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* Task cards for developing a range of maths problem solving strategies.

ctivities cover all k ey learning * A. key t e of the maths curriculum. o areas c .

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Written by Clare Way © 2006 Ready-Ed Publications Published by Ready-Ed Publications (2006) P.O. Box 276 Greenwood Perth 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 669 X


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Introduction

The Primary Maths Problems series is a comprehensive teacher resource containing a variety of reproducible mathematical problem task cards – some with one solution, some with a number of solutions and some open ended. The problems are related to practical everyday mathematical situations, with each activity designed to challenge students to use their knowledge and problem solving skills.

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Problem solving can develop many valuable skills in our students such as logical reasoning, creative thinking and communication skills. Students require perseverance, flexibility in ideas and methods, reflective thinking and confidence if they are going to be successful in this area. The problems will ask students to draw on a number of mathematical strategies in order to solve them. These strategies need to be introduced and taught to students if they are going to gain the skills necessary to solve a variety of problems. For students to solve a problem they first need to read the facts carefully and understand what the problem is asking them to do. They then need to work out a plan for solving the problem, carry out the processes involved and hopefully look back over their answer and assess the results successfully.

Problems can be solved using a number of different strategies. These strategies may include: • Think, estimate and check • Draw a diagram or picture • Look for patterns • Make a model • Act out the problem • Construct a table or a graph • Write a statement • Make a list • Calculate • Reflect and assess results

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Prior to presenting the problems from this book to your students, put a list of these strategies on display. Go through each one and present students with an example to work with. Keep the strategies on display, then as your students work through the various problem cards from this book, ask them which strategies they need to solve each problem. In some cases they may need to use more than one strategy to solve a problem. A checklist included in this book allows teachers and students to keep a record of the strategies used to solve each problem. The above strategies are explained more thoroughly and with examples further on in the teaching notes, which ideally should be worked through with the students.

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The problem cards in this book have been divided into the four main areas of the maths curriculum: • SPACE • NUMBER • MEASUREMENT • CHANCE and DATA The principles of WORKING MATHEMATICALLY and REASONING and STRATEGIES have been incorporated into each of the four main areas.

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Contents

Assessement Checklist

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PROBLEM CARDS: Space and Location STRATEGY Make a model Make a model Look for patterns Make a model Make a model Make a model Make a model Look for patterns Look for patterns Draw a diagram Task 10: Tricky Tangrams Look for patterns Task 11: Symmetrical Letters Look for patterns Task 12: Using Grids Draw picture Task 13: Class Position Draw a diagram Task 14: Flight 125 Draw a diagram Task 15: Carousel Draw a diagram Task 16: Local Map Draw a diagram Task 17: Pizza Delivery Est. and check Make a list Task 18: Fete Plan Draw a diagram Task 19: Lost Cattle Make a list Task 20: Trapped in a Maze Make a list Task 21: Assessment: Make a model Office Building Task 22: Assessment: Draw a diagram School Map Make a list

OUTCOME Identifies lines in our environment and uses them in construction. Recognises, describes and represents perpendicular lines. Recognises, names and classifies various angles. Recognises, names and uses angles for design purposes. Makes and constructs shapes using cubes. Makes and constructs pentominoes using cubes. Identifies and uses triangles to create various shapes and patterns. Visualises and explains the parts of a 3D shape that are not seen. Uses shapes to design a tessellating pattern.

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Manipulates tangram pieces to create shapes and patterns. Identifies line of symmetry in various shapes. Uses a grid square to enlarge or reduce a 2D shape. Demonstrates knowledge of grids and the language of location. Uses and understands the language of location. Demonstrates knowledge of fractions when dealing with location. Identifies and draws simple scale plans of familiar location. Interprets and uses a local map to plan a journey.

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Uses given information and compass points to draw a simple plan. Uses compass points to specify location. Uses language of location to create a path through a maze. Visualises and explains the parts of a 3D shape that are not seen.

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Visualises and plans journeys on simple maps.

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TITLE Task 1: Parallel Tower Task 2: Perpendicular Lines Task 3: Angles Task 4: House Design Task 5: Cubes Task 6: Pentominoes Task 7: Triangles Task 8: Brick Wall Task 9: Tessellating Path

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PROBLEM CARDS: Number TITLE STRATEGY Task 1: Creature Collection Est. and check Draw a picture Task 2: Cross Numbers Est. and check Task 3: Concert Hall Est. and check Calculate Task 4: Four 4s Est. and check, Calculate Task 5: Ages Est. and check Task 6: How Many Days? Calculate Task 7: Making Numbers Make a list Look for patterns Task 8: 200 Metre Sprint Make a list Look for patterns Task 9: Swimming Carnival Calculate Draw a diagram Task 10: AFL Game Est. and check Calculate Task 11: Golf Game Est. and check

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OUTCOME Uses knowledge of number and number processes to solve a problem.

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Manipulates numbers to arrive at a set total. Uses knowledge of number facts and multiplication to solve a problem.

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Constructs and completes number sentences involving the four operations. Selects relevant information to solve a problem using number facts. Uses a calculator to solve a problem involving multiplication and addition. Uses knowledge of number and place value to create numbers.

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Uses knowledge of number and ordinal number to solve a problem.

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Uses knowledge of number and ordinal number to solve a problem.

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Uses knowledge of number operations to solve a problem.

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Uses knowledge of addition and subtraction to solve a problem.

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Contents

PROBLEM CARDS: Number cont. Task 12: Darts

Task 13: Number Sentences Task 14: Equations

Uses knowledge of addition to solve a problem.

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Creates number sentences from a set of numbers.

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Constructs equations using a given set of numbers.

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Uses knowledge of number, time and money to solve a problem. Uses knowledge of number operations and money to solve a problem. Uses knowledge of number facts, patterns and time to solve a problem.

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Uses knowledge of number operations and fractions to solve a problem. Uses knowledge of number facts and patterns to solve a problem.

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Task 18: School Picnic Task 19: Shopping Trolley Task 20: Boat Rescue

Task 21: Melbourne To Brisbane

Task 22: School Supplies Task 23: Uniform Shop Task 24: Toy Sale Task 25: Car Wash Task 26: Cake Shop

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Task 15: Go-Carts Task 16: Museum Task 17: Tennis Tournament

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Est. and check Make a list Est. and check Make a list Est. and check Make a list Est. and check Calculate Make a list Calculate Calculate Look for patterns Calculate Make a list Calculate Calculate Calculate Calculate Look for patterns Est. and check Calculate Calculate Draw a diagram Calculate Make a list Calculate Calculate Calculate Look for patterns Calculate Look for patterns

Orders numbers for a purpose. Uses knowledge of division and fractions to solve a problem. Calculates the cost of items for a purpose.

page page page Applies knowledge of percentages, number operations and money to solve a problem. page Applies knowledge of percentages, number operations and money to solve a problem. page Solves a problem using knowledge of number patterns, multiplication and money. page Uses knowledge of fractions and money to solve a problem. page

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Task 28: School Sports Task 29: Height Order

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Task 30: Dress Maker’s Fabric Task 31: Assessment Cricket Match Task 32: Assessment: Travelling To School

Uses knowledge of numbers and fractions to solve a problem.

Uses knowledge of numbers and fractions to solve a problem. Uses knowledge of decimal number and height to solve a problem.

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Applies knowledge of number operations to decimal numbers. Applies knowledge of number operations and number patterns to solve a problem.

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Uses knowledge of number and fractions to solve a problem.

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PROBLEM CARDS: Measurement TITLE Task 1: Flying Fox

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STRATEGY Est. and check Draw a diagram Task 2: Rose’s Garden Calculate Draw a diagram Task 3: Comparing Students Draw a table Task 4: Lost! Est. and check Write a statement Task 5: Balance Scales Est. and check Act it out Task 6: Smith Family Weight Calculate Task 7: Cave Area Write a statement Act it out Task 8: Oil Drum Calculate Task 9: Petrol Tank Calculate Task 10: Max’s Party Est. and check Make a list

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OUTCOME PAGE Makes judgements and selects appropriate units of measurement for design purposes. page 40

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Selects units of measurement in order to compare two people. page 41 Makes judgements and uses the body as a tool to compare the relative size of objects. page 41

Estimates, compares and measures objects using a balance scale.

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Uses knowledge of number and weight to solve calculations. Estimates, compares and measures area using informal and formal units.

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Uses knowledge of litres and millilitres to solve a problem. page 43 Applies knowledge of number operations to a problem involving kilometres and litres. page 44 Makes judgements and estimates quantities of food and drink for a purpose. page 44


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Contents

Task 13: New Carpet Task 14: Temperature

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Interprets and demonstrates knowledge of graphs and temperature.

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Constructs a model and uses a protractor to measure its angles. Measures and calculates time elapsed from starting and finishing times. Measures and calculates time elapsed from given times. Converts 12 hour time to 24 hour time. Reads timetable correctly to plan a simple journey. Uses and reads a calendar to plan events and dates.

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Uses knowledge of time and volume to solve a problem.

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Uses knowledge of time to plan and prepare a meal.

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PROBLEM CARDS: Chance and Data

TITLE STRATEGY Task 1: Games and Chance Write a statement Task 2: Dice Combinations Act it out Make a list Task 3: Easter Raffle Calculate Task 4: Teacher Splash Write a statement Task 5: Selection Process Calculate Make a list Task 6: Scoring 100 Estimate Write a statement Task 7: Fair/Unfair Write a statement Make a design Task 8: Decision Making Make a list Make a design Task 9: Weather Possibilities Est. and check Task 10: Sports Survey Make a design Task 11: Music Night Make a design Calculate Task 12: Statistics Make a list Task 13: School Rules Make a design Write a statement Task 14: Hot Lunches Calculate Task 15: Beth’s Weight Gain Calculate Draw a graph Task 16: Subject Choices Draw a diagram Task 17: Classroom Temperature Draw a graph Task 18: Take Away Food Write a statement Draw graph Task 19: Pocket Money Calculate Draw graph Task 20: Interpreting Graphs Write a statement Task 21: Assessment: Est. and check Horse Racing Calculate Task 22: Assessment: Make statement Fete Results Calculate

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Calculates area from a plan for a purpose.

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Task 15: Boat Design Task 16: Time Elapsed Task 17: Triathlon Task 18: 24 Hour Time Task 19: Bus Timetable Task 20: Tom’s Calendar Task 21 Assessment: Tap Leak Task 22 Assessment: Christmas Dinner

Calculate Act it out Calculate Interpret a graph Make a model Calculate Calculate Calculate Calculate Calculate Make a list Act it out Calculate Calculate

OUTCOME Understands and uses probability statements in game situations. Carries out and analyses the outcomes from simple chance experiments.

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Examines and orders the outcomes of winning a chance competition. Uses given information to analyse a situation involving chance. Uses given information to analyse a situation involving chance.

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Makes predictions to do with the probability of chance situations.

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Understands and applies the concepts of fair and unfair to simple games.

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Designs a simple device to assist with making decisions.

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Researches and prepares data for presentation to an audience. Prepares a survey using different categories for a purpose.

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Interprets and uses information gathered from a pictograph. Calculates weight gain and presents the information in a line graph.

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Extracts, interprets and presents information in a Venn diagram. Extracts, interprets and presents information on a line graph. Extracts, interprets and presents gathered information in a graph format.

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Extracts, interprets and presents gathered information in a graph format.

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Predicts, interprets and extracts information from a variety of graph styles. Uses given information to analyse a situation involving chance.

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Extracts and analyses information contained in a graph.

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Curriculum Links

The activities in this book can be linked to the following areas in the Mathematics curriculum documents. QUEENSL AND QUEENSLAND Number Number Concepts – N 3.1 Addition and Subtraction – N 3.2 Multiplication and Division – N 3.3 Measurement Length, Mass, Area and Volume – M 2.1 Time – M 2.2 Space Shape and Line – S 3.1 Location, Direction and Movement – S 3.2 Patterns and Algebra Patterns and Functions – PA 3.1 Equivalence and Equations – PA 3.2 Chance and Data Chance – CD 3.1, Data – CD 3.2

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* Incorporates VELS: Number, Space, Measurement, Chance and Data, Structure and Working Mathematically.

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VICTORIA* Number Numbers, Counting and Numeration – 31, 3.2, 3.3, 3.4 Mental Computation and Estimation – 3.1, 3.2, 3.3 Computation and Applying Number – 3.1, 3.2, 3.3 Number Patterns and Relationships – 3.1, 3.2, 3.3 Space Shape and Space – 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 Location – 3.1, 3.2, 3.3, 3.4 Measurement Measuring and Estimating – 3.1, 3.2, 3.3, 3.4, 3.5 Time – 3.1, 3.2 Using Relationships – 3.1 Chance and Data Chance – 3.1, 3.2 Posing Questions and Collecting Data – 3.1, 3.2, 3.3 Summarising and Presenting Data – 3.1, 3.2, 3.3 Interpreting Data – 3.1, 3.2 Reasoning and Strategies Mathematical Reasoning – 3.1, 3.2 Strategies for Investigation – 3.1, 3.2, 3.3, 3.4

NEW SOUTH W ALES WALES Working Mathematically Questioning – WMS 3.1; Applying Strategies – WMS 3.2; Communicating – WMS 3.3; Reasoning – WMS 3.4; Reflecting – WMS 3.5 Number Whole Numbers – NS 3.1; Addition and Subtraction – NS 3.2; Multiplication and Division – NS 3.3; Fractions and Decimals – NS 3.4; Chance – NS 3.5 Patterns and Algebra – PAS 3.1a, PAS 3.1b Data – DS 3.1 Space and Geometry Three-dimensional Space – SGS 3.1; Two-dimensional Space – SGS 3.2a, SGS 3.2b; Position – SGS 3.3 Measurement Length – MS 3.1, Area – MS 3.2, ; Volume and Capacity – MS 3.3; Mass – MS 3.4, Time – MS 3.5

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N.T as. / A.C.T (National Cur riculum) N.T.. / TTas. Curriculum) Working Mathematically Investigating – 3.1; Using Problem Solving Strategies – 3.3; Applying and Verifying – 3.4; Using Mathematical Language – 3.5 Space Spatial Ideas – 3.7a, 3.7b; Visualising, Analysing and Representing Arrangements and Locations – 3.8; Visualising, Analysing and Representing Shapes – 3.9; Visualising, Analysing and Representing Movements and Transformations – 3.10 Number Count and Order – 3.11; Number Patterns – 3.12; Equations – 3.13; Applying Number – 3.14; Mental computation – 3.15; Written computation – 3.16; Calculators – 3.17 Measurement Choosing Units – 3.18; Measuring – 3.19; Estimating – 3.20; Time – 3.21; Using Relationships – 3.22 Chance and Data Understanding, Estimating and Measuring Chance Variation – 3.23; Collecting Data – 3.24; Organising Data – 3.25; Displaying and Summarising Data – 3.26; Interpreting Data – 3.27

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SOUTH AAUSTRALIA USTRALIA Exploring, Analysing and Modelling Data – 3.1, 3.2, 3.3 Pattern and Algebraic Reasoning – 3.9, 3.10, 3.11 Spatial Sense and Geometric Reasoning – 3.12, 3.14 Number – 3.6, 3.7, 3.8 Measurement – 3.4, 3.5

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WESTERN AAUSTRALIA USTRALIA Working Mathematically Contextualise Mathematics – WM 3.1 Mathematical Strategies – WM 3.2 Reason Mathematically – WM 3.3 Apply and Verify – WM 3.4 Space Represent Location – S 3.1 Represent Shape – S 3.2 Represent Transformations – S 3.3 Reason Geometrically – S 3.4 Measurement Understand Units – M 3.1 Direct Measure – M 3.2 Estimate – M 3.3 Indirect Measure – M 3.4 Chance and Data Understand Chance – C&D 3.1 Collect and Organise Data – C&D 3.2 Summarise and Represent Data – C&D 3.3 Interpret Data – C&D 3.4 Number Understand Numbers – N 3.1 Understand Operations – N 2.2 Calculate – N 3.3 Reason About Number Patterns – N 3.4


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Teachers’ Notes

PRESENTING THE PROBLEM CARDS • As a whole class • In small groups • In pairs • Individually • As an extension task • As a homework task

r o e t s Bo r e p ok u S USING THE PROBLEM CARDS

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Prior to presenting the cards, display a list of the strategies needed for solving a problem to your class. Provide an example of each strategy by solving a related problem. The problem cards may be used in a variety of formats, including:

Photocopy the relevant cards suited to the key learning areas your class is covering and distribute according to one of the above formats. Each problem card will contain the following:

1. Task number, key learning area and title; 2. Material required to complete the problem tasks; 3. 1 to 4 problem tasks; 4. A challenge task for early finishers or those needing further extension; 5. A student self assessment area; 6. Relevant indicator/s or learning focus.

