STUDENT JOURNAL
ORIGO Stepping Stones Student Journal Year 3 Copyright 2014 ORIGO Education Senior Authors: James Burnett, Calvin Irons Contributing Authors: Debi DePaul, Peter Stowasser, Allan Turton Program Editors: James Burnett, Beth Lewis, Donna Richards, Stacey Lawson For more information, visit www.origoeducation.com. All rights reserved. Unless specifically stated, no part of this publication may be reproduced, copied into, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of ORIGO Education. ISBN: 978 1 922246 19 6 10 9 8 7 6 5 4 3 2 1
SENIOR AUTHORS James Burnett Calvin Irons contributing authors Debi DePaul Peter Stowasser Allan Turton PROGRAM EDITORS James Burnett Beth Lewis Donna Richards Stacey Lawson STUDENT JOURNAL
CONTENTS MODULE 1 1.1 Reading and Writing Three-Digit Numbers 8 1.2 Revising Three-Digit Numbers 10 1.3 Locating Three-Digit Numbers 12 on a Number Line 1.4 Counting Forwards and Backwards by Tens 14 and Hundreds 1.5 Introducing Comparison Symbols 16 1.6 Comparing and Ordering Two-Digit Numbers 18 1.7 Comparing and Ordering Three-Digit Numbers 20 1.8 Rounding to the Nearest Ten or Hundred 22 1.9 Introducing the Multiplication Symbol ( ) 24 1.10 Using the Multiplication Symbol with Arrays 26 1.11 Using the Multiplication Symbol 28 with Equal Groups 1.12 Revising Division Language (Sharing) 30 MODULE 2 2.1 Estimating with Addition 32 MODULE 4 4.1 Composing Three-Digit Numbers 80 4.2 Bridging Decades to Add One- and Three- 82 Digit Numbers 4.3 Using Jump and Split Strategies to Add Two- 84 and Three-Digit Numbers (with Bridging) 4.4 Using Jump and Split Strategies to Add 86 Three-Digit Numbers (with Bridging) 4.5 Consolidating Addition with Three- 88 Digit Numbers 4.6 Introducing the Compensation Strategy 90 for Addition 4.7 Consolidating the Compensation Strategy 92 to Add Two- and Three-Digit Numbers 4.8 Consolidating the Compensation Strategy 94 to Add Three-Digit Numbers 4.9 Introducing the Kilogram 96 4.10 Working with Kilograms 98 4.11 Introducing Litres and Estimating Capacity 100 4.12 Working with Litres 102 MODULE 5 2.2 Using the Associative Property to Add 34 Three Numbers 2.3 Extending the Count-On Strategy 36 to Three-Digit Numbers 2.4 Using Jump and Split Strategies to Add 38 Two- and Three-Digit Numbers 2.5 Using Jump and Split Strategies to Add 40 Three-Digit Numbers 2.6 Estimating with Subtraction 42 2.7 Revising the Jump Strategy for Subtraction 44 2.8 Revising the Inverse Strategy for Subtraction 46 2.9 Solving Word Problems Involving Addition 48 or Subtraction 2.10 Working with Five-Minute Intervals 50 2.11 Working with Duration (Hours) 52 2.12 Working with Duration (Hours and Minutes) 54 MODULE 3 3.1 Counting in Steps of Two, Five and Ten 56 3.2 Revising Multiplication Concepts 58 3.3 Introducing the Twos Multiplication Facts 60 3.4 Reinforcing the Twos Multiplication Facts 62 3.5 Doubling and Halving Multiples of 10 and 5 64 3.6 Introducing the Tens Multiplication Facts 66 3.7 Introducing the Fives Multiplication Facts 68 3.8 Reinforcing the Tens and Fives 70 Multiplication Facts 3.9 Adding Coin Values 72 3.10 Reading and Recording Dollars and Cents 74 3.11 Constructing a Vertical Column Graph 76 3.12 Interpreting and Constructing a Horizontal Column Graph 78 5.1 Writing Four-Digit Numbers 104 5.2 Representing Four-Digit Numbers 106 5.3 Writing Four-Digit Number Names and 108 Numerals 5.4 Locating Four-Digit Numbers on a Number Line 110 5.5 Revising Fractions 112 5.6 Working with the Area Model of Fractions 114 5.7 Naming Equal Parts of a Whole (Area Model) 116 5.8 Identifying the Numerator and Denominator 118 5.9 Relating Fraction Words and Symbols 120 5.10 Comparing Lengths in Metres 122 5.11 Comparing Lengths in Metres and Centimetres 124 5.12 Writing Lengths in Metres and Centimetres 126 MODULE 6 6.1 Extending the Count-Back Strategy 128 to