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r o e t s Bworking For students at risk at r e o p o u k Upper Primary levels S
rescue maths
Book 1 number: written calculations
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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
o c . By Sandy T asker Tasker c e her r o t s super
© Ready-Ed Publications - 2003. Published by Ready-Ed Publications (2003) P.O. Box 276 Greenwood W.A. 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However, this permission is not transferable and applies only to the purchasing individual or institution. ISBN 1 86397 564 0
Information on the Series About The Books
This series has been created for classroom teachers and parents to use for home or class work - with students of a range of abilities taken into consideration. The focus will be on reinforcement of “the basics” in maths, as well as activities aimed at developing understanding of classroom activities in mathematics. Students with Specific Learning Difficulties experience a range of problems with their academic learning. These aspects include:• Difficulties with word recognition and comprehension • Coping with pages that are too cluttered and with too many differing requirements • Being able to sequence, recall and apply strategies in abstract situations • Striving to process formation - while working to meet deadlines • Having trouble with personal organization with their schoolwork. The books in this series are designed with these problems in mind, and whilst pages are designed for the student with learning difficulties, they can also be used as a simple and straightforward introduction to concepts or a reinforcement of mathematical strategies for the whole class. The books will follow a basic format, with a variety of homework topics usually containing a choice of two worksheets.
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Content of the Books
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The Three Books in the Series Book One: Number - Written Calculations Book Two: Number - Applications Book Three: Measurement, Chance and Data Curriculum Links and Learning Outcomes The aim of the activities is to focus on one concept per page, therefore, only one outcome in a strand from the relevant Mathematics outcomes will usually be addressed. Strands and outcomes focused on in this book are shown on pages 4 to 6. Learning Outcomes for each page are specified at the top of the page. Information in Specific Learning Difficulties This section will contain information from a variety of referenced sources including online literature and recommendations from trained and experienced consultants. Information will include descriptions of the various learning difficulties and ideas for strategies in the classroom and at home. A list of website addresses containing information and ideas is provided for teachers and parents. Student Lifesavers Many students with Specific Learning Difficulties become overwhelmed when expected to recall basic facts when carrying out more complex calculations. Students may grasp a concept, but be unable to apply the strategy because they are struggling to remember tables and combinations. To focus on the teaching point and alleviate stress for students, these tables and charts can be kept within easy access for the students. Charts include multiplication tables, addition and subtraction charts, number lines, rules and formulas and measurement conversions. “Parent Power” Pages The information provided on Specific Learning Difficulties at the beginning of this book can also be photocopied and given to parents who are requesting additional information. However, it should be made clear that this is a guide only, and contact with local recognised Specific Learning Difficulty associations or Child Development Centres should be made if there are any particular concerns. Parent Power pages can be photocopied and sent home at the commencement of each unit and include: • terminology; • mathematical strategies and examples; • learning and practice ideas in the home and community. It is also suggested that teachers photocopy answers to each section and include these when sending home the Parent Power Page. This enables parents to feel confident in checking their child’s work and giving them valuable, immediate feedback. Progress Charts It is widely appreciated that success is built on success, and the more students are able to track their own progress, the more likely they are to be motivated to attempt the next stage in their learning. Students can keep these progress charts as an ongoing record of their homework. Skill Drills Some students work best with structured, timed drills. Drill practice can be very helpful in developing skills in automatic recall. The drill charts in this book are designed so that the length of time and the starting position for the drill can be changed according to the student’s abilities. A record of the score can be kept so that the student can track their progress.
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Contents
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Information on the series ........................................................................................................................ 2 Curriculum Links - State and National Curriculums ........................................................................... 4 - 6 Specific Learning Difficulties .................................................................................................................. 7 How are Individuals With Specific Learning Difficulties Affected? ........................................................... 9 General Strategies for the Home ........................................................................................................... 11 Internet References .............................................................................................................................. 12 Student Lifesavers Tables Chart .............................................................................................................................. 13 Addition Chart ............................................................................................................................ 14 Subtraction Chart ....................................................................................................................... 15 Number Square to 100 ............................................................................................................... 16 Number Lines ............................................................................................................................ 17 Parent Power Maths Words ............................................................................................................................. 18 Symbols .................................................................................................................................... 18 Roman Numerals ....................................................................................................................... 18 Face, Place and Total Value ...................................................................................................... 19 Addition, Subtraction, Multiplication and Division ................................................................ 20 - 24 Progress Chart What Can I Do? ......................................................................................................................... 25 Skill Drills Pairs To 10 ................................................................................................................................ 26 Pairs To 20 ................................................................................................................................ 27 Subtraction Chart ....................................................................................................................... 28 Addition Chart ............................................................................................................................ 29 Multiplication Chart .................................................................................................................... 30 Counting By… ........................................................................................................................... 31 Activity Sheets Digit Value Revision ................................................................................................................... 33 Rounding 1 ................................................................................................................................ 34 Rounding 2 ................................................................................................................................ 35 Rounding 3 - Decimals ............................................................................................................... 36 Rounding and Estimating 1 ........................................................................................................ 37 Rounding and Estimating 2 ........................................................................................................ 38 Other Tricks For Mental Maths 1 ............................................................................................... 39 Other Tricks For Mental Maths 2 ............................................................................................... 40 Addition Regrouping 1 ................................................................................................................ 41 Addition Regrouping 2 ................................................................................................................ 42 Decimal Addition 1 ..................................................................................................................... 43 Decimal Addition 2 ..................................................................................................................... 44 Subtraction Regrouping 1 ........................................................................................................... 45 Subtraction Regrouping 2 ........................................................................................................... 46 Decimal Subtraction 1 ............................................................................................................... 47 Decimal Subtraction 2 ............................................................................................................... 48 Setting Out Sums 1 (Whole Numbers) ....................................................................................... 49 Setting Out Sums 2 (Whole Numbers and Decimals) ................................................................ 50 Multiplication 1 .......................................................................................................................... 51 Multiplication 2 .......................................................................................................................... 52 Multiplication 3 .......................................................................................................................... 53 Multiplication 4 - Multiplication of Decimals ............................................................................... 54 Division 1 - Revision ................................................................................................................... 55 Division 2 - With Regrouping ...................................................................................................... 56 Division 3 - What Kind of Division? ............................................................................................. 57 Division 4 - Larger Numbers ....................................................................................................... 58 Division 5 - Decimals ................................................................................................................. 59 Division 6 – Remainders ............................................................................................................. 60 Division 7 – Remainders ............................................................................................................. 61 Answers Skill Drills .................................................................................................................................. 62 Activity Sheets .......................................................................................................................... 63
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Curriculum Links - State Curriculum Documents Activities in Book One mainly address the following outcomes in the Number Strand of the relevant curriculum documents.
Activity
New South Wales Whole Numbers N 2.1(a), 3.1
Skill Drills
Queensland Number Concepts N 3.1
Number Facts N 2.3(a) 2.3(b) 3.3
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Number Concepts N 3.1
Decimal Digit Value 1 & 2
Whole Numbers N 2.1(a), 3.1
Number Concepts N 3.1
Rounding 1 - 3
Number Operations N 2.4(a), 3.4
Number Concepts N 3.1
Number Operations N 2.4(a), 3.4
Number Concepts N 3.1
Addition 1 & 2
Number Operations N 2.4(a), 3.4
Addition and Subtraction N 3.2
Addition Regrouping 1 & 2
Number Operations N 3.4
Addition and Subtraction N 3.2
Addition Regrouping 3 & 4
Number Operations N 3.4
Addition and Subtraction N 3.2
Subtraction 1 & 2
Number Operations N 3.4
Addition and Subtraction N 3.2
Subtraction Regrouping 1 & 2
Number Operations N 3.4
Addition and Subtraction N 3.2
Subtraction Regrouping 3 & 4
Number Operations N 3.4
Addition and Subtraction N 3.2
Decimal Addition 1 & 2
Number Operations N 3.4
Addition and Subtraction N 3.2
Decimal Subtraction 1 & 2
Number Operations N 3.4
Addition and Subtraction N 3.2
Setting Out Sums 1 & 2
Number Operations N 3.4
Addition and Subtraction N 3.2
Multiplication 1 & 2
Number Operations N 3.4
Multiplication and Division N 3.3
Multiplication Regrouping 1 & 2
Number Operations N 3.4
Multiplication and Division N 3.3
Multiplication Regrouping 3 & 4
Number Operations N 3.4
Multiplication and Division N 3.3
Multiplication Revision
Number Operations N 3.4
Multiplication and Division N 3.3
Number Operations N 3.4
Multiplication and Division N 3.3
Number Operations N 3.4
Multiplication and Division N 3.3
Division with Remainders 1 & 2
Number Operations N 3.4
Multiplication and Division N 3.3
Division with Regrouping
Number Operations N 3.4
Multiplication and Division N 3.3
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Estimating 1 & 2
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Whole Numbers N 2.1(a), 3.1
Digit Value 1 & 2
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Division Revision Division 1 & 2
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Curriculum Links - State Curriculum Documents Activities in Book One mainly address the following outcomes in the Number Strand of the relevant curriculum documents. (Read Activity names from previous page.)
South Australia Number 3.6, 3.8
Victoria Numbers, Counting and Numeration 3.1
Western Australia Understand Numbers N 3.1(a) Understand Operations N 3.2
Number 3.6
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Understand Numbers N 3.1(a)
Numbers, Counting and Numeration 3.1
Understand Numbers N 3.1(a)
Mental Computation and Estimation 3.3
Understand Numbers N 3.1(a)
Mental Computation and Estimation 3.3
Understand Numbers N 3.1(a)
Number 3.8
Computation and Applying Number 3.1
Calculate N 3.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.8
Computation and Applying Number 3.1
Calculate N 4.3, Und. Operations N 3.2
Number 3.6 Number 3.8
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Number 3.8
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Numbers, Counting and Numeration 3.1
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National Curriculum Links
Activities in Book One mainly address the following outcomes in the Number Strand. Most activities fall within Level 3 with revision from Level 2 and Extension into Level 4.
Activity
Count and Order 2.11
Skill Drills Digit Value 1 & 2
3.11
Mental Computation
Written Computation
2.15
2.16
3.15
3.16
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Decimal Digit Value 1 & 2
Estimating 1 & 2
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Rounding 1 - 3
Addition 1 & 2
Addition Regrouping 1 & 2 Addition Regrouping 3 & 4 Subtraction 1 & 2
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Subtraction Regrouping 1 & 2 Subtraction Regrouping 3 & 4 Decimal Addition 1 & 2
Decimal Subtraction 1 & 2
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Setting Out Sums 1 & 2
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Multiplication 1 & 2
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Multiplication Regrouping 3 & 4 Multiplication Revision Division Revision Division 1 & 2 Division with Remainders 1 & 2
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Division with Regrouping 1
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Specific Learning Difficulties (SLDs) What are Specific Learning Difficulties?
Specific Learning Difficulties ARE: • A range of conditions including dyslexia, dyscalculia, dyspraxia and dysgraphia. • Significant difficulties in one or a few areas of learning, whilst demonstrating average to above average abilities in most or all other areas. Specific Learning Difficulties ARE NOT: • A result of global low intelligence, physical conditions such as visual or hearing impairments, or a lack of appropriate parenting or teaching. • Attention difficulties (or behavioural disorders) such as Attention Deficit Disorder (ADD) and Attention Deficit Hyperactivity Disorder (ADHD). Specific Learning Difficulties are founded on a reduced capacity to learn, and attention difficulties stem from a reduced capacity to concentrate and attend to tasks when learning. Specific Learning Difficulties CAN: • Appear to overlap, as learning areas often merge. For example, a person with reading difficulties may struggle in maths in the presence of lengthy word problems or poorly set-out activities (www.dyslexia-speld.com).
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Descriptions of the Types of Specific Learning Difficulties
(www.dyslexia-speld.com)
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Dyslexia is the most commonly recognised and well-researched SLD, characterised by difficulties in: • Recognising, reading and spelling words; • Comprehension of written information; • Relating new written concepts to stored ideas and existing knowledge; • Phonological coding, the process of associating sounds with letter groups; • Producing written work (sequencing letters, recognising letter reversals).
