83 •

Unit 17–1

Student page 49

Outcomes

Indicators

N1.1, S1.3

The student is able to: • use a fold line to produce symmetrical pictures by drawing freehand, folding, cutting, tracing.

Skills • identifying shapes • mirror imaging

Number (N1.1)

Resources • coloured pencils/ crayons • mira or mirrors • pencil • ruler

• match • larger • draw • pattern • shape • count • mirror image • reflection

Main Activity (S1.3) Warm up

• Students open workbooks and use a mira or mirror placed along the dotted line to see what the other half of the drawing will look like.

What to do

• Explain that each drawing is completed by drawing the mirror image (reflection) of the drawing shown on the page. The reflection will be exactly the same size as the drawing shown but on the right hand side of the dotted line.

• Work with the whole class and have them follow your instructions as they draw.

• Place your ruler underneath the top line of the top picture. How many squares does the line cross? (4) Start at the dotted line and draw a line four squares wide to the right of the dotted line, use your ruler as a guide.

• The next line is at an angle to the first line. How many squares does it pass through? (2) From the end of the line you have just drawn, place your ruler so that it passes through two squares and draw a line to finish at the corner of the second square. From the end of this line draw a line one square long down the page. Place your ruler under the next line across the page. How long is this line? (3) Draw this line. The next line is two squares straight down. The next line is how many squares long? (3) This line starts at the end of your last line and moves at an angle away from the dotted line to finish in the corner of the third square. Use your ruler to draw this line. The next line is three squares long and is drawn back towards the dotted line. Draw a line from the end of this line one square up the page. Draw the next line from the end of the last line two squares long towards the dotted line. This line finishes one square out from the dotted line. Draw the next line three squares long, one square out from the dotted line. The final line is from the end of the last line drawn to the end of the bottom line on the original drawing.

• Repeat the process for the second drawing. Start with the top line of four squares and so on.

Note: A mira is a plastic maths tool which both reflects what is in front and lets you see through to what is behind.

Notes

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 16 – 17.

• 84 • New Wave Maths Book A – Teachers Guide

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Unit 17–2

Student page 50

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • concrete materials • pencil

• match • larger • one, two, three, four, five, six • how many

r o e t s Bo r e p ok u S

Notes

Teac he r

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow time for free play.

What to do

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

• Ask students to select a given number of items. Count to check that the quantity is correct. Ask students to remove a given number of items. Count these to check that the correct number have been removed. How many items are left? Count to check.

• Repeat this activity using different numbers of items and removed items each time.

• Written records of this activity may be made using the workbook. Concrete materials may be placed over individual drawings to assist students. Activities may be completed with the class as a whole or individually.

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New Wave Maths Book A – Teachers Guide • 85 •

Unit 17–3

Student page 51

Outcomes

Indicators The student is able to: • order events within the day.

• understand that daily activities are related to time and that many of our activities are influenced by patterns in time.

N1.1, M1.2, WM1.1

Skills • ordering events • measuring time

Number (N1.1)

Resources • coloured pencils/ crayons • pencil • names of days of the week

• match • larger • day • week • Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday

Main Activity (M1.2, WM1.1) Warm up

• Introduce the days of the week to the class.

What to do

• Read the names of the days of the week.

• Put the days in their correct sequence. Ask students what days come before or after given days.

• Discuss the main activities to be undertaken on each day of the week.

• In the space provided in the workbook, draw a picture to show the events or activities that each student may undertake on each day of the week.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 84 – 85.

• 86 • New Wave Maths Book A – Teachers Guide

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Unit 17—Answers

Student pages 49 – 51 Unit 17–2

Unit 17–1 Number 1. Set A has more.

Main Activity 2. 4 3. 6 4. 2 5. 4 6. 1 7. 2

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Number 1. Set A has more.

Main Activity 2.

3.

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• Complete similar activities using 1-cm grid paper (page 196) and simple straight-sided shapes.

Number 1. Set A has more.

Main Activity 2. Teacher check

• Complete similar activities with students working more independently with concrete materials to subtract amounts from up to 10 objects and making written records.

Consolidation 17–3

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• Discuss their workbook pictures with a classmate to compare daily activities.

New Wave Maths Book A – Teachers Guide • 87 •

Unit 18–1

Student page 52

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• coloured pencils/ crayons • pencil • fruit—3 apples, 4 pears, 2 bananas, 3 strawberries, 7 cherries

• match • larger • one, two, six • how many

Main Activity (N1.1, N1.2) Warm up

• Sit the class on the mat, display the fruit for the fruit salad—3 apples, 4 pears, 2 bananas, 3 strawberries and 7 cherries. (Combinations of fruit, type and number are discretionary.)

What to do

• Ask the class to count each type of fruit.

• Select one of the fruit types and remove one or two pieces. Ask students how many were removed. How many of that fruit type are left?

• Students may be selected to remove the nominated items and then have responsibility for cutting the fruit for a fruit salad.

• Repeat for each fruit type.

• If the quantities of fruit used are the same as in the workbook, students may complete workbook exercises as fruit is removed.

• Alternatively, workbook exercises are completed as a follow up to fruit salad-making.

• Finish by eating the fruit salad.

Notes

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Unit 18–2

Student page 53

Outcomes N1.1, C&D1.3

Indicators

Resources

The student is able to: • summarise information by counting.

• coloured pencils/ crayons • pencils • concrete materials

Skills • counting • sorting • ordering • reading graphs

Number (N1.1)

Language

r o e t s Bo r e p ok u S

• match • larger • graph • number • how many • one, three, four • first, second, third • fourth, quarter • how many • altogether

Notes

Teac he r

Main Activity (C&D1.3) Warm up

• Distribute a variety of concrete materials to groups of students. Allow time for free play.

What to do

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• The focus for this unit is one-to-one correspondence or counting to determine the higher amount.

• Direct students to sort a double handful of items into four groups. Describe how they were sorted.

• Arrange the items into rows. Count the items in each row. Which group has the most items? Which group has the least? Can you arrange rows so that you can tell which has the most and the least without counting? This arrangement is a form of a graph. A graph is a presentation of information that makes it simpler for us to read and understand.

• Graphs are most often in pictorial or drawn form.The two graphs in the workbook show information on books read and the number of goals shot in a game of netball.

• By looking at the graph of books - which person read the most books? How can you tell?

(Count or tallest column) Who read the least?

• Ask students to count the books read by each person and record the total in the space provided.

• The graph showing the goals scored shows two quarters having the same number of goals scored. Which two quarters are those? Which quarter had the most goals scored?

• How many goals were scored altogether? Record the answer in the square provided.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

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New Wave Maths Book A – Teachers Guide • 89 •

Unit 18–3

Student page 54

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• ‘act out’ or draw a picture to represent a story involving a small number of things.

• coloured pencils/ crayons • concrete materials • pencil

• match • larger • two, three, four, five • how many • octagons, circles, cubes, pentagons

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow time for free play.

What to do

• Ask students to select a given number of items. Count to check that the quantity is correct.

Ask students to remove a given number of items. Count these to check that the correct number have been removed. How many items are left? Count to check.

• Repeat this activity using different numbers of items and removed items each time.

• Written records of this activity may be made using the workbook. Concrete materials may be placed over individual drawings to assist students. Activities may be completed with the class as a whole or individually.

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• 90 • New Wave Maths Book A – Teachers Guide

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Unit 18—Answers

Student pages 52 – 54 Unit 18–2

Unit 18–1 Number 1. Set B has more.

Main Activity 2.

r o e t s Bo r e p ok u S 3. 9 goals

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Number 1. Set A has more.

Main Activity 2. (a) 1 (b) 0 (c) 1 (d) 3 (e) 1 (f) 1

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Number 1. Set B has more.

Main Activity 2. 6 3. 3 4. 4 5. 3

• Use a variety of objects to sort into three or four groups and line up in rows as described in the warm up. Work with a partner and describe what they have done.

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Consolidation 18–3

• Complete similar activities with students working more independently with concrete materials to subtract amounts from up to 10 objects and making written records.

New Wave Maths Book A – Teachers Guide • 91 •

Unit 19–1

Student page 55

Outcomes

Indicators

N1.1, S1.4

The student is able to: • interpret, and begin to use, language such as ‘flat’, ‘straight’, ‘curved’, ‘side’, ‘round’, ‘corner’.

• recognise shapes which are rectangles, squares, triangles and circles.

Skills • identifying shapes • colouring

Number (N1.1)

Resources • coloured pencils/ crayons • 2-D shapes

• match • larger • shapes • bottom • similar • box • top • same, different

Main Activity (S1.4) Warm up

• Distribute a variety of 2-D shapes to groups of students and allow time for free play.

What to do

• Encourage students to discuss the shapes they are handling, looking at similarities and differences. Suggest that the shapes may be sorted into groups according to similarities.

• Share discussions with the whole class.

• There are two boxes in the workbook with shapes drawn in each. Ask students to find the circle in the top box and colour it. Find a similar shape (circle) in the bottom box and colour it the same colour as the circle in the top box.

• Find a square in the top box. Colour it a different colour from the circle. Find a similar shape (square) in the bottom box. Colour it the same colour as the square in the top box.

• Continue until all shapes are matched. Use shape names or a distinguishing feature such as the number of sides or corners.

• Discuss with the class why shapes are similar but not the same. Different length sides and/ or different sized corners (angles). The shapes have the same name but only similar features.

Notes

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 8 – 9.

• 92 • New Wave Maths Book A – Teachers Guide

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Unit 19–2

Student page 56

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• ‘act out’ or draw a picture to represent a story involving a small number of things.

• coloured pencils/ crayons • pencil • concrete materials

• add • one, three, four, five, six • squares, triangles, octagon • how many

r o e t s Bo r e p ok u S

Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow time for free play.

What to do

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

• Ask students to select a given number of items. Count to check that the quantity is correct. Ask students to remove a given number of items. Count these to check that the correct number have been removed. How many items are left? Count to check.

• Repeat this activity using different numbers of items and removed items each time.

• Written records of this activity may be made using the workbook. Concrete materials may be placed over individual drawings to assist students. Activities may be completed with the class as a whole or individually.

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New Wave Maths Book A – Teachers Guide • 93 •

Unit 19–3

Student page 57

Outcomes

Indicators

N1.1, M1.1, M1.2

The student is able to: • respond appropriately to and use for himself/herself comparative language of length such as ‘shorter’, ‘taller’, ‘longer’, ‘same length’, ‘near’, ‘far’, ‘higher’, ‘lower’.

• select something longer than/shorter than/same length as another thing by matching.

Skills • ordering events • measuring time

Resources • pencil • variety of long items; e.g. pencils, crayons • Base 10 MAB longs • collected items • coloured rods • 1-cm cubes

• add • longest, shortest • green, red • how many • altogether • two • same length • double • order

r o e t s Bo Notes r e p ok u S • line up one end of things in order to make a direct comparison of length.

Number (N1.1)

Language

Main Activity (M1.1, M1.2) Warm up

• Arrange the class into groups and distribute a variety of materials or ask students to each collect five or six items of different lengths—pencils, sticks, rods etc. Put all items into a shared pool for each group.

What to do

• Select one item—find another that is longer, another that is shorter and a third that is the same or nearly the same length as one of the first two.

• Repeat this several times.

• Select five items. Arrange them in order from shortest to longest. Discuss the arrangements.

• Repeat this several times.

• Select one item—lie 1-cm cubes alongside it to measure its length. How many cubes were required? Repeat this several times.

• Work with students on the activities in the workbook. Encourage discussion and reasoning when reaching answers. Record findings in the space provided.

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 82 – 83.

• 94 • New Wave Maths Book A – Teachers Guide

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Unit 19—Answers

Student pages 55 – 57 Unit 19–2

Unit 19–1 Number 1. (a) 2 (b) 3 Main Activity 2. 5 3. 2 4. 5 5. 3

(c) 5

(d) 4

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Main Activity 2.

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• Display and label a variety of 2-D shapes of different sizes for students to refer to. The labels could be a description in students’ own words, especially for irregular sapes.

Consolidation 19–2

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Number 1. (a) 8 (b) 6 Main Activity 2. longest – E shortest – D (a) 5 (b) B and D (c) A (d) D, B, C, A, E 3. longest – B shortest – D

• Use attribute blocks to complete similar activities with students working more independently to subtract amounts from up to 10 and making written records.

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Consolidation 19–3

• Use 1-cm or 2-cm cubes to measure a variety of objects and compile written records. (See warm up.)

New Wave Maths Book A – Teachers Guide • 95 •

Unit 20–1

Student page 58

Outcomes N1.1, N1.2

Skills • counting • subtracting

Number (N1.1)

Indicators

Resources

The student is able to: • match oral names to written numbers into the teens and write recognisable versions of them.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• pencil • concrete materials

Language • add • count • how many • one, two, six • outside • circle

r o e t s Bo r e p ok u S

Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups and allow time for free play.

What to do

• Ask students to select a given number of items. Count to check that the quantity is correct. Ask students to remove a given number of items. Count these to check that the correct number have been removed. How many items are left? Count to check.

• Repeat this activity using different numbers of items and removed items each time.

• Written records of this activity may be made using the workbook. Concrete materials may be placed over individual drawings to assist students. Activities may be completed with the class as a whole or individually.

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

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• 96 • New Wave Maths Book A – Teachers Guide

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Unit 20–2

Student page 59

Outcomes

Indicators

N1.1, C&D1.2, C&D1.3

The student is able to: • suggest how they can answer questions about his/her collections.

• summarise information by counting.

• talk about what he/she has found from their data collections and display.

Skills • counting • sorting • ordering • graphing

Number (N1.1)

Resources

Language

• pencil • coloured pencils/ crayons

• add • graph • survey • most • least

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

Main Activity (C&D1.2, C&D1.3) Warm up

• Explain to the class they will be providing information to be used to complete the graph in their workbook. The information will be collected using a survey—a question asking about the pets students have.

What to do

• Ask the students to stand if they have a cat for a pet. Write the number on the blackboard/ whiteboard.

• Repeat for dog, bird, fish, rabbit, mouse and other pets.

• Ask students to select a coloured pencil/crayon to colour one space above the picture of the cat for each child who has a cat for a pet. How many people have cats as pets?

Colour___spaces. Supervise and assist as required.

• Repeat for other pets.

• When the graph is completed, ask the two questions at the bottom of the page. Students may write the pet name and draw a picture of the appropriate pet.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 94 – 95.

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New Wave Maths Book A – Teachers Guide • 97 •

Unit 20–3

Student page 60

Outcomes N1.1, N1.2

Skills • counting • adding

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’.

• use objects to represent a number story and manipulate the objects to find a solution.

• pencil • concrete materials

Language • add • how many • more • six, seven, nine

r o e t s Bo Notes r e p ok u S

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Direct students to take out a given number of items; for example three. How many more do they need to make 5? Students may wish to select five items and then match them with the three to see how many are different, or to count on from three to five to find how many more items are required. Encourage both methods and any others that students may experiment with.

