Number Strategies Series: Working on Number by Teacher Superstore

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Acknowledgements i. Clip art images have been obtained from Microsoft Design Gallery Live and are used under the terms of the End User License Agreement for Microsoft Word 2000. Please refer to www.microsoft.com/permission.

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The Act allows a maximum of one chapter or 10% of the pages of this book, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that

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Except as otherwise permitted by this blackline master licence or under the Act (for example, any fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address below.

o c . che e r o t r s super Published by: Ready-Ed Publications PO Box 276 Greenwood WA 6024 www.readyed.com.au info@readyed.com.au

ISBN: 978 1 86397 827 9 2

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Any copying of this book by an educational institution or its staff outside of this blackline master licence may fall within the educational statutory licence under the Act.

Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

Numeration

4 5

Real Life Addition

Real Life Subtraction

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How Many Tens Are There?

How Many Hundreds Are tThere?

Numbers in Cubes and Colour

Words to Numbers

Numbers in a Row

Measuring Numbers

Large Numbers

Real Life Addition and Subtraction 35

Multiplication and Division (Teachers’ Notes)

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(Teachers’ Notes)

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Mental Mania 2

36-37

Multiplication or Division

Changing the Order

Mental Multiply 1 Mental Multiply 2 Mental Division

40 41 42

Bring Down © ReadyEdPDivide, ubTimes, l i cTake, at i on s 43 Real Life Multiplication 44 Place• Value f orr evi e w pur posesonl y•45 Real Life Division (Teachers’ Notes) 15-16 Numbers in Columns

How Many Are There?

Describing the Number

Different Groupings

What’s the Number?

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Fractions

(Teachers’ Notes) Cutting Up the Cake Colour the Fraction Slice it Up

o c . che e r o t r s super Addition and Subtraction Grouping Numbers for Addition

Grouping Numbers for Subtraction 23 Estimation

(Teachers’ Notes)

25-26

Add or Subtract?

Mental Strategy 1a and 1b

28-29

Mental Strategy 2

Mental Mania 1

Share Them

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Numbers to Words

47 48 49 50

Which is Larger?

Which of these are the same?

Fractions on a Line

Fractions in Real Life

Answers

Teachers’ Notes This resource is focused on the Number Strand of the Australian Curriculum for students aged between 8 to 10 years old. Although each of the five sections is matched up with an elaboration from the Australian Curriculum, each section can also be thought of as a specific skills area for students to work on.

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Each section contains eight activities and while there are some stand-alone tasks, most activities are arranged in such a way that skills based tasks come first in the section, followed by further practice questions or application problems. Each section is also prefaced by a Teachers’ Notes page, explaining the idea and purpose behind each activity. Included here are methods to extend the activities or modify the activities based on the level of individual student ability.

The majority of activities are scaffolded into two sections: Task A builds up the general skills to be mastered, usually with two digit numbers; Task B explores the skill further with a more in-depth investigation or consideration and often the use of three digit numbers.

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challenges range from Individual Challenges, through to Research and Small Group Challenges. Each of these are designed to complement the activity page, yet extend beyond the material. They are designed to engage student interest and appreciation for Mathematics as well as exposing students to the idea that Mathematics can be a creative and investigative pursuit. Challenges can be included in the lesson of the day, or used as a stand-alone lesson when time permits. Many can be set as homework or assignment tasks over a longer period of time. Research tasks do tend to include the use of internet resources and it is advisable that computer resources are organized in advance.

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It is hoped that Working On Number will be used to help guide teachers in their teaching strategies and methods of presentation. While some activities are designed to be extra practice for students, many others can be used to present and teach students new concepts.

National Curriculum Links Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)

•

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)

•

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

•

Recognise and explain the connection between addition and subtraction (ACMNA054)

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Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

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Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

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Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

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ModelR and represent unit fractions including 1/4,a 1/3, 1/5 and their © e ady E dP ub1/2, l i c t i o n s multiples to a complete whole (ACMNA058) • f Investigate andv use thew properties of r odd and numbers • orr e i e pu p oeven se so(ACMNA071) nl y• •

Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

•

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

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Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

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Investigate equivalent fractions used in contexts (ACMNA077)

•

Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

•

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

•

Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

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Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

Teachers’ Notes

Numeration How Many Tens Are There?

Materials required for this activity: a 30cm ruler with cm and mm markings. As a discussion point you may like to talk about the connection between cm and mm and their different uses depending upon the accuracy required. You can extend Task C by asking students to measure and order other lengths: the distance between their eyes, from elbow to wrist. You can extend this even further by a research assignment on the Golden Ratio and body lengths.

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How Many Hundreds Are There?

This activity is best completed after “How many tens are there?”. As an extension activity for more able students you may like to turn Task C into an activity on numbers greater than 1000, using a separate symbol for 1000.

Large Numbers

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This activity can be made more tangible by asking students to create and cut out their own Xs and Is for this task. Task C can be a casual activity or you may like students to create a more formal “mini test” to try on their partner, with a separate solutions guide.

Measuring Numbers

This activity is designed to expose students to numbers beyond 1000 and their existence in the real world. The above six activities should be completed first.

© ReadyEdPubl i cat i ons This activity can be done without actual MSB cubes, some lower ability Np umbers to s Words •butf o r r e vi ew pu r ose onl y• Once again this task is designed to expose students may like to assemble numbers using cubes before attempting these tasks.

Words to Numbers

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You may like to talk about the different way we say numbers. As an example you can discuss how to say the number 2 307 and when we use the word “and”. Task C will enable students to simultaneously participate in the creation of mathematics and to practise a larger variety of numbers. Take note of each number as they say it so that you can go through all the solutions at the end.