Dyscalculia describes significant difficulties in the area of mathematics. People with dyscalculia may possess average to above average linguistic skills but struggle with: • Mental recall of basic facts; • Accurate calculation; • Understanding and applying mathematical concepts, rules and formulas; • Awareness of time, direction (such as spatial and mapping skills) and sequence; • The ability to estimate and recognise errors in maths work; • Money and budgeting; • Games that involve strategic planning or complex scoring.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• (www.dyscalculia.org)
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Dysgraphia outlines difficulties with the production of written language which may occur in isolation or in conjunction with other SLDs. Underlying causes include difficulties with sequencing and ordering of letters and words, attention difficulties leading to poor fine motor and organisational skills and reduced auditory processing. (www.ldonline.org) Dyspraxia describes difficulties in the ability to plan and execute new or unfamiliar movements in a coordinated manner. During early childhood, many new tasks are being learned, so this is a time where dyspraxia can significantly impact upon daily living. Problems can appear with performing fine and gross motor tasks (Motor Dyspraxia) and / or speech-related tasks (Verbal or oral Dyspraxia). (www.dyspraxiafoundation.org.uk)
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Associated Difficulties
Visual and Visual-Perceptual Difficulties (Source: www.children-special-needs.org)
These difficulties may occur in conjunction with, or as a result of, other learning or attention difficulties. The problems listed below can also place a considerable strain on the reading process for a child, and can often go unnoticed until the child is in primary school, where the he / she spends longer periods of time focusing on print. Myopia (short-sightedness) - may lead to difficulties in reading information written on the blackboard or on charts around the classroom, if not rectified with glasses or contact lenses. Binocular coordination - the action of both eyes moving together, a process required to read effectively. Convergence - the movement of both eyes inwards, reaching an accurate point of focus. Fixation - where the eyes meet on a specific point so that the image is clear. Pursuit - smoothly tracking across an image or follow a moving object. Saccades - a “jump” from one point of focus to another without losing place. This is particularly important as skilled reading involves a series of fixations on words across a line rather than one continuous movement. • Children who have difficulty with any of the above may show signs such as skipping or re-reading lines, misreading small words, using their finger or moving their head as they read.
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Directionality - A convention of the English language is that information is written from left to right. Some children confuse or reverse this direction and may also confuse letters that are the same shape in a different direction, such as d and b, or p and q. Visual Figure-Ground is the ability to distinguish certain forms, words or features amongst irrelevant visual information such as reading print on a cluttered page, successfully scanning for key words within a block of text and editing work for errors. Visual Discrimination relates to the distinction of similar words. Some children, for example, may consistently confuse similar words such as bad and bed, through and thorough. Visual Form Constancy describes the recognition of the same object image or word in a different form, for example, being able to read the same sentence correctly in a variety of fonts, or understanding that a word is the same whether it is represented in capital or lower case letters. Visual Closure can be demonstrated by mentally or physically completing “gaps” in visual images, such as writing the end of a word where only part of it is given or doing “dot-to-dot” and jigsaw puzzles. Visual Memory aids in both reading and writing, as familiar words can be recognised, pronounced and spelt more automatically once they are retained. Students with poor visual memory take longer to learn new words. Visual Sequential Memory refers to the recall of a sequence of shapes, images or words, and the ability to apply what is recalled. For example, looking up at the board to remember and write down a list of spelling words. Visual Motor Integration is the process of integrating visual input with motor output – the coordination of “seeing, planning and doing”. In the classroom context, this skill is used in accurate copying of images and words, staying on the lines when writing and correctly aligning maths calculations, to name a few examples.
Auditory Processing
Auditory processing problems affect the learner’s ability to interpret auditory information. Often under the broad category of Central Auditory Processing Disorder (CAPD), this group of disorders are caused by a dysfunction of the brain, rather than of the ear, and include symptoms such as: • A slower rate of processing auditory information due to a perceived distortion of the incoming sounds; • A sensitivity to excessive noise or background noise – inability to concentrate and distractibility; • Difficulty locating directionality of sound; • Confusion of similar words or sounds; • Poor memory of verbal instructions; • Difficulty interpreting intonation such as jokes, sarcasm, questions, etc.; • Apparent hearing loss, e.g. saying “What?” often despite normal results on hearing tests; • Poor reading and/or writing as a result of some of the above problems. There are several subgroups, which more specifically describe auditory processing disorders and like visual perceptual problems, these can exist in conjunction with other learning or attention difficulties.
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Attention Deficit Disorder
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Attention Deficit Disorder or ADD is a neurological disorder that has been a focus of media attention over the last decade. There are two types that are commonly recognised: Attention Deficit Hyperactivity Disorder (ADHD) is characterized by: • Constant fidgeting or moving about in a seat; • Having trouble waiting a turn; • Impulsivity; • Difficulty listening to and following instructions. Attention Deficit Disorder (ADD) is evident in individuals who: • Are quiet, withdrawn and sluggish; • Demonstrate low self-esteem; • Are often described as “daydreamers”; • Need constant prompting to remain on task. Both types tend to be: • Easily distracted • Forgetful • Disorganised As previously mentioned, Attention Deficit Disorder is a separate entity to Specific Learning Difficulties and each requires some unique strategies to best approach the difficulties. There are, however, instances where an individual may experience both conditions to a certain degree. Initially, it may be difficult for the untrained individual to pinpoint the “cause”. A student with attention difficulties may appear dyslexic because their distractibility leads them to constantly lose their place when reading. Conversely, a student with a specific learning difficulty may become so frustrated that they avoid work or give up easily, appearing to “lose concentration”.
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Source: http://add.about.com
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How are Individuals With Specific Learning Difficulties Affected? Some of the obstacles that students with SLDs can face are: • Being branded as “lazy” because they are capable in most areas, and their difficulties often do not correspond with expectations based on their intelligence; • Becoming frustrated that they understand a concept, but are not able to read or write about it; • Developing a low self-esteem as they struggle to keep up with their peers; • Missing out on educational support and resources during the time it takes to identify their problems. On the positive side, having a SLD can also mean that the individual: • Is constantly seeking out alternative ways of thinking and learning, thus becoming a creative and innovative thinker or a strong leader; • Is an intelligent, capable individual, who can be educated at any level if approached with understanding and a willingness to provide appropriate learning opportunities and strategies; • Can overcome learning difficulties to become successful in their chosen fields. Some examples of these people can be found at: www.nald.ca and www.dyslexiaonline.com
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General Strategies for the Classroom
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Below are some ideas that may be of assistance with any of the areas of difficulty listed above. They are not intended to be specific strategies for any one area. These suggestions are provided as a guide only and it is recommended that teachers and parents seek specialised, individualised assessment and intervention for students who have SLDs. Location - Seat the student where they can: • Read the board; • Hear instructions clearly; • Easily access teacher assistance; • Locate reference charts; • Find personal belongings; • Be free from potential distractions. Organisation - Encourage a desk that: • Is clear of “clutter”; • Contains daily work items in a clear pencil case or a tin (contains only the “essentials” such as pencils, ruler, eraser, scissors, glue and a calculator). A daily or weekly checklist to ensure that all stationery is available may help the student to keep track of when things need to be tidied or replaced. Collaboration - A peer tutor needs to know how to: • Prompt and set good examples for the student; • Help without “spoon-feeding” them with the answers; • Avoid distractions. Support Success - Building self-esteem by: • Drawing attention to any success, even if partial, e.g. “Well done! You are using the formula correctly, you just might like to check your final calculation again”. • Drawing on student’s strengths, e.g. asking them to dictate answers verbally if extended writing is difficult. Break It Down - Aid learning by breaking tasks down into manageable components. • Help the student to plan each stage of a task with a familiar “plan of attack” can be helpful. For example, when approaching a word problem, asking “What sort of sum is this”, then “What numbers will be in the sum”, then “Write the sum”, etc. Allow Extra Time - allowing students additional time in situations such as tests is a fair means of compensating for their difficulties. Additional time can also be given to a student by spending a few minutes explaining a new concept in advance before introducing it to the class, so that the information is consolidated, rather than lost in a panic. Easy On Eyes - Try some of the following and ask the student what they prefer. • Font: simple, clear font with no serifs, such as “Arial”. (This book is typeset in Arial.) • Size: Medium to larger size, for example 14 point. • Line Length: 45 - 75 characters including spaces and punctuation. • Paragraphing: wide margins (1.5 - 2.0 cm), 1.5 or double spacing, short, clearly separated paragraphs. • Alignment: Do not justify - it leads to uneven spacing on the line. • Emphasis: simple headings, using bold instead of italics. Use boxes to highlight information. • Points: Use bullets or numbers to identify a list. • Paper: Use matt paper, and try cream or other pastel colours, as many students with SLDs find white paper harder to read from. • Limit irrelevant pictures, background print and borders. • Additional space for ease of working out. • Guiding lines, boxes and cues to assist students with setting out their work. • Simple pictures, only used to reinforce concepts or problems, not as additional decoration on the page.
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Multisensory Learning - Students with SLDs often learn more successfully if provided with a variety of sensory experiences. To consolidate a concept use some of these – it will help ALL students learn: Look at it; write it in six different colours; write it in the air; trace it on sandpaper; show classmates on the blackboard; sing it or make it into a rhyme; say it to a partner; draw it; act it out; use counters, MAB blocks and plastic money or other real objects.
1x9 bend first finger down
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• Reversals, e.g. 6 + 4 = 4 + 6 • “Tens pairs” (pairs of numbers adding up to 10) e.g. 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 …
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Keep On Track - To avoid “losing track of time”: • Issue regular warnings about how much time is left; • Try a timer on the student’s desk (if this does not cause additional stress); • Highlight a number of items that they should aim to complete before the next time you pass by their desk. Room To Move - Provide an outlet for excess energy by: • A small “fidget toy” such as a palm sized squeeze ball; • Asking the student to take messages to other classrooms. Memory Strategies • Reference charts; • Mnemonics, poems; • Visualising in pictures; • The “9 x table finger” technique, i.e.
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General Strategies for the Home Some of the strategies below may be of assistance when supporting your child in their mathematics homework. • Short and Sweet - Shorter, more frequent sessions of homework minimise the risk of your child losing concentration. Practising a task over a number of days will help to reinforce the concept, so try 10 - 15 minutes of homework each day rather than one hour, once a week.
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• A Friendly Place - Create an environment that is consistent, quiet, comfortable and well lit, with plenty of space for both you and your child to work together. Have a glass of water for your child to drink. Some students also work best if they have small snacks to nibble on whilst they work. • The Right Stuff - Make sure your child has all the necessary equipment before starting. Some handy things to have include highlighters (to emphasise important parts of the homework or examples), eraser (so that mistakes can easily be corrected and there is no mess of scribbling out), sharpener (so that writing is clear and easy to read), lined scrap paper (with relevant sized lines and plenty of space for working out and examples).
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• • In Tune - Background music has been found to be beneficial for some
• Write it Big - A whiteboard may be a useful way of working out problems. It is easy to see, easy to rub out, and another way of introducing a different sensory experience to the child. learners. Classical (Baroque) music has been researched quite extensively and may be of assistance.
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• Check it Off - Using a checklist to tick off tasks that have been done give your child a sense of achievement as well as helping them to keep their place. • Charts are not Cheating - A chart with rules, formulas, definitions and basic maths facts can help your child enormously. Remember that integrating several concepts at once can be overwhelming, and it is best to “isolate” the new skill being learned until your child is confident. For example, if your child is learning how to calculate area, a multiplication chart may be useful until he / she has learned how to use the length x width formula.
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o c . che e r o t r s super • Success is the Best Foundation - Remember that every time your child gets something correct, even if it is just one part of a larger task, praising them for their success is the most effective way to increase their self esteem and to motivate them to continue. Vary your positive comments, make them specific: “Good work for writing the 3 in the correct column!” and give them small rewards for reaching their goals: “You finished the whole page! Let’s go and kick the footy!”
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Internet References The following can be used as alternatives for parents who wish their child to practise basic mathematics online. http://www.math.com - Go to “Homework Help” for a range of explanations on a variety of maths skills. http://schooldiscovery.com - Visit sections such as “Parents”, “Brain Boosters” and “Webmath” for a range of activities.
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www.discover.tased.edu.au - A Tasmanian education site with links to mathematics activities
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www.kevinsplayroom.co.uk - Visit the “Maths” section and explore activities such as the Maths Dictionary, A-Plus Math (including online flash cards), Curious and Useful Maths with interesting tricks and puzzles, and Math Baseball. www.yahooligans.com - Follow the links from School Bell > Math > Real World Math to discover activities for sites such as Math in Daily Life, Cadbury Learning Zone, Cool Math and Figure This.
www.awesomelibrary.org - Follow the links from Maths > Elementary School for a range of activity and article sites.
© ReadyEdPubl i cat i ons Sites with more information on learning difficulties: • f o r r e v i e w p u r p o s e s o nl y• www.dyslexia-speld.com - Western Australian organisation for people with learning difficulties.
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www.ldonline.org - Contains many links for a range of informative sites. www.interdys.org - International Dyslexia Association website.
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www.bda-dyslexia.org.uk - British Dyslexia Association website with ideas for parents and educators.
o c . www.dyscalculia.org c - Information of dyscalculia (specific learning difficulties e her r in maths). o t s s r u e p Contact your local organisation that caters for people with dyslexia and specific learning difficulties, or ask your local child development centre or child health service for more information.