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Note: Challenge questions can be answered using another sheet of paper.

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o c Two assessment task cards are located at the end of each strand for teachers to . c e herchecklist is located r collect and assess. An assessment at the end of the introductory o t sof the strategies and skills su section of this book for teachers to keep ar record e p students are using as they work through each problem card. There is also provision ASSESSMENT AND ANSWERS

on each problem task card for students to note their own self-assessment. They are simply required to shade in an icon to represent how they felt they performed on a task. Answers or possible solutions are also provided at the back of this book with the exception of open-ended problems where answers would vary or require a teacher to check the end results.

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Teaching Points

PROBLEM SOLVING STRATEGIES

Think, estimate and check

This skill is often used subconsciously in problem solving as well as many other areas of maths. It should be the first step taken whenever a student is presented with a problem. Students read the problem at least once, think about what it is asking of them, estimate an answer and then check to see if they are correct. While solving a problem using this method, students may still need to work through a number of other strategies, such as calculating mentally or writing notes or sums, drawing up a table or chart or even checking using mathematical tools such as a calculator, scales, ruler and so on.

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Example:

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If Alex, who is 12 years old, is one quarter the age of his mother and father, half the age of his sister and double the age of his younger brother, how old are all the members of his family combined? STEP 1: Read over the problem with the students and ask them to think about what the problem is asking them to do. As this is a two part problem, point out the following steps that need to be estimated and solved. STEP 2: Work out the age of each member of the family, using Alex’s age to help.

E.g. mother and father are 12 x 4 = 48 (¼ of 48 = Alex’s age), his sister is 12 x 2 = 24 (½ of 24 = Alex’s age) and his younger brother is ½ of 12 = 6.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Therefore Alex’s mother and father are both 48 years old, his sister is 24 years old, his younger brother is 6 years old and Alex is 12 years old. STEP 3: Add the ages of each member of his family to get the combined age.

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Draw a diagram/picture

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E.g. 48 + 48 + 24 + 12 + 6 = 138 years.

This skill can be very useful in helping a student visualise the problem, making it often easier to interpret and solve. In this case students would read over the problem, think about what it is asking and draw a diagram/picture to help them solve it. Example:

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12 friends were at a party enjoying pizzas for a snack. Each pizza had 8 slices. If 6 friends ate 4 slices each, 4 ate 3 slices each and 2 friends had 2 slices each, how many pizzas did they eat altogether? STEP 1: Read the problem and work out what it is asking. STEP 2: Draw the number of slices of pizza mentioned or draw several pizzas and divide them into 8ths and shade the number of slices eaten. STEP 3: Count up the number of pizzas eaten and record the answer. (The answer is 5 pizzas.)

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Teaching Points Look for patterns

As with drawing a diagram or picture, looking for a pattern can also help students to visualise the problem. A pattern may present itself particularly in the areas of space and number. Example:

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A gardener placed some patterned paving stones as shown below to form a path from the house to the washing line. If the pattern continued to grow what would the next three stones look like? STEP 1: Read the problem, look for a pattern and think about how it would look if it continued.

123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123

123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123

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STEP 2: Draw another three blank paving stones and continue the increasing/decreasing pattern.

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© ReadyEdPubl i cat i ons Make a model f or r e vi ew udealing r po se sorelated nl y • and Making• a model works particularly well p when with problems to shape

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Example:

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space. Once again in order for students to visualise the problem it is often useful to construct it or make a model first. Materials such as blocks, 2D and 3D shapes, cubes, sticks, Plasticine, paper, etc. are all handy in representing shapes and structures in our world. If Ben wanted to build a footbridge across a two metre wide stream, what would be the best shapes to use to make his bridge sturdy? Think about the supports, the main walking bridge and the arm rails needed.

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STEP 1: Read the problem and visualise what it is asking.

STEP 2: Gather various 3D shape blocks and begin working on a structure that could theoretically support the weight of people as they cross a stream. STEP 3: Build an example of a bridge. For example use large rectangular prisms for the base, longer flatter rectangular prisms for the walkway and triangles for the handrails. ANSWER: The most effective shapes would be rectangular prisms and triangles.

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Teaching Points Act it out

Acting out a problem can also give students a greater understanding of a problem. In particular if the problem involves things like people, objects, measurement tools or money or things they have easy access to, it can help them visualise the question as well as the answer. A problem that involves being acted out is often also fun and can intrinsically motivate students to find a solution. Example:

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

If you were to drop a small, bouncy ball from a height of two metres, how many bounces would it then take to come to a complete stop?

Teac he r

STEP 1: Read the problem and think about what it is asking. Most students would realise that this is an open-ended problem and therefore the solution would vary.

ew i ev Pr

STEP 2: Locate a bouncy ball and follow the problem by dropping it from a two metre height (a student standing on top of a table may equate to two metres). STEP 3: Count the number of bounces until the ball comes to a stop. Repeat the problem/ experiment and compare answers.

Draw a table/graph

This skill is particularly useful when working with problems in the area of data collection and number. Drawing a table or graph helps present the information in a more organised manner which in turn makes it easer to see the result or answer.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Example:

Jessica has been swimming with the squad for 5 years and Alex for 18 months. Because of this Jessica is able to swim 1 lap in 30 seconds and Alex can swim 1 lap in 40 seconds. How long would it take Jessica to swim 10 laps compared to Alex?

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STEP 1: Read the problem and work out what it is asking?

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STEP 2: Draw up a table comparing Jessica’s times and laps compared to Alex.

STEP 3: Read the table and write the solution. Jessica can swim 10 laps in 5 minutes compared to Alex who takes 6 mins and 40 secs to complete the 10 laps.

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JESSICA 30 sec

10

ALEX

o c . che e r o t r s super 1 lap

40 sec

1 laps

60 sec (1 min)

2 laps

80 sec

2 laps

90 sec

3 laps

120 sec (1 min)

3 laps

120 sec (2 min)

4 laps

160 sec

4 laps

150 sec

5 laps

200 sec

5 laps

180 sec (3 min)

6 laps

240 sec (4 min)

6 laps

210 sec

7 laps

280 sec

7 laps

240 sec (4 min)

8 laps

320 sec

8 laps

270 sec

9 laps

360 sec (6 min)

9 laps

300 sec (5 min)

10 laps

400 sec (6 m 40 s)

10 laps


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Teaching Points

Make a statement

Some problems simply require that you think about the question and make a statement or thought showing your opinion. These types of problems are often evident in the areas of measurement, chance and data. Such a type of problem gives us a good insight into a student’s knowledge and understanding of a presented topic. Example:

Rainfall in Melbourne during Spring

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

The following graph appeared on the news last night during the weather report. Make a statement about what it is telling us. STEP 1: Read the problem and work out what it is asking.

Example of answer: The graph shows Melbourne’s rainfall during the spring months. September had the most rainfall with 75 mm, while only 43 mm of rain fell in October.

Make a list

ew i ev Pr

Teac he r

STEP 2: Look at the graph and the headings and write a statement.

Making a list is a useful skill to use in all areas of the maths curriculum. Students could be required to make a list of people, times, events, numbers, etc. in order to solve a problem. Once again being able to write a list makes it more effective to then visualise the answer to a problem. Alternatively you may need to make a list of answers for your problem.

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Calculate

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© ReadyEdPubl i cat i ons •f orr evi ew pur poseso nl y10•5 3 2 235

Example: The following numbers appear on a dart board. Make a list of as many possible combinations of numbers you would need to hit in order to score 20. STEP 1: Read the problem and work out what it is asking. STEP 2: Think about what possible number combinations add up to 20 and begin listing some of these equations. Example of answer: 10+10, 10+5+5, 5+5+5+5, 10+2+2+3+3, 10+5+2+3, 2+2+2+2+2+2+2+2+2+2 5+5+5+2+3, 5+5+3+3+2+2

This skill is more commonly used in the area of number. Students would be required to read the problem and use mental or written calculations to come up with the answer. In some cases this skill would be required along with another skill, such as, “estimate and check”, “looking for patterns” or “making a list” prior to working on the calculation. Calculators or computers are also a useful tool for this strategy.

o c . che e r o t r s super

Example: Ben had $8.00 to spend at the school Mother’s Day stall. He bought a candle for $3.00, three chocolate hearts at 50c each, a bath bomb for $1.00 and a card for $1.00. How much money did he have left? STEP 1: Read the problem and work out what calculations are required. STEP 2: In order to determine the amount of money Ben has left, students would first need to calculate how much he has spent, then deduct this amount from his total of $8.00. Students may work out the calculations on paper, in their head or using a calculator. STEP 3: Calculations. 1) $3.00 + 50c + 50c + 50c + $1.00 + $1.00 = $6.50 Note: Some students may note that 3 x 50c = $1.50 2) $8.00 - $6.50 = $1.50 Answer = Ben has $1.50 left.

11


STRAND: ESTIMATE AND CHECK

DRAW A DIAGRAM/ PICTURE

LOOK FOR PATTERNS

MAKE MODEL/ DESIGN

ACT IT OUT

DRAW A TABLE/ GRAPH

WRITE A STATEMENT

MAKE A LIST

CALCULATE

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

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Teac he r

TASK

ASSESSMENT CHECKLIST (STRATEGIES)

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s super


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TASK

parallel tower

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

Construct the highest possible tower of parallel lines using blocks. Measure how high it was before it crashed down. Write the height below. ___________________________________________________

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2

SELFAS SES SMENT ASSES SESSMENT

Materials Materials:

Draw an example of each of these line types that can be seen in objects or structures you can see in your classroom. An example would be the vertical line of a window.

Teac he r

1 1

SHAPE AND SPACE (MEASUREMENT)

Challenge:

How could you make a tower of parallel lines more secure so that it didn’t fall? _________________ _________________ _________________ _________________

© ReadyEdPubl i cat i ons SHAPE SPACE orr evi ew pur poses onAND l y • TASK•f Indicator Indicator: Identifies lines in our environment and uses them in construction.

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Materials Materials: •pencil •matchsticks •Plasticine

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1

perpendicular lines

Identify and draw two different sets of perpendicular lines in the classroom.

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2

SELFAS SES SMENT ASSES SESSMENT

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2

o c . che e r o t r s super

Challenge:

Using matchsticks and Plasticine make two different shapes that only contain perpendicular lines. Name the shapes below. ___________________________________________________ ___________________________________________________ Indicator Indicator: Recognises, describes and represents perpendicular lines.

What shapes do not have any perpendicular lines? _________________ _________________ _________________ _________________ _________________ _________________ 13


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TASK

3 1

angles

SELFAS SES SMENT ASSES SESSMENT

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

Group the angles below into three categories (come up with a name for each category)

ew i ev Pr

3

Materials Materials: •pencil •ruler

Identify and draw three right angles you can see in the classroom.

Teac he r

2

SHAPE AND SPACE

Challenge: What is

Identify and draw an angle less than 90° that you can see in the classroom.

a reflex angle? Can you see any in the classroom? If so, where? _____ _______________ _______________ _______________ _______________

© ReadyEdPubl i cat i ons SHAPE ANDl SPACE orr evi ew pur pose son y• TASK •f Indicator Indicator:: Recognises, names and classifies various angles.

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house design

Materials Materials: •pipe cleaners •pencil

SELFAS SES SMENT ASSES SESSMENT

. te

Name the three different types of angles you used in your design.

m . u

An architect has asked for your assistance in designing a house that has at least three different types of angles. Make a model of your design using pipe cleaners.

w ww

4 1 2

o c . che e r o t r s super

______________________________________________________________ ______________________________________________________________

3

___________________________________________________

Name the 2D or 3D shapes you used in your design.

Challenge: If you had

to design a house that had no right angles, what would it look like? Draw a model and label the angles you used on your diagram. Indicator Indicator:: Recognises, names and uses angles for design purposes.

14


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TASK

cubes

Materials Materials: •cubes •pencil

SELFAS SES SMENT ASSES SESSMENT

How many squares are there in a cube? _____________________________ Make five different shapes using only four cubes (Note: the cubes need to share at least one surface when they join). Draw your shapes below.

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

ew i ev Pr

Teac he r

5 1 2

SHAPE AND SPACE

Challenge: Make a rectangular prism using eight cubes. Draw a diagram of this prism on the back of this sheet or on another sheet of paper.

© ReadyEdPubl i cat i ons SHAPE SPACE orr evi ew pur poses onAND l y • TASK•f Indicator Indicator:: Makes and constructs shapes using cubes.

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6

pentominoes

SELFAS SES SMENT ASSES SESSMENT

w ww

1

m . u

Materials Materials: •graph paper •scissors •glue •pencil •computer

Using graph paper, draw as many different shapes (pentominoes) as you can using five squares joined together with at least one common edge. Cut them out and paste them below.

. te

o c . che e r o t r s super

Challenge:

Use a computer drawing package to represent one of these pentominoes for an interesting swimming pool design. Indicator Indicator:: Makes and constructs pentominoes using cubes.

15


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TASK

7

1

triangles

Materials Materials: •triangular tiles or blocks •pencil

SELFAS SES SMENT ASSES SESSMENT

Draw an equilateral triangle.

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

Using four identical triangles make the following shapes, and then draw them below. a) a rectangle b) a square

d) a large triangle

c) a parallelogram

ew i ev Pr

Teac he r

2

SHAPE AND SPACE

Challenge: Create a tiled path using triangles and draw your design below on another sheet of paper.

e) a trapezoid

© ReadyEdPubl i cat i ons ANDl SPACE• orr evi ew pur poseSHAPE son y TASK •f Indicator Indicator:: Identifies and uses triangles to create various shapes and patterns.

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Materials Materials: •triangular tiles or blocks •pencil

Make a list of all the uses of a rectangular prism.

SELFAS SES SMENT ASSES SESSMENT

m . u

brick wall

w ww

8 1

______________________________________________________________

. te

______________________________________________________________

2

o c . che e r o t r s super

A painter was asked to paint the brick wall pictured below. If he has already painted the shaded surfaces, how many more surfaces will he need to paint? (Note: He hasn’t yet painted the back, sides and top of the wall.)

Challenge: How

many square surfaces are there on the cube pictured below?

Indicator Indicator:: Visualises and explains the parts of a 3D shape that are not seen.

16


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TASK

9 1

tessellating path

Materials Materials: •pencil •pencil •paper •shape tiles

SELFAS SES SMENT ASSES SESSMENT

In the space below, draw and label as many 2D and 3D shapes as you can that tessellate.

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

ew i ev Pr

Using only squares, rectangles and triangles create a tessellating pattern that could be used for a garden path. Draw your design below.

Teac he r

2

SHAPE AND SPACE

Challenge: Create

a tessellating pattern using four or more different shapes. Use another sheet of paper for your pattern.

© ReadyEdPubl i cat i ons SHAPE SPACE orr evi ew pur poses onAND l y • TASK•f Indicator Indicator:: Uses shapes to design a tessellating pattern.

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tricky tangrams

m . u

. te

2

SELFAS SES SMENT ASSES SESSMENT

Materials Materials:

Cut out the following seven tangram pieces below and arrange them into a square again.

w ww

10 1

o c . che e r o t r s super

Now create your own pattern/picture using the same seven pieces. Paste your design onto a piece of paper. Indicator Indicator:: Manipulates tangram pieces to create shapes and patterns.

Challenge: Draw up and cut out a large square. Divide the square into an 8, 9 or 10 piece tangram with a ruler. Cut it into these pieces and see if you can arrange your pieces into a square again. 17


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TASK

11 1

SHAPE AND SPACE

symmetrical letters

SELFAS SES SMENT ASSES SESSMENT

Which letters of the alphabet pictured below are symmetrical? Draw the line of symmetry (vertical, horizontal or both) through the symmetrical letters.

A B C D E F G H I N O

Teac he r

J K L M

r o e t s B r e oo P Qp R S T U V W X Y Z u k S

Is your name symmetrical? Write it below in upper case letters and see.

ew i ev Pr

2

Materials Materials: •pencil •ruler

Challenge:

On the back of this sheet, or using another sheet of paper, find and draw a shape from the classroom that is not symmetrical. Explain why it is not symmetrical.