• Repeat many times using different starting numbers and different final totals.

• Written records of these activities may be made using the workbook. Concrete materials may be used to add on to the objects to find how many more are needed to make the given number.

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 98 • New Wave Maths Book A – Teachers Guide

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Unit 20—Answers

Student pages 58 – 60 Unit 20–2

Unit 20–1 (c) 5

(d) 7

(b) 3 (d) 6 (f) 2

Number 1. (a) 7 (b) 8 Main Activity 2. Teacher check 3. Teacher check

(c) 9

(d) 10

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Number 1. (a) 4 (b) 6 Main Activity 2. (a) Teacher check (c) 7

(e) 8

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(d) 6

Consolidation 20–2

(b) 2 (d) 4 (f) 5

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• Compile a class graph on the blackboard/whiteboard of students’ favourite colour or drink.

Consolidation 20–3

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• Choose a given number of items and use concrete materials if necessary to find how many more are needed to make a given number (up to 10).

New Wave Maths Book A – Teachers Guide • 99 •

Unit 21–1

Student page 61

Outcomes

Indicators

N1.1, S1.1

The student is able to: • respond appropriately to the language of movement such as ‘back’, ‘forward’, ‘around’, ‘past’, ‘turn’ and ‘up’.

Skills • following a path

Number (N1.1)

Resources • pencil • coloured pencils/ crayons

Language • add • path • maze • start • finish • through

r o e t s Bo r e p ok u S

Notes

Main Activity (S1.1) Warm up

• Revise finding a way through a maze. Remind students that solid lines can not be crossed.

What to do

• Use an overhead of a maze and ask the class to guide you through it. Use a coloured marking pen to trace the path. If you are led into a dead end, start again with a different pen. Assist the students with hints for them to use to guide you through the maze.

• Use the maze in the workbook as a whole-class activity, with students using their finger to trace the path. Copy the maze onto an overhead and, with student guidance, work your way through it. Use coloured pens as for initial example.

• Ask students to trace the path themselves. Assist those who need help.

• Repeat the process for the second maze or allow students to seek their own path. Remind students to use a different coloured pencil/crayon if they need to start again.

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

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Unit 21–2

Student page 62

Outcomes

Indicators

N1.1, N1.2

The student is able to: • say how many are in visible collections of objects.

• when counting small collections, use the last number said as the answer to ‘How many?’’.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

Skills • counting • difference • grouping

Number (N1.1)

Resources

Language

• pencil • variety of concrete material

• add • number • how many • more than

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 38 – 39.

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New Wave Maths Book A – Teachers Guide • 101 •

Unit 21–3

Student page 63

Outcomes

Indicators

N1.1, M1.2, WM1.2

The student is able to: • select something longer than/ shorter than/same length as another thing by matching.

• ask ‘why’ or ‘how’ mathematical questions of other children.

• suggest how they can answer their own mathematical questions.

Skills • ordering events • measuring time

Number (N1.1)

Resources • pencil • coloured pencils/ crayons • counters • 2-D shapes

Language • add • top • box • around • bottom • biggest

r o e t s Bo Notes r e p ok u S

Main Activity (M1.2, WM1.2) Warm up

• Explain to the class they will be tracing around their hand in a space provided in the workbook. Demonstrate how they are to trace around their hand on the blackboard/ whiteboard. Keep your fingers together.

What to do

• Ask students to practise tracing around their hand using their index (pointer) finger as their tracing tool.

• Now use a pencil and trace around your hand.

• Choose a friend and trace around his/her hand in the space provided.

• How can you check to see who has the bigger hand? Encourage a range of answers then work with the class to try them and discuss with the class what they are doing and what they find.

• Allow students to discuss with their partner who has the bigger hand.

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 78 – 79.

• 102 • New Wave Maths Book A – Teachers Guide

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Unit 21—Answers

Student pages 61 – 63 Unit 21–2

Unit 21–1

3.

(c) 11

(d) 12

Number 1. (a) 5 Main Activity 2. (a) 5 (d) 6 (g) 7

(b) 6

(c) 7

(b) 3 (e) 8 (h) 4

(c) 2 (f) 2 (i) 3

(d) 8

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Number 1. (a) 9 (b) 10 Main Activity 2.

or

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(c) 7

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Consolidation 21–2 • Provide opportunities to complete similar activities explained in the ‘what to do’ section.

Consolidation 21–3

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• Trace and compare the size of a left or right foot with a classmate.

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New Wave Maths Book A – Teachers Guide • 103 •

Unit 22–1

Student page 64

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

Resources • pencil • variety of concrete materials

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting • adding

Language • add • number • how many • more than

• use objects to represent a number story and manipulate the objects to find a solution.

r o e t s Bo r e p ok u S • describe how he/she solved a number problem.

Number (N1.1)

Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

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• The focus for this unit is addition of basic facts using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 38 – 39.

• 104 • New Wave Maths Book A – Teachers Guide

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Unit 22–2

Student page 65

Outcomes

Indicators

N1.1, C&D1.2

The student is able to: • classify objects using one or two familiar criteria.

Skills

Resources

Language

• pencil • chart of days of the week

• measuring • ordering • recognising days of the week

Number (N1.1)

r o e t s Bo r e p ok u S

• take • how many more • larger • days, week • before, after • Wednesday, Saturday, Friday, Monday, Tuesday, Thursday, Sunday • next to

Notes

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• The focus for this unit is subtraction of basic facts using drawings to represent numbers.

Main Activity (C&D1.2) Warm up

• Ask students to name the days of the week. Have the whole class chant the names of the days of the week.

What to do

• Ask students what days come before and after - Monday, Friday, Sunday. Use a chart of the days of the week to assist.

• Work with students to complete the first activity in their workbook. Display a chart of the days of the week to assist.

• For the second activity, ask each student to write his/her own name in the space provided.

Then ask students to write the names of their three best friends. Use cards with student names on to assist individuals to spell names correctly.

• Next to the items on the page, ask each student to write his/her favourite. Assistance will be required to write many of the names of the chosen items.

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New Wave Maths Book A – Teachers Guide • 105 •

Unit 22–3

Student page 66

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

Resources • pencil • variety of concrete materials

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting • subtracting

• use objects to represent a number story and manipulate the objects to find a solution.

Language • take • how many more • larger • group • number • more than

r o e t s Bo Notes r e p ok u S • describe how he/she solved a number problem.

Number (N1.1) Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Also make each group the same at times so the answer will be zero. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 38 – 39.

• 106 • New Wave Maths Book A – Teachers Guide

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Unit 22—Answers

Student pages 64 – 66 Unit 22–2

Unit 22–1 Number 1. (a) 8 Main Activity 2. (a) 6 (d) 6 (g) 8

(b) 9

(c) 6

(b) 2 (e) 4 (h) 4

(c) 4 (f) 2 (i) 4

(d) 7

Number 1. (a) 2 (b) 1 Main Activity 2.

(c) 3

(d) 2

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3. Teacher check 4. Teacher check

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C.Publ i cat i ons Consolidation 22–1o •f orr evi ew u r poses nl y• Unit 22–3p (c) 4

(d) 3

• Provide opportunities to complete similar activities explained in the ‘what to do’ section.

Consolidation 22–2 (b) 4 (e) 4 (h) 4

(c) 4 (f) 3 (i) 2

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Number 1. (a) 1 Main Activity 2. (a) 8 (d) 7 (g) 6

• Arrange flashcards of the days of the week in the correct order.

• List and write favourites for other items such as colour, book or place to visit.

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Consolidation 22–3

• Provide opportunities to complete similar activities explained in the ‘what to do’ section, including equal groups where the answer is zero.

New Wave Maths Book A – Teachers Guide • 107 •

Unit 23–1

Student page 67

Outcomes N1.1, WM1.2, N1.2

Skills • counting • comparing

Number (N1.1)

Indicators

Resources

The student is able to: • suggest how to answer his/her own mathematical questions.

• manipulate objects mentioned in a problem to find a solution.

• describe how he/she solved a number problem.

• pencil • many squares and circles

Language • take • how many more • larger • group • different • square • circles

r o e t s Bo r e p ok u S

Notes

Main Activity (WM1.2, N1.2) Warm up

• Distribute several circles and squares to groups of students. Allow free play with the materials.

What to do

• Ask one student in the group to select a number of squares.

• Ask another student in the group to select a number of squares.

• Ask the group to decide how they can tell who has more items. Encourage much discussion within the groups. Share group items.

• Repeat until every student has had a turn at selecting squares and circles.

• Ask students to look at the squares and circles in their workbook. Show at least one way they are able to tell whether there are more squares than circles.

• If there are other ways they can tell, show these as well. Student representation should be in diagrammatic form unless they are very proficient at writing.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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• 108 • New Wave Maths Book A – Teachers Guide

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Unit 23–2

Student page 68

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

Resources

Language • take • how many more • larger • group • number • more than

• pencil • variety of concrete material

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting • difference • grouping

• use objects to represent number story and manipulate the objects to find a solution.

r o e t s Bo r e p ok u S • describe how he/she solved a number problem.

Number (N1.1)

Notes

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Teac he r

• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Keep the larger number less than 10. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 38 – 39.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 109 •

Unit 23–3

Student page 69

Outcomes

Indicators

N1.1, S1.2, S1.3, WM1.2

The student is able to: • remember the shape of objects and component parts of objects.

• fit figures and objects together based on shape and orientation.

• manipulate objects mentioned in a problem to find a solution.

Skills • working geometrically

Number (N1.1)

Resources • pencil • 2-D shapes

Language • take • how many more • larger • group • shapes • same • different • overlap

r o e t s Bo Notes r e p ok u S

Main Activity (S1.2, S1.3, WM1.2) Warm up

• Distribute a variety of 2-D shapes to groups and allow time for free play.

What to do

• Ask students to make shapes using the 2-D shapes. Describe the new shapes made.

• Ask each student to select up to five different items from the 2-D shapes. The items may be similar to or different from each other.

• Select one shape and place it in the space provided in the workbook. Trace around the shape. Select another shape and place it on the page so that it overlaps the first shape.

Trace around it.

• Colour the new shape made from the overlapping shapes. Provide a name for it.

• Continue to add shapes to their drawings, trace around each and name and colour the new shapes that are made.

• Finish when the space is filled.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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• 110 • New Wave Maths Book A – Teachers Guide

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Unit 23—Answers

Student pages 67 – 69 Unit 23–2

Unit 23–1 (c) 4

(d) 5

Number 1. (a) 3 Main Activity 2. (a) 8 (d) 7 (g) 9

(b) 2

(c) 1

(b) 4 (e) 4 (h) 2

(c) 4 (f) 3 (i) 7

(d) 6

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Number 1. (a) 3 (b) 1 Main Activity 2. Teacher check

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C.Publ i cat i ons Consolidation 23–1o Unit 23–3p •f orr evi ew u r poses nl y• (c) 6

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• Form groups of three and allow students to explain how each of them worked out whether there were more squares than circles.

Consolidation 23–2

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• Provide opportunities to complete similar activities explained in the ‘what to do’ section, with the larger number no more than 10.

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Consolidation 23–3

• Compare his or her drawings with a partner. Swap partners.

New Wave Maths Book A – Teachers Guide • 111 •

Unit 24–1

Student page 70

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

Resources • pencil • variety of concrete materials

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting • adding

• use objects to represent a number story and manipulate the objects to find a solution.

Language • take • how many more • larger • large, small • group • two, three, four • altogether

r o e t s Bo r e p ok u S • describe how he/she solved a number problem.

Number (N1.1)

Notes

Main Activity (N1.1, N1.2) Warm up

• Focus on the use of the addition sign and explain to the class that this is the symbol that tells them items are to be added together to find a total.

What to do

• Distribute concrete materials to groups of students. Allow time for free play.

• Ask students to take out a small number of items. Count them.Take another small number of items. Count them. How many do they have altogether?

• Repeat this many times.

• Direct students to take a set number of items and another set number or items. How many do they have altogether? Repeat this many times.

• Complete the workbook page, focusing on the use of the addition sign.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 54 – 55.

• 112 • New Wave Maths Book A – Teachers Guide

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Unit 24–2

Student page 71

Outcomes

Indicators The student is able to: • suggest how he/she can answer questions about the collections.

• suggest how to answer his/her own mathematical questions.

• say how many are in visible collections of objects.

N1.1, C&D1.2, WM1.2

Skills • counting • sorting • comparing

Number (N1.1)

Resources

Language

• pencil • concrete materials

• take • how many more • larger • group • altogether

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

Main Activity (C&D1.2, WM1.2, N1.1) Warm up

• Organise the class into groups and distribute a variety of concrete materials. Allow time for free play.

What to do

• Ask one student to scoop up two handfuls of items from the set at their group. Working together, sort the material into three to five groups.

• Ask the students to find out how many items are in each group. How many items are there altogether? Ask students how they found the number of items in each group. Ask if they could have found the number of items in each group in another way. Explain and share explanations.

• Repeat using different materials.

• Use the workbook page as a written record of this activity. Use concrete materials to place on pets to show the different groupings if this helps.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

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New Wave Maths Book A – Teachers Guide • 113 •

Unit 24–3

Student page 72

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting • adding on

Resources • pencil • concrete materials • number line (see pages 201 – 202)

• use objects to represent a number story and manipulate the objects to find a solution.

• take • how many more • larger • longer • group • bottom • line • top • number line

r o e t s Bo Notes r e p ok u S • describe how he/she solved a number problem.

Number (N1.1)

Language

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

• Use a large number and individual student number lines to work the following examples.

Ask the students to follow your instructions and repeat what you say. ‘How many more is seven than five?’ Point to 7 in the number line. Point to 5 on the number line. ‘Repeat after me - start at 5, 6, 7. Seven is 2 more than 5. I needed to add on two (count two numbers) to reach 7 from 5’. (Students may keep a record using their fingers or counters to note numbers counted on; e.g. start at 5 - 6, one finger, 7 two fingers - 2 more than 5.)

• Repeat this a number of times then use the workbook examples as written records. Use the same process for written records.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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• 114 • New Wave Maths Book A – Teachers Guide

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Unit 24—Answers

Student pages 70 – 72 Unit 24–2

Unit 24–1 (c) 6

(d) 2

Number 1. (a) 4 (b) 2 Main Activity 3. (a) 3 (b) 4 (c) 1 (d) 3 (e) 1 (f) 2 (g) 14 4. Teacher check 5. Teacher check

(c) 3

(d) 1

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Number 1. (a) 5 (b) 7 Main Activity 2. 7 3. 5 4. 9 5. 5 6. 7

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• Complete similar activities and make written records using the addition sign, with the sum totalling less than 10.

Consolidation 24–2

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• Cut out pictures from magazines of animals, food or toys.

Sort into groups and count items in individual groups and total of all groups. (Keep amounts to less than 20.)

Consolidation 24–3

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• Use a ruler as a number line to assist in similar activities, keeping the higher number 10 or less.