Three-Digit Numbers 6.2 Using Jump and Split Strategies to Subtract 130 Two-Digit Numbers from Three-Digit Numbers 6.3 Using Jump and Split Strategies to Subtract 132 Three-Digit Numbers 6.4 Bridging the Decades to Subtract One-Digit 134 Numbers from Three-Digit Numbers 6.5 Using Jump and Place-Value Strategies 136 to Subtract Three-Digit Numbers 6.6 Consolidating Subtraction of Two-Digit 138 Numbers from Three-Digit Numbers (with Bridging) 6.7 Using Jump and Place-Value Strategies to 140 Subtract Three-Digit Numbers (with BTridging) 6.8 Exploring Rectangles 142 6.9 Exploring Rhombuses 144 6.10 Exploring Quadrilaterals 146 6.11 Exploring Parallelograms 148 6.12 Exploring Reflective Symmetry 150 ORIGO Stepping Stones Year 3
MODULE 7 7.1 Revising Four-Digit Number Names 152 and Numerals 7.2 Comparing and Ordering Four-Digit Numbers 154 from Everday Contexts 7.3 Revising Four-Digit Numbers on a Number Line 156 7.4 Exploring Place Value of Four-Digit Numbers 158 7.5 Investigating Patterns on Number Charts 160 7.6 Exploring Addition and Subtraction Patterns 162 7.7 Identifying Odd and Even Numbers 164 7.8 Exploring Odd and Even Numbers 166 7.9 Introducing Millimetres 168 7.10 Measuring, Comparing and Ordering Lengths 170 (Centimetres and Millimetres) 7.11 Exploring Area in Square Centimetres 172 MODULE 10 10.1 Adding Amounts in Cents (Bridging Dollars) 224 10.2 Rounding Prices to the Nearest Five Cents 226 10.3 Calculating Change (Cents) 228 10.4 Calculating Change (Whole Dollars) 230 10.5 Consolidating Subtraction Strategies 232 (Whole Dollars) 10.6 Counting Fractions on a Number Line 234 (Between 0 and 1) 10.7 Counting Fractions Beyond 1 (Mixed Numerals) 236 10.8 Representing Mixed Numerals (Area Model) 238 10.9 Locating Fractions on a Number Line (Beyond 1) 240 10.10 Revising Litres and Parts of a Litre 242 10.11 Working with Parts of a Litre 244 10.12 Solving Word Problems Involving Capacity 246 CONTENTS 7.12 Exploring Area in Square Metres 174 MODULE 11 MODULE 8 8.1 Introducing the Division Symbol ( ) 176 8.2 Exploring the Relationship Between 178 Multiplication and Division 8.3 Introducing the Tens Division Facts 180 8.4 Introducing the Fives Division Facts 182 8.5 Reinforcing the Tens and Fives Division Facts 184 8.6 Introducing the Twos Division Facts 186 8.7 Reinforcing the Twos Division Facts 188 8.8 Exploring Angles as Openings 190 8.9 Exploring Angles as Amounts of Turn 192 8.10 Reading and Writing Times 194 to the Nearest Minute 8.11 Relating Times Past and To the Hour 196 8.12 Introducing Seconds 198 MODULE 9 9.1 Introducing the Threes Multiplication Facts 200 9.2 Reinforcing the Twos, Threes, Fives and Tens 202 Multiplication Facts 9.3 Exploring Mental Strategies to Multiply 204 by a Multiple of Ten 9.4 Extending the Tens Multiplication Facts 206 9.5 Solving Word Problems Involving Multiplication 208 9.6 Using the Array Model to Relate Multiplication 210 and Division 9.7 Relating Multiplication and Division (Sharing) 212 9.8 Introducing the Three Division Facts 214 9.9 Reinforcing the Threes Division Facts 216 9.10 Exploring Volume 218 9.11 Investigating Volume 220 9.12 Using Cubic Centimetres to Measure Volume 222 11.1 Working with Place Value of Four- 248 Digit Numbers 11.2 Exploring Place Value of Four-Digit Numbers 250 11.3 Partitioning Four-Digit Numbers 252 11.4 Partitioning Four-Digit Numbers 254 in Non-Standard Forms 11.5 Exploring the Relative Position of Numbers 256 to 9999 11.6 Rounding Four-Digit Numbers to the Nearest 258 Ten, Hundred or Thousand 11.7 Identifying Pyramids 260 11.8 Identifying Prisms 262 11.9 Comparing Prisms and Pyramids 264 11.10 Making and Analysing 3D Objects 266 11.11 Exploring Nets 268 11.12 Joining 3D Objects 270 MODULE 12 12.1 Using the Jump Strategy to Add Numbers 272 to 9999 12.2 Partitioning to Add Three- and Four- 274 Digit Numbers 12.3 Using