© ReadyEdPubl i cat i ons ANDl SPACE• orr evi ew pur poseSHAPE son y TASK •f Indicator Indicator: Identifies the line of symmetry in various shapes.

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USING GRIDS

o c . che e r o t r s super

How do grids help someone copy a picture?

__________________________________________________ __________________________________________________ __________________________________________________ Indicator Indicator: Uses a grid square to enlarge or reduce a two-dimensional shape.

18

SELFAS SES SMENT ASSES SESSMENT

m . u

. te

2

Materials Materials: •A4 paper •pencils

Grids can be useful in helping you enlarge and reduce pictures. Enlarge one of the pictures below onto an A4 piece of paper. Rule up faint lines to help you.

w ww

12 1

Challenge: Find a

large picture you like in a magazine or newspaper, draw a grid over the top of it and copy it onto a smaller piece of paper.


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LOCATION

TASK

13 1 2

class position

Materials Materials: •pencil (Challenge: •paper •ruler)

Look at where you are sitting in the classroom and answer the following: a) Who is sitting to your right? b) Who is sitting to your left? ___________________________

_____________________________

Look at the following grid map of Class 6F and answer the questions below.

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

A JOHN JESSICA HARRY MEGAN

B ALEX EMILY BEN JOHN

C MARK JAMES CHRISTY LISA

D ALISON DANIEL KIM JOEL

E LUCY ROSE LUKE NATALIE

Who is sitting at a) C3? ___________ b) F1? ___________ c) B4? ________

d) A2? ___________ e) E3? ___________ f) B2? ________ a) How many students are in 6F altogether? ______________ b) How many are boys?_____

c) How many are girls?_____

F CLARE MARY WIL LIAM

ew i ev Pr

Teac he r

1 2 3 4

3

SELFAS SES SMENT ASSES SESSMENT

Challenge: Make a grid map like the one above of your classroom, showing where everyone is sitting. In what position do you sit? _______________

© ReadyEdPubl i cat i ons LOCATION orr evi ew pur poseson l y• TASK•f Indicator Indicator:: Demonstrates knowledge of grids and the language of location.

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14 flight 125

3

. te

m . u

Last Friday, on Flight 125 to Sydney, Mrs Apple, Miss Peach and Mr Pear were seated together in Row 28 on the right hand side of the plane. At one particular time during the flight Mrs Apple had her tray down, the person sitting next to the window was to the left of the others, Mr Pear was sitting next to Mrs Apple, Mr Pear was wearing headphones, Miss Peach was sitting to the left of Mr Pear, the lady seated in the middle was reading a magazine and Miss Peach was reading a book.

w ww 1 2

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

o c . che e r o t r s super

Who was sitting in the aisle seat?

_____________________________________________________________

Who was sitting in the window seat?

__________________________________________________

Which pieces of information above were not useful in helping you work out where each person was sitting? __________________________________________________ __________________________________________________ Indicator Indicator:: Uses and understands the language of location.

Challenge: If Flight 125 had 38 rows, each seating three passengers on the right and three on the left, how many passengers would there be if the flight was ¾ full?________ 19


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TASK

15

LOCATION

carousel

At the local fete there is a small carousel with four horses for young children to ride. At one point during the day Jessica, Emily, Ben and Kate are sitting on the horses waiting for their ride to start. Jessica is sitting on the front horse, Ben is wearing a blue hat, Kate is 90 right of Jessica, Jessica is crying, Emily is 180 left of Jessica and Kate’s mum is taking her photo.

Teac he r

1

Show where each child is sitting below on the carousel.

SELFAS SES SMENT ASSES SESSMENT

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

Which information above is not useful in working out where the children are sitting? Underline.

If the carousel moved 90o right and then stopped, who would be sitting at the front now? ____________________________

If the carousel moved another 180o right and then stopped, who would be sitting in the front now? __________________

ew i ev Pr

2 3 4

Materials Materials: •pencil

Challenge: If the

carousel was in the position it ended up at in Question 4, and then continued to move around 10 times to the right and stopped, who would be sitting 90° left of the child in front?

© ReadyEdPubl i cat i ons orr evi ew pur posesoLOCATION nl y• TASK •f Indicator Indicator:: Demonstrates knowledge of fractions when dealing with location.

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16

local map

Materials Materials: •pencil •paper (Challenge: •Street directory)

. te

m . u

2

List some times when it is useful to have a map.

w ww

1

A new student has arrived to your suburb and school. Help this student get to know the local area by drawing a map to scale on a piece of paper. Include the main features such as the school, main streets, shops, parks, sporting grounds, and so on.

SELFAS SES SMENT ASSES SESSMENT

o c . che e r o t r s super

________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ Indicator Indicator:: Identifies and draws simple scale plans of a familiar location.

20

Challenge:

Find your school in the street directory. Write answers on the back of this sheet. a) What page is it on? b) What grid reference is it? c) What main streets surround your school?


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TASK

17

LOCATION(NUMBER)

pizza delivery

Materials Materials: •Street directory •pencil

SELFAS SES SMENT ASSES SESSMENT

The local pizza shop has to make the following deliveries:

• 2 pizzas to school office • 6 pizzas to the local police station • 4 pizzas to the local fire department • 2 pizzas to your house • 3 pizzas to the local post office • 2 pizzas to your best friend’s house

ew i ev Pr

2

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

Look up these locations in YOUR local area using a street directory. Work out the most direct path for the delivery person to take and list the places in order below.

Teac he r

1

Challenge: If a quarter

If each pizza is cut into eight pieces, how many slices are there altogether? ____________________________________

of the overall total of pizzas were not eaten, how many slices were eaten? _________________ _________________

© ReadyEdPubl i cat i ons LOCATION orr evi ew pur poseson l y• TASK•f Indicator Indicator: Interprets and uses a local map to plan a journey.

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18 1

fete plan

Materials Materials: •paper •pencil

SELFAS SES SMENT ASSES SESSMENT

. te

• Merry-go-round NORTH EAST • Jumping castle NORTH • Spinning wheel CENTRAL • Animal nursery NORTH WEST • Toilet block WEST • Plant stall SOUTH • Sausage sizzle stand SOUTH WEST • Trash and Treasure stall SOUTH EAST • Lucky dips and mystery bottle stall EAST • Show bag stall to the RIGHT of the plant stall • Drink stall to the LEFT of sausage sizzle • Devonshire tea stall to the EAST of the jumping castle.

m . u

w ww

You have been asked to help set up the school fete. The committee has given you instructions as to where all the stalls and attractions should be located. Follow the instructions and draw a possible plan of the set up on a piece of paper, which includes a simple compass in the top right hand corner.

o c . che e r o t r s super

Challenge: Using a large sheet of paper, design and map out your own idea of what stalls and attractions should be included at a fete.

Indicator Indicator: Uses given information and compass points to draw a simple plan.

21


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TASK

19

LOCATION

lost cattle

2

A herd of cattle has been spilt up by a storm and the farmer is trying to locate them by air in a helicopter. Help out the farmer by looking at the diagram below and writing compass directions as to where he can locate his cattle. Use the back of this sheet.

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

ew i ev Pr

Teac he r

1

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

Challenge:

If the farmer only manages to rescue the cattle in the northern area, how many are left?

How many cattle are there altogether? ___________________

_________________

© ReadyEdPubl i cat i ons orr evi ew pur posesoLOCATION nl y• TASK •f Indicator Indicator:: Uses compass points to specify location.

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20 trapped in a maze 1

Materials Materials: •pencil •paper

SELFAS SES SMENT ASSES SESSMENT

. te

m . u

w ww

Peter has found himself trapped in the middle of a giant maze and has been trying for some time to get out. Look at the maze and write a set of instructions for Peter which he can use to help him get out. (Hint: Use location words such as right turn, left turn, forward, back, north, south, east, west and the number of steps he should take.)

o c . che e r o t r s super

Challenge: Design

2

Draw the path Peter will take to follow your directions out of the maze. Indicator Indicator:: Uses the language of location to create a path through a maze.

22

and draw your own maze for a friend to try and follow a path from the centre to the outside.


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TASK

21

1

SPACE ASSESSMENT

office building

Materials Materials: •pencil •cubes •paper

SELFAS SES SMENT ASSES SESSMENT

In the main street of the city, a new office building has been constructed entirely of square glass panels. Look at the picture and name the shape of this building.

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

_______________________________________

2

_______________________________________

3

ew i ev Pr

Teac he r

How many windows in total would cover the entire building?

Challenge: Design and draw

Construct the same building as above using cubes. How many cubes did you need to use?

your own office building on a piece of paper. What shape is it and what special features does it have?

_______________________________________

_______________________ _______________________

© ReadyEdPubl i cat i ons LOCATION ASSESSMENT orr evi ew pur pose son l y• TASK•f Indicator Indicator:: Visualises and explains the parts of a 3D shape that are not seen.

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school map

w ww

1

. te

Art Room

Italian Room

Year 6

SELFAS SES SMENT ASSES SESSMENT

Look at this map of a primary school. a) Draw a red path from the school office to the Year 6 classroom. b) Draw a blue path from the library to the hall. c) Draw a yellow path from the Year 1 classroom to the toilet block.

o c . che e r o t r s super

Playground

School Library Office

Toilet Block

2

Materials Materials: •pencil •coloured pencils •paper

m . u

22

12345678901 12345678901 12345678901 12345678901 12345678901 Oval 12345678901 12345678901 Hall 12345678901 12345678901 12345678901 12345678901 12345678901

Year 5

Year 4

Year 1

Year 2

Year 3

Using the compass as a guide, write a set of instructions as to how you would travel from the Year 5 classroom to the art room.

Challenge: Design and draw

a map of your own school on another sheet of paper. Draw a path leading from your classroom to the office.

Indicator Indicator:: Visualises and plans journeys on simple maps.

23


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NUMBER

TASK

1 1

Creature collection

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

On Saturday Alex collected 13 beetles, eight spiders, 28 ants and two ladybirds. On Sunday he added 14 slaters, two butterflies and seven snails to his collection. a) How many creatures did he collect altogether on the weekend?

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

_______________________________________________________________

b) How many more insects did he collect on Saturday, compared to Sunday?

2

Alex set up a house for some beetles and spiders he had collected. The legs of these insects totalled 54. How many beetles and how many spiders does he have?

ew i ev Pr

Teac he r

_______________________________________________________________

Challenge: If the legs of a spider and beetle collection totalled 150, how many beetles and how many spiders would there be?

Remember: Spiders have 8 legs and beetles have 6!

________________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator:: Uses knowledge of number and number processes to solve a problem.

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cross numbers

o c . che e r o t r s super

Use the numbers 6, 7, 8, 9, 10 to complete these cross numbers, with the following totals. a) Total = 23

b) Total = 24

c) Total = 25

Indicator Indicator:: Manipulates numbers to arrive at a set total.

24

SELFAS SES SMENT ASSES SESSMENT

m . u

. te

2

Materials Materials: •pencil •paper

Using only the numbers 1, 2, 3, 4, 5 fill in the squares in the cross so that they equal the answers below, when totalling the numbers horizontally or vertically.

w ww

2 1

Challenge:

On another piece of paper, create your own cross combination with the numbers 20, 40, 60, 80, 100 and a total of 180.


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TASK

3 1 2

NUMBER

concert hall

Materials Materials: •pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

At a concert hall there are 20 rows of 12 single seats and 15 rows of bench seats (or bench rows) that hold eight people. What is the maximum number of people the hall can hold? ______________________________________________________________

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

How many people would there be if if the following seats were booked: a) all the single seats and eight bench rows?

b) 15 rows of single seats and all the bench rows?

___________________________________________________

c) 18 rows of single seats and 13 bench rows? ___________________________________________________

Challenge: If the single

ew i ev Pr

Teac he r

___________________________________________________

seat tickets cost $22.00 each and a seat in a bench row costs $18.00 each, how much would the concert hall ticket office take if it was totally booked out? ___________________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f Indicator Indicator:: Uses knowledge of number facts and multiplication to solve a problem.

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four 4S

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

. te

m . u

Using the number 4, exactly four times and the operations +, -, x, ÷ make number sentences that equal 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example: 4 + 4 – 4 – 4 = 0 or (4 + 4) ÷ 4 + 4 = 6

w ww

4 1

o c . che e r o t r s super

Challenge: Try using the same formula with a number of your choice, making as many number sentences as you can that equal 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Does it work? _________________

Indicator Indicator:: Constructs and completes number sentences involving the four operations.

25


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TASK

5 1

NUMBER

ages

SELFAS SES SMENT ASSES SESSMENT

Matilda’s mother is four times as old as Matilda is now. In four years time Matilda will be one third her mother’s age. Use the boxes for your working. a) How old are they now?

Matilda: _____ Mother: ________

At what age will Matilda and her mother be when Matilda is half her mother’s age?

Challenge:

ew i ev Pr

Teac he r

b) How old will they be in four years time?

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

Matilda: _____ Mother: ________

2

Materials Materials: •pencil

•Ben is 6 years younger than his brother. •Ben’s father is three times as old as Ben. •Ben’s brother is half the age of his father. On the back of this sheet, work out: a) How old they are now. b) How old they will each be in 12 years time.

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator:: Selects relevant information to solve a problem using number facts.

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2

3

Materials Materials: •pencils •calculator

How many days old were you when you turned one year old? (Note: Was it a leap year?)

w ww

1

how many days?

. te

SELFAS SES SMENT ASSES SESSMENT

m . u

6

o c . che e r o t r s super

How many days old were you when you turned five years old? (Note: Remember to include leap years!)

Challenge: Work out

How many days old will you be on your next birthday? Use the space below for your working. (Note: Remember to include leap years!)

exactly how many days old you are today. Write the answer below. ____________________

Indicator Indicator:: Uses a calculator to solve a problem involving multiplication and addition.

26


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TASK

7 1

making numbers

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

How many two-digit numbers can be written using the numbers 1, 2, 3 and 4 using each digit only once?

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

How many three-digit numbers can be written using the numbers 1, 2, 3 and 4 using each digit only once? (Hint: A tree diagram may help.)

ew i ev Pr

Teac he r

2

NUMBER

Challenge: How many four-digit numbers can be written using the numbers 1, 2, 3 and 4 using each digit only once? ________________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f SELFMaterials: •pencil 8 200 mETRE sprint Materials AS SES SMENT ASSES SESSMENT Indicator Indicator:: Uses knowledge of number and place value to create numbers.

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. te

2

m . u

w ww

1

If three runners enter in the 200 metre sprint how many different combinations of 1 , 2 and 3 place could there possibly be? (Hint: A list or tree diagram may help.)

o c . che e r o t r s super

If four runners enter in the 200 metre sprint, how many different combinations of 1 , 2 , 3 and 4 place could there possibly be? E.g. Runner 1, 2, 3, 4; Runner 1, 2, 4, 3; Runner 1, 3, 2, 4; Runner 1, 3, 2, 4, etc.

Challenge: If five runners

enter in the 200 metre sprint, how many different combinations of 1st, 2nd, 3rd, 4th and 5th place could there possibly be? ____________________

Indicator Indicator:: Uses knowledge of number and ordinal number to solve a problem.

27


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TASK

9 1

NUMBER

swimming carnival

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

At the school swimming carnival the students were lined up in their coloured team. There were 54 students in Red house, 48 students in Green, 50 in Blue and 42 in Gold house. How many students are there altogether?

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

______________________________________________________________ If every sixth student in line was chosen to compete in the first race how many would represent each team? a) Red – ____ b) Green – ____ c) Blue – ____ d) Gold – ____

2

Teac he r

Of the remaining house team members, every third student in line was chosen to view the race from the stand while the others watch poolside. a) How many students are in the stands altogether?

_______________________________________________

b) How many students are poolside? _______________________________________________

ew i ev Pr

3

Challenge: If each

house team was divided into sixths for the races, how many students would compete in the first three races? __________________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator:: Uses knowledge of number operations and ordinal number to solve a problem.

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afl game

3

______________________________________________________________

. te

If a goal is worth six points what possible combinations of goals and points could Carlton have scored? (Hint: Carlton scored a minimum of 14 goals.)

o c . che e r o t r s super

What possible combinations of goals and points could Richmond have scored? (Hint: Richmond scored a minimum of 10 goals.)

Indicator Indicator:: Uses knowledge of number operations to solve a problem.