Student Lifesavers The following chart can be used as a reference when students are learning their basic operations or as a support when skills such as multiplication are required in more complex problems. Page 12
Book 1
Ready-Ed Publications
Student Lifesavers
Tables Chart Use this chart to learn your tables. Trace your finger down and across from the two numbers being multiplied to find your answer where the two fingers meet.
1
1
1
2
Teac he r
0
3
4
5
6
7
8
r o e t s Bo r 2 3e 4 5 6 7 8 p o u k S 4 6 8 10 12 14 16
9
10
9
10
18
20
2
3
3
6
9
12
15
18
21
24
27
30
4
4
8
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16
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32
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40
5
5© R 10e 15 20 35 40n 45 a dyEd25Pu30 bl i c at i o s
50
7
70
7
• or ev ew ur p36 ose so nl y54• 60 6f 12r 18i 24 p 30 42 48
w ww 8
8
9
9
10
10
14
21
28
35
42
49
56
16
24
32
40
48
56
64
. te18
63
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2
72
81 o c . c e 20 h 30e40 50 60 o 70r 80 90 t r s super 27
36
45
54
63
72
80 90
100
Things to remember:
z Reversals / pairs - If you reverse the question, the answer is the same: 5 x 7 = 35
7 x 5 = 35
z All 2 times tables are even numbers - 2, 4, 6, 8, 10 z All 5 times tables end in 5 or 0 - 5, 10, 15, 20, 25 z All 10 times tables are the number with a zero on the end - 10, 20, 30 Ready-Ed Publications
Book 1
Page 13
Student Lifesavers
Addition Chart Can be used reading the first number across or down. Trace your finger down and across from the two numbers being added to find your answer where the two fingers meet.
1
1
2 3
3
3
4
10 11
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2
5 6 7 8 9 r o e t s Bo r e p 3 u 4 5 6 7 8 o 9 10 k S 2
Teac he r
0
4
5
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7
8
9
10
4
5
6
7
8
9
10
11
4
5
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7
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©7Rea dy Ed Publ i cat i ons 8 9 10 11 12 13 14 15 •f orr evi ew pur posesonl y•
12
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o 18 c . che e r o 18 19 r st su 13 14 15 16 17 r pe 12
13
14
Book 1
15
16
17
19 20
Ready-Ed Publications
Student Lifesavers
Subtraction Chart Subtract the number along the side from the number along the top to find your answer where the two fingers meet.
1
1
0
2
-1
3 4 5
3
4
9
10
8
9
0
1
2
3
4
5
6
7
8
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
©R ea dyEd0Pub l i c at i o ns4 -3 -2 -1 1 2 3 •f orr evi ew pur posesonl y• -4
5
-4
-3
-2
-1
0
1
2
3
4
7
-6
-5
-4
-3
-2
-1
0
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2
3
8
-7
-6
-5
-4
-3
-2
-1
0
1
2
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-5
9
. t -8 e -7
10
-9
Ready-Ed Publications
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5 6 7 8 r o e t s Bo r e p2 3 4 5 6 ok 1u 7 S 2
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Teac he r
0
o 0 c . che e r o st sup -8 -7 r -6 -5 e -4 -3 -2 -1 r -6
-5
-4
Book 1
-3
-2
-1
1 0
Page 15
Student Lifesavers
Number Square to 100 This can be used for addition or subtraction by counting on, or for identifying patterns in number sequences by shading boxes.
2
11
12
6 7 8 9 r o e t s Bo r e p 15 16 17 o 13u 14 18k 19 S 3
4
5
21
22
23
24
25
26
27
28
31
32
33
34
35
36
37
38
41
10 20
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Teac he r
1
29
30
39
40
43
44
45
46
47
48
51
© ReadyEdPubl i cat i ons 52f 53r 54i 56 57 58 59 • or ev ew55pu r po ses onl y•60
61
62
63
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65
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67
68
73
74
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71
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81
. 82 t e83
91
92
Page 16
49
50
69
70
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42
79
89 o c . che e r o t 93 94 r 95 96 97 s 98 99 super 84
85
86
Book 1
87
88
80 90
100
Ready-Ed Publications
4
o c . che e r o t r s super
Book 1
0
0.1
0.2
0.3
0.4
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0.7
Number Line FFor or Decimals
0.8
0.9
1.0
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Use this to assist in rounding or working out more than/less than for decimals.
3
r o e t s Bo r e p ok u S
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Ready-Ed Publications
2
. te
1
ach er
This can be used for quick addition, subtraction or more than/less than calculations, as well as rounding to the nearest 5 or 10.
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Number Line TeTToo 50
Student Lifesavers
Page 17
Parent Power Maths W ords Words Here are some meanings for words that you might read in maths work. Examples are underneath. Addition - Plus, add or “what is the sum of?” e.g. 2+4=6 Subtraction - Minus, take away or “how much is left?” e.g. 5-2=3
r o e t s Bo r e p ok u S
Multiplication / Multiplied by - Times, “lots of” or “what is the product of?” e.g. 3 x 5 = 15
Whole Number - 0, 1, 2, 3, 4… (counting numbers as well as zero) Even Numbers - 2, 4, 6, 8, 10…(numbers divisible by 2) Odd Numbers - 1, 3, 5, 7, 9… (numbers not divisible by 2) Prime Numbers - A number that can only be divided by 1 and itself. e.g. 1, 3, 5, 7, 11, 13, 17, 19, 23, 29
ew i ev Pr
Teac he r
Division / Divided by - Shared into groups or “how many times does x go into y?” e.g. 10 ÷ 2 = 5 or 10 shared into groups of 2 = 5 groups
Composite Numbers - Numbers that have more than 2 numbers (factors) that divide into it, e.g. 2, 4, 6, 8, 9,10, 12, 14, 15, 16, 18 e.g. Factors of 16 are 1, 2, 4, 8 and 16 so it is a composite number.
© ReadyEdPubl i cat i ons Rounding - Finding the closest 10, 100 or 1000 for the number. e.g. •f Round 46r to the = 50 or e vnearest i ew10p ur posesonl y•
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Symbols + Plus or add, e.g. 2 + 5 = 7 – Take away, subtract or minus, e.g. 6 - 3 = 3 × Times, multiply, e.g. 3 x 4 = 12 ÷ Divided by, e.g. 10 - 2 = 5 = Equals, answer to the sum ≠ Not equal, e.g. 4 + 5 ≠ 6 ~ Approximately (close to), e.g. 235 + 220 ~ 500 … Continue the pattern, e.g. 2, 4, 6, 8, … > More than or greater than, e.g. 8 > 4 < Less than, e.g. 5 < 9 % Percent, e.g. 30⁄60 in a test = 50%
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Page 18
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•
Round 530 to the nearest 100 = 500 Round 2978 to the nearest 1000 = 3000 If the number to be rounded is “in the middle”, e.g. 35 is in between 30 and 40, most sources agree that it is best to round up, i.e. round 35 to 40.
Roman Numerals I II III IV V VI VII VIII IV X L C M
= = = = = = = = = = = = =
one two three four five six seven eight nine ten fifty one hundred one thousand
o c . che e r o t r s super
Book 1
Ready-Ed Publications
Parent Power Face, Place and TTotal otal V alue Value Face Value - What the actual numeral itself looks like. e.g. In 2345 the face value of the 3 is 3 Place Value - Relates to where the numeral is. e.g. In 2345 the place of the 3 is hundreds
r o e t s Bo r e p ok u S
Total Value - A combination of place and face value. e.g. The value of the 3 is 3 hundreds or 300
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
1
2
3
4
5
8
1000 000
200 000
30 000
4000
500
80
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Teac he r
Whole Numbers e.g. For the number 1 234 589
Tens
Ones
9
9
©R ea dyEdPubl i cat i ons (one million) (two hundred thousand) •f or r ethousand) vi ew pur posesonl y• (thirty (four thousand) (five hundred) (eighty) (nine)
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So, the value of 1 is 1 000 000 2 is 200 000 3 is 30 000 4 is 4000 5 is 500 8 is 80 9 is 9
Decimal Numbers e.g. For the number 3.9874 Ones
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Decimal Place
3
•
3
•
So, the value of 3 is 3 9 is 9⁄10 8 is 8⁄100 7 is 7⁄1000 Ready-Ed Publications
Tenths
9
9
⁄ 10
Hundredths
Thousandths
8
7
8
⁄ 100
7
⁄ 1000
(nine tenths) (eight hundredths) (seven thousandths) Book 1
Page 19
Parent Power Addition, Subtraction, Multiplication and Division When are these operations used? • For budgeting and banking. E.g. If I earn $560 a week and I spend $56.00 on bills and $72.50 on food, how much do I have left? • For calculating amount required of items. E.g. what is number of cans of paint required if I need 5 cans for the lounge and 3 cans each for four bedrooms. • For sharing amongst the family. E.g. If there are 6 hours of videotape left and 3 people in the family, how much time does each person have to record? • For working out scores. E.g. How many points are there in an AFL game if a team scores 11 goals and 6 points?
r o e t s Bo r e p ok u S
Addition: 464 + 459
+
Working out:
ew i ev Pr
Teac he r
Rule of thumb: Work out sums from right to left - start in the Ones column first.
1
1
4
6
4
4 + 9 = 13
Put down the 3, regroup the 1.
4
5
9
1 + 6 + 5 = 12
Put down the 2, regroup the 1.
9
2
3
1+ 4 + 4 = 9
Put down the 9.
© ReadyEdPubl i cat i ons •964 f o evi ew pur posesonl y• Subtraction: –r 676r
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1
6
6
7
2
8
4 6
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Multiplication: 65 × 3
× 1
Page 20
9
14 – 6 = 8 5–7
Can’t do - regroup 1 from the Tens (the 6 becomes 5) to make 4 into 14. Can’t do - regroup 1 from the Hundreds (the 9 becomes 8) to make 5 into 15.
o c . che e r o t r s super 15 – 7 = 8 8–6=2
Working out:
1
6
Working out: 4–6…
m . u
98
15
5
Multiply each digit in 65 by 3. Start in the Ones column. Write 5 in the Ones column and 1 in the Tens.
3
5 × 3 = 15
5
6 × 3 = 18 + 1 = 19 Multiply 6 x 3 and add 1 (the regrouped number). Book 1
Ready-Ed Publications
Parent Power Multiplication 65 × 35 1
Working out:
2
×
6
5
3
5
Multiply each digit in 65 by 5 FIRST, THEN put down a zero in the Ones column and multiply each digit in 65 by 3. 5 × 5 = 25 Multiply 5 x 5. 6 × 5 = 30 + 2 = 32 Write 5 in the Ones column and regroup the 2 into the tens. Multiply 6 x 5 and add 2 (the regrouped number). 5 × 3 = 15 NEXT, PUT 0 in the ONES, 6 × 3 = 18 + 1 = 19 because now you are multiplying by 3 which is in the TENS. Multiply 5 x 3. Write 5 in the Tens column. Regroup the 1 into the Hundreds. Multiply 6 x 3 and add 1 (the regrouped number). 325 + 1950 = 2275 Add the two subtotals together.
r o e t s Bo r e p ok u S
2
5
1
9
5
0
2
2
7
5
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Teac he r
3
© ReadyEdPubl i cat i ons •f orr evi ew p ur posesonl y• Working out:
Multiplication 2.3 × 6.4
×
1
2.
3
6.
4
w ww 1
3
1
4
9
. te 8 7
2
Do the sum normally, IGNORING THE DECIMAL PLACE.
m . u
1
3 × 4 = 12 2×4=8+1=9 3 × 6 = 18 Still put down the 0 on the second 2 × 6 = 12 + 1 = 13 line.
o c . che e r o t r s super 0 2
92 + 1380 = 1472
Now, count the total number of digits after the decimal point in the original sum. This is how many digits should appear after the decimal point in the answer. 2.3 6.4
One number after the decimal point. One number after the decimal point. TOTAL = 2 numbers after the decimal point, i.e. the answer = 14.72
Ready-Ed Publications
Book 1
Page 21
Parent Power Division In division, you regroup if you cannot divide into the first digit evenly. 2 ) 34
Divide the Tens column first: 3 ÷ 2 = 1 r 1 (Does not divide evenly.) Regroup by writing the remainder next to the ones. Divide the Ones column next: 14 ÷ 2 = 7 (Divides evenly.)
17 2 ) 3 14
Answer = 17
r o e t s Bo r e p ok u S
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Teac he r
1 2 ) 3 14
Division of decimals 9 ) 24.75
Divide the Tens column first: 2 ÷ 9: you can’t do, so try 24 ÷ 9 = 2 r 6.
Regroup by writing the remainder (6) next to the first decimal place (Tenths).
27 9 ) 24. 6745
The 7 in the Tenths column now becomes 67. So do 67 ÷ 9 = 7 r 4. © ReadyEdPubl i cat i ons Regroup by writing the reminder (4) next to the second decimal place (Hundredths). •f orr evi ew pur posesonl y• The 5 in the Hundredths column now becomes 45. So do 45 ÷ 9 = 5.