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Numbers in a Row

This task is best completed after “Words to Numbers”, especially when attempting Task C. You may like to encourage students to cross off each number once they’ve used it to keep track of which numbers are left to order.

students to numbers beyond 1000 and how we read and write them.This is also an opportunity for some small group research and you can extend this further to look at other occupations. A good place is to look at government jobs, where salaries are often numbers like $76 201 and $42 523.

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Numbers in Cubes and Colour

How Many Tens Are There?

* Task a

I iiiiiiiiii

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XXXXXXXXX I iiiiiiiiii XXXXXXXXX

XXXXXXXXX

I iiiiiiiiii XXXXXXXXX

76bl © R e a d y E d P u c at i ons I iiiiiiiiii Ii iiiiiiiiii •f orr evi ew pur posesonl y•

* Task b

Draw the number of tens (X) and ones (I) you need to make each number.

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Hi, I’m a one!

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Hi, I’m a ten!

XXXXXXXXX

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XXXXXXXXX

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Circle the number of tens and ones needed to make each number.

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* Task c: Challenge your partner

Give your partner ten different numbers between 1 and 100 and see if they can draw the correct number of tens and ones. 7

How Many Hundreds Are There?

* Task a

or eBo CCCCCCe Cr Cs Ct p o u k XXXXXXXXX S Hi, I’m a hundred!

912

CCCCCCCCC XXXXXXXXX CCCCCCCCC

827 © R e a d y E d Pub i at o XXXXXXXXX Xl Xc X Xi Xn Xs XXX •f orr evi ew pur posesonl y•

* Task b

Draw the number of hundreds and tens you need to make each number.

275

587

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199

Hi, I’m a ten!

XXXXXXXXX

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CCCCCCCCC

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Circle the number of hundreds and tens needed to make each number.

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your partner * Task c: Challenge Use your imagination to draw your own symbols to represent a

hundred, a ten and a one. Give them to your partner, along with ten different numbers between 100 and 1000 and see if they can draw them with the correct number of hundreds, tens and ones. 8

Numbers in Cubes and Colour Colour in the correct number of cubes needed to make each number.

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* Task a

* Task b

How many of each block do you need to represent each of these numbers?

462 63 ©R eadyEdPubl i cat i ons I need I need blocks •f ohundreds rr evi ew pur poseshundreds onl yblocks • tens blocks

I need

tens blocks

I need

ones blocks

I need

ones blocks

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374

. hundreds blocks hundreds blocks I need te o c . tensc blocks tens blocks I need e her r o t s ones blocks ones blocks s I need r upe

* Task c: Personal Challenge

How many thousands blocks, hundreds blocks, tens blocks and ones blocks do you need to make each of these numbers? 1502

3946

7324

9090

Compare yours answers with your partner. 9

Words to Numbers

Task a

Each of the numbers below are written in words. Next to each one write them using numerals. e) Seven hundred and twenty three _ ______

a) Seventeen _ ______

f)r Ninety _ ______ o e t s B r oo c) One hundred and six _e ______ p g) Four hundred k u S _ ______ and thirteen _ ______ d) Eighty nine

* Task b

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b) Forty five _ ______

Circle the answer that is the correct way to write each number in words.

two OR Seventy and two ©Seventy Rea dyEd Pub l i cat i ons o rr e vi ew u r p s es onl y Three hundred one p OR o Three hundred and• one 301•f Five hundred twelve

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Five hundred and twelve

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* Task c: Class Challenge

Thirty and four

Listen to each person in the class as they say their favourite three digit number. Write down the number they say using numerals. See how many you got correct when your teacher writes the answers on the board.

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Numbers in a Row

* Task a a)

These numbers are in the wrong order. Write them from smallest to largest.

15, 4, 1, 10, 9, 12, 19, 8, 6 __________________________________

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207, 27, 720, 702, 72, 270, 727 __________________________________

* Task b

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These numbers are in the wrong order. Write them from largest to smallest.

420, 370, 810, 590, 840, 960, 720, 630, 110, 340

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•f orr evi ew pur posesonl y• ______________________________________________ ______________________________________________

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612, 745, 315, 621, 361, 872, 782, 351, 827, 754

o c . ______________________________________________ che e r o t r s s r u e p 321, 142, 231, 213, 123, 423, 234, 342, 214, 241 ______________________________________________

Task c: Personal Challenge *These numbers are in the wrong order. Write them from smallest to largest using words.

85, 304, 32, 6, 173, 210, 98, 27, 246, 351, 18 11

Measuring Numbers

* Task a A: 7 cm

Place the letter on the correct position on the 30 cm ruler below. The first one has been done for you. B: 25 cm

C: 12 cm

D: 19 cm

E: 2 cm

F: 21 cm

G: 16 cm

A 2

* Task b

30cm Ruler

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Place the letter on the correct position on the 200 mm ruler below. The first one has been done for you.

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110

120

130

140

200mm Ruler

160

170

180

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* Task c: Class Challenge Use your ruler to measure, in mm, your left hand from the tip of the middle finger to the bottom of your hand. Write your answer on the board. When all answers are on the board, write them in order from smallest to largest.

150

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200

Large Numbers

* Task a

The table below shows how many thousands or hundreds or tens or ones are needed to make each number. The first one is done for you.

Number

Thousands

Hundreds

Tens

Ones

1 243

124

1243

350

4 389

13 437

* Task b

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7 028

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These numbers are in the wrong order. Write them from smallest to largest.