28

SELFAS SES SMENT ASSES SESSMENT

m . u

2

Materials Materials: •pencil

At an AFL football match the final score was Carlton 106 to Richmond 84. How many points did the winning team win by?

w ww

10 1

Challenge: If in the

following week Sydney defeated Richmond by 42 points after Richmond only kicked 4 goals and 9 points, what must Sydney’s winning score have been?

_________________


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TASK

11

1

NUMBER

golf game

Materials Materials:•pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

On Saturday Jack played a round of golf at the local public 18 hole golf course. Of the 18 holes, eight holes were par 3, six holes were par 4 and four holes were par 5. a) If he played each hole to par, what was his final score?

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

_______________________________________________________________

b) If he played a birdie (1 under par) on each hole, what was his final score? _______________________________________________________________

Teac he r 2

ew i ev Pr

c) If he played a double bogey (2 over par) on each hole, what was his final score? Challenge: At the golf On the following Saturday Jack played 36 holes when course Jack was playing on, the par 3s are 150 he went around the course twice. The first time around metres long, the par 4s are he scored a bogey (1 over par) on each hole and the 380 metres long and the par second time around he scored par on each hole. What 5s are 470 metres long. was his final score? What is the total distance of this 18 hole golf course? ____________________________________________ _____________________ Indicator Indicator:: Uses knowledge of addition and multiplication to solve a problem.

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f

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darts

3

80

40 20 10

40 20 10

w ww

Look at the dartboard and the different scores for each section. If the following totals were scored using only three darts, what sections must the darts have hit?

. te

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

m . u

12 1

o c . che e r o t r s super

a) 110 – _________

b) 240 – _________

c) 50 – __________

d) 170 – _________

If only two darts were thrown and both hit the board, what possible scores could be made? _______________________________________________ _______________________________________________

Challenge: If three darts were thrown and all hit a different section of the board, what possible scores could be made? Make a list on the back of this sheet.

Indicator Indicator:: Uses knowledge of addition to solve a problem.

29


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TASK

13 1

NUMBER

number sentences

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

Using the two-digit numbers below, how many different number sentences can you make to equal 100? 10, 12, 15, 20, 28, 30, 34, 40, 45, 50, 55, 60, 62, 66, 70, 80, 85, 90

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

__________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Teac he r

100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900 ________________________________________________ ________________________________________________ ________________________________________________

ew i ev Pr

2

Using the three-digit numbers below, how many number sentences can you make to equal 1000?

Challenge: When added

together which of the following four-digit numbers equal 10,000? 1600, 2500, 2650, 3100, 3590, 4000, 4320, 4850, 5150, 5680, 6000, 6410, 6900, 7350, 7500, 8400. Use the back of this sheet to write your sums.

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator:: Creates number sentences from a set of numbers.

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equations

o c . che e r o t r s super

Using the numbers 10 to 90, place them in the circles below so that each connecting three circles equal 150. Note: The connecting circles must line up and include the centre circle..

Indicator Indicator:: Constructs equations using a given set of numbers.

30

SELFAS SES SMENT ASSES SESSMENT

m . u

E.g. 1 + 6 + 8 = 15

. te

2

Materials Materials: •pencil

Make as many three-step equations as you can that total 15, using the numbers 1 to 9. Note: Each number may only be used once in an equation.

w ww

14 1

Challenge: Complete the following equation:

___ x ___ ( ___ ÷ ___ ) = 100


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TASK

15 1

NUMBER

go-carts

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

At the local festival, one of the attractions was the go-carts. The go-carts travelled around a 200 metre circular course for a time limit of five minutes and at a cost of $4.00 a ride. a) If James drove his go-cart around the enclosure 10 times in the five minutes, how far did he travel altogether?

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

c) If Ben travelled a distance of 1800 metres in five minutes, how many times did he drive around the course?

2

ew i ev Pr

Teac he r

b) If Ruby drove her go-cart twice around the enclosure every minute, how far did she travel altogether?

Challenge: If at

If in one hour 36 children had a ride on the go-carts, how much money would the attendant have taken? __________________________________________________

the end of the day the attendant had taken $920.00, how many children rode the go-carts that day? ______________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f Indicator Indicator: Uses knowledge of number, time and money to solve a problem.

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Materials Materials: •pencil •calculator

w ww

Yesterday 412 people visited the museum. If 198 of those who visited were children, how many adults were there?

2

3

. te

If the entry cost to the museum is $12.00 for adults and $7.00 for children, how much money did the museum take for entries yesterday?

o c . che e r o t r s super

If the following attendances to the museum were recorded over a week, what was the total number to visit the museum for that week? • Mon – 320 • Wed – 368 • Fri – 288 • Sun – 571

SELFAS SES SMENT ASSES SESSMENT

m . u

16 museum 1

• Tues – 412 • Thurs – 390 • Sat – 612

Challenge: Calculate

the average number of attendances to the museum for that particular week. __________________ __________________

Indicator Indicator:: Uses knowledge of number operations and money to solve a problem.

31


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NUMBER

TASK

17 tennis tournament 1

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

For an interschool game of tennis there are two teams of six students. One team is from Hills Primary and one team is from Lake Primary. How many different combinations of players could play each other during the scheduled game time? Use another sheet of paper to draw a diagram of your working and write the answer in the box.

Teac he r

If six pairs of students were given 20 minutes each of playing time, how long would it take to complete this round of play?

ew i ev Pr

2

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

Challenge: If all of the combinations of players in Question 1 played each other for 10 minutes each, how long would it take to complete this round of play? ________________

© ReadyEdPubl i cat i ons orr evi ew pur posesoNUMBER nl y• TASK •f Indicator Indicator:: Uses knowledge of number facts, patterns and time to solve a problem.

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school picnic

Materials Materials: •pencil •calculator

w ww

A school picnic was organised for the end of year Christmas break up. A total of 720 students needed to be transported by buses to the chosen park. If each bus holds 45 students, how many buses are needed? Do your working on the back of this sheet.

2

3

. te

o c . che e r o t r s super

In order to help supervise the students, a ratio of one adult to 10 students is required by law. If this is the case how many adults are needed to attend the picnic? A choice of raspberry and lemonade icypoles were distributed to the students at recess time. If every student at the picnic had an icy-pole and 324 students chose raspberry, how many must have chosen lemonade?

Indicator Indicator:: Uses knowledge of number operations and fractions to solve a problem.

32

SELFAS SES SMENT ASSES SESSMENT

m . u

18 1

Challenge: If three quarters of the students participated in running races while a quarter chose not to join in, how many students chose to be in the running races? __________________


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TASK

19

1

shopping trolley

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

How far did the trolley travel after the fourth stop?

ew i ev Pr

3

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

At the supermarket a shopping trolley is recorded at moving twice the distance it did previously, less two metres, before coming to a stop each time. If it started out moving three metres the first time, how far did it travel the second time? Use the space to show your working.

Teac he r

2

NUMBER

Challenge:

How many stops would the trolley have made before reaching the final distance travelled of 514 metres?

How far did the trolley travel after the seventh stop?

__________________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f Indicator Indicator: Uses knowledge of number facts and patterns to solve a problem.

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Jenny Faith 11 yrs • Daniel West 43 yrs 1234567890123456 1234567890123456 1234567890123456 1234567890123456 • Molly West 45 yrs • Kyle West 20 yrs • Sam West 9 yrs • Kristy Read 28 yrs 1234567890123456 1234567890123456 1234567890123456 • Bridget Read 2 yrs • Nick Williams 84 yrs • Lillian Williams 85 yrs • Frances Hail 41 yrs 1234567890123456 1234567890123456 1234567890123456 1234567890123456 • Ben Hail 39 yrs • Emily Hail 8 yrs • William Hail 7 yrs • Oliver Hail 3 yrs 1234567890123456 1234567890123456

20 boat rescue

2

SELFAS SES SMENT ASSES SESSMENT

m . u

A small ferry off the coast of Sydney has started to sink. There are three rescue boats and 24 passengers. In order to rescue all those on board the captain has decided that all the youngest be put in the first boat, followed by the eldest in the second boat. Look at the passenger list below and work out how many

w ww 1

Materials Materials: •pencil •paper

people will be on the first two boats? _____________________________

. te

o c . che e r o t r s super

Look at the passenger list above. Using another sheet of paper, draw up a table like the one below and use it to work out who should be in each boat.

1 BOAT ST

2

ND

BOAT

Indicator Indicator:: Orders numbers for a purpose.

3

RD

BOAT

Challenge:

How would you decide who should be on the first rescue boat? Write your answer on another sheet of paper. 33


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NUMBER

TASK

21 Melbourne to brisbane

1

Materials Materials: •pencil •calculator

The Jones family travelled from their home in Melbourne to Brisbane for a holiday. If they travelled a total distance of 1725 km over three days, how far did they travel on average each day?

ew i ev Pr

3

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

If they took two days to get there and they travelled a third of the distance on the first day, how far did they travel on the second day?

Teac he r

2

SELFAS SES SMENT ASSES SESSMENT

Challenge: Find out

how many more kilometres the journey would be if the Jones family were to travel onto Cairns. (Hint: The Internet would be useful.)

If they only travelled 345 km each day, how many days would it take them to get there?

________________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator::Uses knowledge of division and fractions to solve a problem.

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school supplies

o c . che e r o t r s super

a) Year 1 – 5 exercise books, 4 pencils, 1 eraser, 1 scissors, 1 packet of crayons and 1 reader cover. b)Year 2 – 6 exercise books, 4 pencils, 1 eraser, 1 ruler, 1 scissors, 1 packet of coloured pencils and 1 reader cover. c) Years 3 and 4 – 8 exercise books, 4 pens, 2 pencils, 1 eraser, 1 ruler, 1 scissors, 1 packet of coloured pencils and 1 reader cover. d)Years 5, 6, 7 – 12 exercise books, 6 pens, 2 pencils, 1 eraser, 1 ruler, 1 scissors, 1 packet coloured pencils and 1 packet of textas.

What is the difference in cost between the Year 1 and the Year 5, 6 and 7 booklist? ________________________________________ Indicator Indicator:: Calculates the cost of items for a purpose.

34

m . u

. te

2

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •calculator

It is approaching the end of the school year and each class has been given a booklist of required school supplies for next year. Look at the items available and work out the cost required for each year level.

w ww

22 1

Challenge:

What is the average cost of the booklists? ____________


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NUMBER

TASK

23 1

uniform shop

Materials Materials: •pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

The school uniform shop is having a special sale for the start of the school year. Look at the specials below and fill out the chart below to show the savings. ITEM

Teac he r

SAVING

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

Find the cost of the following orders at the sale cost. a) Jessica: 3 pairs of school socks, 1 hat and 1 dress

b) Joel:

4 pairs sports socks, 1 shorts and 1 shirt

c) Ben:

1 pair school socks, 2 hats, 1 shorts and 2 shirts

ew i ev Pr

2

NORMAL COST SALE COST

Challenge: Who

out of Jessica, Joel and Ben made the greatest saving on their orders? ______________ ______________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f Indicator Indicator:: Uses knowledge of percentages, number operations and money to solve a problem.

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24 toy sale 1

Materials Materials: •pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

. te

a) SARAH:

2

o c . che e r o t r s super

A jewellery making set, dive sticks and Brats doll. b) MATTHEW:A Bionnical kit, a game boy game and a water pistol. c) JOHN: A craft set, football wallet, dive sticks and water pistol. d) MARY: A craft set, diary set and game boy game. How much would it cost at the original and discounted cost if you purchased one of each item? a) Original cost = ______ b) Discounted cost = ______ Indicator Indicator::

m . u

w ww

With Christmas approaching, the local toy shop is having a sale. All items are marked 20% off or one fifth less than the original cost. Look at the items listed below and calculate the sale cost for each of the children’s Christmas lists.

Challenge:

Which child’s list showed the greatest saving? ________________ ________________

Applies knowledge of percentages, number operations and money to solve a problem.

35


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NUMBER

TASK

25 car wash 1

Materials Materials: •pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

A local car wash earns $5.00 a car wash. In the first week the car wash earns $5.00, in the second week it earns $10.00, $20.00 in the third and so on, doubling each week.

2

a) How much will they earn on the 10 week?

_____________________

b) How much will they earn on the 15 week?

_____________________

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

How many cars would have to be washed to earn the following amounts? a) $45.00

b) $120.00

________________

c) $335.00

________________

Teac he r

________________

3

ew i ev Pr

Challenge:

Following the pattern above, how many weeks would it take for the car wash to earn at least $655,360.00?

How much money would the car wash take after washing 147 cars?

_______________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator: Solves a problem using knowledge of number patterns, multiplication and money.

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cake shop

a) cheesecake

m . u

. te

o c . che e r o t r s super /

$ _______

1 slice $ _______

7

/10

$ _______

1 slice $ _______

c) apple pie

1

/3

$ _______

1 slice $ _______

d) chocolate log

4

/5

$ _______

1 slice $ _______

e) fruit cake

2

/16

$ _______

1 slice $ _______

f) custard tart

½

$ _______

1 slice $ _______

b) lemon tart

Indicator Indicator:: Uses knowledge fractions and money to solve a problem.

36

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

The cakes pictured below as displayed at the local cake shop could be purchased as a whole or in slices. Work out the following fractional costs.

w ww

26 1

Challenge: What

would be the cost if you purchased a quarter of each cake? _________________


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TASK

27 1

NUMBER

party time

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

Chloe invited 40 people to her dress up party for her 12 birthday. If of those 40 people ½ dressed as pop stars, ¼ dressed as dancers and / dressed as horse riders, how many people did not dress up?

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

Out of those 40 people / gave Chloe a gift. How many did not give her a gift?

Challenge: If, at the party,

(Hint: A pizza is divided into eight slices.)

4

ew i ev Pr

If half the people at the party ate one slice of pizza and half ate two slices of pizza, how many pizzas would have been eaten?

Teac he r

2 3

/5 of the people had to leave early, how many left early and how many stayed until the end? 2

If ¾ of the people blew up three balloons each, how many balloons did they have altogether?

a) left early:

______

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK•f Indicator Indicator:: Uses knowledge of numbers and fractions to solve a problem.

b) stayed:

______

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school sports

A total of 400 students were divided into four house teams in order to participate in the school sports day. If / of each team was required to parade around with their house flag, how many students were chosen altogether for the four houses?

w ww 2 3 4

Materials Materials: •pencil

. te

SELFAS SES SMENT ASSES SESSMENT

m . u

28 1

o c . che e r o t r s super

If ¾ of each house had to be spectators for the first event, how many from each house participated in that event? If 1/20 of each house was chosen for the relay event, how many participated in that event altogether? If 1/10 of the total number of students had won a prize by the end of the day, how many students did not receive a prize?

Indicator Indicator:: Uses knowledge of numbers and fractions to solve a problem.

Challenge: If 4/5 of each

team house participated in at least one event, while 1/5 of each house participated in all the events, how many students altogether participated in all of the events? _____________________ 37


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TASK

29 1

NUMBER (MEASUREMENT)

height order

Materials Materials: •pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

A group of upper primary maths quiz winners recorded their height in metres. Their teacher has asked them to write a list ordering their heights from shortest to the tallest for a school photo. Using their notes, help them write their list. ___________ ____________

2 3

r o e t s Bo r e p ok u S ___________

____________

___________

____________

___________

____________

___________

____________

___________

____________

What is the difference in height between the tallest and shortest student? Work out the average height for this group of students.

Challenge: If, on

ew i ev Pr

Teac he r

Justin 1.34 m Samantha 1.29 m Harry 1.38 m Madeline, 1.35 m James 1.51 m Kate 1.32 m Liam 1.45 m Hannah 1.39 m Lisa 1.36 m Joshua 1.40 m Jack 1.46 m Ruby 1.49 m

average, girls grew 4 cm a year and boys grew 6 cm a year, what would be the total increase in height of this group of students in three years time? ______________

© ReadyEdPubl i cat i ons NUMBER orr evi ew pur poseson l y• TASK •f Indicator Indicator: Uses knowledge of decimal numbers and height to solve a problem.

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dressmaker’s fabric

w ww

A dressmaker ordered the following amounts of fabric from the material shop: 3.2 m satin, 1.8 m cotton, 4.8 m linen, 1.3 m denim and 6.5 m of polyester. How much fabric did she order altogether?

2 3

. te

SELFAS SES SMENT ASSES SESSMENT

o c . che e r o t r s super

How much more polyester fabric did she order compared to the cotton? The following week she doubled her order of cotton, denim and polyester and tripled her order of satin and linen. How much fabric did she purchase altogether this week?