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275
9 ) 24. 6745
There is nothing that needs regrouping.
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2 9 ) 24. 675
o c . che e r o t r s super
Now, count the total number of digits after the decimal point in the original sum. This is how many digits should appear after the decimal point in the answer. 2. 7 5 24.75 Two numbers after the decimal point, i.e. the answer = 2.75 9 ) 24. 6745
Page 22
Book 1
Ready-Ed Publications
Parent Power Activities at Home: Place tables charts around the home where children see them regularly, such as on the fridge or inside the toilet door.
•
Keep counters or charts to help with checking mental calculation.
•
Draw pictures to reinforce problems, e.g. draw 12 lollies and circle them into groups of 4 to calculate 12 ÷ 4.
•
Make a card with the word “True” on one side and “False” on the other. Ask a question and give an answer – the child holds up a card to say whether the answer is true or false.
•
In sports games, e.g. football, netball or soccer, work out points from goals by multiplying, or work out goals by dividing into total points.
•
Play competitions during long car trips by announcing a sum (using either +, -, x, or ÷ or a mixture) and “buzzing in” when the answer is known. Keep a tally of the results or just play for fun.
•
Roll two dice and as you roll, call out “add”, “subtract” or “times”. Your child must use the two numbers to complete the sum, e.g. if a 3 and a 5 are rolled, the sum would be “Five take 3 is 2”. Multiple-sided dice can be purchased at educational stores and some newsagencies.
r o e t s Bo r e p ok u S
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Teac he r
•
© ReadyEdPubl i cat i ons Show your child how repeated addition is multiplication by sharing things out, e.g. •plates f or evi e p ur ose • stacking intor groups of 4.w Three piles ofp 4 equals 12.s 4 +o 4 +n 4l =y 12 and
•
3 x 4 = 12.
•
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Introduce terms such as double (explain how this is the same as multiplying by 2) and half (this is the same as dividing by 2).
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Provide grid paper for your child to set out sums. The squares on the grid paper may assist in aligning the numbers (write one digit per square when setting out sums vertically).
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o c . che e r o t r s super
Play “Magic Number”. Write a number, such as 12, in the centre of a blank page and fold it into quarters. In each corner, write +, -, x, or ÷. See how many different sums your child can think of for each quarter (see example below).
+
-
9 + 3 = 12
6 + 6 = 12
1 + 11 = 12
13 - 1 = 12
24 - 12 = 12
20 - 8 = 12
4 + 8 = 12
5 + 7 = 12
10 + 2 = 12
17 - 5 = 12
19 - 7 = 12
50 - 38 = 12
36 ÷ 3 = 12
48 ÷ 4 = 12
×
÷
4 × 3 = 12
3 × 4 = 12
1 × 12 = 12
6 × 2 = 12
2 × 6 = 12
12 × 1 = 12
Ready-Ed Publications
24 ÷ 2 = 12
Book 1
Page 23
Parent Power •
Play “Buzz”. In this game, each person in the circle says one number in a regular counting sequence, but each time a certain number is reached, the person must say “buzz” instead of the number, for example: Any multiple of 3: “1, 2, buzz, 4, 5, buzz, 7, 8, buzz …” Any number that is either a multiple of 6 or contains the number 6: “1, 2, 3, 4, 5, buzz, 7, 8, 9, 10, 11, buzz, 13, 14, 15, buzz, 17, buzz, 19, 20, 21, 22, 23, buzz …” To make this trickier, any number that is both, such as 36, would be “buzz buzz”.
r o e t s Bo r e p ok u S
•
Encourage your child to keep score during a game such as ten-pin bowling. Also practise concepts such as “tens pairs”, e.g. “You have knocked 7 pins over – how many more do you need to knock over to get all 10?”
•
Play “Guess the Number”. Give clues until the child guesses the number, e.g. “I am thinking of a number between 1 and 10 that is even”. “This number is divisible by 4.” “The number is greater than 6” (the number is 8).
Teac he r
Play card games such as “21”, that require your child to calculate in their head, or modify a game of “Snap” so that a snap is any two cards that add to equal 10.
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Book 1
Ready-Ed Publications
Progress Chart
What Can I Do? Colour the lines in as you learn something new: Encourage your child to use their own judgement for colouring in. The first square can be coloured in straightaway. Getting some right: Approx 4/10; Getting most right: Approx 6/10 to 8/10; I can do this: Consistently getting more than 8/10 and confidently trying more complex problems
Rounding and Estimating
r o e t s Bo r e p ok u S
Starting to learn
Getting some right Getting most right
I can do this!!
Starting to learn
Getting some right Getting most right
Decimal Addition Starting to learn
Getting some right Getting most right
Subtraction Regrouping
I can do this!!
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Teac he r
Addition Regrouping
I can do this!!
© Re adyEdPubl i cat i on s Getting some right Getting most right I can do this!! •f orr evi ew pur posesonl y•
Starting to learn
Decimal Subtraction Getting some right Getting most right
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Multiplication
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Starting to learn
Getting some right Getting most right
I can do this!!
m . u
Starting to learn
I can do this!!
o c . Decimal Multiplication che e r o Starting to learn Getting some right Getting most right I can do this!! t r s super Division Starting to learn
Getting some right Getting most right
I can do this!!
Getting some right Getting most right
I can do this!!
Decimal Division Starting to learn Ready-Ed Publications
Book 1
Page 25
Skill Drills
Learning Outcome: Students will identify pairs of numbers that add to equal 10.
Pairs TTo o 10 Fill in the number that adds to give 10. The first few have been done for you:
4+6
2+8
6+
8+
5+
9+
1+
7+
3+
1+
6+
3+
5+
4+
8+
2+
9+
5+
7+
8+
6+
4+
2+
9+
9+
r o e t s Bo r e p ok u S
4+
5+
1+
7+
2+
9+
6+
3+
6+
4+
5+
3+
8+
1+
9+
2+
8+
3+
4+
2+
7+
6+
1+
5+
1+
6+
5+
1+
7+
4+
3+
8+
6+
3+
2+
8+
6+
9+
7+
1+
4+
7+
©8 +Rea dy9Ed4 P ub l i ca t i o8n s5 + 1+ + + 2+ 7+ + •f orr evi ew pur posesonl y•
9+
3+
2+
. te 4+
1+
9+
3+
o c . che e r o t r s super 8+
5+
2+
9+
1+
5+
6+
4+
7+
8+
2+
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7+
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3+7
1+
6+
8+
3+
7+
Time Taken: __________________ Number Completed: ___________________ Number Correct: __________________ Keep this sheet and try to beat your score next time! Page 26
Book 1
Ready-Ed Publications
Skill Drills
Learning Outcome: Students will identify pairs of numbers that add to equal 20.
Pairs TTo o 20 Fill in the number that adds to give 20. The first few have been done for you:
13 + 7
4+6
1+
16 +
12 + 8
6+
18 +
5+
19 +
1+
17 +
3+
13 +
15 +
4+
18 +
2+
19 +
5+
17 +
18 +
6+
4+
12 +
19 +
9+
11 +
7+
12 +
9+
16 +
3+
10 +
14 +
5+
13 +
8+
11 +
9+
12 +
18 +
3+
14 +
2+
17 +
6+
11 +
5+
Teac he r 5+
©R ea dyEdP ub12l i ca t i on s 5+ 8+ 1+ 19 + 4+ + 7+ 18 + •f orr evi ew pur posesonl y• 16 +
1+
17 +
4+
13 +
8+
16 +
3+
12 +
8+
16 +
9+
17 +
1+
14 +
7+
17 +
3+
9+
12 +
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15 +
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19 +
13 +
o c . che e r o t r s super
14 +
8+
15 +
2+
19 +
1+
1+
15 +
6+
14 +
10 +
18 +
2+
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1+
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14 +
r o e t s Bo r e p ok u S
1+
16 +
8+
3+
17 +
Time Taken: __________________ Number Completed: ___________________ Number Correct: __________________ Keep this sheet and try to beat your score next time! Ready-Ed Publications
Book 1
Page 27
Skill Drills
Learning Outcome: Students will mentally subtract whole numbers up to 100.
Subtraction Chart Try these sums in your head. You might like to time yourself. Try working a different way each time - down, across or diagonally. Write the answer underneath the sum. 6-4
9-3
8-3
7-5
9-8
17 - 8
19 - 15
27 - 8
83 - 5
95 - 74 69 - 34 74 - 36
7-6
8-4
7-3
13 - 2
19 - 6
27 - 4
48 - 3
34 - 23 78 - 25 57 - 29
4-3
6-1
7-6
14 - 1
17 - 5
39 - 3
56 - 1
50 - 19 51- 20 54 - 37
2-1
8-5
9-5
18 - 6
15 - 0
27 - 2
49 - 6
13 - 12 97 - 87 42 - 35
19 - 5
16 - 11
28 - 6
56 - 4
76 - 20 48 - 39 92 - 84
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Teac he r
3-1
3-0
-2 15 - 4 16 - 5 28 - 0 67 - 6 24 - 21 52 - 20 71 - 58 © 7R ea dyEdPubl i cat i ons • f o5r r e14v-i ew pur posesonl y• 5-1 -2 3 17 - 3 78 - 7 97 - 5 23 - 20 93 - 32 25 - 18
4-2
9-2
6-3
w ww
8-4
15 - 1
15 - 3
50 - 0
65 - 4
32 - 21 75 - 51 83 - 48
18 - 5
13 - 1
38 - 6
70 - 0
25 - 14 14 - 12 70 - 37
3-1
5-2
6-2
2-2
7-1
8-6
. te
m . u
1-1
o c . che e r o t r s super 13 - 3
19 - 3
65 - 0
64 - 9
63 - 53 89 - 66 90 - 76
Time Taken: __________________ Number Completed: ___________________ Number Correct: __________________ Keep this sheet and try to beat your score next time! Page 28
Book 1
Ready-Ed Publications
Skill Drills
Learning Outcome: Students will mentally add whole numbers up to 100.
Addition Chart Try these sums in your head. You might like to time yourself. Try working a different way each time - down, across or diagonally. Write the answer underneath the sum. 3+1
6+4
8+3
7+5
6+7
8+4
4+3
2+1
9+3
17 + 8 19 + 15 27 + 8
83 + 5 74 + 95 69 + 34 74 + 36
7+3
13 + 2
19 + 6
27 + 4
48 + 3 34 + 23 78 + 25 57+ 29
6+1
7+6
14 + 1
17 + 5
39 + 3
56 + 1 50 + 19 51 + 20 54 + 37
8+5
9+5
18 + 6
15 + 0
27 + 2
49 + 6 13 + 12 97 + 87 42 + 35
7 + 2 15 + 4 16 + 5 28 + 0 67 + 6 24 + 21 52 + 20 71+ 58 ©R eadyEdPubl i cat i ons • f or r evi ew pur posesonl y• 5+1 5 + 2 14 + 3 17 + 3 78 + 7 97 + 5 23 + 20 93 + 32 25 + 18 6+3
9+2
w ww
8+4
15 + 1
15 + 3
50 + 0
65 + 4 32 + 21 75 + 51 83 + 48
18 + 5
13 + 1
38 + 6
70 + 0 25 + 14 14 + 12 70 + 37
3+1
5+2
6+2
2+2
7+1
8+6
. te
m . u
4+2
r o e t s Bo r e p ok u S 9+8
Teac he r 3+0
56 + 4 76 + 20 48 + 39 84 + 92
ew i ev Pr
1+1
19 + 5 16 + 11 28 + 6
o c . che e r o t r s super 13 + 3
19 + 3
65 + 0
64 + 9 63 + 53 89 + 66 90 + 76
Time Taken: __________________ Number Completed: ___________________ Number Correct: __________________ Keep this sheet and try to beat your score next time! Ready-Ed Publications
Book 1
Page 29
Skill Drills
Learning Outcome: Students will mentally multiply whole numbers up to 100.