11 351, 13 268, 10 267, 19 521, 10 627, 12 368, 11 531, 15 921_

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6 023, 2 545, 3 278, 10 420, 2 455, 6 302, 2 554, 3 287, 9 580

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______________________________________________

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* Task c: Research Challenge

On the internet, go to the following url: 4http://www.ozlotteries.com/play Write down each of the jackpot amounts from smallest to largest for all the games playing this week. 13

Numbers to Words

* Task a

Write each of the following numbers in words.

_____________________________________________________

282

_____________________________________________________

1 015 _____________________________________________________

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d) 823

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716 __________________________________________

2 458 _____________________________________________________

* Task b

Write these much larger numbers in words.

64 305

___________________________________________________

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___________________________________________________ . t e o c . c e e) 26 089 ________________________________________ her r o t s super d) 8 042

110 395 ___________________________________________________

* Task c: Small Group Challenge In a group of three or four, use the internet to find out the different salaries that teachers make. Write your findings, from smallest to largest, in words. 14

Teachers’ Notes

Place Value Numbers in Columns

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This activity acts as a basic review of place value and how groupings of 100s, 10s and 1s can be converted into place value. You may like to allow students to work with MSB blocks to enable a more tangible approach to the exercise.

How Many Are There?

This activity helps students understand how many lots of 1s, 10s and 100s are needed to create numbers. This is in contrast to thinking about place value. Task C can be extended by asking students to create a larger worksheet or a mini test for their partner. If you photocopy each student’s created task then you can create a database of tasks for students to attempt.

The previous three activities in this section should be completed before attempting this activity, in particular the Describing the Number task. Building on the detail in the curriculum where students are required to describe numbers flexibly, this task helps guide students in the variety of ways they can group numbers using a combination of 1s, 10s, 100s and 1000s.

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Different Groupings

For example, in Task A, if we were to find the different groupings of the number 4 136, we could have each of the following different groupings: 4 136 is made up of:

4 thousands + 13 tens + 6 ones © ReadyEdP oru b l i cat i ons 4 136 ones orp o 4 thousands +o 136 ones • f o r r e v i e w p u r s e s nl y• or 4 thousands +1 hundred + 3 tens + 6 ones Describing the Number

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or or or

41 hundreds + 36 ones 41 hundreds + 3 tens + 6 ones 413 tens + 6 ones.

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It is important to note that this activity is about the total number of 1s, 10s or 100s found in the number, not just the number in the place value column. As described in the curriculum, it is important that students are able to describe a number from a number of different perspectives.

While Task A asks students to consider a few of the different possible groupings, Task B asks students to find the total number of different groupings. For students who find the task challenging, you might encourage them to write down all possible combinations on a separate piece of paper first.

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For example, if examining the number 5 327, we could describe this number as having 5 thousands, or 53 hundreds, or 532 tens or 5 327 ones. Task B extends this idea by asking students to describe the number without any scaffolding. Task C is a show and tell type activity and students should be encouraged to record their answers individually, rather than sharing their answers with their peers.

Task C is designed to make students aware that numbers and research go hand in hand. You can turn this task into a more formal assignment and extend the number of dinosaurs that students research.

Teachers’ Notes

Place Value What’s the Number? This task can be presented more as a game, with tasks A and B acting as preliminary warmups. It is important that students have completed Describing the Number and Different Groupings prior to this activity to ensure they have a sound understanding of the concepts involved. As an alternative to Task C you may like to have students write their clues on a card. These cards can then be shuffled and handed out to students in small groups.

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Grouping Numbers for Addition

For example, to add 52 + 34, we can see we have 5 tens + 3 tens, plus 2 ones + 4 ones.

52 + 34

= 5 tens + 3 tens + =

8 tens +

6 ones

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This is a powerful and useful method for students to learn mental addition strategies. Building on the place value ideas developed in the previous few activities, students can utilise their understanding of place value to help them add numbers more easily. These activities are designed to guide students away from written strategies, as advised by the curriculum.

2 ones + 4 ones

86 © ReadyEdP ubl i cat i ons •f orr evi ew pur posesonl y• If we take a slightly more difficult example, like 48 + 13, we see we have 4 tens + 1 ten, plus In total we have 8 tens and 6 ones, and by our understanding of place value we know the number is 86.

8 ones + 3 ones. We then end up with 5 tens and 11 ones. Since 11 ones is 1 ten and 1 one, we end up with 6 tens and 1 one. Therefore we have an answer of 61.

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Grouping Numbers for Subtraction

This task is similar to, and best completed after, the Grouping Numbers for Addition task. While this task encourages students to learn and develop mental strategies, you may also like to ask students to check their answers using the written algorithm method.

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For example, if we wish to calculate 356 – 83, then we can first see that we have 35 tens – 8 tens, plus 6 ones – 3 ones. We therefore have 27 tens plus 3 ones which results in an answer of 273.

356 − 83 =

35 tens − 8 tens +

= 27 tens +

6 ones − 3 ones

3 ones

= 273

Estimation This estimation activity can be completed at any time. An important, yet often overlooked skill, estimation is an important way for students to gauge whether their answers are close to the correct answer. It is also a way for students to begin to understand rounding. You may wish to add other activities to Task C to extend the estimation practice for the class. 16

Numbers in Columns

* Task a

Circle the number in the hundreds column. Look at the first example, in the number 743 there is a 7 in the hundreds column, a 4 in the tens column and a 3 in the ones column.