Indicator Indicator: Applies knowledge of number operations to decimal numbers.

38

Materials Materials: •pencil •calculator

m . u

30 1

Challenge: If the

polyester cost $3.50 a metre, how much did she spend on this fabric over the two weeks? _________________ _________________


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TASK

31

1

cricket match

Materials Materials: •pencil •calculator (optional)

SELFAS SES SMENT ASSES SESSMENT

During an interschool cricket match Lachlan managed to score 92 runs. Of those 92 runs, if 20 of them were singles, how many 4s and 6s could he have possibly made? Show your working below.

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

Teac he r

In another cricket match, ten players all scored the same amount of runs. The other batter managed to score 35 more runs than each of the others. If the team scored a total of 651, how many did each player score? Ten batters scored ____________ each The other batter scored ____________

ew i ev Pr

2

NUMBER ASSESSMENT

Challenge: Three batters

scored a total of 258 runs. If their totals were three consecutive numbers, what were the scores of each of these batters? ___________________

© ReadyEdPubl i cat i ons NUMBER ASSESSMENT orr evi ew pur pose son l y• TASK•f Indicator Indicator:: Applies knowledge of number operations and number patterns to solve a problem.

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32

3

. te

m . u

2

SELFAS SES SMENT ASSES SESSMENT

Use the spaces below to show your working. Of the 36 students in Year 5 surveyed, / caught the bus to school, / walked to school and / rode their bike to school. If the remaining students travelled to school by car, how many used this form of transport?

w ww

1

travelling to school

Materials Materials: •pencil

o c . che e r o t r s super

If out of the students who travelled by car to school, / always arrived late, how many arrived on time?

If half the students who rode their bike or walked to school said they would prefer to travel by car while the other half said they were happy with how they travelled to school, how many students would prefer to go by car?

Challenge: If 3/8 of the

96 students travelled to school by bus, how many of the students used other methods of transport? ___________________

Indicator Indicator:: Uses knowledge of number and fractions to solve a problem.

39


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TASK

1 1

2

MEASUREMENT

flying fox

Materials Materials: •pencil •tape measure or metre ruler

SELFAS SES SMENT ASSES SESSMENT

A flying fox is going to be included in the senior area playground. To be safe, when a student rides it they must clear the ground by at least 40 cm. How would you work out what height the handle bar should be for upper primary students in your school?

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

Challenge:

ew i ev Pr

Teac he r

Draw your flying fox plan below and include height and width measurements.

How would your design and measurements change if the flying fox was to be used by adults? _________________ _________________

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poses onl y• TASK •f Indicator Indicator: Makes judgements and selects appropriate units of measurement for design purposes.

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rose’s garden

3

. te

o c . che e r o t r s super

Rose also wants to plant some lettuces in her vegetable patch. If the patch is two metres long and lettuces need to be planted 40 cm apart, how many lettuce plants does she need to buy?

If a tomato plant was to grow on average 15 cm high each week, how long would it take to reach a height of 1.2 m?

Indicator Indicator:: Uses knowledge of length and number to solve a problem.

40

SELFAS SES SMENT ASSES SESSMENT

m . u

2

Materials Materials: •pencil •1 metre ruler

Rose wants to plant some pansies in her three metre long garden bed. If she has 12 pansy plants, how far apart should she plant them? Show your working here.

w ww

2 1

Challenge: Rose also

decided to plant out a 6 m by 1.2 m garden bed with bulbs. If each bulb needs a 40 cm area to grow (width and length), how many bulbs would Rose need to purchase? ______________________


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TASK

3

MEASUREMENT

comparing students

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil, •tape measure or 1m ruler, •bathroom scales

1

Your teacher has asked you to compare the differences in physical appearance between yourself and a friend. Present the information in the table below.

Skin colour

Challenge: If you

were to grow on average 3 mm every five days, how much would you have grown in three months (90 days)?

Foot length Shoe size Clothes size

3

ew i ev Pr

Teac he r

2

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

What was the greatest difference between yourself and your friend?

_______________

© ReadyEdPubl i cat i ons orr evi ew pur poseso nl y• MEASUREMENT TASK•f Indicator Indicator:: Selects units of measurement in order to compare two people.

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4

lost!

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

1

2

3

. te

m . u

w ww

Patrick has become lost in a forest after breaking away from his hiking group to get a drink from a nearby stream. All he has with him is a bottle of water and a map. From looking at the map of the area he noticed the edge of the forest was located 75 metres north from their campsite. He also remembered being told that there were new trees planted on the edge of the north side of the forest that were only 1 metre high.

o c . che e r o t r s super

If Patrick is 142cm tall, how might he use his height to locate the small trees on the edge of the forest?

______________________________________________________________

Once Patrick has located the north side edge of the forest, how might he work out how far he needs to move to get back to his campsite?

___________________________________________________ Find and name something or someone in the classroom that is as tall as you. __________________________________________________

Challenge: Using

another sheet of paper, make a list of useful parts of our bodies that can help us to compare and measure things. List some things you could measure with them.

Indicator Indicator:: Makes judgements and uses the body as a tool to compare the relative size of objects.

41


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TASK

5

1

balance scales

SELFAS SES SMENT ASSES SESSMENT

A jeweller has four small bars of gold, however he knows one of them is counterfeit (which has a slightly different weight than that of real gold). Using only a balance scale, explain how can the jeweller find the counterfeit bar? _____________________________________________________________

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

_____________________________________________________________

ew i ev Pr

Using a balance scale find out which object weighs more and fill in the blank with heavier or lighter.

Teac he r

2

MEASUREMENT

Challenge:

a) A pair of scissors is _________ than a ruler.

Find and name three objects in the classroom that weigh approximately 1 kg. _________________

b) A stapler is __________ than a calculator. c) A pencil is __________ than an eraser. d) A glue stick is __________ than a pair of scissors.

_________________ _________________

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poses onl y• TASK •f Indicator Indicator: Estimates, compares and measures objects using a balance scale.

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smith family weight

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •bathroom scales •calculator

w ww

1

2

3

David Smith weighs 94 kg. His wife Julie weighs 36 kg less than her husband. Their eldest son Jack weighs 11 kg more than his mother and their youngest son Michael weighs 9 kg less than his mother. What is the total weight of the Smith family?

. te

o c . che e r o t r s super

Over the next four years Jack continues to put on half a kilo a year and Michael puts on 1 kg a year. David has lost 3 kg and Julie has added 2 kg. What is the new total weight of the Smith family? David wants to lose a further 6 kg. If it takes him four weeks to lose this weight (losing the same amount of weight each week), how much does he lose each week?

Indicator Indicator:: Uses knowledge of number and weight to solve calculations.

42

m . u

6

Challenge: Weigh

yourself and four other classmates and calculate the group’s total weight. Then find the average weight for your group. Total weight = ______ Average =

______


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TASK

7 1

MEASUREMENT

cave area

Materials Materials: •pencil •ruler or tape measure

SELFAS SES SMENT ASSES SESSMENT

A miner is trapped inside a cave beneath the ground. There is a small hole through which he has been able to communicate to the rescue team outside. The rescue team have asked him to estimate the floor area he is trapped in. Make some suggestions as to how he might do this.

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

_____________________________________________________________

Use an object or part of your body to estimate the area of your class desk/ table top. What did you use and what was the area?

3

___________________________________________________

Name three items in the room that have a larger area than your desktop. ___________________________________________________ ___________________________________________________ ___________________________________________________

Challenge:

ew i ev Pr

Teac he r

2

_____________________________________________________________

a) What formula do we normally use to measure area? _________________

b) What is the area of your desk in cm2?

_________________

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poseso nl y• TASK•f Indicator Indicator: Estimates, compares and measures area using informal and formal units.

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8 1

At a car repair garage a 60 litre drum of oil was used to fill fifteen 1 litre (L) containers and twenty four 500 ml containers. How much oil was left in the drum?

2

The next day the same oil drum was used to fill twelve 750 ml containers and ten 1.5 L containers. How much oil is now left in the drum?

w ww 3

. te

m . u

oil drum

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

o c . che e r o t r s super

It was discovered nine days later that one of the 500 ml containers had been leaking at a rate of 20 ml a day. How much oil would be left in that container?

Challenge: The

remaining oil in the drum (from Question 2) also had a leak of 25 ml a day. How much oil would be remaining in the drum after 16 days?

Indicator Indicator:: Uses knowledge of litres and millilitres to solve a problem.

43


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TASK

MEASUREMENT

9 1

Amy filled her 75 litre tank from empty with petrol at a cost of $1.14 a litre. How much did the petrol cost her?

2

If her car uses petrol at a rate of 6 km per litre, how much petrol did Amy use after travelling:

petrol tank

c) 84 km?

3

SELFAS SES SMENT ASSES SESSMENT

r o e t s Bo r e p ok u S b) 39 km?

d) 240 km?

ew i ev Pr

Teac he r

a) 24 km?

Material Materials: •pencil •calculator

Challenge: If a 4WD

with a petrol tank of 120 litres travelled 600 km before running out of petrol, how many kilometres does this car travel per litre of petrol?

How many kilometres could Amy travel before she ran out of petrol?

__________________

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poses onl y• TASK •f Indicator Indicator:: Applies knowledge of number operations to a problem involving kilometres and litres.

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each ____ x 1 dozen 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 d) Doughnuts ____ each ____ x packs of 6 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 e) Lollipops ____ each ____ x packs of 10

10 1

max’s party

Materials Materials: •pencil •paper

SELFAS SES SMENT ASSES SESSMENT

. te

f) Cup cakes

2

m . u

w ww

Max is having 24 people (including himself) to his 12 birthday party this weekend. His mother is trying to work out a shopping list for the party. Help her work out the amounts of food and drink to buy by filling in the table below.

o c . che e r o t r s super ____ each

g) Small chips packs

____ each

____ x packs of 10

h) Snakes

____ each

____ x packs of 20

Max had a large birthday cake divided into 24 slices. If only three quarters of the guests had a slice, how many slices of cake does he have left over? Indicator Indicator:: Makes judgements and estimates of quantities of food and drink for a purpose

44

Challenge: Plan your

next party, including how many guests you would invite and a shopping list of food you would include. Use another sheet of paper for your planning.


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TASK

11 photo frame 1

MEASUREMENT

Materials Materials: •pencil •ruler •cardboard •textas or pencils

SELFAS SES SMENT ASSES SESSMENT

2

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

ew i ev Pr

Teac he r

Design, make and decorate a cardboard frame for a photo that is 15 cm wide by 20 cm long. The frame needs to have a width of at least 3 cm. Use the space below to plan your design.

Challenge: Measure

What is the perimeter of the inside and outside of your frame? a Inside perimeter

= ___________________________

b) Outside perimeter

= ___________________________

and find something in the classroom that has a perimeter greater than 150 cm. What is it and what is its exact perimeter? ________________

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poseso nl y• TASK•f Indicator Indicator:: Draws and constructs objects using accurate measurements.

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Materials Materials: •pencil •compass •trundle wheel

You have been asked to set up an orienteering course for your school. The course is to be 5 km in length, starting at your school and finishing at the local park. There are to be check points every 500 metres moving in all directions (north, south, east and west). Use another sheet for your working and write your answers in the boxes below.

w ww

1

orienteering course

SELFAS SES SMENT ASSES SESSMENT

m . u

12

. te

o c . che e r o t r s super

a) How many checkpoints will you need? ____________________________ b) What equipment will you need? _________________________________

2

If you were to move from your classroom door to the following areas of your school, which direction would you need to move each time? a) the office:

______

b) the oval:

_______

c) the hall:

______

d) the senior playground:

_______

f) the toilet block:

_______

e) the library: ______

Indicator Indicator:: Selects and uses appropriate instruments suitable for a specific task.

Challenge:

Using a trundle wheel, find out the distance between the front entrance and the opposite end of the school. _______________

45


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123456789012345678901 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 1234567890123456 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 •pencil •1 metre 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 ruler or tape measure (Challenge) 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 123456789012345678901 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 1234567890123456 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 Scale 1 cm = 1 m 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 BEDROOM 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123456 1234567890123 123456789 1234567890123456789012 3 1234567890123456 1234567890123 123456789 1234567890123456789012 STUDY 1234567890123456 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 RUMPUS ROOM 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123456 BEDROOM 1234567890123 123456789 1234567890123456789012 1234567890123456 1234567890123456 1234567890123 1234567890123456789012 1234567890123456 1234567890123 1234567890123456789012 1234567890123456 2 1234567890123456 1234567890123 1234567890123456789012 1234567890123456 1234567890123 1234567890123456789012 12345678901234567 1234567890123456 1234567890123456 12345678901234567 1234567890123456 12345678901234567 1234567890123456 1234567890123456 12345678901234567 1234567890123456 1234567890123456 12345678901234567 1234567890123 LAUNDRY 1234567890123456 1234567890123 12345678901234567

MEASUREMENT

TASK

new carpet

Materials Materials:

SELFAS SES SMENT ASSES SESSMENT

A carpet supplier has been given a plan of a house with the rooms that require new carpet shaded. Help the supplier work out the area of each room so that he can provide the correct amount of carpet.

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

1234567890123 12345678901234567 1234567890123 12345678901234567 1234567890123 12345678901234567 1234567890123 12345678901234567 LOUNGE ROOM 1234567890123 12345678901234567 BEDROOM 12345678901234567 ENSUITE1234567890123 1234567890123 12345678901234567 1 1234567890123 12345678901234567 1234567890123 12345678901234567 1234567890123 12345678901234567 1234567890123 12345678901234567

ew i ev Pr

Teac he r

BATHROOM

13 1

Challenge:

KITCHEN

Measure and calculate the carpeted area of your classroom.

a) Area of bedroom 1 = b) Area of bedroom 2 = c) Area of bedroom 3 = d) Area of lounge room = e) Area of rumpus room = f) Area of study = What is the total area of the house that requires carpet?_____

2

______________ ______________

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poses onl y• TASK •f Indicator Indicator:: Calculates area from a plan for a purpose.

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temperature

a) What is the graph showing?

o c . che e r o t r s super ○

○ ○

b) Which day has the greatest difference between day and overnight temperatures?

Celsius o

. te

2

3

Sun Mon Tues Wed Thurs Fri

c) Which day has the least difference between day and overnight temperatures?

Sat

Calculate the average daily temperature for that week. ___________________________________________________ Calculate the average nightly temperature for that week. ___________________________________________________ Indicator Indicator:: Interprets and demonstrates knowledge of graphs and temperature.

46

SELFAS SES SMENT ASSES SESSMENT

m . u

Look at the graph and answer the following questions on the back of this sheet.

w ww

14 1

Challenge:

Select three different countries and investigate on the Internet what their current daily and overnight temperature is. Type up your findings.


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TASK

15

MEASUREMENT

boat design

SELFAS SES SMENT ASSES SESSMENT

Materials Materials:

1

Using popsticks, matchsticks and Plasticine, design a 3D model of a boat that has at least three different angles.

2

Circle below the angles you used in your design and record their measurement using a protractor.

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

Challenge: Find and

ew i ev Pr

Teac he r

acute ____________________________________________

obtuse ___________________________________________

draw a piece of furniture in the classroom that has more than two angles. Record the angles and their measurements on your diagram.

right (90°) _______________________________________

© ReadyEdPubl i cat i ons orr evi ew pur posesMEASUREMENT onl y• TASK•f Indicator Indicator:: Constructs a model and uses a protractor to measure its angles.

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1234567890123456 Jarrod 7:00am 8:25am 8:45am 1234567890123456 1234567890123456 1234567890123456 ____________ 1234567890123456 1234567890123456 Jessica 7:30am 8:45am 8:50am 1234567890123456 1234567890123456 1234567890123456 b) Which student’s data shows 1234567890123456 1234567890123456 1234567890123456 Daniel 6:30am 8:20am 8:30am 1234567890123456 the shortest time elapsed 1234567890123456 1234567890123456 1234567890123456 Emily 7:45am 8:35am 8:40am between waking and arriving 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 to school? 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456

time elapsed

2

3 4

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

. te

m . u

The chart below shows wake up, leave home and arrive at school times for five students.

w ww

16 1

o c . che e r o t r s super

a) Which student takes the longest time to travel to school? _______________________ b) Which students take the shortest time to travel to school? _______________________ c) Which two students take 10 minutes to travel to school? _______________________

___________

Which two students have the same amount of time elapsed between waking and leaving home? _________________________ How much time elapses between the time you wake up and arrive at school? _______________________________________________

Challenge: How

much time does Daniel spend in total between waking up and leaving home over the course of a school week? ________________

Indicator Indicator:: Measures and calculates time elapsed from starting and finishing times.