Multiplication Chart Try these sums in your head. You might like to time yourself. Try working a different way each time - down, across or diagonally. Write the answer underneath the sum. 4×4
2×5
1×6
6×3
3×5
5×4
4×8
8×2
2×9
9×5
5×7
7×4
4×5
5×1
1×7
7×2
2×9
9×6
6×3
3×8
8×6
6×6
6×4
4×5
5×3
3×8
8×1
1×9
9×2
2×4
8×3
3×4
4×2
2×7
7×6
6×1
1×5
5×9
1×6
6×8
6×5
8×2
5×9
9×1
1×7
7×3
r o e t s Bo r e p ok u S
3×1
ew i ev Pr
Teac he r
3×2
4×2
2×8
9×9
9×1
5×1
×1 1×9 9×4 ×2 2×7 7×8 8×5 ©8R ea dyEd4P ub l i ca t i on s 5×5 •f o7r r e4v i ew pu r po ses on9l y •2 × 2 1×7 ×4 ×3 3×8 8×6 6×3 3×9 ×2
2×8
8×6
9×7
7×1
1×4
4×7
7×3
8×8
5×5
2×9
9×9
1×1
7×7
3×9
4×4
9×2
2×1
1×5
. te
3×1
1×8
6×6
8×7
m . u
w ww
6×9
o c . che e r o t r s super 5×6
6×4
4×7
7×8
8×3
3×7
7×5
Time Taken: __________________ Number Completed: ___________________ Number Correct: __________________ Keep this sheet and try to beat your score next time! Page 30
Book 1
Ready-Ed Publications
Skill Drills
Learning Outcome: Students will identify number patterns of multiplication tables up to the 10x table.
Counting By… Complete the number patterns to count by… Twos:
2, 4, 6, 8, ___________________________________________________ 20
Threes: 3, 6, 9, _____________________________________________________ 30
r o e t s Bo r e p ok u S
Fives:
5, 10, 15, ____________________________________________________ 50
Sixes:
6, 12,18, ____________________________________________________ 60
Teac he r
4, 8, 12,_____________________________________________________ 40
ew i ev Pr
Fours:
Sevens: 7, 14, 21, ____________________________________________________ 70
Nines: Tens:
8, 16, 24, ____________________________________________________ 80
© ReadyEdPubl i cat i ons 10, 20, 30, ___________________________________________________ 100 • f orr evi ew pur posesonl y• 9, 18, 27, ____________________________________________________ 60
w ww
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m . u
Eights:
o c . che e r o t r s super
Time Taken: __________________ Number Completed: ___________________ Number Correct: __________________ Keep this sheet and try to beat your score next time! Ready-Ed Publications
Book 1
Page 31
How To Use The Following Activity Pages
r o e t s Bo r e p ok u S
ew i ev Pr
Teac he r
Each topic will focus on a single maths concept with a choice of two separate activity sheets. The teacher is able to introduce and explain the sheet to the whole class and then select which worksheet is assigned to each student. As both worksheets focus on the same content, only differing by the level of complexity, there is no need to isolate students by giving them separate instructions. Teachers may also choose to give all students the first sheet, and then follow up with the second sheet if the student is able to complete the first with minimal difficulties. Some topics in this book have 3 or 4 sheets. These should be completed in sequential order. Note: Although the second worksheet is designed for the more “able” students in the classroom, this certainly does not discount students with learning difficulties. Research shows that many students with Specific Learning Difficulties can work at an average to above average level, provided that their needs are taken into consideration. With this in mind, both worksheets have been designed so that ALL students have the opportunity to be extended.
w ww
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Page 32
m . u
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
o c . che e r o t r s super
Book 1
Ready-Ed Publications
Learning Outcome: Students will identify the value of a digit in a whole or decimal number up to 3 decimal places.
Name:
Digit V alue Revision Value Digit Value tells you how much a digit is worth in a number: The last whole digit is 6. It goes in the ONES column. The first decimal digit is 5. It goes into the TENTHS column.
1 874 296.523
Digit
Millions
Hundred Ten Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Thousands Thousands
1
8
r o e t s Bo r e p ok u S 4
2
9
6.
5
2
3
70 000
4 000
200
90
6
0.5
0.02
0.003
ew i ev Pr
Teac he r
Value 1 000 000 800 000
7
Write the value of the bold number for each of these:
Number
Value
Number
848 .......... 40
Value
5.251 ....... 0.05
Number
Value
$4.65 ........ $0.05
__________ 7.231 ...... $32.40 ...... __________ © Ready E d__________ Publ i ca t i o ns 7 432 ...... __________ 6.285 ...... __________ $199.00 .... __________ •f orr evi e w pur poses onl y•
2 396 ......
__________
3.021 ......
__________
$0.90 ........ __________
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m . u
7 211 ......
Place a decimal point in these amounts so that they make sense, and then write the digits in the correct columns.
Item
. te
Amount
An ice-cream $ 2 5 0 A CD
$2795
A stereo
$56300
An apple
$060
o c . che e r o t r s super Decimal
Thousands Hundreds Tens Ones Tenths Hundredths
$2.50
2
5
0
An old car $ 8 5 6 0 0 0
Ready-Ed Publications
Book 1
Page 33
Learning Outcome: Students will round whole numbers to the nearest 10.
Name:
Rounding 1 Rounding means finding the closest whole or decimal number that is asked for. Use the bold numbers to find the closest 10. 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
r o e t s Bo r e p ok u S
Circle the number 12. Is it closer to 10 or 20? 12 is closer to 10. So you round 12 to 10.
ew i ev Pr
Teac he r
When the number ends in 5, you can round up OR down (usually up).
Round these numbers to 10 or 20 (the nearest 10).
7 = ______
14 = ______
19 = ______
20 = ______
15 = ______ or ______
© ReadyEdPubl i cat i ons 20 f 30r 40i 60 90 • or ev ew50 pu r po70ses80onl y•100
Use these numbers to find the rounded answers to the nearest 10:
21 = ______
45 = ______ or ______
63 = ______
99 = ______
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m . u
10
Circle the correct rounding to the nearest 10 for these numbers. Hint: Look at the tens column first, then the ones. Do you round up or down?
. te 10 Circle the correct one o Round to the nearest c . c e her r 466 460 400 465 470 o t s super
Page 34
912
900
920
910
950
599
590
600
650
500
1 347
1 340
1 350
1 300
1 400
44 444
44 400
44 445
44 450
44 440
Book 1
Ready-Ed Publications
Learning Outcome: Students will round whole numbers to the nearest 10, 100, 1000 or 10 000.
Name:
Rounding 2 When rounding whole numbers you need to find the nearest number that is asked for: Look at 47 931
Number 4
Thousands Hundreds 7
9
Tens
Ones
3
1
r o e t s Bo r e p ok u S
To the nearest HUNDRED =
47 900 (3 is less than 5 so round DOWN.)
To the nearest THOUSAND =
48 000 (9 is more than 5 so round UP.)
To the nearest TEN THOUSAND =
50 000 (8 is more than 5 so round UP.)
Teac he r
47 930 (1 is less than 5 so round DOWN.)
ew i ev Pr
Rounded to the nearest TEN =
When the number ends in 5, you can round up OR down (usually up).
Number
Round to Nearest 10 (Ten)
Nearest 100 (Hundred)
Nearest 1 000 (Thousand)
Nearest 10 000 (Ten Thousand)
©R e a dyEd Publ i c a t i ons e.g. 24 470 27 500 27 000 30 000 •f orr evi ew pur posesonl y• 82 339 27 472
m . u
18 901
w ww
30 789 44 762 91 994
. te
o c . che e r o t r s super
A car costs $58 782 Round this to the nearest TEN THOUSAND dollars. $
An area of the city has 23 424 houses. Round this to the nearest THOUSAND.
An 11-year-old has lived for 96 362 hours. Round this to the nearest HUNDRED.
Ready-Ed Publications
Book 1
Page 35
Learning Outcome: Students will round numbers of up to 3 decimal places to the nearest 1, 1/10, 1/100 or 1/1000.
Name:
Rounding 3 - Decimals When rounding decimals you need to find the nearest number that is asked for: Look at 4.763
Ones
Decimal
Tenths
4
.
7
Hundredths Thousandths 6
3
r o e t s Bo r e p ok u S
Rounded to the nearest ONE = 5 (The next number, 7, is more than 5 so round UP.) To the nearest TENTH or 1 decimal place = 4.8 (6 is more than 5 so round UP.)
ew i ev Pr
Teac he r
To the nearest HUNDREDTH or 2 decimal places = 4.76 (3 is less than 5 so round DOWN.) When the number ends in 5, like 5, 1.5, 2.5, you can round up OR down (usually up).
Round to Nearest One
Nearest Tenth
(No decimal place)
(1 decimal place)
Number
Nearest Hundredth
Nearest Thousandth
(2 decimal places) (3 decimal places)
© ReadyEdPubl i cat i ons orr evi ew pur posesonl y• 8.901•f 7.472
7
7.5
7.47
7.472
2.339
4.762
w ww 1.994
. te
m . u
3.789
o c . che e r o t r s super
* A swimmer finishes a race in 12.343 seconds.
Round his time to the nearest HUNDREDTH or 2 decimal places = _________ seconds. * I need 7.679 cm of material.
Round this amount to the nearest TENTH or 1 decimal place = _____________ cm. * Round all of these prices to the nearest 10c (0.10, 0.20, 0.40, 0.50, …). $6.36 = $6.40
$3.21 = ___________
$7.59 = ___________
$2.05 = ___________
$9.47 = ___________
$0.99 = ___________
Page 36
Book 1
Ready-Ed Publications
Learning Outcome: Students will use rounding to estimate the answer to whole number and decimal addition sums.
Name:
Rounding and Estimating 1 Rounding numbers and estimating the answer can give you an IDEA of what the answer will be. This can help when you are checking your sums. Round numbers and do the sum: 31 + 58 Answer 89
Estimate: 30 + 60 = 90 Count up by 10’s in your head.
31 is close to 30 58 is close to 60
Teac he r
Estimate by rounding each number in the sum to the nearest Ten. Work out the real sum on a spare piece of paper:
ew i ev Pr
r o e t s Bo r e p ok u S
37 + 22
Estimate: 40 + 20 = 60
Answer: 59
Was it close? Yes
52 + 39
Estimate: ____________
Answer: _______
Was it close? _______
56 + 58
Estimate: ____________
Answer: _______
Was it close? _______
© ReadyEdPubl i cat i ons •f o rr evi ew pur posesAnswer onl y• 310 + 680 Estimate: 300 + 700 = 1 000 = 990 Estimate by rounding each number in the sum to the nearest Hundred. Work out the real answer with a calculator.
Answer: _____________
194 + 392
Estimate:________________________
Answer: _____________
Estimate:________________________
Answer: _____________
104 + 512
. te
m . u
Estimate:________________________
w ww
482 + 494
o c . che e r o t r s super
Estimate by rounding each number in the sum to the nearest One (whole number). Work out the real answer with a calculator.
3.10 + 6.79
Estimate: 3 + 7 = 10
Answer = 9.89
3.82 + 5.92
Estimate:________________________
Answer: _____________
1.09 + 0.98
Estimate:________________________
Answer: _____________
7.86 + 3.53
Estimate:________________________
Answer: _____________
Ready-Ed Publications
Book 1
Page 37
Learning Outcome: Students will use rounding to estimate the answers to whole number and decimal multiplication processes.
Name:
Rounding and Estimating 2 Rounding numbers and estimating the answer can give you an IDEA of what the answer will be. This can help when you are checking your sums. Round numbers and do the sum: 31 × 8 Answer 248
Estimate: 30 × 8 The best way to do this is to remove the zero, i.e. 3 × 8 = 24, then replace the zero, i.e. = 240.
31 is close to 30
r o e t s Bo r e p ok u S
Teac he r
So the estimate, 240, was close to the answer, 248.
37 x 2
52 x 9
Remove 0 = 4
Sum: 4 x 2 = 8
Replace 0 = 80
Round: 52 = 50
Remove 0 = 5
Real answer = 74
Sum: R 5 xe 9 = 45 Replace = 450 Real answer = 468 © a dyE dP0u bl i ca t i o ns Round: 89 = 90 0=9 •f orr evi ewRemove pur posesonl y• Sum: 9 x 8 =72
Replace 0 = 720
Real answer = 712
m . u
89 x 8
Round: 37 = 40
ew i ev Pr
Round each first number in the sum to the nearest Ten, then remove the zero, work out the sum, then replace the zero. Work out the real sum with a calculator:
w ww
Estimate by rounding each number in the sum to the nearest Hundred. Work out the real answer with a calculator.
. te
310 × 3
Estimate: 300 x 3 = 900
Answer = 930
482 × 4
Estimate: _________________________
Answer: _____________
194 × 2
Estimate: _________________________
Answer: _____________
104 × 8
Estimate: _________________________
Answer: _____________
o c . che e r o t r s super
Estimate by rounding each number in the sum to the nearest One (whole number). Work out the real answer with a calculator. 3.10 × 6.79
Estimate: 3 × 7 = 21
Answer = 21.049
4.85 × 6.92
Estimate: _________________________
Answer: _____________
8.09 × 1.98
Estimate: _________________________
Answer: _____________
Page 38
Book 1
Ready-Ed Publications
Learning Outcome: Students will use a range of strategies in order to carry out mental calculations more efficiently.