743

302

1 204

952

3 001

12 367

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Circle the number in the tens column for these numbers:

* Task b

Tom has made different numbers with his blocks. What number would go in the tens column for each?

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Task c: Personal Challenge * How many of these

and of these would you need to make each of the following numbers?

136

1013

458

2367

How Many Are There?

* Task a

How many of these do you need to make these numbers? a)

104

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How many of these do you need to make these numbers?

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How many of these do you need to make these numbers? c)

400

2 300

How many tens do you need to make these numbers?

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380

680

o c . How many hundreds c e h r1000 s r o do you need to make 300 e t 800 4 500 s r u e p these numbers?

* Task c: Challenge Your Partner

Write down 5 numbers larger than 1000. Ask your partner to write down how many hundreds are needed to make each number. When your partner has finished check and discuss their answers.

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How many ones do you need to make these numbers?

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Describing the Number

* Task A a)

Let’s see the different ways we can describe a number. Fill in each of the empty boxes below. Remember, we are writing the TOTAL number of ones, tens, hundreds or thousands. Some have been done for you to give you some clues.

has 52 ones

has

tens

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r o e t s Bo r e 324 has p ones 324 has o hundreds u k S 32 tens 324 has

852

has

tens

852

2351 has

ones

2351 has 23

hundreds

7245 has

tens

7245 has

hundreds

has

hundreds

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Task B Describe how many ones, tens, hundreds and thousands there are in

a. 72

b. 634

TOTAL in each of these numbers.

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Task c: class challenge *Each student in the class will think of a number between 0 and 5 000. Each student will say their number out loud and you have to write down the total number of tens in their number. When everyone is finished each student will tell the class how many tens were in their number and you have to see how many you got correct. 19

Different Groupings Task A * Fill in each of the empty boxes to see how many different groupings you can make for each number. a)

923

is made up of

92 tens + 3 ones

r o e t s Bo r e ok 203 is madep up of = tens + ones u 203 isS made up of = 2 hundreds + ones 923

hundreds +

1362 is made up of

thousands +

1362 is made up of

hundreds +

1362 is made up of

tens +

3067 is made up of

thousands +

3067 is made up of

tens +

ones

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is made up of

tens +

62 ones ones

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ones

Task B * Write as many different groupings for the following numbers as you can.

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Compare your answers with three other students in your class. a. 67 b. 451

Research Challenge *Use Taskthe C:Internet or the Library to find the weights in kilograms of these Dinosaurs:

Tyrannosaurus, Megalosaurus, Velociraptor, Triceratops and Stegosaurus. Write their weights in as many different groupings as you can. Compare your answers with your partner.

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What’s the Number?

* Task a

Clue: I have 12 tens plus 5 ones.

I am

Clue: I have 36 tens plus 7 ones.

Clue: I have 3 hundreds plus 27 ones.

I am

r o e t s r Clue:B e o p I have 42 ones. o u k I am I am S d)

I am

Clue: I have 78 hundreds and 12 ones.

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Clue: I have 2 thousands plus 54 tens plus 3 ones

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Read each of the clues carefully to help you guess the number.

I am

Look at each number on the right and use it to fill in the empty box. * Task b © ReadyEdPubl i cat i ons a) I have ones. I am 56 •f orr evi ew pur posesonl y• I have

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I have

tens plus two ones. hundreds plus 16 ones.

I am 432

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I am 516

. ones. I am 2304 te tens plus o c . c e he r I have thousands plus 72 tens plus ones. I am 4726 o t r s super

* Task c: class challenge

Think of a number and write down the clues for your number. For example, if you are the number 485 you might write down “I have 48 tens and 5 ones. Who am I?”. Each student will then go up, one at a time, to the front of the class and read their clue. Guess the number for each student and write it down. Each student will reveal which number they were so you can check your results. 21

Grouping Numbers for Addition Fill in each of the empty boxes to help you add each pair of two digit numbers. In the first example you can see that we split each number into groups of tens and ones.

45 + 23

4 tens + 2 tens + 5 ones + 3 ones tens +

ones

tens +

ones

tens +

ones

tens +

ones

tens +

ones

hundreds +

r o e t s Bo r e p o u k = tens + tens + ones + ones 15 S tens + ones = =

65 + 27

ones +

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72 +

ones

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82 + 95

214 + 35 =

ones +

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48 + 39

ones

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ones +

ones

Grouping Numbers for Subtraction

Fill in each of the empty boxes to help you subtract each pair of two digit numbers. In the first example you can see that we split each number into groups of tens and ones.

76 − 32

7 tens − 3 tens + 6 ones − 2 ones tens +

r o e t s Bo r e p tens − tens + oneso − ones 21 = u k S tens + ones = =

234 − 51

= =

tens −

tens +

ones

ones −

ones

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53 − 25

tens +

ones

tens −

tens +

= =

ones −

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85 −

ones

. te= 2 tens + 13 ones − 5 ones o c . ones = c tens + e her r o t = s super

451 − 67 =

tens −

tens +

ones −

tens +

ones −

ones

tens +

ones

= 23

Estimation To estimate an answer we can think about what each number is close to. The number 43 is close to 40. 162 is close to 160.

* Task a a)

Fill in each of the empty boxes to help you estimate what the answer should be. The first one is done for you. b)

61 + 8 is about 60 + 10 .

32 + 11 is about

r o e t s r So theB answer is about e o p ok u S − . 151 + 39 is about + 79 − 19 is about +

So the answer is about 70 .