New Wave Maths Book A – Teachers Guide • 115 •

Unit 25–1

Student page 73

Outcomes

Indicators The student is able to: • convey the essential spatial features of common mathematical figures in his/her drawings.

• recognise shapes which are rectangles, squares, triangles and circles.

• give some examples of shapes being used for particular purposes.

N1.1, S1.2, S1.4, WM1.1

Skills • identifying shapes • drawing shapes

Number (N1.1)

Resources • pencil • variety of 2-D shapes • playground

Language • take • how many more • larger • group • shape • match • rectangle, triangle, circle, square

r o e t s Bo r e p ok u S

Notes

Main Activity (S1.2, S1.4, WM1.1) Warm up

• Provide groups of students with a variety of 2-D shapes and allow time for free play.

What to do

• Ask students to select a rectangle, square, triangle and a circle. Discuss the features of each shape.

• ‘Look around the classroom. Are you able to see any shapes in the classroom that are the same as those you have? Describe the shapes, where they are and what they are.’

• Ask for a range of descriptions.

• Write one object in the workbook.

• Take the shapes and workbook out to the playground. Find shapes in the playground the same as the four shapes. Draw a picture of where the shape was found.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 10 – 11.

• 116 • New Wave Maths Book A – Teachers Guide

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Unit 25–2

Student page 74

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting on • adding • difference • grouping

Resources

Language

• pencils • concrete materials • counters

• use objects to represent a number story and manipulate the objects to find a solution.

r o e t s Bo r e p ok u S • describe how he/she solved a number problem.

Number (N1.1)

• take • how many more • larger • group • altogether • add • number sentence • answer • equal

Notes

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

Main Activity (N1.1, N1.2) Warm up

• Focus on the use of the addition sign and explain to the class that this is the symbol that tells them items are to be added together to find a total.

What to do

• Distribute concrete materials to groups of students. Allow time for free play.

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

• Use counters to show 2 and counters to show 7. How many counters are there altogether?

How did they find the total? Count on, count together or use any other method.

• Continue to use counters (if required) to complete the rest of the exercise.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 56 – 57.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 117 •

Unit 25–3

Student page 75

Outcomes

Indicators

N1.1, M1.2

The student is able to: • use informal units repeatedly to match the length of things and say how many fit.

Skills

Resources • pencil • 1-cm cubes • 2-cm cubes

• measuring

Number (N1.1)

Language • take • how many more • larger • group • long

r o e t s Bo Notes r e p ok u S

Main Activity (M1.2) Warm up

• Provide 1- and 2-cm cubes to groups of students and encourage them to use the cubes to measure objects of their own choosing.

What to do

• Direct students to use the 1-cm cubes to measure the length of the drawings of pencils in their workbook. Record the number of 1-cm cubes required in the space provided at the end of each drawing.

• Repeat using 2-cm cubes for each of the drawings.

Note: Students measure to the nearest even number of cubes.

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• The focus for this unit is the basic facts of subtraction using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 78 – 79.

• 118 • New Wave Maths Book A – Teachers Guide

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Unit 25—Answers

Student pages 73 – 75 Unit 25–2

Unit 25–1 (c) 2

(d) 1

Number 1. (a) 9 (b) 8 Main Activity 2. (a) 4 + 4 = 8 (b) 3 + 3 = 6 (c) 4 + 5 = 9 (c) 4 + 4 = 8 3. (a) 9 (d) 7 (b) 7 (e) 6 (c) 3 (f) 9

(c) 7

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(g) 7 (h) 8 (i) 8

(d) 6

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Number 1. (a) 4 (b) 3 Main Activity 2. Teacher check 3. Teacher check

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Consolidation 25–2

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• Provide opportunities for further activities using the addition sign and counters (if required).

Consolidation 25–3

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• Use 1- and 2-cm tiles to complete similar measuring activities.

New Wave Maths Book A – Teachers Guide • 119 •

Unit 26–1

Student page 76

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are visible collections of objects.

Skills

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting on • adding • difference • grouping

Resources • pencil • concrete materials • counters

• use objects to represent a number story and manipulate the objects to find a solution.

Language • add • how many • altogether • square, triangle, circle, rectangle, octagon • equal • number sentence

r o e t s Bo r e p ok u S • describe how they solved a number problem.

Number (N1.1)

Notes

Main Activity (N1.1, N1.2) Warm up

• Focus on the use of the addition sign and explain to the class that this is the symbol that tells them items are to be added together to find a total.

What to do

• Distribute concrete materials to groups of students. Allow time for free play.

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

• Use counters to show 2 and counters to show 1. How many counters are there altogether?

How did they find the total? Count on, count together or use any other method.

• Continue to use counters (if required) to complete the rest of the exercise.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 56 – 57.

• 120 • New Wave Maths Book A – Teachers Guide

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Unit 26–2

Student page 77

Outcomes N1.1, C&D1.2, C&D1.3

Skills • sorting • ordering • graphing

Number (N1.1)

Indicators

Resources

The student is able to: • classify objects using one or two familiar criteria.

• summarise information by counting.

• pencil • students • number line (see pages 201 – 202)

Language • add • count • blue, brown, green, hazel • most • least • order

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is the basic facts of addition using drawings to represent numbers.

Main Activity (C&D1.2, C&D1.3) Warm up

• Explain to the class that we often need to sort items according to given criteria.

What to do

• Use students to sort into—boys and girls—left-handed and right-handed—with 0, 1, 2, 3 or more brothers and sisters.

• Use the workbook to record the sorting as asked for. Group students according to eye colours of blue, brown, green and hazel. Write the total in the workbook.

• Order colours from most to least. Use a number line to assist if required.

• Sort students according to footwear: shoes, sports shoes, boots or sandals.

• Order footwear from most to least.

• Have a general discussion of other things around the school that could be counted and ordered. Students may write their own description or copy one from the blackboard/ whiteboard.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 94 – 95.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 121 •

Unit 26–3

Student page 78

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting • grouping

Resources • pencil • counters • interconnecting cubes

• use objects to represent a number story and manipulate the objects to find a solution.

Language • add • how many • lots of • two, three, four • altogether • equal

r o e t s Bo Notes r e p ok u S • describe how he/she solved a number problem.

Number (N1.1) Main Activity (N1.1, N1.2) Warm up

• Distribute counters, unifix and/or other similar materials to groups of students. Allow time for free play.

What to do

• Ask each individual to select two of the same items - counters or interconnecting cubes.

Select another two of the same items and keep in a group separate from the first two.

How many groups do they have? (2) How many are there in each group? (2) How many are there altogether? (4) • Repeat this many times for groups of 2, 3 or 4. Keep the overall total to 10 or less.

Encourage students to verbalise; e.g. ‘I have 2 groups of 2. I have 4 altogether. 2 groups of (or lots of) 2 make (equal) 4.’

• Written records of this activity may be made in the workbook. Use concrete materials to assist if required.

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• The focus for this unit is the basic facts of addition using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 42 – 43.

• 122 • New Wave Maths Book A – Teachers Guide

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Unit 26—Answers

Student pages 76 – 78 Unit 26–2

Unit 26–1 (c) 12

(d) 13

Number 1. (a) 7 (b) 8 Main Activity 2. Teacher check 3. Teacher check 4. Teacher check 5. Teacher check 6. Teacher check

(c) 9

(d) 10

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(g) 8 (h) 8 (i) 9

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Number 1. (a) 10 (b) 11 Main Activity 2. (a) 6 + 2 = 8 (b) 3 + 2 = 5 (c) 5 + 5 = 10 (d) 3 + 4 = 7 3. (a) 3 (d) 6 (b) 7 (e) 6 (c) 7 (f) 7

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C.Publ i cat i ons Consolidation 26–1o Unit 26–3p •f orr evi ew u r poses nl y• (c) 14

(d) 15

• Cut out pictures from magazines of the four 2-D shapes and create four wall charts to display.

Consolidation 26–2 9 altogether 8 altogether 4 altogether 6 altogether 6 altogether

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• Count and order one or more suggestions given for Exercise 6.

Consolidation 26–3

• Provide opportunities for further activities to group up to 10 objects into 1s, 2s, 3s, 4s or 5s.

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New Wave Maths Book A – Teachers Guide • 123 •

Unit 27–1

Student page 79

Outcomes

Indicators

N1.1, WM1.2, WM1.4

The student is able to: • suggest how to answer his/her own mathematical questions.

• respond to a direct challenge.

Skills • counting • comparing

Number (N1.1)

Resources • pencil

Language • add • count • triangles • how many • shapes • same • number

r o e t s Bo r e p ok u S

Notes

Main Activity (WM1.2, WM1.4) Warm up

• Read through all instructions in the workbook to the whole class.

What to do

• Ask students to count the triangles. Check to confirm there is agreement.

• Ask students to count the stars. Check to confirm there is agreement.

• Ask students to think about how they can be sure there are the same number of triangles as stars. All have counted and checked, but mistakes can be made counting—how can students be sure the count was correct?

• Share ideas. Try ideas on blackboard/whiteboard or overhead using a transparency of the page.

• Write an explanation on the board for the class to copy or allow capable students to give their own explanation in writing.

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• The focus for this unit is the basic facts of addition using drawings to represent numbers.

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Unit 27–2

Student page 80

Outcomes

Indicators

N1.1, N1.2

The student is able to: • say how many are in visible collections of objects.

• from a collection, circle sets of objects.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

Skills • counting on • sharing • grouping

Number (N1.1)

Resources

Language

• pencil • counters • interconnecting cubes

• add • equal • sets • two, three, four

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is the basic facts of addition using drawings to represent numbers.

Main Activity (N1.1, N1.2) Warm up

• Distribute counters and interconnecting cubes or similar to groups of students. Allow time for free play.

What to do

• Ask students to take four of the same items from the group. Make 2 equal sets (groups) using these four items. How many items are there in each group?

• Repeat this many times using different quantities up to and including ten, sharing into equal sets of 2, 3 or 4.

• Emphasise the use of language and encourage students to talk their way through each activity.

• A written record of this activity may be made in the workbook. Use concrete materials to assist by placing them over the drawings if this helps.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 42 – 43.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 125 •

Unit 27–3

Student page 81

Outcomes

Indicators

N1.1, M1.2

The student is able to: • use informal units repeatedly to match the length of things and say how many fit.

Skills

Resources • pencil • 1-cm cubes • 2-cm cubes

• measuring

Number (N1.1)

Language • add • measure • length • how many • cubes • longest, shortest

r o e t s Bo Notes r e p ok u S

Main Activity (M1.2) Warm up

• Distribute 1- and 2-cm cubes to groups of students and encourage them to use the cubes to measure objects of their own choosing.

What to do

• Direct students to use the 1-cm cubes to measure the length of the drawings of pencils in their workbook. Record the number of 1-cm cubes required in the space provided at the end of each drawing.

• Repeat using 2-cm cubes for each of the drawings.

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• The focus for this unit is basic facts of addition using drawings to represent numbers.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 78 – 79.

• 126 • New Wave Maths Book A – Teachers Guide

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Unit 27—Answers

Student pages 79 – 81 Unit 27–2

Unit 27–1 (c) 10

(d) 11

Number 1. (a) 12 (b) 13 (c) 14 Main Activity 2. (a) 3 books in each set (b) 3 squares in each set (c) 2 trains in each set (d) 2 triangles in each set (e) 2 soldiers in each set

(d) 15

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Number 1. (a) 8 (b) 9 Main Activity 2. (a) 8 (b) 8 (c) 16 3. Teacher check 4. Teacher check

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(d) 13

• Discuss with a partner how each of them solved Exercises 3 and 4.

Consolidation 27–2 (b) 5 (d) 10

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• Provide opportunities for further activities to make equal sets from up to 10 objects.

Consolidation 27–3

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• Find objects in their desks that are a set number of 1- or 2cm cubes (or tiles) in length.

New Wave Maths Book A – Teachers Guide • 127 •

Unit 28–1

Student page 82

Outcomes WM.1.1, WM1.2

Skills • working mathematically • discussing • explaining • observing

Indicators

Resources

The student is able to: • give examples of some of the ways in which he/she and his/her family uses numbers.

• offer questions when prompted by their teacher.

• ask ‘why’ or ‘how’ mathematical questions of other children.

• pencil • signs in the environment with numbers • photographs or pictures of signs from magazines etc. (optional)

Language • number • numeral • sign • symbol • registration number • postcode • address • speed limit

r o e t s Bo r e p ok u S

Notes

Main Activity (WM1.1, WM1.2)

• The aim of the activity is to identify and discuss how and why numbers are used in their environment.

• This activity can be completed individually, with a partner or as a whole class. Assistance in writing the answer may be required.

• Direct students to look at each number sign in their workbook. Individually, perhaps after class or partner discussion, students make a written explanation about what the numbers in each sign are used for.

• Words and phrases could be written on a blackboard/whiteboard before students write in their workbooks.

• A follow-up activity could be to show photographs or pictures of number signs and discuss them. Students can also brainstorm signs and these can be drawn on the blackboard/ whiteboard.

Note: The car licence plate has been altered to avoid inadvertently identifying a real motor vehicle.

The name and address on the letter are fictitious, though 6024 is Greenwood’s postcode.

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What to do

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Unit 28–2

Student page 83

Outcomes

Indicators

N1.1, C&D1.2, C&D1.3

The student is able to: • suggest how he/she can answer questions about the collections.

• summarise information by counting.

• talk about what he/she has found from the data collection and display.

Skills • sorting • ordering • graphing

Number (N1.1)

Resources

Language • add • how many • counted

• pencil • coloured pencils/ crayons

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is basic facts of addition using drawings to represent numbers.

Main Activity (C&D1.2, C&D1.3) Warm up

• Revise graphs. Use students to stand in lines, one for boys and one for girls. Change the graph to hair colour, eye colour, type of clothes etc. Ask students how many in each group, which group has the most, least, etc.

What to do

• Remind students that the graph they will be completing will have one picture to show one item just as one child showed one person for each of the human graphs just made.

• Ask students to stand if they have a dog as a pet. Write the number on the blackboard/ whiteboard. Continue for cat, bird, fish, guinea pig or other pets, recording the total each time.

• Ask students to draw a picture of the pet or a person for each person who had a particular type of pet; e.g. five dogs as pets, draw five dogs in the column above the word dogs, or draw five people.

• Continue for each different type of pet, showing the totals.

• Discuss the final graph with the class. Discuss most types of pets, least types and how many pets there are altogether.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 129 •

Unit 28–3

Student page 84

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting on • adding • grouping • comparing

Resources • pencil • concrete materials • number line (pages 201 – 202)

Language • add • how many • more than

• use objects to represent a number story and manipulate the objects to find a solution.

r o e t s Bo Notes r e p ok u S • describe how he/she solved a number problem.

Number (N1.1) Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group. It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

• Emphasise the comparison of the two sets and the difference between the two sets.

Discuss how students will find the difference – direct comparison, adding on from smaller group (coupling), counting back from larger group.