Name:
Other TTricks ricks FFor or Mental Maths 1 Tens pairs – all of these pairs add to give 10. 1+9
2+8
3+7
4+6
5+5
Find the Tens pairs in these sums and add them up:
r o e t s Bo r e p ok u S = 20
4+3+5+7+5
= 4 + 10 + 10
= _______
3+5+3+7+7
= _____________________
= _______
20 + 4 + 6
= _____________________
= _______
37 + 25 + 25 + 23
= _____________________
= _______
Twentys pairs – all of these pairs add to give 20.
ew i ev Pr
= 10 + 10
Teac he r
2+4+8+6
© a3d Ed b5l i t i o 2 +R 18e +y 174 +P 16u +c 15a 6 +n 14s 7 + 13 •f orr ev wp r po nl y• 8i +e 12 9u + 11 10s +e 10so
1 + 19
= 40
4 + 13 + 15 + 7 + 5
= 4 + 20 + 20
= _______
13 + 5 + 3 + 17 + 7
= _____________________
= _______
20 + 14 + 6
. te
Removing Zero
m . u
= 20 + 20
w ww
2 + 14 + 18 + 6
o c . che e r o t r s super = _____________________
= _______
Any multiplication sum with a zero in one of the numbers can be worked out by removing the zero, working out the sum, then replacing the zero. Sum: 20 x 3 Remove: 2 x 3 = 6 Replace: 20 x 3 = 60 Sum: 60 x 5
Remove: _______ = _______
Replace: _______ = _______
Sum: 90 x 7
Remove: _______ = _______
Replace: _______ = _______
Ready-Ed Publications
Book 1
Page 39
Learning Outcome: Students will understand and use the concept of repeated addition as a means of mental multiplication and vice versa.
Name:
Other TTricks ricks FFor or Mental Maths 2 Repeated Addition Multiplication is simply repeated addition. 3×5 =5+5+5
= 15
r o e t s Bo r e p ok u S
4×5 =5+5+5+5
= 20
Teac he r
You can use repeated addition to help you with your tables: e.g.
ew i ev Pr
If you forget 7 × 9, but you know that 6 × 9 = 54, you just add one more 9. 54 + 9 = 63
You can use your multiplication tables to help you with repeated addition – this is like taking a short cut: e.g.
If I sleep for 8 hours a night, how many hours do I sleep for in a week (7 days)? It is easier to remember that 8 × 7 = 56 than to add 8 + 8 + 8 + 8 + 8 + 8 + 8.
© ReadyEdPubl i cat i ons Addition Multiplication Answer •f orr evi ew p ur poseson16l y• 4+4+4+4 4×4 Change these repeated additions to multiplication sums and work out the answer:
2+2+2+2+2+2+2+2
w ww
m . u
6+6+6 7+7+7+7 9+9+9
. te
o c . che e r o t r s super
5+5+5+5+5+5+5+5
Make these into two multiplication sums and then work out the answer. Addition 7+7+7+3+3
Multiplication
Sum
Answer
3 × 7 and 2 × 3
21 + 6
27
5+5+5+5+9+9 2+2+4+4+4+4
Page 40
Book 1
Ready-Ed Publications
Name:
Learning Outcome: Students will add whole numbers up to 1000 with regrouping.
Addition Regrouping 1 (previously known as carrying) +
565 359
First add the ones, 5 + 9 14
WORK FROM RIGHT TO LEFT
r o e t s Bo r e p ok u S Ones
1
4
Look at the number 14:
Regroup 1 to the Tens.
Put 4 in the Ones. T
5
6
3
5
O
1
5
9
+
5
6
4
3
5
2 6
Add all the digits in the Tens. 1 6 + 5 12
ew i ev Pr
Teac he r
H
+
Tens
Hundreds
Tens
1
2
regroup 1 to the Hundreds.
© ReadyEdPubl i cat i ons 5 •f 6o 4s r4r evi ew5pu6r po esonl y•
Put 2 in the Tens and 1
3
2
2
6
w ww
5
1
4
+
+
. 6t e4 1
4
5
9
2
3
5
2
9
2
6
m . u
+
1
o c . c e 9 h + 4 4 7 + 1 r er o t s super 2
5
7
7
7
6
3
5
3
Now try without the box: +
667 363
Ready-Ed Publications
+
355 476
+
Book 1
265 649
+
563 178
Page 41
Learning Outcome: Students will add whole numbers up to 1000 with regrouping.
Name:
Addition Regrouping 2 (previously known as carrying) WORK FROM RIGHT TO LEFT Start by adding all the digits in the Ones column. Each time the answer is 10 or more, you must regroup the Tens digit, usually a 1, into the next column. 1
4
6
4
5
Working out:
9
2
4 + 9 = 13
Put down the 3, regroup the 1.
9
1 + 6 + 5 = 12
Put down the 2, regroup the 1.
3
1+ 4 + 4 = 9
Put down the 9.
Try these:
+
587 236
+
239 495
173 + 659
+
578 244
+
468 495
+
258 358
+
768 269
+
199 334
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 367 + 457
w ww
+
336 485
378 + 469
. te
+
m . u
+
r o e t s Bo r e p ok u S 4
ew i ev Pr
Teac he r
1
789 247
o c . che e r o t r s super Try these on some spare lined paper:
295 + 425
697 + 286
236 + 139
457 + 358
4357 + 3294
6946 + 2385
1582 + 2786
3484 + 3269
9654 + 1298
2575 + 2579
6478 + 2493
9918 + 1696
Page 42
Book 1
Ready-Ed Publications
Learning Outcome: Students will add decimal numbers to 2 decimal places with regrouping.
Name:
Decimal Addition 1 Adding decimals is like regular adding. You regroup the same way. Just remember to keep the decimal point in the same place. No regrouping
Regrouping 1 column
Regrouping 2 columns
r o e t s Bo r e p ok u S 1
+
9. 94
10. 17
WORK FROM RIGHT TO LEFT
Try these:
No regrouping +
+
1
8. 39 1. 78
ew i ev Pr
Teac he r
8. 67
+
1
5. 79 4. 15
2. 25 5. 32
+
4. 43 3. 14
+
3. 58 4. 13
+
$6. 79 $2. 55
+
6. 28 1. 60
© ReadyEdPubl i cat i ons 4. 34f 3.p 66u 4. 36 • o r r e v i e w r p o s e s o n l y• 3. 31 + 5. 22 + 3. 51
w ww
Regrouping 1 column +
5. 27 2. 13
+
5. 37 2. 24
. te
+
m . u
+
3. 45 5. 22
6. 47 2. 38
o c . che 4. 59 e 4. 27 r o r +s 1. 28 st + 4. 65 u per
Regrouping 2 columns +
$4. 46 $1. 85
Ready-Ed Publications
Book 1
+
$4. 48 $2. 87
Page 43
Learning Outcome: Students will Add decimal numbers to 2 decimal places, (including numbers of differing decimal places) with regrouping.
Name:
Decimal Addition 2 Adding decimals is like regular adding. You regroup the same way. Just remember to keep the decimal point in the same place. No regrouping
Regrouping 1 column 1
r o e t s Bo r e p ok u S 5. 79 + 4. 3
3. 45 + 5. 2
10. 09
Try these:
WORK FROM RIGHT TO LEFT
HINT: PUT 0 IN THE GAPS TO HELP.
1. 40 4. 12
+
+
5. 6 4. 14
+
ew i ev Pr
Teac he r
8. 65
3. 4 1. 59
© ReadyEdPubl i cat i ons 4. 8 1. 9 + 5. 95 + 5. 89 •f orr evi e w pur poses onl y•
m . u
3. 47 + 5. 8
w ww
When you write the decimals for a sum, make sure the decimal point is lined up. Example: 2.45 + 3.6 + 0.78 + 5 (Putting 0 into the gaps helps neat setting out!) Wrong: 2.45 3.6 0.78 + 5
. te
o c . che e r o t r s super Right: 2. 45 3. 60 0. 78 + 5. 00
Try lining this sum up in the space here:
.
5.37 + .4 + 23.55 + 7
. .
Page 44
+
.
=
.
Book 1
Ready-Ed Publications
Learning Outcome: Students will subtract whole numbers up to 1000 with regrouping.
Name:
Subtraction Regrouping 1 ( previously known as borrowing)
To subtract, –
WORK FROM RIGHT TO LEFT
964 676
Take away the Ones. T
9
6
6
7
1
8
–
5
r o e t s Bo r e p ok u S O 4
–
6
9
6
6
7
5
1
9
4
6
–
6
15
1
6 7
4 6
8
1
In the Tens 6 becomes 5.
4
In the Hundreds 9 becomes 8.
7 R 6e © adyEdPubl i cat i ons r8r evi ew pur posesonl y• 2 •f 8o 6
w ww
Try these:
4
2 . te 8 4
1
7
5
–
8
m . u
–
You can’t do 5 – 7 so, regroup 10 from the Hundreds.
ew i ev Pr
Teac he r
H
You can’t do 4 – 6 so, regroup 10 from the Tens.
4
15
6
1
7
5
4
3
8
6
9
o 3 c . che e r o t r s super 8 –
–
6
1
8
3
Now try without the box:
–
727 349
Ready-Ed Publications
–
938 269
–
Book 1
743 268
–
842 178
Page 45
Learning Outcome: Students will subtract whole numbers up to 10 000 with regrouping.
Name:
Subtraction Regrouping 2 ( previously known as borrowing)
To subtract,
WORK FROM RIGHT TO LEFT
964 – 676 You can’t do 4 – 6 … so
You can’t do 5 – 7 … so
regroup 10 from the Tens.
regroup 10 from the Hundreds.
6
5
6
7
1
4
9
6
–
6
8
1
5
1
7
4
6
–
6
8 In the Tens 6 becomes 5.
–
426 159
–
1
4 6
8
8
In the Hundreds 9 becomes 8.
© ReadyEdPubl i cat i ons 246 823 827 •f or e i ew p–u279 r poseso y• –r 189v – n 159l
w ww
–
5 7
2
Try these:
821 165
1
8
328 179
–
. te –
947 379
–
826 187
–
m . u
–
r o e t s Bo r e p ok u S
ew i ev Pr
Teac he r
9
Now finish the sum.
902 547
o c . che e r o t r s super 723 547
–
515 257
–
950 273
Try these on some spare lined paper:
642 – 129
735 – 167
845 – 378
745 – 388
5463 – 2187
9824 – 2975
8725 – 6512
8613 – 3748
Page 46
Book 1
Ready-Ed Publications
Learning Outcome: Students will subtract decimal numbers to 2 decimal places with regrouping.
Name:
Decimal Subtraction 1 Subtracting decimals is like regular subtraction. You regroup the same way. Just remember to keep the decimal point in the correct place so it lines up and down the column. Examples:
r o e t s Bo r e p ok u S
No regrouping 5. 45 – 3. 22
Regrouping 2 columns 7 12 1 8. 36 – 1. 78
1. 59
6. 58
WORK FROM RIGHT TO LEFT
Try these:
No regrouping –
7. 55 2. 24
–
3. 12
ew i ev Pr
Teac he r
2. 23
Regrouping 1 column 6 1 5. 74 – 4. 15
–
5. 28 2. 23
–
9. 67 1. 50
–
2. 63
–
1. 23
w ww
–
m . u
© ReadyEdPubl i cat i ons • orr evi ew8.p r poseso2.n87l y• 7. 43f 89u
–
$6. 56 $2. 79
Regrouping 1 column
. te
–
8. 47 2. 19
–
8. 42 3. 17
–
5. 74 2. 26
–
$8. 32 $4. 57
6. 76 1. 39
o c . che e r o 5. 43 7. 36 t r s s r u e p – 2. 28 – 3. 28
Regrouping 2 columns –
$7. 52 $1. 86
Ready-Ed Publications
Book 1
Page 47
Learning Outcome: Students will subtract decimal numbers to 2 decimal places, (including numbers of differing decimal places) with regrouping.
Name:
Decimal Subtraction 2
Subtracting decimals is like regular subtraction. You regroup the same way. Just remember to keep the decimal point in the correct place so it lines up and down the column. Examples: No regrouping
r o e t s Bo r e p ok u S Regrouping 1 column 4
5. 45 3. 2
–
–
Regrouping 2 columns 5 14 1
1
5. 39 4. 7
–
2. 77
0. 69
Try these:
WORK FROM RIGHT TO LEFT
Putting 0 as a place marker helps you to work the sum out. 7. 30 5. 12
–
–
8. 6 3. 13
–
ew i ev Pr
Teac he r
2. 25
6. 50 3. 73
9. 6 1. 28
–
m . u
© R e a d y E d P u b l i c a t i o n s 8. 37 4. 3 7. 7 5. 8 •f – 1. 79 – 3. 25 orr evi ew pur poseso nl y•
w ww
When you write the decimals for a sum, make sure the decimal point is lined up. Example: 8.45 – 5 Wrong:
–
8.45 5
. te
o c . che e r o t r s super Right:
–
8. 45 5. 00
Putting 0 as a place marker helps neat setting out.