So the answer is about

289 − 32 is about

So the answer is about

−

So the answer is about .

ew i ev Pr

Teac he r

531 − 49 is about

So the answer is about

52 + 9 =

89 − 32 =

w ww

. te

368 + 11 =

370

380

m . u

390

o c 831 − 29 = c 790 800 810 . e h r e o t r s uper * Task c: small group challenge s

Form a small group of 4 to 5 students. • Measure your heights in centimeters and then estimate the total of your heights. • Write down the time it takes for each of you to travel to school in minutes and then estimate your total travel time. • Write down the amount of television each of you watches each week in minutes and then estimate your total television viewing time.

Height (centimeters) Travel time to school (minutes) Television viewing per week (minutes)

Teachers’ Notes

Addition and Subtraction number) to allow ease of calculation.

Add or Subtract?

Task A makes students aware that addition and subtraction are the opposite of each other. Included in Task B are ideas on changing subtraction to addition and using mental grouping strategies to assist with mental calculations.

r o e t s Bo r e p o u 84k + 21 S = 84 + 20 +

ew i ev Pr

It is advisable that you spend time demonstrating the ideas behind the mental strategy used in Task B before students attempt this task. If we take for example 92 – 48, we can instead see how much we need to add to 48 to get to 92. To do this, we first bridge to the nearest 10. We can set our working out as follows: 48 to 50 then 50 to 90 then 90 to 92 = 2 plus 40 plus 2 = 44

Teac he r

For example, if we wish to calculate 84 + 21, we can say we have 84 + 20 + 1. Here we have partitioned 21 into 20 ones plus 1 one. Working from left to right we then have 104 + 1 and then finally 105.

= 104 + 1 = 105

As another example, if we calculate 745 – 231, we can say we have 745 – 200 – 30 – 1. We have partitioned the 231 into 200 ones plus 30 ones plus 1 one. Working from left to right we then have: 545 – 30 – 1 = 515 -1 = 514.

w ww

To simplify this further, students might like to instead say: 48 to 50 then 50 to 60 then 60 to 70 then 70 to 80 then 80 to 90 then 90 to 92 = 2 + 10 + 10 + 10 + 10 + 2 =44

. te

745 − 231 = 745 − 200 − 30 − 1

m . u

2 + 40 + 2

= 545 − 30 − = 514

o c . c Mental Strategy 1a and 1b e her r o t s super

The aim of the curriculum is to equip students with as many mental strategies for addition and subtraction as possible. In doing so it is hoped that students will work confidently and flexibly with a method that they like and understand best. Here is yet another strategy for students to try. Task 1a uses only two digit numbers while task 1b extends to three digit numbers.The idea in this strategy is that students will partition one of the numbers (usually the second

Task C allows students to create their own calculations and to observe the way in which their peers might approach this strategy.

Mental Strategy 2

These tasks revisit the mental strategy of bridging to 10 and bridging to 100, as outlined in the Add or Subtract? task. As an example of bridging to 100, let’s consider calculating 624 – 281. We begin as follows: 25

Teachers’ Notes

Addition and Subtraction 281 to 300 plus 300 to 600 plus 600 to 624 = 19 + 300 + 24 = 319 + 24 =343

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

624 − 281 = 281

300

600

624

+ 19 + 300 + 24

= 319 + 24 = 343

Task C can be turned into a project that students can work on over a few lessons and the finished products can be reused often to help students work on their mental abilities.

Real Life Subtraction

Tasks A and B may be set as individual tasks or small group work tasks. Asking each group to work on a selection of the problems and explain how they did them to the class is a useful way for students to consolidate how they know what they know. It also serves as a useful way for students to communicate mathematically and for students to share their methods. Task C is aimed as a way for students to explore some of the patterns to be found in addition and subtraction.

ew i ev Pr

Teac he r

their methods.

Real Life Addition and © R e a d y E d P u bl i cat i ons Subtraction Mental Mania 1 & 2 These eight problems can be set as an This set of 40 questions can be used • f or r ev i ew puassignment r pos es n • task and o used asl ay measure as a timed activity if desired. This of students’ progress in this unit of work. It will enable students to demonstrate their ability to work mathematically and solve worded problems.

m . u

w ww

should be completed after Mental Strategy 1 and Mental Strategy 2 and it is worth spending time beforehand reminding students of the different mental strategies that they can use. You could allow less able students to use written methods for the last half of the questions.

. Real Life t Addition e o c . che e r o t r s super

Add or Subtract?

* Task a

Fill in each of the empty boxes to make each calculation true.

d. 124 − 6 =

a. 24 + 5 =

+ 6 = 124

− 5 = 24

e. 430 + 50 = r o e t s B r e o 480 − = 430 30 + = 40 p o u k S f. 1110 − 200 = c. + 3 = 42

ew i ev Pr

Teac he r

− 10 = 30

+ 200 = 1110

− 3 = 39

Describe what you notice in each of the calculations above:

______________________________________________________________ ______________________________________________________________

© ReadyEdPubl i cat i ons Sometimes when we need to subtract, it is easier to do addition instead. * •f Fillr in the empty boxes circles to help you calculate these o r e vi e wandp ur p os e son l ysubtractions. • Task b

The first one has been done for you.

25 − 17 = 17

53 − 36 =

w ww

+ 3 + 5

= 3 . t e

87 − 28 = 28 + =

+ 5 =

o c . che e 72 − 47 = r 30 80 7 o r st super

m . u

= 59

+ =

Task c: Personal Challenge * Describe and show how you would calculate 257 + 1 340 using a written method.