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• The focus for this unit is basic facts of addition using drawings to represent numbers.

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Unit 28—Answers

Student pages 82 – 84 Unit 28–2

Unit 28–1 Number 1. (a) 13 (b) 12 Main Activity 2. Teacher check 3. Teacher check

(c) 11

(d) 10

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Main Activity Teacher check Answers should indicate: • car registration number so car and owner can be traced.

• house number on letterbox informs visitors, mail deliveries etc.

• number informs drivers of the speed limit.

• letter shows the postcode for mail sorting purposes; house number for delivery; cost of required stamp.

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• Students create a display or a class book of number signs in their environment. Direct students to look for signs going to and from school, visiting shopping centres or community centres etc.

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• Make a pictograph of hair colour, eye colour, favourite toys from a small selection etc.

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Consolidation 28–3

• Complete similar activities with concrete materials or pictures.

New Wave Maths Book A – Teachers Guide • 131 •

Unit 29–1

Student page 85

Outcomes

Indicators The student is able to:

N1.1, S1.1, S1.2

• respond appropriately to the language of position and orientation such as ‘under’, ‘behind’, ‘in front of’, ‘below’, ‘on’, ‘alongside’, ‘near’, and ‘right’ and ‘left’.

Skills • discussing • drawing • recognising shapes • recognising position

Resources • counters or similar • pencil • coloured pencils

• draw pictures or make things which illustrate the meaning of words relating to position and orientation.

Language • add • two • in front • taller • leads • from, to

• draw or make a thing from an oral description which involves spatial language or implies shape.

Number (N1.1)

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Notes

Main Activity (S1.1, S1.2) Warm up

• Hold a general discussion with the whole class on what a house looks like. Discuss the shape of the front of the house. Ask, ‘What would you probably see on the front wall of the house?’ (Door(s), window(s)) ‘What would be on top of the wall?’ (Roof.) ‘What shape might the roof be? Would there be anything on the roof?’ (TV aerial, chimney, solar panels) ‘What might be in front of or near the house?’ (Garden, trees, shrubs, fences)

What to do

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• The focus for this unit is basic facts of addition.

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• With assistance from the students draw a house on the blackboard/whiteboard as they agree on shapes and features as discussed above.

• Use the instructions in the workbook, read and ask students to draw each item as it is described. Some students may draw a 3-D perspective of a house, others will draw a 2-D perspective. Accept both but discuss why there are different perspectives.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 2 – 3.

• 132 • New Wave Maths Book A – Teachers Guide

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Unit 29–2

Student page 86

Outcomes

Indicators The student is able to:

N1.1, N1.2

• say how many are in visible collections of objects.

Skills

• when counting small collections, use the last number said as the answer to ‘How many?’.

• counting on • adding • grouping • comparing

Resources

Language

• counters or similar • pencil • concrete materials

• add • how many • more than

• use objects to represent a number story and manipulate the objects to find a solution.

r o e t s Bo r e p ok u S • describe how he/she solved a number problem.

Number (N1.1)

Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

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• The focus for this unit is basic facts of addition.

• Direct students to take out 5 items. Ask them to take another 3 items. Which group has the most? How many more than the smaller group? It may help students if items from each group are placed in a line and the items are paired where possible to assist students to find the differences between quantity in the two groups.

• Repeat this many times. Make the first group the larger at times and on other occasions make the second group larger. Encourage students to verbalise their work at all times.

• Written records of this activity may be made by completing the workbook page. Concrete materials may be used to place over the drawings if this will assist students.

• Emphasise the comparison of the two sets and the difference between the two sets.

Discuss how students will find the difference—direct comparison, adding on from smaller group (coupling), counting back from larger group.

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New Wave Maths Book A – Teachers Guide • 133 •

Unit 29–3

Student page 87

Outcomes N1.1, M1.2, WM1.2

Skills • measuring

Number (N1.1)

Indicators

Resources

The student is able to: • count informal units to measure the area of given shapes.

• manipulate objects mentioned in a problem to find a solution.

• counters or similar • pencil • counters • assorted concrete materials

Language • add • shape • more • cover • inside

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Main Activity (M1.2, WM1.2) Warm up

• Distribute counters and the concrete materials among groups of students. Allow them time for directed play. Ask students to use the materials to cover items of their choice.

Discuss with the whole class the activities that each group has been involved in.

What to do

• Ask students to use counters only to cover the top shape in their workbook. Ask, ‘How many counters did you use? Why did different people use different numbers of counters?

Does it matter about the spaces left or the overlap of counters outside the boundary?‘ Allow students to determine their own stance.

• Repeat for the second shape. Ask ‘Which shape, A or B, required more counters to cover it? Discuss findings.

• Ask students to repeat the exercise using different shapes or materials to cover shapes A and B. Discuss the findings.

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• The focus for this unit is basic facts of addition.

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Unit 29—Answers

Student pages 85 – 87 Unit 29–2

Unit 29–1 (c) 2

(d) 5

Number 1. (a) 8 (b) 3 Main Activity 2. (a) 3 (b) 5 (c) 2 (d) 3 (e) 5 (f) 2

(c) 9

(d) 6

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Number 1. (a) 4 (b) 7 Main Activity 2. Teacher check

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• Complete similar activities using oral instructions to draw objects in a variety of positional orientations. Settings could be in a park or at the beach.

Consolidation 29–2

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• Provide further opportunities for students to find the difference between two sets by direct comparison, coupling or counting back.

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Consolidation 29–3

• Students continue using informal units to estimate and check the amount needed to cover given shapes or objects.

New Wave Maths Book A – Teachers Guide • 135 •

Unit 30–1

Student page 88

Outcomes

Indicators

N1.1, N1.2

The student is able to: • say how many are in visible collections of objects.

• make or draw collections of a given size.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

Skills • counting • adding • difference

Number (N1.1)

Resources • counters or similar • pencils • counters • interconnecting cubes • coloured rods • other concrete materials

Language • add • two, three • squares • circle • how many • lots of • triangle

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Notes

Main Activity (N1.1, N1.2) Warm up

• Distribute materials among groups of students and allow free play.

What to do

• Ask students to select one item, select one more item and place it apart from the first item. Initially, asking students to use counters only as the selected item may assist in developing the concept. Language can be more specific in selecting one counter, such as take one more counter. Ask, ‘How many counters are there in each group? How many counters are there altogether?’ and so on. ‘How many items are there in each group?’ (1) ‘How many lots of one?’ (2) ‘How many items are there altogether? (2) ‘Two lots of one equal 2.’

• Repeat this activity and the vocabulary used above many times using lots of one, two, three or four to make totals to 10.

• Written records of this activity may be made in the workbook. Concrete materials may be used to place in the circles.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 42 – 43.

• 136 • New Wave Maths Book A – Teachers Guide

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Unit 30–2

Student page 89

Outcomes N1.1, C&D1.2, C&D1.3

Skills • sorting • ordering • graphing

Number (N1.1)

Indicators

Resources

The student is able to: • classify objects using one or two familiar criteria.

• suggest how he/she can answer questions about the collections.

• draw a picture as a record of the results.

• summarise information by counting.

• counters or similar • pencil • coloured pencils/ crayons • students

Language • add • number • graph • box • blonde, brown, black, red

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Notes

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• The focus for this unit is basic facts of addition.

Main Activity (C&D1.2, C&D1.3) Warm up

• Revise graphs—one item (box or picture) shows one member of that group. Practise sorting students into boys and girls. Count the number in each group. Pair group members to see which is the larger group.

What to do

• Organise another sorting into those with only sisters, only brothers, brothers and sisters or no brothers or sisters. Match group members to see which is the largest.

• Sort students according to hair colour – blonde, brown, black or red. Others need to be set aside or placed in a group as close to their hair colour as possible.

• Match groups to see which are the largest and the smallest. Record total group numbers on the blackboard/ whiteboard.

• Assist students to complete the graph in the workbook. Count the number of boxes until the total number of blonde children is reached. Ask students to colour all the boxes, up to and including the last they counted, yellow. This represents the number of blonde students in the class.

• Repeat for other hair colours.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

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New Wave Maths Book A – Teachers Guide • 137 •

Unit 33–1

Student page 97

Outcomes N1.1, N1.4, S1.4

Skills • drawing • following patterns • creating patterns

Number (N1.1)

Indicators

Resources

The student is able to: • copy and continue in materials the pattern of the counting numbers.

• recognise shapes which are rectangles, squares, triangles and circles.

• pencil • interconnecting cubes • counters or similar materials • coloured pencils/ crayons

Language • pattern • next • three • shapes • same • pair

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Notes

Main Activity (N1.4, S1.4) Warm up

• Distribute the interconnecting cubes, counters and/or other concrete materials to groups of students. Allow free play.

What to do

• Direct students to make patterns with the materials. Ask them to describe their patterns to other group members, or if the whole group is making the pattern, to describe the pattern to the class.

• Allow time for several pattern-making activities.

• Work with the students to determine what pattern the next card in each of the two series in the workbook will look like. It may help to draw the blank card on the blackboard/ whiteboard and have students describe what the next card will look like. Complete the description on the board—encourage discussion to determine final satisfaction with the pattern.

• Use coloured pencils/crayons to colour the pairs of shapes the same colour in Exercises 4 and 5. (Note: The triangle in Exercise 5 can not be paired.)

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Unit 33–2

Student page 98

Outcomes

Indicators

N1.1, N1.4

The student is able to: • say how many are in visible collections of objects.

• sort coins and notes and realise that coins and notes have different values.

• copy and continue repeating patterns.

Skills • counting on • working with money

Number (N1.1)

Resources

Language

• counters or similar • pencils • plastic coins • interconnecting cubes • coloured rods or similar patternmaking materials • coloured pencils/ crayons

• count • how much • money • copy • pattern

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Notes

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• The focus for this unit is adding on.

Main Activity (N1.1, N1.4) Warm up

• Distribute pattern-making materials and plastic coins to groups of students. Allow time for free play.

What to do

• Direct students to make small sets of the same coin. Count to see how much money is in each set. Students may be directed to use given numbers of coins.

• Use the workbook page to make written records of this activity. Use coins if it helps.

• Ask students to choose colours to colour the patterns on their workbook page. When the patterns are coloured, students are to draw a copy of the pattern below that is shown in the workbook.

• Students may be directed to make and discuss their own patterns made with the concrete materials.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 46 – 47.

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New Wave Maths Book A – Teachers Guide • 139 •

Unit 33–3

Student page 99

Outcomes N1.1, S1.2, S1.3

Skills • recognising shape • colouring

Number (N1.1)

Indicators

Resources

The student is able to: • remember the shape of objects and component parts of objects.

• fill in patterns where lines are provided to enable direct matching of component shapes.

• counters or similar • pencil • coloured pencils/ crayon

Language • squares • frame • circles • different • regions

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Main Activity (S1.2, S1.3) Warm up

• Ask students to open their workbook page.

What to do

• The drawing on the page shows squares, rectangles and circles.

• Choose one colour and colour only the circles.

• When completed, choose another colour and colour only the squares with nothing drawn in them.

• Choose a third colour and colour the regions left in the squares and rectangles that have the circles drawn in them.

• Ask students if they coloured the whole shape. (The answer will be ‘yes’ if they have correctly identified the shapes.)

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Unit 33—Answers

Student pages 97 – 99 Unit 33–2

Unit 33–1 Number 1. (a) 1 (b) 2 Main Activity 2.

3.

(d) 4

Number 1. (a) 1 (b) 1 Main Activity 2. (a) $6 (b) 20c 3. Teacher check

(c) 3

(d) 5

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4.

(c) 4

5. It is not possible to pair the shapes.

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• Create number patterns with concrete objects and ask another classmate to describe it. Give the answer if necessary.

Consolidation 33–2

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Number 1. (a) 1 (b) 5 Main Activity 2. Teacher check

• Provide opportunities to practise counting a given number of the same coins.

• Students can create their own pictorial number patterns and share these with classmates.

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Consolidation 33–3

• Compare frames with other classmates to discuss the visual effects different colour choices make.

• Complete other pattern frames using three or four colours.

New Wave Maths Book A – Teachers Guide • 141 •

Unit 34–1

Student page 100

Outcomes N1.1, N1.2, M1.2

Skills • counting • sharing • grouping

Number (N1.1)

Indicators

Resources

The student is able to: • share numbers into equal groups.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• count informal units of length.

• counters or similar • pencils • 1-cm cubes • 2-cm cubes • concrete materials

Language • subtract • share • numbers • groups • long

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Notes

Main Activity (N1.1, N1.2, M1.2) Warm up

• Distribute 1- and 2-cm cubes and concrete materials to groups of students. Allow time for free play.

What to do

• Ask students to select 9 items. Share them into three equal groups. Ask, ‘How many groups do you have?’ (3) ‘How many items are there in each group?’ (3) ‘How many items did you start with?’ (9) ‘9 can be shared into 3 groups of 3.’

• Repeat this activity many times, sharing up to 20 items into groups of 2, 3, 4 or 5. Encourage students to verbalise their actions at all times.

• Written records of this activity can be made in the workbook. Students write the number to be shared in each shape. Use concrete materials if this assists.

• Direct students to line 1-cm cubes along the first fish. How many are used? Write this number in the space provided.

• Repeat this with 2-cm cubes.

• Repeat process for second fish.

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Unit 34–2

Student page 101

Outcomes

Indicators

WM1.2

The student is able to: • offer questions when prompted by their teacher asking.

• ask ‘why’ or ‘how’ mathematical questions of other children.

Skills • working mathematically • problem-solving • discussing • explaining • counting

Resources

Language

• pencil • coloured pencils • Smarties™ (optional)

• counting • number • decide • decision • problem • adding • tally

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Notes

Main Activity (WM1.2)

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What to do

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• The activity can be completed individually, with a partner, in a small group or as a whole class. Some students may be more successful in mixed-ability groups rather than sameability groups (or partners). Some groups/partners will be able to work independently while others may need guidance.

• Individually, or after partner, group or class discussion, students count the Smarties™ and use words and/or pictures to explain how they counted them.

• Discuss the methods used and difficulties encountered. For example, if they crossed them out as they counted, one or more could have been missed; if they counted by colour, made a tally of each and added the totals, a miscalculation could have been made.

• A follow-up activity could be to count the number of actual Smarties™ in a box. Can any of the same methods be used as in the workbook activity?

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New Wave Maths Book A – Teachers Guide • 143 •

Unit 34–3

Student page 102

Outcomes N1.1, N1.2

Skills • counting • grouping

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• share collections into equal groups.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• counters or similar • pencil • counters • interconnecting cubes • coloured or similar materials

Language • subtract • share • how many • shapes • two • groups

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Main Activity (N1.1, N1.2) Warm up

• Share the concrete materials among groups of students and allow free play.

What to do

• Ask students to select 9 items. Share them into three equal groups. Ask, ‘How many groups do you have?’ (3) ‘How many items in each group?’ (3) ‘How many items did you start with?’ (9) ‘9 can be shared into 3 groups of 3.’