Work out the answer to the RIGHT sum.
Challenge: On the back of this sheet, try this one: 7 – 4.59 Page 48
Hint: Make 7 into 7.00. Book 1
Ready-Ed Publications
Learning Outcome: Students will use understanding of place value to align and calculate written addition sums with whole numbers up to 5000.
Name:
Setting Out Sums 1
(Whole Numbers)
It is always important to set out sums neatly, especially when: You have many numbers in the sum: 3 2 2
Right:
+
Wrong:
3465 2874 4987 9826
1 2 2 1 1
3465 2874 4987 + 9826
r o e t s Bo r e p ok u S
3011897
The numbers in the sum have different place values: Right:
+
1 1
Wrong:
2852 127
+
ew i ev Pr
Teac he r
21152
2852 127 4122
2979
Rule: Always make sure that the Ones, Tens, Hundreds and Thousands are lined up the same.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
w ww
m . u
Use these grids to practise lining up the sums below:
. te
o c Answer . che e r o t 2736 + 2873 + 2985r +s 1284 2874 s + 1002 + 1276 + 1874 uper +
562 + 1938 + 17 Ready-Ed Publications
4274 + 201 + 20 Book 1
Page 49
Learning Outcome: Students will use understanding of place value to align and calculate written addition sums with whole numbers up to 5000 and numbers with up to 2 decimal places.
Name:
Setting Out Sums 2
(Whole Numbers and Decimals) Make sure the place values are lined up when you add these. Use lined paper to work out the answers. 2736 + 1562 + 1814 + 1562
r o e t s Bo r e p ok u S
2753 + 2781 + 4826 + 1725 4326 + 2635 + 4835 + 3612
ew i ev Pr
Teac he r
1452 + 7214 + 3872 + 1423
2788 + 5325 + 3 + 2537 1427 + 88 + 43 + 253 1427 + 5 + 15 + 1572
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
2 + 21 + 2543 + 12
2653 – 142
w ww
m . u
7635 – 55 9988 – 9
. tedecimal points are lined up when you add these.oUse lined Make sure the c . paper to work out the answers. ch e r e o t r s super 3.01 + 0.9 + 25.42 43.02 + 1.46 + 0.05 652.842 + 0.01 + 7.7 45.9 – 0.01 36.8 – 2.8 Page 50
Book 1
Ready-Ed Publications
Learning Outcome: Students will multiply whole numbers up to 100 by numbers up to 10, with and without regrouping.
Name:
Multiplication 1 64 × 2
Do the ONES first: 4 × 2 = 8 (put down in the ONES column) Do the TENS next: 6 × 2 = 12 (put the 2 into the TENS)
128
Regroup the 1 into the HUNDREDS.
r o e t s Bo r e p ok u S
83 × 2
42 × 4
71 × 5
81 × 2
91 × 4
71 × 6
51 × 2
ew i ev Pr
Teac he r
62 × 2
© ReadyEdPubl i cat i ons Regrouping •f orr evi ew pur posesonl y• 1
75
Do the ONES first: 5 × 3 = 15 (put the 5 in the ONES) Regroup the 1 into the TENS.
w ww
Do the TENS next: 2 × 3 = 6 + 1 = 7 (ADD the regrouped number.)
26 × 4
. te
Ready-Ed Publications
m . u
25 × 3
o 28 c . × 2 che e r o t r s super
19 × 4
16 × 9
Book 1
Page 51
Learning Outcome: Students will multiply whole numbers up to 100 by numbers up to 100, with and without regrouping.
Name:
Multiplication 2 Using 65 × 35 as an example: 2 (regrouping for the first line) 1 (regrouping for the second line)
Working out:
6 ×
3 2
r o e t s Bo r e p ok u S 5
5
1
9
5
0
2
2
7
5
Multiply 5 x 5 Write 5 in the Ones column and 5 × 5 = 25 regroup the 2 into the tens. 6 × 5 = 30 + 2 = 32 Multiply 6 x 5 and add 2 (the regrouped number). For 32, write 2 in the tens and regroup 3 into the hundreds. 5 × 3 = 15 6 × 3 = 18 + 1 = 19 NEXT, PUT 0 in the ONES column, because now you are multiplying by 3 which is in the TENS. Multiply 5 x 3 (=15). Write 5 in the Tens column. Regroup the 1 into the Hundreds. Multiply 6 x 3 and add 1 (the regrouped number).
ew i ev Pr
Teac he r
3
5
Multiply each digit in 65 by 5 FIRST, THEN put down a zero in the Ones column and multiply each digit in 65 by 3.
w ww
Try these:
. te 5
× 2
m . u
© ReadyEdPubl i cat i ons •f orr ev i ew pur posesonl y• 325 + 1950 = 2275 Add the two subtotals together.
o c . che e r o t r s super
3
8
2
7
6
6
×
9
6
5
9
Do the second line.
0
Page 52
Book 1
Ready-Ed Publications
Learning Outcome: Students will multiply whole numbers up to 1000 by numbers up to 10, with and without regrouping.
Name:
Multiplication 3 Try these: 4 1 (regrouping for the first line) 1 (regrouping for the second line)
1 ×
4
51
5
9
Teac he r
34
+
2
1
r o e t s Bo r e p ok u S 3
9
61
8
6
0
2
8
×
5
0
2
6
+
ew i ev Pr
1
5
6 + 6 = 12 Regroup the 1.
2 4 2 © R ea7dyEdPubl i cat i on s4 × 2 1 × 3 •f orr evi ew pur posesonl y•
+
w ww
. te
8
m . u
+
6
o c . che e r o t r s super Try these on some spare lined paper:
139 × 71
712 × 12
568 × 15
399 × 25
705 × 16
890 × 11
168 × 35
236 × 36
Ready-Ed Publications
Book 1
Page 53
Learning Outcome: Students will multiply numbers with up to 2 decimal places by numbers with up to 2 decimal places, with regrouping.
Name:
Multiplication 4 -
Multiplication of Decimals
Using 2.3 × 6.4 as an example. 1
Working out:
1
2. ×
6. 9 8
1
4
7
Teac he r
3
Do the sum normally, IGNORING THE DECIMAL PLACE.
r o e t s Bo r e p ok u S 4
2
0 2
3 × 4 = 12 2×4=8+1=9 3 × 6 = 18 Put down the 0 on the second line. 2 × 6 = 12 + 1 = 13
ew i ev Pr
1
3
92 + 1380 = 1472
Now, count the total number of digits after the decimal point in the original sum. 2.3 One number after the decimal point. 6.4 One number after the decimal point. TOTAL = 2 numbers after the decimal point, i.e. the answer = 14.72.
© ReadyEdPubl i cat i ons Try these: •f orr evi ew pur posesonl y• 5
6.
3
w ww
. te
×
9.
8
4.
6
m . u
×
4.
o c . che e r o t r s super
Try these. You may wish to set them out on grid paper to help you keep the correct position of the digits: $2.60 × 3
Page 54
$1.95 × 52
$3.45 × 19
Book 1
$6.99 × 25
Ready-Ed Publications
Learning Outcome: Students will divide whole numbers up to 100 by whole numbers up to 10.
Name:
Division 1 - Revision Using 24 ÷ 2 =
2 ) 24
This means how many times will 2 go into 24?
Divide the Tens column first 2 ÷ 2 = 1.
12 2 ) 24
Divide the Ones column next 4 ÷ 2 = 2.
Try these:
r o e t s Bo r e p ok u S
2 ) 84
4 ) 44
3 ) 63
Division With Remainders
5 ) 55
2 ) 25R This many times will 2i go into © ea dmeans yEhow dP ub l i c at on s25? •Divide f or r evi ew pur posesonl y• the Tens column first: 2 ÷ 2 = 1 (write 1 on top of the 2).
25 ÷ 2 =
12 r1 2 ) 25
w ww
Divide the Ones column next:5 ÷ 2 = 2 remainder 1 (will not go three times).
m . u
1 2 ) 25
ew i ev Pr
Teac he r
1 2 ) 24
Answer = 12 remainder 1 or 12 r 1
. te
Try these: 2 ) 85
o c . che e r o t r s s r u e p 4 ) 46 6 ) 61
3 ) 67
2 ) 23
4 ) 89
3 ) 68
9 ) 99
4 ) 45
3 ) 69
4 ) 80
5 ) 59
Ready-Ed Publications
Book 1
Page 55
Learning Outcome: Students will divide whole numbers up to 100 by whole numbers up to 10 with regrouping.
Name:
Division 2 - With Regrouping In division, you regroup if you cannot divide into the first digit evenly.
2 ) 34
Divide the Tens column first: 3 ÷ 2 = 1 r 1 (Does not divide evenly)
r o e t s Bo r e p ok u S
Regroup by writing the remainder next to the Ones. 4 becomes 14.
17 2 ) 3 14
Answer = 17
Teac he r
Divide the Ones column next: 14 ÷ 2 = 7 (Divides evenly)
ew i ev Pr
1 2 ) 3 14
Try these:
3)8 7
w ww
2)7 6
7)8 4
. te
6)7 2
7)9 1
4)9 6
4)6 4
5)8 5
m . u
5)9 0
© ReadyEdPubl i cat i ons )4 5 2)5 4 4)6 8 •f orr e vi ew pur p3o sesonl y•
6)8 4
o c . che e r o t r s super 3)8 1
6)9 6
3)4 8
Work these out below: 98 ÷ 8
Page 56
64 ÷ 4
76 ÷ 4
Book 1
Ready-Ed Publications
Learning Outcome: Students will understand that there are different processes used in division and use the correct method.
Name:
Division 3 - What Kind of Division? Can the first digit divide evenly? Yes: Write the answer on top.
Teac he r
42 2 ) 84
Look at the first example and then try the other one!
r o e t s Bo r e p ok u S 4 ) 44
Yes: Write the answer on top.
Too Small: Write 0 (it goes into the number 0 times). Then write the second digit as a remainder. 4 cannot go into 3 - it goes 0 times, so the 3 becomes the remainder.
12
3 ) 36
ew i ev Pr
Can the second digit divide evenly?
5 ) 55
© ReadyEdPubl i cat i ons 20 r 3 • f o r r e v i e w p u r p o sesonl y• ) 4 83 Too Large:
w ww
13 r 1 2 ) 27
4 ) 89
3 ) 92
m . u
Divide and then write the leftovers as the remainder.
. te divide evenly? o Can the first digit c . che e r o t r s super Too Large: Divide and regroup the remainder into the ones. Divide into the regrouped remainder. 5÷2=2r1 Regroup 1: 8 becomes 18.
Too Small: Divide into the tens and the ones together. 6 cannot go into 3, so do 6 into 37.
13 r 1 2 ) 5 18
Ready-Ed Publications
6r1 4)6 4
6 ) 37
Book 1
9 ) 86
Page 57
Learning Outcome: Students will use a variety of processes, including regrouping, when dividing whole numbers up to 1000 by whole numbers up to 10.
Name:
Division 4 - Larger Numbers Look at the first examples and then try the rest. No regrouping or remainders: 110 5 ) 550
r o e t s Bo r e p ok u S) ) 2 ) 642
3 ) 963
4 ) 884
6 689
4 955
2 )8 5 7
4 )6 6 4
4 )8 7 2
Regrouping and remainders:
Teac he r
2 )7 5 8
Combining the first two digits:
ew i ev Pr
226 r 1 5 ) 67 19
6 )9 4 8
© Re adyEdPu bl i cat i ons 3 )2 5 6 6 )4 6 8 3 )2 8 8 •f orr evi ew pur posesonl y• 4 )3 5 5
2 )1 9 8
5 )2 1 9
7 )2 4 2
8 )2 6 1
w ww
5 )4 1 8
. t Word Problemse
6 )2 4 7
m . u
64 r 1 7 )4 4 9
9 )7 5 2
o c Write these as sums and work them out on a separate page: . ch e r ethesu o st There are 4 sports groups inr school andr 377 children. How many e p children are in each group? Are there any children left over? What would you do with the left over children? I have read the same number of pages in my book each day for 7 days. If I have read 245 pages, how many pages do I read each day?
Page 58
Book 1
Ready-Ed Publications
Learning Outcome: Students will divide numbers with up to 2 decimal places by whole numbers up to 10 with regrouping.