Describe and show how you would calculate 847 – 260 using a written method. 27

Mental Strategy 1a Fill in each of the empty boxes to help you add these two digit numbers together. Look at how the first calculation has been done. The 23 has been split into 20 ones plus 3 ones.

45 + 23

E.g.

32 + 27

= 45 + 20 + 3

= 32 +

= 65 + 3

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

53 + 34

87 − 21 = 87 −

−

66 − 14 =

−

78 − 25 =

. te

56 + 23

−

+ 30 + 3

w ww

−

65 + 33 =

−

95 − 73 =

−

m . u

ew i ev Pr

Teac he r

= 68

82 + 17

−

o c . che35 + 47 e r o t r s 89 − 32 super =

−

Mental Strategy 1b Fill in each of the empty boxes to help you add these three digit numbers together. Look at how the first calculation has been done. The 142 has been split into 100 ones plus 40 ones plus 2 ones.

325 + 142

510 + 120

r o e t s r + + B = − e o p ok u = − S = +

= 325 + 100 + 40 + 2

= 425 + 40 + 2

= 467

795 − 342 =

−

− −

998 − 452 =

−

= − − = © +Ready Ed Pu bl i ca t i o−ns − + f = w p − u = o −l y• • orr evi e r poses n +

w ww

821 + 237

473 + 215

ew i ev Pr

Teac he r

= 465 + 2

678 − 123

. te+

546 − 423 =

−

m . u

E.g.

742 + 435 =

o c . che = − = + e r o t r s s r u e p = = =

−

Task c: Challenge your partner * Write twenty calculations, similar to those above, for your partner to try using their mental

mathematics skills. When they are finished mark their work.

Mental Strategy 2

* Task a: Bridging to 10

Fill in the empty boxes and circles to help you calculate these subtractions. The first one has been started for you. a

36 − 13 = 13 +

45 − 28 =

+ + + r o e t s B r e o p = + u= 23 +o = k S

62 − 37 =

93 − 45 =

+ +

ew i ev Pr

Teac he r

© ReadyEdPubl i cat i ons * Fill in the empty boxes and circles to help you calculate these subtractions. • f o r r e v i e w p u r p o s e sonl y• The first one has been started for you. Task b: Bridging to 100

320 − 180 = 180 200 300 320

w ww +

+ . te

431 − 145 =

+ =

+ +

670 − 190 =

= 140

m . u

o c . ch e 732 − 384 = 400 r er o t s s r u e p + + + + d

Group Challenge * Small In a group of three or four students, plan and develop your own mental maths game. Write down the rules and how a player wins the game. When you are finished, try out the game on another group in your class. 30

Mental Mania 1 Use the different mental strategies you’ve learnt to calculate each of the following.

24 + 32

21. 55 – 27

16 + 82

22. 41 + 77

76 – 15

Teac he r

r o e t s Bo r 86 – 22 e 24. 73 – 55 p ok u 21S + 45 25. 83 + 54

23. 35 + 48

26. 22 + 78

12 + 47

27. 92 – 57

19 – 11

28. 43 – 25

33 + 46

29. 84 – 47

ew i ev Pr

95 – 73

eadyEdPub l i c at ons 10. © 72 R + 17 30. 75 +i 42

•f orr evi ew pur posesonl y• 31. 23 + 10 + 45

12. 89 – 15

32. 32 + 51 + 12

w ww

13. 24 + 31

m . u

11. 67 – 42

33. 58 + 27

34. 53 -24 . t e– 14 15. 78 35. 68 – 11c –o 25 . ce e r 16. 58 + 41 h 36. 87 o – 12 – 35 r st super 14. 67 + 12

17. 88 – 56

37. 84 + 32

18. 32 + 47

38. 74 – 36

19. 94 – 33

39. 95 – 49

20. 43 + 35

40. 62 – 47 31

Mental Mania 2 Use the different mental strategies you’ve learnt to calculate each of the following.

110 + 54

21. 435 + 225

368 – 20

22. 782 + 516

452 +105

785 – 203

Teac he r

r o e t s r 24. B 238 + 491 e o p o u k 623 + 111 25. 549 + 625 S

23. 637 + 271

26. 754 – 236

124 + 345

27. 887 – 293

587 – 365

28. 945 – 762

784 + 213

29. 672 – 538

ew i ev Pr

583 – 222

ReadyEdPu bl i ca i ons 10. 956© – 354 30. 453 –t 236

•f orr evi ew pur posesonl y• 31. 542 + 813

12. 864 – 741

32. 775 – 491

w ww

13. 381 + 416

16.

33. 262 + 374

34. 995 – 128 . t o 324 +e 563 35. 724 + 269 c . c e r 120 + 235 + h 342 36. t 529 er o s – 381 super

14. 659 – 325 15.

m . u

11. 252 + 345

17. 550 + 235 – 162

37. 341 + 923

18. 895 – 342 – 121

38. 462 – 225

19. 234 + 421 + 534

39. 246 + 671

20. 688 – 432 – 144

40. 949 – 362

Real Life Addition Task a * 1

Answer each of these word problems and be sure to show how you got your answer. 2

If James has $25 and Melissa has $32 more than James, how much does Melissa have?

r o e t s Bo r e p ok u S In the summer months the Brett and Susie are going on a 4

ew i ev Pr

Teac he r

The Kirtz family drank 5423 mL of milk last week and this week they’ve drunk 2374 mL of milk. How much milk have they drunk in two weeks?

Bradley household uses 742 units of electricity and in the winter months they use 595 units of electricity. How much have they used altogether?

holiday. They drive 175 km from Perth to Bunbury and then another 279 km. How far is the total journey?