• Repeat this activity many times, sharing up to 20 items into groups of 2, 3, 4 or 5. Encourage students to verbalise their actions at all times.

• Written records of this activity can be made in the workbook. Use concrete materials if this assists.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 42 – 43.

• 144 • New Wave Maths Book A – Teachers Guide

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Unit 34—Answers

Student pages 100 – 102 Unit 34–2

Unit 34–1 Main Activity 1. There are 40 Smarties™.

2. Answers will vary.

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Number 1. (a) 7 (b) 5 (c) 1 (d) 3 Main Activity 2. (a) 2, 2, 2, 2 (b) 2, 2, 2 (c) 3 (d) 3, 3, 3 (e) 3, 3, 3, 3 3. (a) 8 x 1-cm cubes 4 x 2-cm cubes (b) 6 x 1-cm cubes 3 x 2-cm cubes

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• Provide further opportunities to share up to 20 items into equal groups.

• Use 1- and 2-cm cubes to measure other items; e.g. fallen leaves or twigs.

Consolidation 34–2

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• Record ways of counting large collections of other items such as a variety of buttons, counters, plastic animals or packets of balloons.

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• Provide further opportunities to share up to 20 items into equal groups.

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New Wave Maths Book A – Teachers Guide • 145 •

Unit 30–3

Student page 90

Outcomes N1.1, N1.2, N1.3

Skills • counting • grouping

Number (N1.1)

Indicators

Resources

Language

The student is able to: • say how many are in visible collections of objects.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• say the number sequence of 2s, e.g.

2, 4, 6, …

• counters or similar • pencils • assorted concrete materials • number line (see pages 201 – 202)

• add • how many • sets • altogether • count • total • twos • number line • squares, circles, triangles • ten, three, one, six, seven, nine

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Main Activity (N1.1, N1.2, N1.3) Warm up

• Distribute materials to groups of students. Allow free play.

What to do

• Direct students to make two sets of two items each. Check how many items are in each group. (2) ‘How many items are there altogether?’ (4) ‘Two lots of two equal four.’ Encourage students to verbalise their actions.

• Repeat this many times using different numbers (1 – 5) in sets to a total of 10.

• Written records of this activity may be made in the workbook.

• Before completing Exercises 3(d) and 4, give students practice in counting by twos, starting at different numbers and using a number line to assist.

• Work through the remaining activities in the workbook with the students.

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Unit 30—Answers

Student pages 88 – 90 Unit 30–2

Unit 30–1 (b) 5

(c) 8

(d) 9

(b) 8 (b) 9 (b) 10

Number 1. (a) 5 (b) 7 Main Activity 2. Teacher check

(c) 4

(d) 9

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• Provide further opportunities for students to practise using the vocabulary ’how many?’ and ‘lots of ’ in activities with concrete materials and totals no more than 10.

Consolidation 30–2 (d) 8

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• Brainstorm to find other things students can use to graph.

Consolidation 30–3

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• Practise using a number line to assist in counting 2s to 10, starting and finishing at different numbers.

New Wave Maths Book A – Teachers Guide • 147 •

Unit 31–1

Student page 91

Outcomes

Indicators The student is able to:

N1.1, S1.1

• respond appropriately to the language of position and orientation such as ‘under’, ‘behind’, ‘in front of ’, ‘below’, ‘on’, ‘alongside’, ‘near’, and ‘right’ and ‘left’.

Skills • drawing • following paths

Resources • counters or similar • pencil • coloured pencils/ crayons

• use some of the language of position and orientation for himself/herself.

• respond appropriately to the language of movement such as ‘back’, ‘forward’, ‘around’, ‘past’, ‘turn’ and ‘up’.

Language • add • path • centre • maze • ends • belong

r o e t s Bo r e p ok u S • use some of the language of movement for himself/herself.

Number (N1.1)

Notes

Main Activity (S1.1) Warm up

• Display a maze using an overhead transparency and work with the class to find the way through it. Ask the students to direct you. If the path finishes in a dead end, start again from the beginning. Use a different coloured pen for each path started.

• Encourage students to use positional and orientational language such as ‘left’, ‘right, ‘across’, ‘next’, ‘turn’.

What to do

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• Ask students to find the path through the workbook maze. Most should find the shortest route themselves.

• Ask students to find an alternative path. (Use a different colour.) Share the findings with the whole class. This may be done on the overhead by following the path as described by the student or by copying his/her path onto the overhead.

• Ask students to trace along the two pieces of string, using a different colour for each, to find the matching ends.

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Unit 31–2

Student page 92

Outcomes N1.1, N1.2

Skills • counting on • sharing • grouping • comparing

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• make or draw collections of a given size.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• counters or similar • pencil • concrete materials

Language • add • two, four • lots of • how many

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Notes

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• The focus for this unit is addition to 20.

Main Activity (N1.1, N1.2) Warm up

• Distribute materials to groups of students. Allow free play.

What to do

• Direct students to make two sets of two items each. Check how many items are in each group. (2) ‘How many items are there altogether?’ (4) ‘Two lots of two equal four.’ Encourage students to verbalise their actions.

• Repeat this many times using different numbers (1 – 5) in sets to a total of 10.

• Written records of this activity may be made in the workbook. Concrete materials can be placed in the circles before drawing chosen objects or pictures in the circles.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 42 – 43.

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New Wave Maths Book A – Teachers Guide • 149 •

Unit 31–3

Student page 93

Outcomes N1.1, M1.1, M1.2, WM1.1

Skills • measuring • ordering

Number (N1.1)

Indicators

Resources

The student is able to: • refer to familiar recurring events when describing time.

• order events within the day.

• understand that daily activities are related to time and that many of our activities are influenced by patterns in time.

• counters or similar • pencil • coloured pencils/ crayons

Language • add • order • number

r o e t s Bo Notes r e p ok u S

Main Activity (M1.1, M1.2, WM1.1) Warm up

• Hold a whole-class discussion of the activities that are done at school during the school day.

What to do

• Ask students to list the activities they do in order. Ask what should be done if different activities are completed at the same time in different ways. List these items beside each other or in a group on the blackboard/whiteboard.

• Ask students to choose six items they will draw pictures of in the workbook.The pictures are to be drawn in the order that they occur. Number pictures in the correct order.

• Students should share their finished order within groups or with the whole class.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 86 – 87.

• 150 • New Wave Maths Book A – Teachers Guide

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Unit 31—Answers

Student pages 91 – 93 Unit 31–2

Unit 31–1

3.

Number 1. (a) 17 (b) 12 Main Activity 2. 8 3. 9 4. 8

(c) 12

(d) 13

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Number 1. (a) 15 (b) 11 (c) 10 (d) 8 Main Activity 2. Two possible solutions are shown.

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• Complete further maze activities. Draw a scribble pattern with two lines similar to Exercise 3. Give to a classmate to solve.

Consolidation 31–2

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• Provide further opportunities to draw sets of objects and count the total.

Consolidation 31–3

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• Extend the day to include what students do at home and school on a school day, or choose a day on the weekend.

New Wave Maths Book A – Teachers Guide • 151 •

Unit 32–1

Student page 94

Outcomes

Indicators

Resources

Language

N1.1, N1.3, C&D1.2, C&D1.3

The student is able to: • say the number sequence of 2s.

• suggest how he/she can answer questions about the collections.

• draw a picture as a record of his/ her results.

• summarise information by counting.

• counters or similar • pencil • number line (see page 201 – 202)

• subtract • count • twos • how many • group • four • picture • graph • number • most, least • most common

Skills • counting • adding • picture graphing

Number (N1.1)

r o e t s Bo r e p ok u S

Notes

Main Activity (N1.3, C&D1.2, C&D1.3) Warm up

• Distribute counters to students. Direct students to make sets of 2 counters. Count by twos to find the total in the sets made.

What to do

• Students complete Exercise 2 in the workbook, independently if possible.

• Use a number line to assist and extend counting to 20 and beyond if students are able.

• Organise the class into groups of four.

• Revise picture graphs. In the graph to be drawn, one picture of a boy shows one boy and one picture of a girl shows one girl. In the group, each student will need to write the student’s family name in the space provided and then draw a picture of a boy or a girl for each brother and sister in the family above the family name; e.g. one brother and two sisters will see one boy and two girl pictures drawn.

• Work with the whole class to assist each group complete the questions asked about the graph. Answers will differ but be consistent within each group.

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• The focus for this unit is basic facts of subtraction.

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Unit 32–2

Student page 95

Outcomes N1.1, C&D1.1, C&D1.2, C&D1.3

Skills • sorting • ordering • graphing

Number (N1.1)

Indicators

Resources

Language

The student is able to: • recognise and take into account the possibility of different results for repetitions of the same simple action, such as throwing a die for a game.

• suggest how he/she can answer questions about their collections.

• summarise information by counting.

• counters or similar • pencil • dice • coloured pencils/ crayons

• subtract • die • ten • times • record • results • number • first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth • graph

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Notes

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• The focus for this unit is basic facts of subtraction.

Main Activity (C&D1.1, C&D1.2, C&D1.3) Warm up

• Distribute dice among groups of students and allow time for free play.

What to do

• Direct students to their workbook and explain that they will each have ten throws of the die. Each time the student throws the die, he/she records the number shown next to the number of the throw—if the first throw is a 3, write 3 next to ‘First’.

• When all members of the group have had their 10 throws, the numbers shown on the die are recorded on the graph. If first throw was 3, one box above the number 3 on the graph is coloured. If the second throw was a 1, the first box above the number 1 is coloured.

• Continue until one box for each of the ten throws has been coloured.

• The graph will now show how often each number on the die showed up and which was the number that showed most, least and in between.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 94 – 95.

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New Wave Maths Book A – Teachers Guide • 153 •

Unit 32–3

Student page 96

Outcomes N1.1

Skills • counting • grouping

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• make or draw collections of a given size.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• counters or similar • pencil • concrete materials

Language • subtract • how many • set • altogether

r o e t s Bo Notes r e p ok u S

Main Activity (N1.1) Warm up

• Distribute materials to groups of students. Allow free play.

What to do

• Direct students to make two sets of two items. Check how many items are in each group.

(2) ‘How many items altogether?’ (4) ‘Two lots of two equal four.’ Encourage students to verbalise their actions.

• Repeat this using two lots of three, two lots of four and two lots of five.

• Written records of this activity may be made in the workbook.

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• The focus for this unit is basic facts of subtraction.

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Unit 32—Answers

Student pages 94– 96 Unit 32–2

Unit 32–1 (c) 3

(d) 6

Number 1. (a) 7 (b) 6 Main Activity 2. Teacher check 3. Teacher check

(c) 2

(d) 5

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Number 1. (a) 2 (b) 6 Main Activity 2. 8 3. Teacher check

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• Share each group’s graphs and compare answers to the questions.

Consolidation 32–2

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3. (a) 4 (b) 4 (c) 8 4. 4

• Repeat the activity and discuss the results this time. Repeat another time and discuss.

Consolidation 32–3

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• Provide opportunities for students to practise doubling numbers to 10 with concrete objects.

New Wave Maths Book A – Teachers Guide • 155 •

Unit 35–1

Student page 103

Outcomes N1.1, C&D1.2, C&D1.3

Skills • grouping • sorting • classifying

Number (N1.1)

Indicators

Resources

The student is able to: • classify objects using one or two familiar criteria.

• summarise information by counting.

• counters or similar • pencils • concrete materials

Language • count • set • graph

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Notes

Main Activity (C&D1.2, C&D1.3) Warm up

• Distribute a variety of concrete materials to groups of students. Specific items (e.g. animals, vehicles, shapes etc.) may be given to each group, then the groups rotated. Allow time for free play.

What to do

• Direct students to sort, classify and arrange the items in each group into rows. Discuss how each group sorted its items and the number of items in each row. Select more items or rotate groups and repeat.

• Work with students to complete the activity in their workbook.

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• The focus for this unit is adding on.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 96 – 97.

• 156 • New Wave Maths Book A – Teachers Guide

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Unit 35–2

Student page 104

Outcomes

Indicators

N1.1, N1.2, WM1.1

Skills

• counting • grouping • sharing

Number (N1.1)

The student is able to: • say how many are in visible collections of objects.

• share collections into equal groups.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• explain that the value of coins depends upon the number on the coin rather than on the size of the coin and that the numbers enable one to exchange coins.

Resources

Language

• counters or similar • pencil • counters • interconnecting cubes • coloured rods or similar materials

• different • colours • share • three, nine • equal • amounts • how many • sets of

r o e t s Bo r e p ok u S

Notes

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• The focus for this unit is adding on.

Main Activity (N1.1, N1.2, WM1.1) Warm up

• Share the concrete materials among groups of students and allow free play.

What to do

• Ask students to select 9 items. Share them into three equal groups. Ask, ‘How many groups do you have?’ (3) ‘How many items are there in each group?’ (3) ‘How many items did you start with?’ (9) ‘9 can be shared into 3 groups of 3.’

• Repeat this activity many times, sharing up to 20 items into groups of 2, 3, 4 or 5. Encourage students to verbalise their actions at all times.

• Written records of this activity can be made in the workbook. Use concrete materials if this assists.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 42 – 43.

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 157 •

Unit 35–3

Student page 105

Outcomes

Indicators

N1.1, M1.2, C&D1.3

The student is able to: • count informal units of capacity.

• summarise information by counting.

• talk about what he/she has found from the data.

Skills • measuring • graphing • comparing

Number (N1.1)

Resources • counters or similar • pencil • cup • ice-cream container • sand • aerosol cap • tin can

Language • cup • container • fill • how many • plastic aerosol cap • tin can • graph

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Main Activity (M1.2, C&D1.3) Warm up

• Organise the class into groups. Each group is to have a cup, an ice-cream container, a plastic aerosol cap and sand.

What to do

• This activity is best completed in the sandpit. Allow the class time for free play when they first get to the sandpit or when they first have all their equipment ready.

• Direct students to use the cup, fill it with sand and pour the sand into the ice-cream container. Continue until the ice-cream container is full. Count the number of cups used to fill the ice-cream container. One student in the group can keep a record.

• Repeat for the aerosol caps and the tin can.

• Complete the questions and the graph in the workbook with their results. Discuss any discrepancies among groups.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 76 – 77.

• 158 • New Wave Maths Book A – Teachers Guide

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Unit 35—Answers

Student pages 103 – 105 Unit 35–2

Unit 35–1 (c) 5

(d) 6

Number 1. (a) 14 (b) 7 (c) 14 Main Activity 2. $1.05 in each group 3. 3 sets 4. 3 sets

(d) 10

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Number 1. (a) 11 (b) 9 Main Activity 2.

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• Students sort and classify pictures of animals or transport cut from magazines. Create a class picture graph to display and discuss.

Consolidation 35–2

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• Provide opportunities for sharing amounts of coins into equal amounts. After grouping the coins, students may attempt to count the amount.