Name:
Division 5 - Decimals When dividing by a decimal number, keep the amount of digits after the decimal place the same: Look at the first examples and then try the rest: No regrouping or remainders: 1.6 6 ) 9.36
r o e t s Bo r e ) ) p ok u S 3 6. 6
Regrouping but no remainders: 1.90 5 ) 9.450
4 ) 7. 8 4
3 ) 8. 5 8
3 ) 7. 4 1
8 ) 9. 6 0
7 ) 8. 5 4
4 ) 4. 8
ew i ev Pr
Teac he r
2 6. 2
6 ) 9. 5 4 6 ) 9. 3 6
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Combine the first two digits. Use the boxes to help you estimate.
w ww
6 ) $4. 2 6
. te
8 ) $3 1 . 9 2
Estimate: How many times does 7 go into 52? (7 × 7 = 49)
m . u
7.49 7 ) 5 2. 34 63
Estimate: If I share $4 amongst 6 people, do they get less than $1? Would they get more than 50 c?
o c Estimate: How can I round 31.92 to get. a number that 8 c e he r goes into easily. Your answer o should t r s be close to this! super
4 ) $2 1 . 9 2
Estimate: How many times does 4 go into $21? What two amounts will the answer be between?
9 ) $0 . 2 7
Estimate: Will your answer be in dollars or cents? How many times does 9 go into 27?
Ready-Ed Publications
Book 1
Page 59
Name:
Learning Outcome: Students will divide whole numbers up to 1000 and numbers with up to 2 decimal places by whole numbers up to 10 recognising and correctly stating remainders.
Division 6 – Remainders Remainders can be rounded up, written as a fraction, or left out.
Rounded up (Best for things like money or time where there is only a maximum of 2 decimal places that we usually use.) Example:
r o e t s Bo r e p ok u S
Rob needs to earn $570.00 this month. If he gets $9.00 an hour, how many hours does he have to work?
ew i ev Pr
Teac he r
63.33 r 3 9 ) 570.00
It would be easiest for Rob to work for 64 hours (round the answer up) and earn $576.00.
Written as a fraction (Best for things that can be divided up when left over.) There are 5 children in the Smith family, and Mrs Smith makes 12 small pizzas. How many pizzas does each child get?
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
2r2 5 ) 12
w ww Child 1
. te
Child 2
Child 3
Child 4
m . u
Each child gets 2 pizzas – and there are 2 pizzas left. Each of the remaining pizzas can be divided into fifths, so each child can have 2 and 2/5 pizzas.
Child 5
o c . che e r o t r s s r u e p Left out (Best for things that cannot be divided up when left over.) Pizzas left divided into 5ths:
1
3
1
3
2
4
5
2
5
4
How many 7 cm boxes can I stack along a wall that is 696 cm across? 99 r 3 7 ) 696 The 3 means that there is 3/7 of a 7 cm space left over – not enough for another box, so ignore the remainder – only 99 boxes can really fit! Page 60
Book 1
Ready-Ed Publications
Learning Outcome: Students will decide the most appropriate way to express a remainder following a division process.
Name:
Division 7 – Remainders Work out these problems and decide whether to round up, write as a fraction or leave out. There are 76 children going on an excursion, with one adult needed for every 6 students. How many adults are needed? Write the sum:
r o e t s Bo r e p ok u S )
Teac he r
How many children are left over? _________
Round up (One more adult?) Write as a fraction (Can we use a fraction of an adult?) Leave out (Have no extra adult.)
ew i ev Pr
What will be done with this remainder? ________________________________
© ReadyEdPubl i cat i ons I have $265.00 to share between my 3 children. How much will each get? •f orr evi ew pur posesonl y• Write the sum:
w ww
m . u
How much is left over? (Make sure you have worked out the sum to 2 decimal places.) _________
. te
Round up? (Give each child an extra cent – where does it come from?)
o c . Write as a fraction ofc a cent. (Do we have fractions of cents?) e her r o t s Leave out. (How much will eachs child uget?) per
_______________________________________________________________
Think about the smallest coin we have – 5c. Work out the true amount each child can really have in notes and coins. Multiply this amount by 3 to make sure it is not more than $265.00. Challenge: How much is left over that is difficult to share between 3 in coins? _________c Ready-Ed Publications
Book 1
Page 61
ANSWERS - Skill Drills Page 27 - Pairs to 10
Page 28 - Pairs to 20
6
8
4
2
5
1
9
3
7
7
16
8
14
2
15
1
19
3
17
9
4
7
5
6
2
8
1
5
3
19
4
7
5
16
2
18
1
15
3
6
5
9
3
8
1
4
7
2
4
6
15
9
13
8
11
4
17
2
14
4
6
5
7
2
9
1
8
6
8
10
6
15
7
12
9
11
8
16
8
2
7
6
8
3
9
4
2
9
1
5
9
3
6
7
8
2
4
1
3
3
7
6
2
5
1
8
9
5
4
r o e t s Bo r e p ok u S 4
9
5
1
1
2
17
6
18
3
14
9
15
1
11
6
8
3
2
5
19
4
12
19
1
16
8
13
2
15
2
4
7
1
8
5
19
3
16
7
12
4
17
1
18
9
6
3
7
9
8
12
4
11
3
19
6
13
7
19
8
1
9
4
2
3
17
6
12
5
18
1
19
4
12
6
3
2
7
3
11
8
19
5
14
Page 29 - Subtraction
Page 30 - Addition
2
2
6
14
5
22
52
56
9
8
4
10
12
24
27
5
2
1
9
4
19
78
21
35
38
11
12
17
25
34
1
4
4
1
5
1
1
3
4
0
3
5
3
4
2 2
6
10
2
17
34
60
96
87 176
35
88 169 103 110
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 13
23
45
11
53
28
13
12
10
15
25
13
12
36
55
31
31
17
7
7
13
15
22
12
15
25
43
1
10
7
3
13
14
24
11
11
28
61
3
32
13
2
9
9
3
9
14
71
92
3
61
7
3
6
7
4
14
12
50
61
11
24
35
6
3
4
13
12
32
70
11
2
33
6
2
10
16
65
55
10
23
14
. te
Page 31 - Multiplication 6
16
10
30
6
18
15
20
5
24
3
31
51
57 103 86
42
57
69
15
29
55
25 184 77
19
21
28
73
45
7
17
20
85 102 43 125 43
11
12
16
18
50
4
7
8
23
14
44
70
4
8
14
16
22
65
73 116 155 166
69
71
91
72 129
51 126 111
m . u
11
w ww
0
ew i ev Pr
Teac he r
7
39
26 107
o c . che e r o t r s super Page 32 - Counting by ...
16
45
9
7
21
3
20
32
16
18
45
35
28
7
14
18
54
18
24
48
36
20
15
24
8
9
18
8
8
16
24
12
8
14
42
6
5
45
81
9
6
48
8
9
36
8
14
56
40
25
5
7
28
12
16
48
18
27
18
4
16
48
54
63
7
4
28
21
3
8
49
27
16
64
25
18
81
1
36
56
18
2
5
30
24
28
56
24
21
35
2, 4, 6, 8, 10, 12, 14, 16, 18, 20 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 8, 16, 24, 42, 40, 48, 56, 64, 72, 80
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Page 33 - Digit Value Revision: 6, 7000, 10; 0.2, 6.0, 0.001; $30.00, $100.00, $0.90; $27.95, $563.00, $0.60, $8560.00; Check that digits are written in the correct columns. Page 34 - Rounding 1: 10, 10, 20, 20, 10 or 20; 20, 40 or 50, 60, 100; 470, 910, 600, 1350, 44 440 Page 35 - Rounding 2: 82 340, 82 300, 82 000, 80 000; 18 900, 18 900, 19 000, 20 000; 30 790, 30 800, 31 000, 30 000; 44 760, 44 800, 45 000, 50 000; 91 990, 92 000, 92 000, 90 000 $60 000, 23 000, 96 400 Page 36 - Rounding 3: 2, 2.3, 2.34, 2.339; 9, 8.9, 8.90, 8.901; 4, 3.8, 3.79, 3.789; 5, 4.8, 4.76, 4.762; 2, 2.0, 1.99, 1.994; 12.34 seconds; 7.7 cm; $6.40, $3.20, $7.60, $2.00 or $2.10, $9.50, $1.00 Page 37 - Rounding and Estimating 1: 50 + 40 = 90, Answer = 91;60 + 60 = 120, Answer = 114; 500 + 500 = 1000, Answer = 976; 200 + 400 = 600, Answer = 586; 100 + 500 = 600, Answer = 616; 4 + 6 = 10, Answer = 9.74; 1 + 1 = 2, Answer = 2.07; 8 + 4 = 12, Answer = 11.39 Page 38 - Rounding and Estimating 2: 500 x 4 = 2 000, Answer = 1928; 200 x 2 = 400, Answer = 388; 100 x 8 = 800, Answer = 832; 5 x 7 = 35, Answer = 33.562; 8 x 2 = 16, Answer = 16.0182 Page 39 - Other Tricks For Mental Maths 1: 24, 3 + 7 + 3 + 7 + 5 = 25, 20 + 4 + 6 = 30, 37 + 23 + 25 + 25 = 110; 44, 13 + 7 + 3 + 17 + 5 = 45, 20 + 14 + 6 = 40; 6 x 5 = 30, 60 x 5 = 300; 9 x 7 = 63, 90 x 7 = 630 Page 40 - Other Tricks For Mental Maths 2: 2 x 8 = 16, 6 x 3 = 18, 4 x 7 = 28, 3 x 9 = 27, 5 x 8 = 40; 5 x 4 and 9 x 2, 20 + 18 = 38; 2 x 2 and 4 x 4, 4 + 16 = 20 Page 41 - Addition Regrouping 1: 704, 911; 1030, 831, 914, 741 Page 42 - Addition Regrouping 2: 821, 832, 822, 1037; 823, 824, 963, 533; 734, 847, 616, 1036 720, 983, 375, 815; 7651, 9331, 4368, 6753; 10 952, 5154, 8971, 11614 Page 43 - Decimal Addition 1: 7.57, 7.57, 7.88; 7.65, 8.88, 7.87; 7.40, 7.71, 8.85; 7.61, 5.87, 8.92; $6.31, $9.34, $7.35 Page 44 - Decimal Addition 2: 5.52, 9.74, 4.99; 9.27, 10.75, 7.79; 11.83, 36.32 Page 45 - Subtraction Regrouping 1: 368, 578; 378, 669, 475, 664 Page 46 - Subtraction Regrouping 2: 656, 57, 544, 668; 267, 568, 639, 355; 149, 176, 258, 677; 513, 568, 467, 357; 3276, 6849, 2213, 4865 Page 47 - Decimal Subtraction 1: 5.31, 3.05, 8.17; 4.31, 6.26, 1.64; 6.28, 3.48, 5.37; 5.25, 3.15, 4.08; $5.66, $3.75, $3.77 Page 48 - Decimal Subtraction 2: 2.18, 5.47, 8.32; 2.57, 4.45, 2.51; 3.45, 2.41 Page 49 - Setting Out Sums 1: 9878, 7026, 2517, 4495 Page 50 - Setting Out Sums 2: 7674, 12 085, 15 408, 13961; 10653, 1811, 3019, 2578; 2511, 7580, 9979. 29.33, 44.53, 660.552, 45.89, 34.0 Page 51 - Multiplication 1: 124, 168, 355, 162; 166, 364, 426, 102; 104, 76, 144, 56
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Page 52 - Multiplication 2: 1026, 5664 Page 53 - Multiplication 3: 3900, 5187, 9348; 9869, 8544, 8520, 9975, 11 280, 9790, 5880, 8496 Page 54 - Multiplication 4: 28.35, 45.08; $7.80, $101.40, $65.55, $174.75 Page 55 - Division 1: 42, 11, 21, 11; 42 r 1, 11 r 2, 10 r 1, 22 r 1; 11 r 1, 22 r 1, 22 r 2, 11; 11 r 1, 23, 20, 11 r 4 Page 56 - Division 2: 18, 27, 15, 17; 29, 12, 13, 17; 38, 24, 16, 14; 12,27,16,16; 12 r 2, 16, 19 Page 57 - Division 3: 11, 11, 22 r 1, 30 r 2, 16, 9 r 5 Page 58 - Division 4: 321, 321, 221; 114 r 5, 238 r 3, 428 r 1; 379, 166, 218, 158; 85 r 1, 78, 96; 83 r 3, 88 r 3, 99, 41 r 1; 43 r 4, 34 r 4, 32 r 5, 83 r 5; 94 in each faction, 1 left over. Put them in one of the factions; 35 pages. Page 59 - Division 5: 3.1, 2.2, 1.2; 1.96, 2.86, 1.59; 2.47, 1.20,1.22, 1.56; $0.71, $3.99, $5.48, $0.03 Page 60 - Division 6: No answers – information sheet only Page 61 - Division 7: 12 r 4 6) 76 There are 4 children left over. As these children need supervision, you need to round up, i.e. 13 adults. 88.33 r 1 3) $265.00 We do not have fractions of a cent, and we cannot round up something that does not exist, so it is best to leave it out, i.e. each child gets $88.33. In reality, we only have 5 coins as the smallest, so each child can have $88.30 Check: 88.30 x 3 = $264.90. There is 10c to spare, which cannot be divided up between 3 children in coins.
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