the Split Strategy to Add Three- 276 and Four-Digit Numbers 12.4 Using the Jump Strategy to Subtract 278 from Four-Digit Numbers 12.5 Partitioning to Subtract Three- and Four-Digit 280 Numbers from Four-Digit Numbers 12.6 Using the Split Strategy to Subtract Three- and 282 Four-Digit Numbers from Four-Digit Numbers 12.7 Using Simple Maps 284 12.8 Using Grid References 286 12.9 Constructing and Interpreting Picture Graphs 288 12.10 Collecting Data and Constructing 290 Column Graphs 12.11 Predicting Outcomes of a Chance 292 Experiment 12.12 Exploring the Variation in Results 294 ORIGO Stepping Stones Year 3 Index 296
Step In Counting in Steps of Two, Five and Ten Colour green the numbers you say when you start at 10 and count in steps of ten. What do you notice? Colour blue the numbers you say when you start at 5 and count in steps of five. What patterns do you see? Colour red the numbers you say when you start at 2 and count in steps of two. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 8 89 90 91 92 93 94 95 96 97 98 99 100 What do you notice? Look at the numbers that show all three colours. What do you know about these numbers? Step Up Use this number chart to answer Questions 1 and 2 on page 57. 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 56 3.1 ORIGO Stepping Stones Year 3
1. Start at 110 and count in steps of ten. Colour yellow the numbers you say. Start at 105 and count in steps of fi ve. Colour green the numbers you say. c. Write in order the numbers you said when you counted in steps of both ten and fi ve. 2. Start at 102 and count in steps of two. Colour red the numbers you say. What do you notice about these numbers? 3. Look at the numbers below. 172 185 474 190 225 360 162 285 400 Colour blue the numbers you say when you start at 5 and count in steps of fi ve. Colour red the numbers you say when you start at 2 and count in steps of two. c. Colour green the numbers you say when you start at 10 and count in steps of ten. Step Ahead There are four parts in this Venn diagram. Write two numbers in each part. Numbers That We Say Count by Twos Count by Fives ORIGO Stepping Stones Year 3 3.1 57
Step In Revising Multiplication Concepts I packed 3 stacks of boxes. There were 8 boxes in each stack. How many boxes did I pack? Use cubes to help work out the answer. Write an addition sentence to match your cubes. How does your addition sentence relate to the story problem? Write a multiplication sentence to match your cubes. Write a multiplication sentence to match your cubes. The symbol for multiplication is. How does your multiplication sentence relate to the story problem? Step Up 1. Draw a picture to help solve each problem. Then write the matching multiplication sentence. Each container holds 3 tennis balls. How many tennis nis balls will fi ll 4 containers? Each car needs 5 tyres. How many tyres are needed for 4 cars? balls tyres 58 3.2 ORIGO Stepping Stones Year 3
2. Complete these. Show your thinking. Balloons cost 5 cents. How much would you pay for 9 balloons? How many stamps are on a sheet that has 5 rows of 6 stamps? cents c. Chloe had 4 bags. She placed 8 oranges in each. How many oranges did she have in total? = stamps d. William cut 5 lengths of rope. Each piece was 4 metres long. What was the total length of rope? oranges metres Step Ahead Complete this table. Number of feet 2 3 4 5 8 9 10 Number of toes 10 How did you work out the number of toes on 8 feet? ORIGO Stepping Stones Year 3 3.2 59
Step In Introducing the Twos Multiplication Facts What do you see in this picture? I see double 6. What multiplication number sentences could you write for the picture of eggs? What do you see in this picture? Write two related number sentences to match. = How did you work out the total? What are some other problems you could solve by doubling? I can use doubles to solve any problem that involves two. Step Up 1. Write a twos number fact and its turnaround for each picture. c. 60 3.3 ORIGO Stepping Stones Year 3