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Consolidation 35–3

• Repeat the activity using a container different from the icecream container.

New Wave Maths Book A – Teachers Guide • 159 •

Unit 36–1

Student page 106

Outcomes N1.1, N1.2

Skills • counting • sharing • grouping

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• share collections into equal groups.

• use objects to represent a number story and manipulate the objects to find a solution.

• describe how he/she solved a number problem.

• counters or similar • pencil • interconnecting cubes and/or other concrete materials

Language • subtract • two, three • circles • brown, green • how many • altogether • around

r o e t s Bo r e p ok u S

Notes

Main Activity (N1.1, N1.2) Warm up

• Share the concrete materials among groups of students and allow free play.

What to do

• Ask students to select 9 items. Share them into three equal groups. Ask, ‘How many groups do you have?’ (3) ‘How many items are there in each group?’ (3) ‘How many items did you start with?’ (9) ‘9 can be shared into 3 groups of 3.’

• Repeat this activity many times, sharing up to 20 items into groups of 2, 3, 4 or 5. Encourage students to verbalise their actions at all times.

• Written records of this activity can be made in the workbook. Use concrete materials if this assists.

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• The focus for this unit is basic facts of subtraction.

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Unit 36–2

Student page 107

Outcomes

Indicators

N1.1, C&D1.2, C&D1.3

The student is able to: • classify objects using one or two familiar criteria.

• display, in one-to-one correspondence, pictures or objects which represent themselves.

• summarise information by counting.

Skills • sorting • ordering • graphing • classifying

Number (N1.1)

Resources

Language • subtract • Carroll diagram • groups

• counters or similar • pencil • students • interconnecting cubes

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Notes

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• The focus for this unit is basic facts of subtraction.

Main Activity (C&D1.2, C&D1.3) Warm up

• Revise graphs with students. Ask for their descriptions of graphs they have completed.

What to do

• Introduce Carroll diagrams. There are times when just the number of a group of items is recorded so that the total in each group can be read and the largest number can be seen.

• A Carroll diagram can be used to show boys and girls and their eye colour. All boys with blue eyes stand here. All girls with blue eyes stand next to the boys but not with them.

Use interconnecting cubes to show how many boys and girls there are in each group. All boys with green eyes stand next to the boys with blue eyes. Girls with green eyes stand in a group beside the girls with blue eyes and the boys with green eyes. Continue for the rest of the eye colours. There will be a row of groups of boys and a row of groups of girls and columns of eye colours.The interconnecting cubes will have recorded this. Alternatively, a blank of the Carroll diagram may have been drawn on the blackboard/whiteboard and the numbers in each group filled in as the groups are arranged.

• Repeat for hair colour, family size (includes parents and children) and for birthplace.

These activities may be spread over more than one session.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 94 – 95.

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New Wave Maths Book A – Teachers Guide • 161 •

Unit 36–3

Student page 108

Outcomes N1.1, N1.2

Skills • counting • grouping • comparing

Number (N1.1)

Indicators

Resources

The student is able to: • say how many are in visible collections of objects.

• use objects to represent a number story and manipulate the objects to fined a solution.

• describe how he/she solved a number problem.

• counters or similar • pencil • concrete materials

Language • subtract • more • how many • longer • count

r o e t s Bo Notes r e p ok u S

Main Activity (N1.1, N1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to select five items and arrange them in a line. Select another seven items and arrange them in a line so that there is a pair made with as many in the first line as possible. Ask, ‘Which line has more in it? How many more items are there in the longer line? There are 5 items in the first line and 7 items in the second line. There are 2 items more in the second line.’

• Repeat this with different numbers with up to 20 in any one line. Encourage students to verbalise their workings.

• Written records of this activity may be made in the workbook.

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Unit 36—Answers

Student pages 106 – 108 Unit 36–2

Unit 36–1 (c) 5

(d) 1

Number 1. (a) 4 (b) 5 Main Activity 2. Teacher check 3. Teacher check 4. Teacher check 5. Teacher check

(c) 1

(d) 7

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Number 1. (a) 4 (b) 7 Main Activity 2. 6 3. 4 4. (a) 3 (b) 6

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• Provide further opportunities to share up to 20 items in equal groups. Use pictures as well as concrete materials.

Consolidation 36–2

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• Other ideas to record using Carroll diagrams could include which boys and girls like specified colours, foods, toys or sports.

Consolidation 36–3

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• Provide further opportunities to arrange different numbers of objects in rows with up to 20 in any one line. Work with a partner and verbalise their workings.

New Wave Maths Book A – Teachers Guide • 163 •

Unit 37–1

Student page 109

Outcomes

Indicators The student is able to:

N1.1, S1.1

• respond appropriately to the language of position and orientation such as ‘under’, ‘behind’, ‘in front of’, ‘below’, ‘on’, ‘alongside’, ‘near’, and ‘right’ and ‘left’.

Skills • following paths

• use some of the language of position and orientation.

• respond appropriately to the language of movement such as ‘back’, ‘forward’, ‘around’, ‘past’, ‘turn’ and ‘up’.

Resources • counters or similar • pencil • coloured pencil/ crayon • overhead of a school plan (see page 224)

Language • path • left, right • across • up, down

r o e t s Bo r e p ok u S • use some of the language of movement.

Number (N1.1)

Notes

Main Activity (S1.1) Warm up

• Ask individual students to describe the path they would take to move to given locations around the school. Accept alternative paths if others wish to provide them.

What to do

• Use an overhead showing a school plan and the grounds. Ask students to show, (or trace the path described by a student) the path they would take to move between two given locations; e.g. classroom and office, playground climbing equipment and toilets and so on.

• Encourage students to use positional and orientational language such as ‘across’, ‘left’, ‘right’, ‘up’ and ‘down’.

• Ask students to draw the path they would follow, using the bicycle path, on the map in their workbook to move from home to school. Are there other paths that could be used?

Which is the shortest path? Which is the longest path? Which path should Amy follow to the shops? Show them, using different colours.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 6 – 7.

• 164 • New Wave Maths Book A – Teachers Guide

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Unit 37–2

Student page 110

Outcomes N1.1, WM1.1

Skills • recognising different coins

Number (N1.1)

Indicators

Resources

Language

The student is able to: • sort coins and notes and realise that coins and notes have different values.

• explain that the value of coins depends on the number on the coin rather than on the size of the coin and that the numbers enable one to exchange coins.

• counters or similar • pencil • coloured pencils/ crayons • plastic coins • coins of the same value showing commemorative features instead of an animal

• colour • coins • red, blue, green, yellow • 5 cents, 10 cents, 20 cents, 50 cents, one dollar

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Notes

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• The focus for this unit is adding on.

Main Activity (N1.1, WM1.1) Warm up

• Distribute plastic coins to groups of students. Allow time for free play.

What to do

• Direct students to find a 5 cent coin. What animal does it have on it? (Echidna) • Find a 10 cent coin. What animal does it have on it? (Lyrebird) • Find a 20 cent coin. What animal does it have on it? (Platypus) • Find a 50 cent coin. What animal does it have on it? (Coat of arms - kangaroo and emu) • Find a $1 coin. What animal does it have on it? (Kangaroo) • Do all coins of the same value have the same animal? (No. Some have special commemorative features.)

• Find the five cent coins in the workbook and circle them red.

• Find the other coins and circle them as directed.

• How many $1 coins are there?

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 64 – 65.

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New Wave Maths Book A – Teachers Guide • 165 •

Unit 37–3

Student page 111

Outcomes N1.1, S1.2, S1.3

Skills • measuring • graphing • comparing

Number (N1.1)

Indicators

Resources

The student is able to: • remember the shape of objects and component parts of objects.

• fill in patterns where lines are provided to enable direct matching of component shapes.

• counters or similar • pencil • coloured pencils/ crayons

Language • colour • pattern • guide • yellow, blue, red, orange

r o e t s Bo Notes r e p ok u S

Main Activity (S1.2, S1.3) Warm up

• Ask students to find yellow, blue, red and orange pencils or crayons.

What to do

• There is a pattern shown on the page of overlapping oval shapes. Point to the centre of one of these overlapping shapes. Check to see that all have the correct shape. Colour the shape yellow. Colour all the other central shapes yellow.

• Point to the side pieces of the overlapping ovals. Check that students have the correct pieces. Colour these blue. All the same pieces on the pattern are coloured blue.

• Find the end pieces and check student responses. Colour these pieces red.

• The final shape is coloured orange. Complete colouring the pattern so the whole area is coloured.

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• The focus for this unit is adding on.

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Unit 37—Answers

Student pages 109 – 111 Unit 37–2

Unit 37–1 (c) 1

(d) 2

Number 1. (a) 12 (b) 8 Main Activity 2. Teacher check 3 dollar coins

(c) 8

(d) 4

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• Compare the paths they chose with classmates.Think of other paths to follow.

Consolidation 37–2

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• Make a collection of coins featuring the usual animal design as well as those with commemorative features.

Consolidation 37–3

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• Complete other tessellating patterns but direct different groups of students to use different colours. Compare and discuss the visual effects.

New Wave Maths Book A – Teachers Guide • 167 •

Unit 38–1

Student page 112

Outcomes N1.1, N1.2, WM1.1

Skills • recognising coins

Number (N1.1)

Indicators

Resources

Language

The student is able to: • sort coins and notes and realise that coins and notes have different values.

• identify money needed in exchange for goods.

• explain that the value of coins depends upon the number on the coin rather than on the size of the coin and that the numbers enable one to exchange coins.

• counters or similar • pencil • coloured pencils/ crayons • plastic coins

• subtract • colour • one • coin • buy • 10 cents, 5 cents, 20 cents • how much • money

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Notes

Main Activity (N1.1, N1.2, WM1.1) Warm up

• Distribute plastic coins to groups of students and allow time for free play.

What to do

• Ask students to find different valued coins. Repeat several times.

• Ask students to find the coin they would need to buy a 10 cent pencil; a 20 cent lolly; a 50 cent lucky dip; a 5 cent lolly; a $1 gift etc.

• Students use a coloured pencil/crayon to circle the correct coin on the page of the workbook. Read the instructions to the class. Check their coin identification. Ask them to check the drawing with the plastic coins if need be to see that they match.

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• The focus for this unit is basic facts of subtraction.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 66 – 67.

• 168 • New Wave Maths Book A – Teachers Guide

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Unit 38–2

Student page 113

Outcomes N1.1, C&D1.2

Skills • sorting • ordering • graphing • classifying

Number (N1.1)

Indicators

Resources

The student is able to: • classify objects using one or two familiar criteria.

• summarise information by counting.

• counters or similar • pencil • concrete materials

Language • subtract • Venn diagram • sort • number • circle

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Notes

Main Activity (C&D1.2) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

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• The focus for this unit is subtraction of whole numbers.

• Direct students to select a handful of items and sort these into two groups. Have them describe why they sorted them as they did. Can they sort them into two different groups?

• Repeat for different selections of items as often as required.

• Ask students to sort the animals shown in their workbook into two groups as shown, one group to have wild animals, the other to have farm animals. Tell the students to write the number near the animal in the correct box to show where the animals belong. The horse could be either—encourage, if questioned, the notion that this is a farm animal.

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New Wave Maths Book A – Teachers Guide • 169 •

Unit 38–3

Student page 114

Outcomes N1.1, WM1.1

Skills • counting • adding coins

Number (N1.1)

Indicators

Resources

The student is able to: • sort coins and notes and realise that coins and notes have different values.

• explain that the value of coins depends upon the number on the coin rather than on the size of the coin and that the numbers enable one to exchange coins.

• counters or similar • pencil • plastic coins

Language • subtract • how much • money • line • difference • total

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Main Activity (N1.1, WM1.1) Warm up

• Distribute plastic coins to groups of students and allow time for free play.

What to do

• Direct students to take out four 5 cent coins and arrange these in a line.Take another three 5 cent coins and arrange them in a line, paired where possible with the first line. What is the total of each line? What is the difference in value between the two lines?

• Repeat using a variety of coin denominations.

• Ask students to select a ten cent coin and two five cent coins and arrange them in a line.

Select one ten cent coin and place it below the line. What is the total of each line? What is the difference in value between the lines?

• Repeat this with a variety of combined denominations.

• Written records of this activity may be made in the workbook. Use plastic coins to place over pictures if this assists.

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• The focus for this unit is subtraction of whole numbers.

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Unit 38—Answers

Student pages 112 – 114 Unit 38–2

Unit 38–1 (c) 4

(d) 4

Number 1. (a) 7 (b) 7 (c) 8 (d) 5 Main Activity 2. Farm animals – 2, 3, 6, 9, 10 Wild animals – 1, 4, 5, 7, 8, 11, 12

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Number 1. (a) 6 (b) 8 Main Activity 2. Teacher check 3. Teacher check 4. Teacher check, 30c

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Consolidation 38–2 • Sort farm animals and pets or animals that can or can not fly. (Include insects in the latter.)

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• Make written records of the combinations made in activities outlined in the ‘What to do’ section.

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New Wave Maths Book A – Teachers Guide • 171 •

Unit 39–1

Student page 115

Outcomes N1.1, S1.1

Skills • following paths

Number (N1.1)

Indicators

Resources

The student is able to: • respond appropriately to the language of position and orientation such as ‘under’, ‘behind’, ‘in front of ’, ‘below’, ‘on’, ‘alongside’, ‘near’, and ‘right’ and ‘left.

• use some of the language of position and orientation.

• respond appropriately to the language of movement such as ‘back’, ‘forward’, ‘around’, ‘past’, ‘turn’ and ‘up’.

• use some of the language of movement.

• counters or similar • pencil • coloured pencils/ crayons • school map (see page 224)

Language • lot of • path • describe • follow

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Notes

Main Activity (S1.1) Warm up

• Display the map of the school grounds.

What to do

• Ask students to describe the path they would take to move from one place to another; e.g. class to oval; library to canteen; classroom to carpark and so on. Trace each path on the overhead as it is described. Ask students if there are alternative routes that may be followed. Trace these also.

• Encourage students to use positional and orientational language such as ‘across’, ‘left’, ‘right’, ‘up’ and ‘down’.

• Direct students to their workbook and ask them to find a path from Room Five to the office.

• Direct them to use a coloured pencil/crayon to trace the path each has found.

• Ask a number of students to describe the path they have traced.

• If students are able, ask them to write a description of this path in the workbook. (This could also be scribed by the teacher or helper.)

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• The focus for this unit is basic multiplication facts.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 6 – 7.

• 172 • New Wave Maths Book A – Teachers Guide

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Unit 39–2

Student page 116

Outcomes N1.1, WM1.1

Skills • recognising different coins • adding coins

Number (N1.1)

Indicators

Resources

The student is able to: • sort coins and notes and realise that coins and notes have different values.

• explain that the value of coins depends upon the number on the coin rather than on the size of the coin and that the numbers enable one to exchange coins.