47


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TASK

17 1

triathlon

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

If Kate’s time last year for the same event was 106 minutes and 30 seconds, by how much time has she improved this year?

ew i ev Pr

3

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

Kate has been training for a triathlon event in which she needs to run 8 km, swim 2 km and ride 10 km. If her total best time for this event is 97 minutes, which includes 34 minutes for the first leg, 8 more minutes for the second leg and half the second leg time for the third leg, how long does it take her to ride her 10 km? Show your working below.

Teac he r

2

MEASUREMENT

Challenge: Kate has been

If Kate aims to improve by the same amount next year, what will her time be next year?

training for five years. Each year she has improved her time by 90 seconds. If her best time was recorded at 97 minutes this year, what was her time five years ago?

© ReadyEdPubl i cat i ons MEASUREMENT orr evi ew pur poses onl y• TASK •f Indicator Indicator:: Measures and calculates time elapsed from given times.

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24 hour time

. te

a) Start time: ________________

b) Finish time: _________________

o c . che e r o t r s super

On Friday night John has a party to go to and there’s also a movie he would like to tape on Channel 9 starting at 8:30pm. The movie finishes two hours and 15 minutes later. What 24 hour times does he need to set his VCR to start and finish the tape? a) Start time: ________________

3

b) Finish time: _________________

On the night of the party John did not get home until 23:15. What time is this in 12 hour time? _______________________________________________ Indicator Indicator:: Converts 12 hour time to 24 hour time.

48

SELFAS SES SMENT ASSES SESSMENT

m . u

2

Materials Materials: •pencil

John’s favourite TV show is on tonight on Channel 10 at 6:30pm for half an hour. During that time he is playing basketball. As his VCR works in 24 hour time what time does John need to set it to start and finish the tape?

w ww

18 1

Challenge:

On the back of this sheet, make a list of all the places 24 hour time is used. To help you with your list investigate 24 hour time on the Internet.


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TASK

19

1 2

MEASUREMENT

bus timetable

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil

Use the bus timetable below to answer the following questions:

a) How often do the buses run on this timetable? ______________________ Renee wants to catch a bus from the bottom of her street (Errol St) to the cinema in time to meet her friends for an 11:15am movie.

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

a) Which bus should she catch? ___________________________________ b) How long will the trip take? _____________________________________ Jack lives near the Pitt St stop and wants to meet his friends at the West Oval at 3pm for a cricket match. a) Which bus should he catch? ________________________

b) How long will the trip take? _________________________

4

Mr Parker also lives near the Pitt St stop and works at the cinema, starting work at 8am. a) Which bus should he take? _________________________ b) How long will the trip take? _________________________

ew i ev Pr

Teac he r

3

Challenge: Suppose

each bus, after it arrived at the cinema, departed back on the same route after 10 minutes. What time would each of these buses arrive at Neil St? List each Neil St return time on the time table below in red.

© ReadyEdPubl i cat i ons STOPS Pitt St Errol St Neil St West Oval Cinema orr evi ew pur posesonl y• TASK•f Indicator Indicator:: Reads a timetable correctly to plan a simple journey.

6:05

6:15

6:20

6:30

6:40

6:45

6:55

7:00

7:10

7:20

7:25

7:35

7:40

SELFAS SES SMENT ASSES SESSMENT 7:50

8:00

8:05

8:15

8:20

8:30

8:40

8:45

8:55

9:00

9:20

9:25

9:35

9:40

10:05

10:15

10:20

10:00

m . u

6:00

. te

o c . che e r o t r s super

9:10

9:50

10:30

10:40

10:45

10:55

11:00

11:20

11:25

11:35

11:40

12:00

12:05

12:15

12:20

12:30

12:40

12:45

12:55

1:00

1:10

1:20

1:25

1:35

1:40

1:50

2:05

2:15

2:20

2:30

2:40

2:45

2:55

3:00

3:10

3:20

3:25

3:35

3:40

3:50

4:00

4:05

4:15

4:20

4:30

4:40

4:45

4:55

5:00

5:10

5:20

5:25

5:35

5:40

5:50

6:00

6:05

6:15

6:20

6:30

2:00

PM

BUS TIMETABLE

w ww

AM

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11:10 11:50

49


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TASK

MEASUREMENT

20 tom’s calendar 1 2

Materials Materials: •pencil •Internet (Challenge)

SELFAS SES SMENT ASSES SESSMENT

Use the calendar below to answer the following questions:

Tom had a dental check-up on Tuesday 3 October, and has been asked to return in ten weeks for a second visit. What date will that be? __________

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

On Thursday 23 November, Tom broke his left arm and had to have it put in plaster. If the doctor said it would need to be in plaster for six weeks, what date could the plaster come off? ___________________________________

3

a) What date will it be for 2006? ___________________ b) What date was it in 2005? ______________________

4

If Tom’s mother sends overseas Christmas cards exactly three weeks before Christmas day, what day and date will she send them in 2006? ______________________________________________

Challenge: Select a

ew i ev Pr

Teac he r

Every year Tom’s family have a Christmas party with their friends the Sunday before Christmas Eve.

calendar from another culture (e.g. Chinese, Muslim, Aboriginal, Hindu, etc.) and list the differences between their calendar of special events and ours. The Internet will be a useful tool in helping you solve this problem.

© ReadyEdPubl i cat i ons NOVEMBER 2006 OCTOBER 2006 •f or r evi ew pur p o s e s on l y • TASK M T W T F S S Indicator Indicator:: Uses and reads a calendar to plan events and dates.

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TASK

21

1

tap leak

A kitchen tap has a leak of 50 ml an hour. How much water would be lost after one day? (Hint: You may wish to act this task out.)

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

If the tap continued to leak at the same rate for five days, how much water would be lost? Show your working.

ew i ev Pr

3

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •measuring cup •water •jug or bucket •calculator

Teac he r

2

MEASUREMENT ASSESSMENT

Challenge: If a tap was

If the tap doubled its rate of leaking and a plumber reported that 9.6 litres had been lost through the leak, how many days would it take to lose this much water?

to leak at a rate of 25 ml per hour, how many hours would it take to lose one litre? __________________ __________________

© ReadyEdPubl i cat i ons MEASUREMENT ASSESSMENT orr evi ew pur po seson l y• TASK•f Indicator Indicator:: Uses knowledge of time and volume to solve a problem.

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22 christmas dinner 1

Materials Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

. te

a) turkey -

o c . che e r o t r s super

c) roast pumpkin -

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w ww

The Ryan family are preparing their traditional Christmas lunch which they plan to have at 1:30pm. They have a turkey which will need 2 ¾ hours cooking time, roast potatoes which will need one hour, roast pumpkin which will need 45 minutes and vegetable bake which will only need 20 minutes. The other vegetables will be steamed for five minutes before serving. At what times will they need to start cooking the different foods? _______

b) roast potatoes –

_______

_______

d) vegetable bake –

_______

If the pudding needs to be boiled for 3 ½ hours, what time would they need to start cooking it if they wish to eat the pudding at 2:30pm? __________________________________________________ Rebecca Ryan made some shortbread biscuits for Christmas gifts. If she was able to bake 24 biscuits at a time for 20 minutes how long did it take her to cook the six dozen? _________________________________________________ Indicator Indicator:: Uses knowledge of time to plan and prepare a meal.

Challenge: If Rebecca

baked her shortbreads for one hour and 40 minutes, then gave away half of the biscuits, how many biscuits did she keep for herself? _________________ 51


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TASK

1 1

CHANCE

games & chance

Materials: •pencil

SELFAS SES SMENT ASSES SESSMENT

Jack and Lachlan are playing a game of “Trouble” where you need to roll a 6 to begin. a) Do either have a better or equal chance of rolling a 6? ____________________________________________________________

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

b) What percentage of chance do they have of rolling a 6 on the first roll?

____________________________________________________________

a) What percentage of chance does Jack have of winning? _____________ b) What percentage of chance do they have of drawing the game? _______________

3

If you were playing a game with three other people (four in total), what percentage of chance would you have of winning? _______________ __________________________________________________

ew i ev Pr

Teac he r

2

Challenge: Create a game using a die where you have a 50% chance of winning. Explain and draw your game (if possible) on another sheet of paper.

© ReadyEdPubl i cat i ons CHANCE orr evi ew pur poseson l y• TASK •f Indicator Indicator:: Understands and uses probability statements in game situations.

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Materials Materials: •pencil •cardboard •coloured pencils/textas •scissors

w ww

1

dice combinations

SELFAS SES SMENT ASSES SESSMENT

m . u

2

a) How many possible number totals could you roll using two dice? _________________________________

. te

o c . che e r o t r s super

b) What chance do you have of rolling the same number? _____________

2

a) Make a die by cutting and pasting together six cardboard squares of the same size. Shade each face with the following colours – red, blue, yellow, green, pink, black. Working with a friend and their coloured die, how many possible colour Challenge: If you were combinations could there be if you roll both dice? to roll two dice, what would be the likelihood/ ________________________________________________ percentage of rolling two sixes? b) What percentage do you have of rolling the same colour? ________________________________________________

Indicator Indicator:: Carries out and analyses the outcomes from simple chance experiments.

52

__________________


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CHANCE (NUMBER)

TASK

3 1

Material Material:•pencil

SELFAS SES SMENT ASSES SESSMENT

Cara’s class is holding an Easter raffle to win a basket of Easter eggs. Each ticket is 50c or five for $2.00. There are 100 tickets to be sold. a) How much would the class raise if all the tickets were purchased at 50c each? b) How much would the class raise if all the tickets were purchased at 5 for $2.00?

r o e t s Bo r e 3 p ok u S

How many tickets would Cara need to purchase to have the following chances of winning? a) 1/100 chance: _____

Number these students in order 1 to 6 from the most likely (1) to win to the least likely (6) to win the raffle given the number of tickets they have purchased. a) Emily – 2 tickets b) Luke – 5 tickets

b) 1/20 chance:

_____

c) 1/10 chance:

_____

d) Rose – 3 tickets

d) 1/4 chance:

_____

e) Kyle – 10 tickets

c) Matt – 7 tickets

f) Sarah – 1 ticket

ew i ev Pr

Teac he r

2

easter raffle

Challenge: How

many tickets would you need to purchase and at what cost to have _ 2/5 chance of winning the raffle? _________________

© ReadyEdPubl i cat i ons orr evi ew pur posesonCHANCE l y• TASK•f Indicator Indicator:: Examines and orders the outcomes of winning a chance competition.

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4

teacher splash

. te

m . u

a) b) c) d) e) f)

2

SELFAS SES SMENT ASSES SESSMENT

One of the students’ favourite attractions at the school fete this year was the teacher splash. A teacher sits on a stool and if someone manages to throw the ball at the small target then this triggers the stool to collapse, making the teacher fall into a swimming pool of water – SPLASH!! Look at the student’s hobbies/sports and make an assumption as to what chance they have of hitting the target if it is 5 metres away.

w ww 1

Materials Materials: •pencils

o c . che e r o t r s super

Joseph (cricket, softball) Diane (netball, tennis) Harry (reading, swimming) Rose (dancing, gym) Linda (drawing, keyboard) Nick (baseball, football)

likely unlikely some chance no chance certain

What chance would you have of hitting the target from these distances? a) 5 m likely unlikely some chance no chance certain b) 2 m likely unlikely some chance no chance certain c) 10 m likely unlikely some chance no chance certain d) 1 m likely unlikely some chance no chance certain

Challenge:

Devise a competition or attraction for a fete where there are different chances of winning. Use another sheet for your planning.

Indicator Indicator:: Uses given information to analyse a situation involving chance.

53


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TASK

5 1

selection process

SELFAS SES SMENT ASSES SESSMENT

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

Another draw is then going to be held to select three representatives out of five finalists from your region, to have lunch with the Prime Minister. What are the chances of having your name drawn out this time? _______________________________________________

ew i ev Pr

3

Materials Materials: •pencils

Three upper primary students are going to be selected to represent your school at a special meeting with the Prime Minister at Parliament House in Canberra. If there are 75 final year students, including yourself, and the names are going to be drawn out of a hat, what chance do you have of being selected?

Teac he r

2

CHANCE

Challenge: How many

If you and your friend are both representatives, what are the chances that both of you will be selected from the group of five finalists? (List the possible combinations that could occur, e.g. Person 1, 2, 3, 4, 5.)

possible combinations could be drawn from the hat if two finalists are chosen from a group of 10 representatives. (Hint: It may help to list them, e.g. Person 1-10.)

______________________________________________

© ReadyEdPubl i cat i ons CHANCE orr evi ew pur poseson l y• TASK •f Indicator Indicator:: Uses given information to analyse a situation involving chance.

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3

____________________________________

. te

100

o c . che e r o t r s super

What chance do you believe you would have of hitting the 100 target within five throws of a dart? ________________________________

Who from your class do you believe would have the highest chance of hitting the 100 target in the first shot? Why? _________________________________________________

4

What possible scores could you make after throwing two darts that both hit the dart board? _________________________________________________ Indicator Indicator:: Makes predictions to do with probability of chance situations.

54

SELFAS SES SMENT ASSES SESSMENT

m . u

Look at the dart board pictured. What do you believe are your chances of scoring a hit on the 100 target in the first shot?

50 20 10

2

Materials Materials: •pencils

50 20 10

scoring 100

w ww

6 1

Challenge: What possible scores could you make after throwing three darts that all hit the dart board? __________________ __________________ __________________


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CHANCE

TASK

7

Name some games where you have a 50/50 chance of winning.

_______________________________________________________________ Name a game that has fair and unfair aspects. Describe what is fair and unfair about it. You can write more on the back of this sheet if you need to.

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

Name of game –

___________________________________

Fair –

___________________________________

Unfair –

___________________________________

Design a simple board game that allows the players to have an equal chance of winning. Plan your game below.

ew i ev Pr

3

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •cardboard •coloured pencils/textas

Teac he r

1 2

fair/unfair

Challenge:

Design a simple board or card game that is unfair to some players. Use another sheet for your planning and design.

© ReadyEdPubl i cat i ons orr evi ew pur posesonCHANCE l y• TASK•f Indicator Indicator:: Understands and applies the concepts of ‘fair’ and ‘unfair’ to simple games.

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w ww

1

decision making

Materials Materials: •circle of cardboard •cardboard for arrow •scissors •spilt pin •coloured textas / pencils

Make a list of all the decisions you make in a day.

SELFAS SES SMENT ASSES SESSMENT

m . u

8

______________________________________________________________

. te

o c . che e r o t r s super

______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________

2

Design a spinner that can help you with one area of decision making in your day, e.g. What to wear, what to have for breakfast, what to have for lunch, when to do homework, etc. Indicator Indicator:: Designs a simple device to assist with making decisions.

Challenge: On the back of this sheet: a) Name a career / job where you would need to make many decisions in a day. b) List the decisions you might need to make.

55


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TASK

9

1

CHANCE

weather possibilities

Materials Materials: •pencil •newspaper or Internet (Challenge)

Order these weather possibilities from 1 (most likely) to 5 (least likely) to occur at school today. a) rain____

c) cloudy____

d) stormy____ e) snow____

a) Melbourne _____

b) Sydney

_____

c) Canberra _____

d) Brisbane

_____

e) Darwin

_____

f) Perth

g) Adelaide

_____

h) Hobart

_____

_____

Would you change your order as above, if the day was in January? If so, how? ___________________________________________________

ew i ev Pr

3

r o e t s Bo r e p ok u S b) sunny____

Order the likelihood of rain occurring today in the main cities of Australia from l (most likely) to 8 (least likely).

Teac he r

2

SELFAS SES SMENT ASSES SESSMENT

Challenge: Check

and record the reported weather in all the capital cities of Australia today. You may wish to use the internet or a newspaper.

© ReadyEdPubl i cat i ons DATA orr evi ew pur posesonl y• TASK •f Indicator Indicator:: Orders events from least likely to most likely using given information.

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2 3

The school is trying to work out which team sports they should include in the senior sports program next year. You have been asked to design a survey for the upper primary students asking their preferences. You need to decide whether to have Yes / No answers, a “tick the box” system or provisions for answers. You may wish to use the computer to design your survey.