2. Write the twos fact that matches each array. Then write the turnaround fact. c. 3. Draw a line to match each multiplication sentence with its turnaround below. Then write the answers. 2 9 = 12 2 = 11 2 = 2 14 = 2 12 = 2 11 = 9 2 = 14 2 = Step Ahead Write the missing numbers. IN OUT IN OUT 7 5 4 10 double 9 2 24 22 6 ORIGO Stepping Stones Year 3 3.3 61
Step In Reinforcing the Twos Multiplication Facts What pictures could you draw to match this fact? Anton drew rows of apples. How does his picture match the fact? 2 7 = 14 2 rows of 7 apples, that's 14 in total. Lyrra drew bags of marbles. How does her picture match the fact? How could you represent the same fact on a number line? You could draw 2 jumps of 7 on a number line. Step Up 1. Draw a picture to match each word story. Then complete e the number sentence. 5 oranges in each bag 2 bags of oranges 3 rows of strawberries 2 strawberries in each row 62 3.4 ORIGO Stepping Stones Year 3
2. Complete the number sentence. Draw jumps on the number line to show your thinking. 2 6 = 0 4 2 = 0 c. 2 5 = 0 d. 9 2 = 0 3. Write the missing number in each number sentence. 8 2 = 2 = 10 c. 10 20 d. 3 = 6 e. 2 20 f. 14 = 2 g. 2 8 h. 12 = 6 Step Ahead Write a multiplication sentence you could use to solve each problem. There are 9 boxes of shoes. Each box holds 2 shoes. How many shoes in total? Koki cuts a piece of rope into 2-m lengths. The rope is 14 metres long. How many lengths can he cut? ORIGO Stepping Stones Year 3 3.4 63
Step In Doubling and Halving Multiples of 10 and 5 What do you know about doubling and halving that involves the number 20? I know that two 20c coins is equal to 40c, so half of 40 must be 20. How could you work out double 15? 15 is the same as 1 ten and 5 ones. Double 10 is 20, double 5 is 10. How could you work out half of 50? I think of sharing 5 tens blocks. I can put 2 tens in each group but I'd need to split the last block to share it equally. Jasmine drew this picture to show what she knew about doubling and halving. What does it tell you? What other numbers could you use in the picture? How do you know? double 20 40 halve 64 3.5 ORIGO Stepping Stones Year 3
Step Up 1. Complete these sentences. so Double is 4 so Half of 6 is Double is 40 Half of 60 is c. d. so Half of 8 is so Double is 10 Half of 80 is Double is 100 2. Complete the sentence and write the answer. Double 15 is the same as double 10 plus double 5. Double 45 is the same as double plus double. Double 15 is. Double 45 is. c. Double 35 is the same as double plus double. Double 35 is. d. Double 25 is the same as double plus double. Double 25 is. Step Ahead Draw lines to connect the cards that have the same value. Some cards have more than one match. Some cards have no match. Double 25 20 Halve 100 Double 40 35 Halve 40 Halve 70 50 Double 10 ORIGO Stepping Stones Year 3 3.5 65
Step In Introducing the Tens Multiplication Facts Six students held up their hands in front of the class. How many fingers are there in total? How can you work it out quickly? What multiplication sentence could you write to describe the number of fingers? Step Up 1. Work out the total. Write the matching number sentence. fi nger s shoes c. d. bananas c 66 3.6 ORIGO Stepping Stones Year 3
2. Write two facts to match each array. c. = = d. = = Step Ahead Heena has fi ve 10-cent coins. Noah has ten 5-cent coins. Does Noah have more money than Heena? Explain your answer. ORIGO Stepping Stones Year 3 3.6 67