. te

school there are 24 students in Year 1, 31 students in Year 2 and 29 students in Year 3. How many students are there in total in these three year groups?

m . u

w ww

Michael is 12 years older than Nicole. Nicole is 32 years older than Jamie. Jamie is 8 years old. How old is Michael?

o c . Max looks at his bank statement c e he r and sees that he spent $230 on o t r s super clothes, $157 on groceries and $75 on petrol. How much did he spend altogether?

Samantha is writing a story. On Monday she wrote 435 words, on Tuesday she wrote 240 words and on Wednesday she wrote 562 words. How many words has she written so far?

ask c: Research Challenge * TEach evening this week watch the weather report and write down the maximum and minimum temperatures for each day. How much did the temperature increase by each day this week? 33

Task a * 1

Real Life Subtraction Answer each of these word problems and be sure to show how you got your answer. 2

Jonathon is 12 years younger than Amy, who is 44 years old. How old is Jonathon?

r o e t s Bo r e p ok u S at SeaWorld. Martin is reading a book that has Jack has $50 to spend 4

Teac he r

A group of friends are playing Passthe-Parcel at Cynthia’s birthday. Cynthia’s mum wrapped the parcel 20 times and 7 layers of paper have been removed. How many layers are left?

ew i ev Pr

He has already spent $23. How much money does he have left to spend?

356 pages. So far he has read 125 pages. How many pages does he have left to read?

Task b Answer eache of these word problems beu sureb to l show how youi got n yours answer. ©R ad yEdandP i c at o * 2 1 Tania is watching an YouTube f o e vi ew u r po seso l y• The Lims• have ar jarr of money in p

w ww

m . u

video which is 195 seconds long. She pauses the video and sees she has 80 seconds left to watch. How much has she watched already?

their kitchen with $75 in it. Lucy took $11, Mrs Lim took $22 and Mr Lim took $32. How much money is left in the jar?

. t The Dibley family haveo 25 000 On a particulare TV game show, c . MB of internet data to use each ch Team A has 125 points, Team B e r month. So far they have used o has 187 points and Team e C has t r s s r u e p 13 500 MB. How much do they 163 points. How many points does Team A need to beat Team B?

have left to use this month?

Challenge *Start Taskwithc:theResearch number 18 and add 9 to this number ten times. Each time you add 9, write down the number you get. What do you notice about these numbers? Start with the number 98 and subtract 9 from this number ten times. Each time you subtract 9, write down the number you get. What do you notice about these numbers? Does this always work? Investigate this with different starting numbers. 34

Real Life Addition and Subtraction Answer each of these word problems and be sure to show how you got your answer. 1

A set of triplets have just been born. Timothy weighs 2 200 grams, Teneille weighs 3 100 grams and Tash weighs 2 750 grams. How much do the triplets weigh altogether?

r o e t s Bo r e p ok u S 4

Rebecca’s dad is 186 cm tall. Rebecca is 55 cm shorter than her dad. How tall is Rebecca?

Sam and Emily are on the same team playing a computer game. Sam has scored 245 points and Emily has scored 223 points. Oliver and Jane are on the other team and Oliver has scored 195 points and Jane has scored 264 points. Which team is winning?

There are 18 433 cities and towns in the USA. Pierre has visited 125 cities and 62 towns. How many places hasn’t he been to in the USA?

w ww

m . u

There are 40 320 ways to arrange 8 people in a line for a photo. The fussy photographer has so far tried 280 different ways to arrange these 8 people. How many more ways can the photographer arrange these 8 people?

. te

ew i ev Pr

Teac he r

Michelle is writing a short story for her teacher. It has to be 1 200 words long. So far Michelle has written 865 words. How many more words does she need for her story?

o c . che e r o t r s r upe The McKay family are doing as Paul has 16 000 MB of space on his 8

1000 piece jigsaw puzzle. Kelly has completed 123 pieces of the jigsaw. Michael has completed 340 pieces of the jigsaw. Mr McKay has completed 238 pieces of the jigsaw. How many pieces do they have left to complete?

phone. He has used 8 200 MB for his photos, 4 300 MB for his songs and 245 MB for his phone list. How much space does he have left?

Teachers’ Notes

Multiplication and Division Multiply or Divide?

82 × 4 = 80 × 4 + 2 × 4

r o e t 320 B8 s r e o p ok 328 u S

Changing the Order

In this activity students will learn and explore that multiplication is commutative while division is not. There is also the opportunity for students to explore various multiples in Task C and you may like to extend this by asking them to do the same activity with numbers like 24 or 200.

Task B requires students to extend this idea to three digit numbers. For the first problem students would partition 143 into 100 + 40 + 3 before continuing with the multiplication. You may like to encourage students to follow the setting out as given in Task A. More able students may like to attempt these mentally.

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Teac he r

The idea behind these tasks is to make students aware that multiplication and division are the opposite of each other and are therefore complementary. To approach Task C you may like to have students watch this first as a class, and then in small groups allow them time to discuss the “faults” that they see in the explanations. Small groups can be encouraged to report their findings back to the class.

Task C is an excellent game to teach students their multiplication tables and multiples, and the multiples used to represent Fizz and Buzz can be changed each lesson to suit the focus of your multiplication practice.

. te

Mental Multiply 2

After students have completed Mental Multiply 1 this activity allows for more practice. Those students who are less able may like to work on some of these using written and visual strategies to consolidate their learning.

m . u

w ww

By grouping numbers into their 100s, 10s and 1s, students can more flexibly, effectively and easily multiply numbers mentally. This activity can be further supplemented with more multiplication practice and students can work on the problems mentally or with the written approach demonstrated.

o c Mental Division . che e r o r st super

This task demonstrates the method of portioning to simplify the multiplication calculations. In Task A we partition every two digit number and then calculate each sum using the distributive property.