. te

o c . che e r o t r s super

At what stage of this year should you distribute your survey?

______________________________________________________________

How would you make sure each upper primary student completes a survey?

__________________________________________________ __________________________________________________ __________________________________________________ Indicator Indicator:: Designs and prepares a survey for a purpose.

56

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •paper •computer and printer (optional)

w ww

1

sports survey

m . u

10

Challenge: How

would you change your survey if it was to be aimed at the junior grades of the school? On the back of this sheet, explain some of the modifications you would need to make.


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TASK

11 1

DATA (NUMBER)

music night

Materials Materials: •pencils •computer (optional)

SELFAS SES SMENT ASSES SESSMENT

Mrs Chime the music teacher has been asked to organise the school’s Music Night where each primary year level sings and performs two of their favourite songs. To be fair Mrs Chime has decided to distribute a survey to each student to find out their favourite songs. Design a survey she could use for the whole school. You might like to type it on a computer.

_____________________________________________

Mrs Chime has only received ¾ of the surveys from each year level. How many surveys does she still need to collect? Show your working below.

Challenge: Of the 336 students,

ew i ev Pr

3

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

If Mrs Chime has distributed the survey to 336 students, on average how many surveys would she need to give to each year level? (Note: There are seven different year levels.)

Teac he r

2

exactly 1/12 of them did not attend the music night. If half of those students attending had two audience members attend and the other half had three audience members attend, how many were in the audience altogether?

______________________

© ReadyEdPubl i cat i ons DATA orr evi ew pur posesonl y • TASK•f Indicator Indicator:: Designs, prepares and calculates numbers for the purpose of a survey.

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12 statistics

SELFAS SES SMENT ASSES SESSMENT

What is your favourite sport/team/player?

. te

m . u

Statistics tell you all the information/facts you need to know about a particular topic.

w ww 1 2

Materials Materials: •pencils

_____________________________________________________________

o c . che e r o t r s super

Present a list of statistics on your chosen sport/team/player.

______________________________________________________________ ______________________________________________________________

3

__________________________________________________ How could you present and distribute this information so that more people in the wider community are aware of these statistics? _________________________________________________ _________________________________________________

Challenge: Research

a sport or team you don’t know much about and list ten facts or statistics about them. Write them on another sheet of paper.

Indicator Indicator:: Researches and prepares data for presentation to an audience.

57


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DATA

TASK

13

1

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •paper •computer (optional)

What do your classmates think of the school rules? To find out, set up a survey listing some of your main school rules with a section for your classmates to answer Agree / Unsure / Disagree. (You may wish to use the computer to set up your survey.)

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

Teac he r

Distribute your survey to at least ten classmates, and then read the results. Write a statement about the results.

__________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________

Challenge: Do you think your survey accurately found out what students really think of the school rules? If not, how could you alter it? Write your ideas on the back of this sheet.

ew i ev Pr

2 3

school rules

© ReadyEdPubl i cat i ons orr evi ew pur posesonDATA l y• TASK •f Indicator Indicator:: Prepares a survey using different categories for a purpose.

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Materials Materials: •pencils •calculator

w ww

The canteen decided to make a report as to how many hot lunches are sold over a term. They set out the information in the form of a pictograph. If one picture represents 50 items, how many of the following items were sold over the last term? a) pies

2

3

. te

o c . che e r o t r s super

_______

b) hamburgers _____

c) chips

_______

d) hotdogs _______

e) pizza

_______

If hamburgers cost $3.00, pizzas cost $2.50, pies cost $2.10, hotdogs cost $2.00 and hot chips cost $1.70, which item did the canteen take the most money for? __________________________________________________

How might the canteen use this information for their ordering for next term? __________________________________________________ Indicator Indicator:: Interprets and uses information gathered from a pictograph.

58

SELFAS SES SMENT ASSES SESSMENT

m . u

14 hot lunches 1

Challenge: If the

canteen makes 50% profit on the hot food items, how much profit did they make this term? _________________ _________________


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TASK

15 1

DATA

beth’s weight gain

SELFAS SES SMENT ASSES SESSMENT

Teac he r

Beth is 12 years old. She was looking at her weight chart which recorded her weight from aged 1 to 12 years of age. At 1 she weighed 9 kilograms (kg), at 2 years she weighed a third more. By the age of 3, Beth had only gained 2 kg and at 4 she doubled that increase. When she was 5 years old she had increased by 2 kg and at the age of 6 she had the same increase as she had gained at age 4. At 7 she put on the same amount of kilograms as the number that is one third of her current age. When Beth was 8 years old she weighed another 3 kg, at 9 she doubled that increase less 1kg, and at 10 she gained the same amount as the previous year. By 11 Beth had gained 3 more kg and at 12 years she added 1 more kg to the increase she had of the previous year. How much does Beth weigh now? Show your working on the back of this sheet. Challenge: Using the graph paper again, graph what you believe Using the graph paper, plot Beth’s weight in the form of a has been your weight line graph. Count in multiples of 2, 3, 4 or 5 up the vertical gain over the last three axis and remember to label both axes. years and predict what it will be over the next three years. Be sure to clearly label your graph.

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

ew i ev Pr

2

Materials Materials: •pencil •graph paper

© ReadyEdPubl i cat i ons DATA orr evi ew pur posesonl y • TASK•f Indicator Indicator:: Calculates weight gain and presents the information in a line graph.

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subject choices MUSIC

m . u

ART

. te

a) How many students only chose one subject? ______________________ b) How many students like only music and sport? ______________________ c) How many students chose two subjects? ______________________ d) Who likes all three subjects? ______________________

o c . che e r o t r s super •Jacob •Darcy

•Kyle •Liam•James •Michael •Ben •Jack•Lucy •Alana

2

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •computer (challenge)

A group of students were surveyed to find out which of the following subjects they liked – ART, SPORT or MUSIC. (Note: they could choose more than 1.) Study the results presented in the Venn diagram below and answer the questions.

w ww

16 1

SPORT Survey 10 of your classmates as to whether they like Maths or English or both and present your findings in a Venn diagram. Indicator Indicator:: Extracts, interprets and presents information in a Venn diagram.

Challenge:

Give some other suggestions where Venn diagrams are useful for presenting information. You may find the Internet useful for this information.

59


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TASK

17

1

2

classroom temperature

SELFAS SES SMENT ASSES SESSMENT

Materials Materials: •pencil •graph paper •temperature gauge

Last Tuesday the classroom temperature gauge recorded 12°C in the morning. By mid-morning it was half that amount again, by lunchtime it had increased by 2°C and by the end of the day it had risen by double the previous increase. What was the temperature at the end of the day? _______________________

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

The following temperatures were recorded hourly in the same classroom a day later. Plot these temperatures on a line graph using the graph paper.

Teac he r

•9am – 11°C •10am – 12°C •11am – 15°C •1pm – 18°C •2pm 20°C •3pm 24°C

•12 midday – 17°C •4pm – 26°C

a) At what time was the largest increase in temperature recorded?

ew i ev Pr

3

DATA

Challenge: Record the

temperature in your classroom for at least three hours (more if possible). Did it change?

b) What time of year/season do you think these temperatures were recorded? c) Approximately what do you believe would be the temperature by 7pm?

__________________

d) What do you think the temperature might be by 11pm?

© ReadyEdPubl i cat i ons orr evi ew pur posesonDATA l y• TASK •f Indicator Indicator:: Extracts, interprets and presents information on a line graph.

__________________

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18 take away food 1

b) What was the most favourite take away food?

____________________

c) What was the least favourite take away food?

____________________

o c . che e r o t r s super

Suggest some ways Nicholas could present this information so that it was easier to read. __________________________________________________ __________________________________________________

3

Choose one of your suggestions and present Nicholas’s results. Indicator Indicator:: Extracts, interprets and presents gathered information in a graph format.

60

SELFAS SES SMENT ASSES SESSMENT

m . u

____________________

w ww

Nicholas surveyed the students in his class on their favourite take away food. Here is his recorded tally. a) How many students were surveyed?

. te

2

Materials Materials: •pencil •graph paper •paper (Challenge)

Challenge:

Survey and keep a tally of your classmates’ favourite take away food. On the back of this sheet, write two statements about your findings.


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DATA

TASK

19

pocket money

Materials Materials: •pencil •graph paper •coloured pencils/textas Ten students each from Years 2, 4 and 6 were randomly selected and asked how much pocket money they received each week (if any). The information is displayed on the table below. Year 2 Year 4 Year 6

1

1

2

3

4

5

6

7

8

9

10

$2

$5

Nil

Nil

$2

$4

$3

$2

Nil

Nil

$4

$4

$5

$3

Nil

$2

$4

Nil

$5

$6

Nil

$5

$6

$5

$8

$10

$5

$7

$4

$5

SELFAS SES SMENT ASSES SESSMENT

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

2

a) Year 2:

___________________________

b) Year 4:

___________________________

c) Year 6:

___________________________

ew i ev Pr

Teac he r

What is the average amount of pocket money each age group receives?

Challenge:

Based on the above information predict what the average pocket money would be for the following year levels: a) Year 1: _______ b) Year 5: _______ c) Year 7: _______

Transfer the above information onto a bar graph, using the graph paper. Remember to label each axis and use a different colour for each year level.

© ReadyEdPubl i cat i ons DATA orr evi ew pur posesonl y • TASK•f Indicator Indicator:: Extracts, interprets and presents gathered information in a graph format.

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20

interpreting graphs

w ww

Look at each graph below and write a statement about the information each graph is showing. Use another sheet of paper for your statements.

1

. te

2

Harry

o c . che e r o t r s super CAR

Liz Carmel

William

Jessica

Helen Emily

Peter

BIKE

BUS

100

LK WA

TRAIN

110

3

m . u

SELFAS SES SMENT ASSES SESSMENT

Mary

Bridget

Challenge: Find a pie

graph, line graph or bar graph in a magazine or newspaper. Cut it out and write a statement about the information it is giving us. Use the sheet of paper you used for the other statements.

Indicator Indicator:: Interprets, predicts and extracts information from a variety of graph styles.

61


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CHANCE ASSESSMENT

TASK

21 horse racing 1

Material Materials: •pencil •calculator

SELFAS SES SMENT ASSES SESSMENT

10 horses are to run in the first race, all with an equal chance of winning and equal odds.

a) If you were to select one horse to win, what is your chance of winning? ______ b) If you selected three horses, what is your chance of winning? _______________

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

c) If you wanted a 50% chance of winning, how many horses would you need to put a bet on? _______________________________________________________ In the second race there are only five horses racing, each with the following odds: Horse 1 = 5-1 Horse 2 = 2-1 Horse 3 = 20-1 Horse 4 = 12-1 Horse 5 = 3-1

Teac he r

2

a) Which horse has the greatest chance of winning? _______

ew i ev Pr

Challenge: The horse that

b) Which horse has the least chance of winning? __________

3

won the fourth race was owned by 12 people. If the total prize money is $72,600, how much money did each share holder receive?

c) Which horse would give you a return of $12.00 if you bet $1.00 for it to win? ________________________________ In the third race the horse that won was owned by nine people. If the total prize money was $31,500, how much money did each owner receive? ________________________

______________________

© ReadyEdPubl i cat i ons DATA orr evi ew pur pose soASSESSMENT nl y• TASK •f Indicator Indicator:: Uses given information to analyse a situation involving chance.

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fete results

o c . che e r o t r s super

b) Which stalls raised about the same amount of money?

3

BBQ Stall

_____________________________

When planning for next year’s fete how could you use this information? (i.e. which stalls would you include and which might you leave out?)

Show B

ags

Challenge: If $21,000

Make a suggestion as to other ways you could find out what students may want to include at their fete?

was raised at the fete, use the pie graph to work out approximately how much was raised at each stall.

__________________________________________________

__________________

________________________________________

Indicator Indicator:: Extracts and analyses information contained in a graph.

62

/ s es e n t d Ri s e m u Am

& sh r e Traeasu Tr Craft Ar t & n Cor er

. te

SELFAS SES SMENT ASSES SESSMENT

m . u

a) Which stall raised the most money? _____________________________

2

Materials Materials: •pencils

The following pie graph appeared in a school newsletter last week. Use the graph to answer the questions below.

w ww

22 1


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ANSWERS

SPACE

TASK 1 PARALLEL TOWER 1) Teacher to check. 2) Teacher to check. Challenge: Answers will vary but should mention need for horizontal support.

d) Jessica e) Luke f) Emily. 3) a) 24, b) 12, c) 12. Challenge: Teacher to check.

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

TASK 3 ANGLES 1) Teacher to check / answers will vary. 2) Three groups: right angles, greater than, less than (or acute, obtuse angles). 3) Teacher to check. Challenge: Over 180° and under 360°. Where? Answers will vary.

b) Square

c) Parallelogram d) Triangle

e) Trapezoid

Challenge: Teacher to check / answers will vary.

TASK 14 FLIGHT 125 1) Mr Pear. 2) Miss Peach. 3) Mrs Apple had her tray down and Mr Pear was wearing headphones. The info about sitting on the right hand side of the plane. Challenge: 171 passengers.

ew i ev Pr

TASK 2 PERPENDICULAR LINES 1) Teacher to check. 2) Teacher to check. Challenge: Circle, oval, cylinder, cone.

Teac he r

triangles. a) Rectangle

TASK 15 CAROUSEL 1) Jessica (front centre), Ben (left), Emily (centre back), Kate (right). 2) Ben is wearing a blue hat, Jessica is crying, Kate’s mum is taking her photo. 3) Ben 4) Kate Challenge: Jessica

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

TASK 5 CUBES 1) 6 2)

TASK 9 TESSELLATING PATH 1) Teacher to check. 2) Teacher to check. Challenge: Teacher to check.

Challenge: Teacher to check.

TASK 10 TRICKY TANGRAMS 1) Teacher to check. 2) Teacher to check / answers will vary. Challenge: Teacher to check.

. te

TASK 6 PENTOMINOES 1) 12 possible answers.

TASK 16 LOCAL MAP 1) Teacher to check. 2) Should mention: Locating new house or street, travelling by car on holiday, visiting a new place. Challenge: Teacher to check.

m . u

TASK 8 BRICK WALL 1) Answers will vary. 2) 88 Challenge: 96

w ww

TASK 4 HOUSE DESIGN 1) Teacher to check. 2) Answers will vary. 3) Answers will vary. Challenge: Teacher to check.

TASK 17 PIZZA DELIVERY 1) Teacher to check. 2) 152 slices. Challenge: 114 slices.

o c . che e r o t r s super

Challenge: Teacher to check.

TASK 11 SYMMETRICAL LETTERS 1) Letters not symmetrical = F, G, J, K, L, N, P, Q, R, S, Z. 2) Answers will vary. Challenge: Teacher to check / answers will vary.

TASK 12 USING GRIDS 1) Teacher to check. 2) Answers will vary but should mention that it is easier to copy each individual square. Challenge: Teacher to check.

TASK 18 FETE PLAN 1) Teacher to check. Challenge: Teacher to check / answers will vary. TASK 19 LOST CATTLE 1) 10 north east, 12 south, 9 south west, 20 north west, 6 east. 2) 57 Challenge: 27 TASK 20 TRAPPED IN A MAZE 1) Teacher to check / answers may vary. 2) Teacher to check. Challenge: Teacher to check.

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ANSWERS

TASK 21 SPACE ASSESSMENT: OFFICE BUILDING 1) Rectangular prism. 2) 32 3) 16 Challenge: Teacher to check / answers may vary.

TASK 6 HOW MANY DAYS OLD? 1) 365 or 366 (leap year). 2) 1826 (1 leap year) or 1827 (two leap years). 3) Teacher to check. (Note: leap years.) Challenge: Answers will vary.

TASK 22 LOCATION ASSESSMENT: SCHOOL MAP 1) Teacher to check. 2) Teacher to check / answers may vary. Challenge: Teacher to check.

TASK 7 MAKING NUMBERS 1) 12, 2) 24, Challenge: 24

TASK 1 CREATURE COLLECTION 1) a) 74 b) 28 2) 5 beetles and 3 spiders. Challenge: 9 beetles and 12 spiders. TASK 2 CROSS NUMBERS 1) a) b)

2 3 1 4 =8 2 5 2) a) b) 7 9 6 8 =23 6 10

TASK 10 AFL GAME 1) 22 2) Combinations may include: 14 goals and 22 points;15 goals and 16 points; 16 goals and 10 points; 17 goals and 4 points. 3) Combinations may include: 10 goals and 24 points; 11 goals and 18 points; 12 goals and 12 points; 13 goals and 6 points; 14 goals. Challenge: 75

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

40 20 60100 =180 80

TASK 11 GOLF GAME 1) a) 68, b) 50, c) 104 2) 154 Challenge: 5360 metres.