• counters or similar • pencil • coloured pencils/ crayons • plastic money

Language

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• lots of • money • more • difference between • amounts • share • four • equal • total • value

Notes

Main Activity (N1.1, WM1.1) Warm up

• Distribute plastic coins to groups of students and allow time for free play.

What to do

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• The focus for this unit is basic facts of multiplication.

• Direct students to select six 10 cent coins and arrange them in a row. Select three more 10 cent coins and arrange these in a row below the first row, pairing coins where possible.

Which row has more coins? What is the difference between the number of coins in each row?

• Repeat this with several different selections, using the same monetary denomination in each row.

• Direct students to select three 5 cent coins, three 20 cent coins and three $1 coins. Share the coins into three equal amounts.

• Repeat this several times using the same numbers of different valued coins and sharing into equal amounts.

• Ask students to pick up a small handful of coins.

• Find the total value of the coins. Ask a group member to check.

• Repeat this activity several times.

• Direct students to their workbook to complete the activities there. Read the activities with the students to help them. Use plastic coins to place over the drawings if this assists.

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New Wave Maths Book A – Teachers Guide • 173 •

Unit 39–3

Student page 117

Outcomes N1.1, M1.2, WM1.2

Skills • measuring • comparing

Number (N1.1)

Indicators

Resources

The student is able to: • compare the area of two regions.

• offer questions when prompted by their teacher.

• ask ‘why’ or ‘how’ mathematical questions of other children.

• counters or similar • pencil • 2-D shapes • concrete materials

Language • lots of • two • shapes • bigger • area

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Main Activity (M1.2, WM1.2) Warm up

• Distribute materials (2-D shapes) among groups of students. Allow time for free play.

What to do

• Direct students to their workbook. Look at the two drawings, the foot and the hand.

Explain that the space inside the line outlining the foot and the hand is known as the area.

• Ask students how they can decide which of the two shapes has the bigger area.

• Allow students to discuss options within their groups.

• Encourage students to experiment and test ideas.

• Ask for explanations within the groups and for selections from the groups to be shared with the whole class.

• Students who are able to should record their working out on the page. (This can also be scribed.)

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• The focus for this unit is basic facts of multiplication.

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Unit 39—Answers

Student pages 115 – 117 Unit 39–2

Unit 39–1 (c) 4

(d) 3

Number 1. (a) 4 (b) 6 Main Activity 2. (a) Bob (b) 15c 3. 35c 4. 50c

(c) 10

(d) 2

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• Use the map on page 115 of the workbook to trace paths from different classrooms to other places around the school.

Consolidation 39–2

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• Provide opportunities to share coins into equal amounts using different valued coins.

Consolidation 39–3

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• Complete a similar activity using tracings of shoes, similar sized books or other objects.

New Wave Maths Book A – Teachers Guide • 175 •

Unit 40–1

Student page 118

Outcomes N1.1, N1.4, WM1.2

Skills • following patterns • creating patterns

Number (N1.1)

Indicators

Resources

The student is able to: • copy and continue repeating patterns.

• use simple language such as ‘pattern’, ‘over and over’, ‘repeat’, ‘again’ to describe patterns and to say what is the same about two versions of the same pattern.

• ask ‘why’ or ‘how’ mathematical questions of other children.

• counters or similar • pencil • 2-D shapes

Language • lots of • rearrange • shapes • different • patterns

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Notes

Main Activity (N1.4, WM1.2) Warm up

• Distribute materials (2-D shapes) among groups of students. Allow time for free play.

What to do

• Ask students to make patterns with the shapes. Share patterns with group members.

• Look at the patterns of shapes in the workbook.

• Use the same shapes to draw different patterns. (Not all shapes need to be drawn for each pattern.)

• Describe the pattern made to your partner.

• Draw different patterns until the page is completed.

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• The focus for this unit is basic facts of multiplication.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 48 – 49.

• 176 • New Wave Maths Book A – Teachers Guide

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Unit 40–2

Student page 119

Outcomes N1.1, C&D1.2, C&D1.3

Skills • counting • collecting information • reading graphs • completing graphs

Number (N1.1)

Indicators

Resources

The student is able to: • classify objects using one or two familiar criteria.

• draw a picture as a record of his/ her results.

• summarise information by counting.

• counters or similar • pencil • coloured pencils

Language • lots of • picture graph • most, least • how many • difference between

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Notes

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• The focus for this unit is basic facts of multiplication.

Main Activity (C&D1.2, C&D1.3) Warm up

• Revise picture graphs. Remind students that each drawing shows one item. A sample showing means of coming to school (bus, car, walk, bike etc.) may be made as a demonstration.

What to do

• Ask students to choose five ice-cream flavours, including vanilla, chocolate and strawberry.

• All students are to decide which is their favourite of the five flavours chosen. When the flavour is named, students are to stand. Count the number standing and write it on the blackboard/whiteboard.

• Ask students to draw one ice-cream in the space above the flavour name to show each student who chose that as his/her favourite ice-cream.

• When all flavours have been completed, work with the class as a whole to answer the questions under the graph.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 66 – 67.

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New Wave Maths Book A – Teachers Guide • 177 •

Unit 40–3

Student page 120

Outcomes

Indicators The student is able to:

N1.1, N1.4, WM1.2

• copy and continue repeating patterns.

Resources • counters or similar • pencil

• use simple language such as ‘pattern’, ‘over and over’, ‘repeat’, ‘again’ to describe patterns and to say what is the same about two versions of the same pattern.

Skills • following patterns

Language • lots of • error • patterns • correctly • draw

• suggest how to answer his/her own mathematical questions.

r o e t s Bo Notes r e p ok u S • manipulate objects mentioned in a problem to find a solution.

Number (N1.1)

Main Activity (N1.4, WM1.2) Warm up

• Direct students to their workbook. Either ask students to work independently to complete the activities or work with the class as a group.

What to do

• (Work as a group.) ‘There is an error in the first pattern, can you see it? What is the error?

How can it be corrected?’

• Draw the pattern in the space provided without the error.

• Repeat for each pattern.

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• The focus for this unit is basic facts of multiplication.

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For a relevant assessment activity refer to RIC-0028 Maths Assessment – Level 1 pages 48 – 49.

• 178 • New Wave Maths Book A – Teachers Guide

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Unit 40—Answers

Student pages 118 – 120 Unit 40–2

Unit 40–1 (c) 9

(d) 8

Number 1. (a) 12 (b) 16 Main Activity 2. Teacher check

(c) 20

(d) 20

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Number 1. (a) 12 (b) 10 Main Activity 2. Teacher check

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• Use concrete materials such as buttons, counters, gumnuts or 2-D shapes to create repeating patterns and discuss with a partner. Also try repeating patterns with bead threading.

Consolidation 40–2

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• Construct picture graphs of students’ favourite fast food, dinner, breakfast cereal or sandwich filling.

Consolidation 40–3

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• Work with partners. Each student makes a repeating pattern with concrete materials with an error in it. Partners have to find and correct the error.

New Wave Maths Book A – Teachers Guide • 179 •

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Additional Activities

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Space Activities...............................................................................................................................182 – 183 Measurement Activities............................................................................................................................ 184 Number Activities....................................................................................................................................... 185

New Wave Maths Book A – Teachers Guide • 181 •

Space Activities S1.1

1. Involve students in discussions as to how the classroom can be best arranged to provide for more floor space at the front, rear or between desks.

2. Involve students in discussions as to how seating might be arranged within the classroom – single desks, groups, rows, direction to face and so on.

3. Students plan pin-up displays of their own.

4. Use the picture on page 221 of New Wave Maths Teachers Guide to instruct the students to find: • the cat under the seat and colour it black.

• the bird above the house and colour it brown.

• the car behind the tree and colour it red.

• the seat beside the tree and colour it blue.

• the bicycle in front of the house and colour it yellow.

• the nest in the tree and colour it brown.

• the large tree near the path and colour it green.

• the house at the end of the path – colour the roof red, the walls light blue and the door dark blue.

S1.2

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1. Use boxes and have students cover the sides with paper. Lead a discussion focused on the number of sides, and the shapes of sides. Boxes may be used for storage or to make models such as robots, towers or other structures. Focus on language of best fit, shapes made, and shapes placed together. Compare shapes used in each other's constructions. This could be done as a group activity.

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C.Publ i cat i ons •f orr evi ew pur posesonl y• 2. Copy teacher-made structures using building blocks, construction kits or the like.

3. Use modelling clay to make shapes and change these to other shapes. Direct activities; for example, roll into a pencil shape, make a hoop, change into a ball; or make a ball, change to a flat disk, change to a bowl.

Allow students to make their own changes, discuss with them what they have done. Select students to share with the class.

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4. Use different materials to make constructions that are tall, long, flat. Materials could include paper, card, straws, construction kits and blocks.

5. View building shapes and make models of the buildings using blocks, boxes and the like.

6. Use the shapes on pages 207 – 209 of New Wave Maths Teachers Guide to have students cut out shapes and make animals or people. Final design can be glued into a book.

• 182 • New Wave Maths Book A – Teachers Guide

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Space Activities cont.

S1.3

1. Students trace around their foot on a piece of paper or with chalk in the playground. Students trace around their shoe and then glue over their foot (on paper) or place their foot in the playground.

Activity may be repeated using hands and making a glove, or tracing around the body in the playground then using newspaper to make clothes for the body.

2. Use the sun to form shadows with students' bodies. Trace around the shadows with chalk.

Make a longer, shorter, wider, narrower shadow. Trace around each – perhaps use a different coloured chalk for each shadow.

Discuss with students what they did each time.

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3. A similar activity may be done using large shapes and the sun, or smaller shapes and the overhead projector.

S1.4

4. Complete jigsaw puzzles and match shapes in picture sticker books.

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1. Find objects that make a given 3-D shape. These may be displayed for all to see and discuss the attributes and common features.

2. Integrate with measurement using arbitrary units to then determine why certain objects are given height, width or spacing.

Discuss door shapes and sizes.

Discuss desk heights – student vs teacher or older students.

Discuss chair and desk heights – match sizes.

3. Discuss why certain shapes are preferred in given situations. For example, for ease of stacking, use boxes not cylinders or spheres.

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4. Discuss with students those shapes that occur in the environment. Compare them with the shapes of known objects. Question why certain shapes are more frequently used in given situations – bricks on walls and in paving, rectangular car parks, rectangular doors etc.

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5. Use modelling clay to make shapes and alter them by squeezing, stretching, dropping or pushing against a firm surface.

Students describe what happens in each case.

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New Wave Maths Book A – Teachers Guide • 183 •

Measurement Activities M1.1

1. Use a variety of materials in a freely structured environment that focuses on a discussion of length, width and height. Students should be encouraged to think about measurement while playing and be encouraged to discuss their findings.

2. Use a variety of materials in free-play situations, using balances, where students are able to verbalise their perceptions of the mass of different objects.

Teacher questions should develop the concept of heavier and encourage the use of balance scales to support the students' claims.

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3. Use modelling clay with students shaping and reshaping the amount they have and discussing the mass and the models they have made.

1. Use a variety of free-play sessions, including art, to allow students to paint, colour, and cover pages or surfaces of objects.

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M1.2

2. Students should be allowed many opportunities to pour from and fill containers with a variety of materials (water, sand, grains). Focus on discussion of how much the container holds, which holds the most, which holds the same etc.

Encourage students to understand the need to pour easily and note which containers are easiest to pour from.

3. Direct students to fill containers to given levels. Levels can be marked with felt-tip pens or elastic bands. Discuss how the student knows the container is half full.

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C.Publ i cat i ons •f orr evi ew pur posesonl y• 4. Stack objects to fill containers; e.g. blocks into boxes.

5. Pour contents (water, sand or grain) from one container to another to compare the capacity of each. Use the labels on page 217 of New Wave Maths Teachers Guide to record the results.

This activity should be repeated many times throughout the year.

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M1.3

6. Find objects that will balance with a given object placed in one pan of a set of balance scales.

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1. Manipulation of puzzles, including jigsaws and simple puzzles, pattern blocks and the like develops an awareness of area.

Students should freely discuss what they are doing.

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2. Use a variety of materials—some similar, others different—to develop the concept of mass by hefting, balancing or throwing. Students compare objects by working through these activities.

3. Students make direct comparisons of pairs of objects by hefting or by using balance scales.

Students may select their own objects or be given pairs of objects by the teacher to ensure there is a difference in the mass of the objects or that the mass is the same.

Lead students to discuss their findings.

• 184 • New Wave Maths Book A – Teachers Guide

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Number Activities N1.1

1. Students play freely with a variety of self-chosen or teacher-given objects. Building and construction work should be closely monitored for language development. As concepts begin to develop, teacher questions will focus on matching and comparing objects, leading to one-to-one correspondence. Use the labels on page 216 of New Wave Maths Teachers Guide to help with language development. They can be used to name, match and count items around the classroom; for example, square window, tall door, large cupboard.

2. Students use the number tracks on pages 201 and 202 of New Wave Maths Teachers Guide to practise counting.

N1.2

4. Students follow sequences of movements along the number track; for example, 'Start at three, move two places forward, move three places back, move one place back, move six places forward, move three places forward, move seven places back. Say the number you land on each time.'

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5. The initial language of adding and subtracting may be introduced during number track activities; for example, 'Three and two more make (equal) …'

1. Use students to form lines to show those with a given eye colour, hair colour, with the same size families, born in Australia, Western Australia or overseas, families that have the same pets.

Count the number in each group.

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2. Objects may be placed in order of length, width or the like.

3. Set up a class shop with items priced in given coin amounts, 5c, 10c, 20c, 50c and permutations of these combinations to 50c. Change is given using plastic coins or cardboard coins copied from page 222 of New Wave Maths Teachers Guide. Purchases are made by a direct match to the price tag.

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4. Repeat the above activity, this time using price tags, and distributing coins so change is required.

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3. Number tracks may be glued into a book or laminated and taped to the student's desktop.

1. Students devise their own mental number stories to use imagery to mentally add and subtract; e.g. 'I can see two forks and three spoons. How many are there altogether?'.

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2. Practise counting in 2s, 5s or 10s.

3. Use a calculator to assist in counting in 3s or 4s etc.

N1.4

1. Use interconnecting cubes or similar to make counting patterns.

2. Make number patterns by threading coloured beads onto string.

3. Use musical instruments to create their own repeating number patterns.

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Assessment

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Reference to Student Outcomes....................................................................................................... 188 Record Sheets – Blank.................................................................................................................189 – 193 Proforma – Blank.......................................................................................................................................... 194

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New Wave Maths Book A – Teachers Guide • 187 •

Student Outcomes Working Mathematically

Number

WM1.1 The student talks about some of the ways numbers, shapes and time are used by self and family.

WM1.2 The student, with guidance, poses questions which can be answered by classifying, matching, ordering or counting objects and represents mathematical questions by acting out a story, or showing it with objects or pictures.

WM1.3 No outcomes specified at Level 1.

WM1.4 The student begins to show some self-correcting behaviour in mathematical activities.