Step In Introducing the Fives Multiplication Facts Look at this array and the number sentences. How could you work out the products? 4 5 = 5 4 = How is this array different from the one above? How could you work out the products of these number sentences? 4 10 = 10 4 = I halved the product in the tens fact. 10 fours is 40 so 5 fours is half of that. t. I counted in steps of 5. Use a halving strategy to work out 6 5. You can draw an array to help. Step Up 1. Complete the tens fact. Colour half the array and then complete the two fi ves facts to match. 3 10 = 2 10 = 3 5 = 5 3 = 2 5 = 5 2 = 68 3.7 ORIGO Stepping Stones Year 3
2. Write the product for the tens fact. Colour half the array and then write the two fi ves facts to match. 7 10 = 6 10 = c. 9 10 = d. 8 10 = Step Ahead Write two tens facts to match this picture. Cross out one hand on each card. Write two multiplication facts to match the new picture. c. How did you work out what facts to write? ORIGO Stepping Stones Year 3 3.7 69
Step In Reinforcing the Tens and Fives Multiplication Facts CLOSED OPENED 6 5 = 5 6 = How can you use the tens fact on the opened card to help work out the number of dots showing on the closed card? What other methods could you use to work out the product of 6 5? 6 10 = 10 6 = I would skip count by fives: 5, 10, 15, 20, 25, 30. Step Up 1. Work out the total and write the matching number sentence. c c 70 3.8 ORIGO Stepping Stones Year 3
2. Draw coins to match the price tag. Then write a matching number sentence. 2 40c c c 3. Write the missing number in each number sentence. 6 10 = 4 20 c. 5 = 35 d. 10 = 40 e. 80 = 8 f. 5 = 15 g. 5 45 h. 30 = 6 4. Write a number sentence to match each story. Jacob has a set of 10 toy cars. The total length of all the cars laid end to end is 70 cm. Each car is 7 cm long. Ella had 30 stickers to pack into bags. She put 5 stickers in each bag. When she fi nished she had 6 bags of stickers. = Step Ahead IN These IN numbers are multiplied by 10 and then halved before they come OUT. Write the missing numbers. OUT 5 50 25 8 10 halve 100 9 ORIGO Stepping Stones Year 3 3.8 71
Step In Adding Coin Values How many 10-cent coins can you trade for 20 cents? How do you know? How many 5-cent coins can you trade for 20 cents? How many 5-cent coins can you trade for 50 cents? Look at this coin. How many 20-cent coins can be traded for one dollar? How many 20-cent coins make 40 cents? How many make 80 cents? Look at this coin. What coin is it? What is its value in dollars? How many 10-cent coins could you trade for one dollar? How do you know? How many 5-cent coins could you trade for one dollar? Step Up 1. Write the missing numbers. Two 20-cent coins is c One 50-cent coin is c Three 10-cent coins is c Two 10-cent coins is c One 5-cent coin is c Four 5-cent coins is c The total is c The total is c 72 3.9 ORIGO Stepping Stones Year 3
2. Loop together the coins that equal one dollar. Then write the total amount. dollar and cents left over dollar and cents left over 3. Read the story. Write the missing numbers. Haroon had two 50-cent coins, two 10-cent coins and three 5-cent coins in his wallet. He had dollar and cents. Haroon gave his sister 10 cents. He then found 20 cents on the footpath. Now he has dollar and cents. Haroon s aunty gave him three 20-cent coins. Now he has dollars and cents. Step Ahead Scarlett has 4 coins in her pocket. The total is more than 50 cents but less than 70 cents. Draw two different pictures to show the coins she might have in her pocket. 10c 20c 50c ORIGO Stepping Stones Year 3 3.9 73
Step In Reading and Recording Dollars and Cents How could you work out the value of these coins? What helps you work out the total quickly? How could you work out the value of these coins in dollars and cents? What do you know about this coin? How many cents is it worth? How do you know? What coins can be traded for two dollars? Step Up 1. Loop together coins that show whole dollars. Then complete the sentences. dollar and cents left over dollars and cents left over c. d. dollars and cents left over dollars and cents left over 74 3.10 ORIGO Stepping Stones Year 3