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TASK 3 CONCERT HALL 1) 360 2) a) 304 b) 300 c) 320 Challenge: $7440.00

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TASK 12 DARTS 1) a) 80, 20, 10 b) 80, 80, 80 c) 20, 20, 10 d) 80, 80, 10. 3) 20, 30, 40, 50, 60, 80, 90, 100, 120, 160 Challenge: 70, 110, 130, 140.

o c . che e r o t r s super

TASK 4 FOUR 4S 1) 4 + 4 - 4 - 4 = 0; (4 + 4 - 4) ÷ 4 = 1; (4 ÷ 4) + (4 ÷ 4) = 2, (4 + 4 + 4) ÷ 4 = 3; (4 x 4 + 4) ÷ 4 = 4; 4 x 4 + 4 ÷ 4 = 5; (4 + 4) ÷ 4 + 4 = 6; 4 - (4 ÷ 4) + 4 = 7; 4 x (4 ÷ 4) + 4 = 8; 4 + 4 + (4 ÷ 4) = 9. Challenge: Teacher to check / answers may vary. (Note: does not work for all answers.) TASK 5 AGES 1) a) Matilda 8 years, Mother 32 years; b) Matilda 12 years, Mother 36 years. 2) Matilda 24 years, Mother 48 years.

Challenge:

a) Ben 12 years, Brother 18 years, Father 36 years; b) Ben 24 years, Brother 30 years, Father 48 years.

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TASK 9 SWIMMING CARNIVAL 1) 194 2) a) 9, b) 8, c) 8, d) 7 3) a) 53 b) 109 Challenge: 96

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Challenge:

c)

1 1 3 4 =9 2 5 3 =10 5 4 c) 7 8 8 10 =24 9 10 6 =25 9 7

TASK 8 200 METRE SPRINT 1) 6, 2) 24 Challenge: 120

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NUMBER

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TASK 13 NUMBER SENTENCES 1) E.g. 10+90, 20+80, 30+70, 60+40, 50+50; 12+28+60, 15+85, 34+66, 45+55; 55+15+30, 62+28+10. 2) E.g. 100+900, 200+800, 300+700, 400+600; 500+500, 150+850, 250+750, 350+650; 450+550, 100+300+600, 200+300+500; 150+450+400, 250+350+400. Challenge: 1600+8400, 2500+7500; 2650+7350, 3100+6900, 4000+6000; 4850+5150, 3590+6410, 4320+5680.


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ANSWERS

TASK 22 SCHOOL SUPPLIES 1) a) $15.70, b) $17.15, c) $20.25, d) $24.30. 2) $8.60 Challenge: $19.35

TASK 15 GO-CARTS 1) a) 2000 m, b) 2000 m, c) 9 times. 2) $144.00 Challenge: 230 children.

TASK 24 TOY SALE 1) a) $40, b) $44, c) $28.40, d) $48. 2) a) $137.50, b) $110. Challenge: Mary $12.

TASK 16 MUSEUM 1) 214 adults. 2) $3954.00 3) 2961 Challenge: 423

TASK 25 CAR WASH 1) a) $2560.00, b) $81,920.00 2) a) 9, b) 24, c) 67. 3) $735.00 Challenge: 18 weeks.

TASK 17 TENNIS COMPETITION 1) 36 2) 2 hours. Challenge: 6 hours.

TASK 26 CAKE SHOP 1) a) $9, $3, b) $14, $2 c) $4, $2, d) $12, $3, e) $3, $1.50, f) $4, $1. Challenge: $28.75

TASK 18 SCHOOL PICNIC 1) 16 2) 72 3) 396 Challenge: 540

TASK 27 PARTY TIME 1) 5 2) 5 3) 7½ 4) 90 Challenge: a) 16, b) 24

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TASK 23 UNIFORM SHOP 1) a) $2, b) $1, c) 0.55c, d) $1, e) $1.50, f) $2.20. 2) a) $34.75, b) $32.50, c) $49.90. Challenge: Ben, $5.10 saving.

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TASK 14 EQUATIONS 1) Answers may include: 1+8+6, 7+3+5, 5+6+4, 9+5+1, 9+4+2, 7+6+2. (There are many more to be found.) 2) Answers will vary. One solution is to place 50 in the middle circle and then running clockwise from centre top: 20, 90, 40, 70, 80, 10, 60, 30. Challenge: Answers will vary. One solution could be: 5 x 10 (8 ÷ 4) = 100.

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TASK 19 SHOPPING TROLLEY 1) 4 m, 2) 10 m, 3) 66 m Challenge: 10

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TASK 20 BOAT RESCUE 1) 16 2) First boat: J.C. 12 months, B.R. 2 years, O.H. 3 years, H.C. 4 years, J.C. 6 years, W.H. 7 years, E.H. 8 years, S.W. 9 years; Second boat: L.W. 85 years, N.W. 84 years, S.H. 78 years, M.R. 63 years, J.S. 54 years, N.S. 53 years, M.S. 45 years, D.W 43 years; Third boat: F.H. 41 years, B.H. 39 years, D.C. 34 years, K.C. 30 years, K.R. 28 years, K.W. 20 years, R.F. 17 years, J.F. 11 years. Challenge: Answers will vary.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• TASK 28 SCHOOL SPORTS 1) 40 2) 25 3) 20 4) 360 Challenge: 80

o c . che e r o t r s super

TASK 21 MELBOURNE TO BRISBANE 1) 575 km. 2) 1150 km. 3) 5 days. Challenge: Approximately 1750 km.

TASK 29 HEIGHT ORDER 1) 1.29 m, 1.32 m, 1.34 m, 1.35 m, 1.36 m, 1.38 m, 1.39 m, 1.40 m, 1.45 m, 1.46 m, 1.49 m, 1.51 m. 2) 0.22 m or 22 cm. 3) 1.395 m Challenge: 1.8 m or 180 cm. TASK 30 DRESSMAKER’S FABRIC 1) 17.6 m 2) 4.7 m 3) 43.2 m Challenge: $68.25

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ANSWERS

TASK 31 ASSESSMENT – CRICKET MATCH 1) 12 x 6(s) + 0 x 4(s); 10 x 6 +3 x 4; 8 x 6 + 6 x 4; 6 x 6 + 9 x 4; 4 x 6 +12 x 4; 2 x 6 +15 x 4. 2) 10 batters scored 56 runs each; the other batter scored 91. Challenge: The three scores were 85, 86 and 87.

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

TASK 1 FLYING FOX 1) Answer should mention: Measure the height of the tallest students. 2) Teacher to check. Challenge: Answer should mention: Higher, longer, sturdier (support a greater weight). TASK 2 ROSE’S GARDEN 1) 25 cm, 2) 5, 3) 8 weeks Challenge: 45

TASK 8 OIL DRUM 1) 33 litres. 2) 9 litres. 3) 320 ml. Challenge: 8 litres and 600 ml or 8.6 litres.

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TASK 32 ASSESSMENT – TRAVELLING TO SCHOOL 1) 3/6 or 18 2) 12 3) 6 Challenge: 60

MEASUREMENT

TASK 7 CAVE AREA 1) Answers may include: Use miner’s hand or foot to estimate. 2) Answers will vary. 3) Answers will vary. Challenge: a) Length x Width = Area; b) Teacher to check.

TASK 9 PETROL TANK 1) $85.50 2) a) 4 litres, b) 6½ litres, c) 14 litres, d) 40 litres. 3) 450 km Challenge: 5 km TASK 10 MAX’S PARTY 1) Answers will vary / teacher to check. 2) 6 slices. Challenge: Teacher to check.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

TASK 4 LOST! 1) Answer should mention: Compare Patrick’s height to those of the one metre high new trees. 2) Answer should mention: Use Patrick’s stride (approx. 1 m) to mark out 75 m/paces. 3) Teacher to check / answers will vary. Challenge: Answer should include: Foot, hand, stride, height, arm span, leg length and finger length.

TASK 12 ORIENTEERING COURSE 1) a) 10, b) Answer should mention: Use a compass and trundle wheel to work out distance between checkpoints, sign at each check point and starting and finishing points. 2) a) to f) Teacher to check. Challenge: Teacher to check.

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o c . che e r o t r s super

TASK 5 BALANCE SCALES 1) Answer should mention: Measure all four bars on balance scales and the one that is different (lighter or heavier) is the counterfeit. 2) Teacher to check. (Answers may vary depending on the size and weight of the object.) Challenge: Teacher to check / answers will vary. TASK 6 SMITH FAMILY WEIGHT 1) 94 + 58 + 69 + 49 = 270 kg. 2) 91 + 60 + 71 + 53 = 275 kg. 3) 1½ kg Challenge: Teacher to check / answers will vary.

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TASK 11 PHOTO FRAME 1) Teacher to check. 2) Inside should be 70 cm, outside answers will vary / teacher to check. Challenge: Answers will vary.

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TASK 3 COMPARING STUDENTS 1) Teacher to check. 2) Answers will vary. Challenge: 54 mm

TASK 13 NEW CARPET 1) Teacher to check. 2) Teacher to check. Challenge: Teacher to check.

TASK 14 TEMPERATURE 1) a) Melbourne’s daily and overnight temperature recorded over a week, b) Monday (11°C), c) Sunday (6°C). 2) 21°C 3) 13°C. Challenge: Teacher to check.


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ANSWERS

TASK 15 BOAT DESIGN 1) Teacher to check. 2) Teacher to check / answers will vary. Challenge: Teacher to check / answers will vary.

TASK 1 GAMES & CHANCE 1) a) No, equal chance, b) 16.6% or 1 in 6 chance. 2) a) 50%. b) Answers will vary (small %). 3) 25%. Challenge: Teacher to check / answers will vary.

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

TASK 16 TIME ELAPSED 1) a) Daniel (2 hours) b) Emily (55 minutess). 2) a) Jarrod 20 minutes. b) Jessica and Emily 5 minutes. c) Luke & Daniel. 3) Luke and Emily. 4) Answers will vary. Challenge: 9 hours and 10 minutes. TASK 17 TRIATHLON 1) 21 minutes. 2) 9 minutes 30 seconds 3) 87 minutes 30 seconds. Challenge: 104 minutes 30 seconds.

TASK 18 24 HOUR TIME 1) a) 18:30, b) 19:00. 2) a) 20:30, b) 22:45. 3) 11:15pm. Challenge: Teacher to check / answers will vary.

TASK 2 DICE COMBINATIONS 1) a) 36, b) 6 chances out of 36 or 1 in 6 (1/6). 2) a) 36, b) 6 out of 36 or 1 in 6 (1/6). Challenge: 6 chances out of 36 or 1 in 6 (1/6). TASK 3 EASTER RAFFLE 1) a) $50, b) $40. 2) a) 1, b) 5, c) 10, d) 25. 3) a) 5, b) 3, c) 2, d) 4, e) 1, f) 6. Challenge: 40 tickets $16 (5 for $2).

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CHANCE & DATA

TASK 4 TEACHER SPLASH 1) Answers will vary. 2) Answers will vary. Challenge: Teacher to check / answers will vary.

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TASK 20 TOM’S CALENDAR 1) 12 December, 2) 4th January, 2007. 3) a) 17 December, b) 18 December. 4) Monday 4 December. Challenge: Teacher to check.

TASK 6 SCORING 100 1) Answers will vary. 2) Answers will vary. 3) Answers will vary. 4) 200, 150, 120, 110, 100, 70, 60, 40, 30, 20. Challenge: 300, 200, 170, 160, 150, 140, 130, 120, 110, 90, 80, 70, 60, 50, 40, 30.

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TASK 19 BUS TIMETABLE 1) Every 40 minutes. 2) a) 10:45am, b) 25 minutes. 3) a) 2:40pm, b) 20 minutes. 4) a) 7:20am, b) 30 minutes. Challenge: Neil St - 6:55am, 7:35am, 8;15am, 8:55am, 9;35am, 10:15am, 10:55am, 11:35am, 12:15pm, 12:55pm, 1:35pm, 2:15pm, 2;55pm, 3:35pm, 4:15pm, 4:55pm, 5:35pm, 6:15pm, 6:55pm.

TASK 5 SELECTION PROCESS 1) 3/75 or 1/25 or 4%. 2) 3/5 or 60%. 3) 2/5 or 40%, Possible combinations – 123, 124, 125, 134, 135, 145, 234, 235, 245, 345. Challenge: 45 different combinations.

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TASK 21 ASSESSMENT – TAP LEAK 1) 1200 ml or 1.2 litres. 2) 6000 ml or 6 litres. 3) 4 days. Challenge: 40 hours.

TASK 22 CHRISTMAS DINNER 1) a) 10:45am, b) 12:30pm, c) 12:45pm, d) 1:10pm. 2) 11am. 3) 1 hour. Challenge: 60.

TASK 7 FAIR/UNFAIR 1) Teacher to check / answers will vary. 2) Teacher to check / answers will vary. 3) Teacher to check. Challenge: Teacher to check.

TASK 8 DECISION MAKING 1) Teacher to check / answers will vary. 2) Teacher to check. Challenge: Teacher to check / answers will vary. TASK 9 WEATHER POSSIBILITIES 1) Teacher to check. 2) Teacher to check / answers may vary. 3) Teacher to check / answers may vary. Challenge: Teacher to check.

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ANSWERS

TASK 17 CLASSROOM TEMPERATURE 1) 24°C 2) Teacher to check. 3) a) 3pm b) Answers will vary (spring/summer). c) Answers will vary. d) Answers will vary. Challenge: Teacher to check.

TASK 10 SPORTS SURVEY 1) Teacher to check. 2) Answers will vary. 3) Answers will vary. Challenge: Answers will vary.

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TASK 18 TAKE AWAY FOOD 1) a) 77, b) Pizza, c) Red Rooster. 2) Answers will vary but should mention various types of graphs. 3) Teacher to check / answers will vary. Challenge: Teacher to check.

TASK 12 STATISTICS 1) Teacher to check. 2) Teacher to check. 3) Answers will vary. Challenge: Teacher to check.

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TASK 11 MUSIC NIGHT 1) Teacher to check. 2) 48 3) 84 Challenge: 770

TASK 19 POCKET MONEY 1) a) $1.80, b) $3.30, c) $5.50. 2) Teacher to check. Challenge: Answers will vary.

TASK 13 SCHOOL RULES 1) Teacher to check. 2) Teacher to check. 3) Teacher to check. Challenge: Teacher to check / answers will vary.

TASK 20 INTERPRETING GRAPHS 1) Answers will vary. 2) Answers will vary. 3) Answers will vary. Challenge: Teacher to check / answers will vary.

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TASK 15 BETH’S WEIGHT GAIN 1) 48 kg, Age Kg 1 9 2 12 3 14 4 18 5 20 6 24 7 28 8 31 9 36 10 41 11 44 12 48 2) Teacher to check graph. Challenge: Teacher to check.

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TASK 22 DATA ASSESSMENT – FETE RESULTS 1) a) BBQ stall, b) Rides/amusements and Show bags. 2) Teacher to check / answers will vary. 3) Survey students (answers may vary slightly). Challenge: Answers may vary but may include approximate totals such as BBQ stall $8400.00, rides/amusements $4200.00, Show bags $4200.00, Art and Craft $3150.00, Trash and Treasure $1050.00.

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TASK 16 SUBJECT CHOICES 1) a) 18, b) 4, c) 7, d) Erin, Kate, Joel. 2) Teacher to check. Challenge: Answers will vary.

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TASK 21 CHANCE ASSESSMENT – HORSE RACING 1) a) 1/10 or 10% b) 3/10 or 30% c) 5 horses. 2) a) Horse 2, b) Horse 3, c) Horse 4. 3) $3500.00 Challenge: a) $6050.00

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TASK 14 HOT LUNCHES 1) a) 625, b) 550, c) 400, d) 700, e) 450. 2) Hamburgers. 3) Answers may vary but should mention that they would order approximately the same number of items next term. Challenge: $3083.75

Primary Maths Problems Series: Book 3  

The Primary Maths Problems Series is a 3-book series (Junior, Middle and Upper Primary) aimed at developing a range of problem solving skill...