S1.4

The student visualises self-generated or orallypresented number stories and partitions of small numbers, and represents them in materials, drawings, with a calculator or by role playing.

The student uses counting and other strategies to mentally solve self-generated or orally-presented questions from stories involving small numbers.

The student copies, continues and makes repeating and counting patterns and uses numbers to represent these patterns.

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The student uses and interprets familiar everyday language for the position of things, their movements, and paths between them.

The student pays attention to shape in making or drawing things which are remembered, imagined, seen or handled.

The student repeats, reorients and turns over things when matching shapes and making pictures and patterns.

The student talks about likenesses and differences between things which can be seen or handled and begins to connect shape, movement and function.

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S1.3

N1.2

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The student reads, writes and says small whole numbers, using them to say how many things there are, makes collections of a given size and describes order.

N1.4

Space S1.1

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The student understands everyday comparative language associated with length, mass, capacity and time.

M1.2

The student directly compares and orders ‘straight’ lengths and events in time and counts informal units of length, capacity, mass and time to decide ‘how many fit or match’.

The student makes non-numerical estimates of size involving everyday movements and actions.

No outcomes specified at Level 1.

M1.3 M1.4

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Chance and Data

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C&D1.1 The student shows some recognition of the element of chance in familiar daily activities.

C&D1.2 The student participates in classifying and sequencing objects and pictures and, with guidance, poses questions about them.

C&D1.3 The student displays objects and pictures and describes data in words and numbers.

C&D1.4 No outcomes specified at Level 1.

Extracted from Mathematics Outcomes and Standards Framework – Student Outcome Statements, Education Department of Western Australia 1998.

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New Wave Maths Book A – Teachers Guide • 189 •

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Space—Record Sheet

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Measurement—Record Sheet

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New Wave Maths Book A – Teachers Guide • 191 •

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Chance and Data—Record Sheet

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Number—Record Sheet

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New Wave Maths Book A – Teachers Guide • 193 •

Proforma This proforma has been provided for you to copy and use with your class. You can either:

• select an activity and evaluate the whole class; or

• select a small group of students and evaluate their work.

The indicators are found on the relevant page in the New Wave Maths Teachers Guide.

1. Photocopy this page.

2. Write the appropriate date, strand, outcome(s) and indicators.

3. Photocopy enough for one per student being assessed.

4. Inform the students they are being assessed on the activity they are about to complete.

5. Students complete the activity in the workbook.

6. Mark the work completed by the student.

7. Attach the proforma to the appropriate workbook page.

8. Record evaluation as required. ✄

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Outcome(s)

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Opportunity

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Photocopiable Resources

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Grid Paper.........................................................................................................................................196 – 199 Number Charts and Cards......................................................................................................200 – 204 Spinners – Blank..............................................................................................................................205 – 206 2–D Shapes.......................................................................................................................................207 – 209 Classification Chart.................................................................................................................................... 210 Sorting Circles.................................................................................................................................211 – 212 Sorting Activities............................................................................................................................213 – 214 Labels....................................................................................................................................................215 – 217 Venn Diagram – Blank............................................................................................................................... 218 Carroll Diagram – Blank..................................................................................................................................................219 Line or Bar Graph – Blank............................................................................................................................................220 Picture Talk....................................................................................................................................................... 221 Coins................................................................................................................................................................... 222 Clocks................................................................................................................................................................. 223 Graph and Table – Blank........................................................................................................................... 233 Map...................................................................................................................................................................... 224 New Wave Maths Book A – Teachers Guide • 195 •

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1-cm grid paper.

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2-cm grid paper.

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New Wave Maths Book A – Teachers Guide • 197 •

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1-cm dot grid paper.

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1-cm triangle grid paper.

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New Wave Maths Book A – Teachers Guide • 199 •

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Number Cards

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Photocopy onto coloured card. Cut out and laminate. You may wish to enlarge to A3.

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New Wave Maths Book A – Teachers Guide • 201 •

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100 Chart

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New Wave Maths Book A – Teachers Guide • 203 •

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0 – 99 Chart

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Spinners

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New Wave Maths Book A – Teachers Guide • 205 •

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Spinners

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2-D Shapes

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New Wave Maths Book A – Teachers Guide • 207 •

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2-D Shapes

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Note: These shapes can be copied onto stiff card, cut out and distributed for sorting.

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New Wave Maths Book A – Teachers Guide • 209 •

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Note: This worksheet can be copied onto card and laminated for continuous use. Students name each group on the lines provided before sorting objects.

Classification Chart

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Sorting Circles

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New Wave Maths Book A – Teachers Guide • 211 •

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Sorting Circles

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Sorting Activity – Zoo

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Sorting Activity – Farm

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Note: This worksheet can be enlarged to A3 size if more space is required.

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Note: These labels may be used to assist students with directed sorting and classifying when using Venn or Carroll diagrams or any other sorting sheet. Some have been left blank for teacher use. Laminating will help to preserve the cards.

Attribute Labels

New Wave Maths Book A – Teachers Guide • 215 •

Classroom Labels

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Cut and glue to match the picture with its name.

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Capacity Labels

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New Wave Maths Book A – Teachers Guide • 217 •

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Venn Diagram

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Carroll Diagram

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Line or Bar Graph

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Picture Talk

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Look at this picture and listen to your teacher.

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To be used in conjunction with the activity outlined on page 182 S1.1.4.

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New Wave Maths Book A – Teachers Guide • 221 •

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Coins

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Clocks

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Waterman Primary School

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Parent Information

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Expectations of Knowledge of Basic Facts..............................................................................................226 Primary School Mathematics..........................................................................................................................227 Developing Mathematical Awareness........................................................................................................228 Concrete to Mental.............................................................................................................................................229 Mathematical Learning Areas..........................................................................................................................230

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New Wave Maths Book A – Teachers Guide • 225 •

Parent Information Expectations of Knowledge of Basic Facts Year 1 An informal, general introduction to number and combinations.

Year 2 Discovery approach (manipulating concrete material) to finding and learning addition and subtraction facts.

Year 3

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Discovery and some recall of addition and subtraction facts. Use the terms 'add' or 'subtract' rather than 'plus' or 'minus'.

Learn basic multiplication facts of 2, 3, 4 and 5 and multiples of 10, to 10 times 10.

Year 4

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Consolidate basic sums to 18, and differences taking from 18. Extend recall of basic multiplication and division facts to facts of 6, 7, 8 and 9 times tables.

Year 5

Recall basic addition, subtraction, multiplication and division facts.

Years 6 and 7

Automatic response is desirable.

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The following suggestions can be used at home to assist your child in becoming more proficient in gaining automatic recall of the basic number facts. The ideas are not exclusive, many alternatives may be used.

1 'Flashcards' – with all combinations of basic facts, hold up, child responds with the answer.

Flashcards can be easily made from light card (cereal packet) or by purchasing blank playing cards and writing basic facts on these.

2 'Snap' – played with flashcards.

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Play as for ordinary snap.

A variation – write pairs of numbers on cards, or blank playing cards, without operation signs. Child may add, subtract, multiply or divide the pair of numbers to find a matching pair.

3 Throw two dice then either add, subtract or multiply the two numbers shown.

4 Race the calculator.

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Call out a basic fact, while you work out the answer using the calculator your child attempts to race you to the correct answer working mentally.

5 'Sums, Differences, Products' (add, take, multiply) – The game is played using a hundred chart.

Call a pair of numbers from the basic facts. Your child covers the sum, the difference and the product of the two numbers called on the hundreds chart.

Play for a given time—for example, five minutes—or until all of a set of basic facts have been used.

6

'Bingo' – The game is played as for ordinary bingo. You call a basic fact, use basic number fact sheet, your child covers the correct answer if it is on the card. First to cover the card or a line wins the game.

7 When using board games encourage your child to add onto the total when throwing the die, or add the total of the dice, rather than counting on.

8

'Numero' is one of the best mathematical games available which can be used at home to develop mathematics skills.

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Parent Information Primary School Mathematics The Algorithm The mathematics syllabus aims at standardising the recording of the algorithms throughout Western Australia. However, there will still be some minimal variance within and between schools.

The following examples show the recommended method of recording the written algorithm for each of the four processes.

These formats are not prescriptive, but are recommendations. In all cases, the ultimate aim is to arrive at the simplest (usually the shortest) form of recording the algorithm. A simplistic progression is shown for the development of each algorithm from Year 1 to Year 7.

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Combining and Separating – Addition and Subtraction

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Year 1 – Concrete activities are recorded in number sentence form – first written recordings may possibly be made late in Year 1. The same form of recording is used in Years 2 and 3. In Year 3, adding and subtracting without regrouping are also recorded in vertical form. Vertical recording continues through to Year 7, with regrouping and increased difficulty of examples.

When subtracting, always start with the top number.

Year 1 Use concrete materials to manipulate and arrange objects with either oral or written answer in addition and subtraction.

Year 2 Using basic facts to 9 + 9 =18 and adding three numbers each less than 6. It is recommended that concrete materials are used.

Grouping and Sharing – Multiplication and Division

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Commencing in Year 2, concrete activities are recorded, using the multiplication symbol in number sentence from late Year 2 or as ready. Number sentence recording of concrete activities is carried on into Year 3.

The written algorithm is introduced in its extended form in Year 4, working to the abbreviated form when the child understands the process.

Year 1 Counting equivalent sets by twos, threes, fours and fives up to 20.

Sharing objects in practical situations.

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Year 2 Symbol 'x' is introduced to assist with grouping. Use of language to support activities – 'lots of', 'sets of' or 'groups of' to 20 or 30.

Division experience is through sorting, sharing and grouping activities using concrete materials.

Introduction to open number sentences.

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The New Wave Maths series is presented in levels to allow for progressive development by individual students. Levels do not equate specifically to Year levels.

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New Wave Maths Book A – Teachers Guide • 227 •

Parent Information Developing Mathematical Awareness Dear Parent(s) Set homework is not expected at this level; however, you can help your child develop an awareness of mathematics and its place in the real world by involving him/her in simple activities as outlined here: • allowing your child to help with cooking – making simple measures • reading the time for your child • estimating how long it takes to complete activities; for example, shower, travel to school or shops etc.

• counting objects • recognising numbers in the environment • counting by twos; for example, car or truck tyres, legs on dogs, cats etc.

• grouping objects by shape, size, colour, use • discussing placement of objects, people or animals; for example, near, beside, below, above, in, inside, under, between, in front, behind, etc. to develop the language of mathematics.

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• encouraging your child to combine or separate sets – add or subtract – when in small quantities; less than ten • comparing lengths, heights, widths, cover surfaces with materials with your child. Encouraging him/her to talk about these activities with you.

Above all, encourage and support your child in his/her mathematical endeavours.

Kind regards

Teac he r

r o e t s Bo r e p ok u S

Classroom Teacher

© R. I .

C.Publ i cat i ons Parent Information •f orr evi ew pur posesonl y• ✄

Developing Mathematical Awareness

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Dear Parent(s) Set homework is not expected at this level; however, you can help your child develop an awareness of mathematics and its place in the real world by involving him/her in simple activities as outlined here: • allowing your child to help with cooking – making simple measures • reading the time for your child • estimating how long it takes to complete activities; for example, shower, travel to school or shops etc.

• counting objects • recognising numbers in the environment • counting by twos; for example, car or truck tyres, legs on dogs, cats etc.

• grouping objects by shape, size, colour, use • discussing placement of objects, people or animals; for example, near, beside, below, above, in, inside, under, between, in front, behind, etc. to develop the language of mathematics.

• encouraging your child to combine or separate sets – add or subtract – when in small quantities; less than ten • comparing lengths, heights, widths, cover surfaces with materials with your child. Encouraging him/her to talk about these activities with you.

Above all, encourage and support your child in his/her mathematical endeavours.

Kind regards

o c . che e r o t r s super

Classroom Teacher

• 228 • New Wave Maths Book A – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Parent Information Concrete to Mental – Including the Calculator

r o e t s Bo r e p ok u S

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Teac he r

Dear Parent(s) There are a number of different means of completing the four algorithms.

Children start by using concrete materials to work through the algorithms to develop understandings. As their knowledge and understanding develop, students move to more abstract means of achieving the solutions to the algorithms. These solutions may be achieved by pencil and paper calculations or by working the solutions mentally (the ultimate aim).

During these developmental phases children will encounter algorithms that are complex, difficult or are a means to another step or the final solution. In such cases, the child should be encouraged to use a calculator to find the solution to the algorithm.

The calculator is an invaluable aid in mathematics and its use is to be encouraged from the very beginning of a child's days at school.

Children who have great difficulties in completing algorithms are to be encouraged to use the calculator to find the solutions after first estimating the answer. Estimation skills are essential in showing the development of mathematical knowledge.

Should you encounter any problems, please contact me.

Kind regards

Classroom Teacher

© R. I .

C.Publ i cat i ons Parent • Information f orr evi ew pur posesonl y• ✄

Concrete to Mental – Including the Calculator

. te

m . u

w ww

Dear Parent(s) There are a number of different means of completing the four algorithms.

Children start by using concrete materials to work through the algorithms to develop understandings. As their knowledge and understanding develop, students move to more abstract means of achieving the solutions to the algorithms. These solutions may be achieved by pencil and paper calculations or by working the solutions mentally (the ultimate aim).

During these developmental phases children will encounter algorithms that are complex, difficult or are a means to another step or the final solution. In such cases, the child should be encouraged to use a calculator to find the solution to the algorithm.

The calculator is an invaluable aid in mathematics and its use is to be encouraged from the very beginning of a child's days at school.

Children who have great difficulties in completing algorithms are to be encouraged to use the calculator to find the solutions after first estimating the answer. Estimation skills are essential in showing the development of mathematical knowledge.

Should you encounter any problems, please contact me.

Kind regards

o c . che e r o t r s super

Classroom Teacher

R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book A – Teachers Guide • 229 •

Parent Information Mathematical Learning Areas Mathematics comprises a series of learning areas. These learning areas are outlined for teachers in the Student Outcome Statements document produced by the Education Department. There are seven learning areas, each of which is outlined briefly below.

Appreciating Mathematics Appreciate the role of mathematics in their own and other communities.

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Working Mathematically

Space

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Thinking about ideas, investigating, applying, verifying and reasoning mathematically. In brief, problem-solving.

Knowledge of location (place), shape, transformations (changes), and reasoning geometrically (angles, constructions and other geometrical relationships).

Measurement

Understand units of measure, measure objects using measuring units, estimate measures and calculate measurements.

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• Chance and Data

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Number

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Understand chance events. Collect and organise data and information. Summarise and represent data. Interpret data.

Understand number and the relationships, order, count, place value. Understand addition, subtraction, multiplication and division and be able to calculate using these operations. Work out number patterns.

Pre-Algebra

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o c . che e r o t r s super

Understand symbols and graphs. Represent variation. Solve equations and inequalities.

• 230 • New Wave Maths Book A – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au