2. Loop together coins that show whole dollars and add to whole dollars. Then complete the sentences. dollars and cents left over c. dollars and cents left over dollars and cents left over d. dollars and Step Ahead Callon has five coins in his wallet with a total of 4 dollars and 20 cents. Draw coins to show two different combinations that he could have. cents left over ORIGO Stepping Stones Year 3 3.10 75
Step In Constructing a Vertical Column Graph Hannah would like to know the seasons in which her classmates were born. She knows some of the months in each season. Write the missing months and season. Season Months Summer December February Autumn April May August What question should she ask her classmates? sm Spring September October Step Up 1. Write the season in which you were born. 2. Ask each student in your class to name the season in which they were born. Record the results in this tally chart. Season Tally Total 3. Most students were born in. The fewest number of students were born in. c. students in total were born in Summer and Autumn. d. What is the total of students born in Winter and Spring? 76 3.11 ORIGO Stepping Stones Year 3
4. Complete this column graph to show your results from Question 2. Title: 9 8 Number of students 7 6 5 4 3 2 1 0 Season Step Ahead This column graph has some mistakes. Describe four mistakes you see. 7 6 5 4 3 1 0 Summer Autumn Winter ORIGO Stepping Stones Year 3 3.11 77
Step In Interpreting and Constructing a Horizontal Column Graph Owen asked his classmates to vote for their favourite type of music. This column graph shows the results. Favourite Music Type of music Hip Hop Pop Rock Country 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Number of votes Each student voted once. How many students voted for each type of music? Which type of music was most popular? How many more students voted for Hip Hop than Country? How do you know? How many students voted altogether? How do you know? If your classmates voted for their favourite music, what do you think the results would look ok like? Step Up 1. Ask each student in your class to vote for their favourite type of music. Record the results in this tally chart. Type of music Tally Total Hip Hop Pop Rock Country Classical 78 3.12 ORIGO Stepping Stones Year 3
2. Show your results from Question 1 on this column graph. Title: Hip Hop Type of music Pop Rock Country Classical 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Number of votes 3. What is the most popular type of music? What is the least popular type of music? c. students ts in total voted for Pop and Hip Hop. d. students s in total voted for Classical and Country. 4. How many students voted altogether? How did d you work it out? Step Ahead Think about the music that students in Year 1 listen to. What type of music do you think they listen to the most? Is this different from the music that you listen to? ORIGO Stepping Stones Year 3 3.12 79
ORIGO Stepping Stones is an award-winning mathematics program developed by specialists for Australian primary schools. This revolutionary online program integrates print and digital technology to deliver comprehensive coverage of the F 6 Australian Curriculum and even more! ORIGO Stepping Stones was developed by mathematics specialists for Australian primary schools to: make maths more focused and coherent foster students thinking and reasoning skills deliver multiple ways to differentiate classroom instruction provide a valuable source of professional learning for the teacher offer methods to assess deep understanding and skills provide online and print resources that engage all students IT S SIMPLY A SMARTER APPROACH Milli the possum Split the kangaroo Dart the echidna Digit the wombat Plato the platypus Tally the turtle Cubit the koala THIS BOOK BELONGS TO 3 Product Code: SSJ 196 1