Changing division questions into multiplication questions is a useful mental strategy. The activity serves to explicitly inform students that they can see multiplication as the inverse of division and use this to help make calculations easier. Task C exposes students to the effects of multiplying and dividing by powers of 10 and it may be an interesting task to explore further.

For example, if we wanted to calculate 82 × 4 we could set out our method as follows: 82 can be partitioned into 80 + 2. We then multiply each part by 4: 80×4 + 2×4 =320 + 8 =328 * If YouTube access is a problem, try KeepVid to download it first. 36

Teachers’ Notes

Multiplication and Division Divide, Times, Take, Bring Down

*Step 2: 5 × 1 = 5

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

As the title of this activity suggests, there are four steps involved in this process, which are to be followed in order until there are no more numbers left that we can divide into.

5 90

*Step 3:

9−5=4

5 90 5 5 90 − 5

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Teac he r

Long division is a useful method for dividing into larger numbers. This method is often more powerful than short division and helps students understand the relationship between multiplication and division. Students are unlikely to be able to attempt this activity without prior instruction and this activity is designed as extra practice if you should choose to teach your students this technique. This activity demonstrates how the process works and you might like to provide a few more examples to your class to help them consolidate the process.

*Step 1: 90 ÷ 5

*Step 4: Bring down the 0.

Repeat until you end up with zero.

5 90 − 5

5 90 − 5 40 40 0

So 90 ÷ 5 is 18

For example if we wish to use this method to divide 90 by 5 we would proceed as follows:

. te

m . u

w ww

Divide: We divide 9 by 5 and we get 1. We write this 1 above the 9. Times: We multiply the 5 by the 1. We get 5 and write it underneath the 9. Take: We subtract the 5 from the 9. We get 4 and write it underneath the 5. Bring Down: Now that the first part is complete, we bring down the next number, in this case the zero. We start the process again. Divide: We divide the 40 by 5 and we get 8. We write this beside the 1, on top of the division symbol. Times: We multiply the 8 by 5 and we get 40. We write this below the first 40. Take: We subtract 40 from 40 and we get 0. When our subtraction results in a zero we then know the process is complete (no remainders) and we have our answer. In this case, 18.

Asking each group to work on a selection of the problems and explain how they did them to the class is a useful way for students to consolidate how they know what they know. It also serves as a useful way for students to communicate mathematically and for students to share their methods.

o c . che e r o t r s super Real Life Division

These eight problems may be set as individual tasks or small group work tasks. Asking each group to work on a selection of the problems and explain how they did them to the class is a useful way for students to consolidate how they know what they know. It also serves as a useful way for students to communicate mathematically and for students to share their methods.

Multiplication or Division?

* Task A

Fill in each of the empty boxes to make each calculation true. 7

a. 14 ÷ 2 = 7 ×

= 14

b. 9 ×

= 18

d. 48 ÷

= 12 × 4 = 48

18 ÷

Teac he r

c. 6 ×

÷ 4 = 6

* Task B

36 ÷

ew i ev Pr

= 10 e. 30 ÷ r o e t s B r e ×o 3 = 30 = 9 p o u k S = 36 f. 4 × = 24 = 4

Fill in each of the empty boxes to make each calculation true.

d. 96 ÷

a. 120 ÷ 10 =

= 8

©=R120 eadyEdP8u×b l i ca i ons =t 96 •f orr evi ew pur posesonl y•

12 ×

e. 111 ×

w ww

c. 500 ÷

÷ 3 = 111

= 10

240 ÷

= 10

. te

× 50 = 500

= 333

f. 100 ×

m . u

b. 10 × 24 =

= 1000

1000 ÷ 100 =

o c . * Can you describe anything you see in the calculations above? cinteresting e her r o t s super ______________________________________________________________ Challenge * Task c: Small Group In a small group of 3 to 4 students watch the YouTube video of Ma and Pa Kettle doing Mathematics. You can use the link below. Watch carefully and discuss in your group who is doing the maths correctly. Is it Ma and Pa Kettle or is it their friend? Write down who was right and why. 4www.youtube.com/watch?v=Bfq5kju627c 38

Changing the Order

* Task a

Fill in the empty box to make each calculation true.

a. 2 × 3 × 8 = 3 × 2 ×

d. 3 ×

b. 6 ×

e. 10 ×

×5 = 2×5×

×7 =

×4×3

×4 = 4×2×

Teac he r

r o e t s Bo r f. ×2×5= 5×9× ×4 c. 4 × 5 × 1 = 5 × e p ok u S Task b Circle True or False for each question below. a

4×5 = 5×4

7÷2=2÷7

10 × 13 = 13 × 10

false True false © Re ady EdPub l i ca t i ons false True •f orr evi e ur poses nl y• e wp f o

200 ÷ 100 = 100 ÷ 200

w ww

True

15 – 7 = 7 – 15

True false

false

25 + 13 = 13 + 25

m . u

True

ew i ev Pr

True

false

. t einteresting you noticed about which calculations were Trueco Write down anything and which were False. . che e r ______________________________________________________________ o t r s s r u e p ______________________________________________________________ * Task c: Personal Challenge

Write the number 48 as the multiple of as many different numbers as you can. For example, 48 = 24 × 2 or 48 = 4 × 2 × 3 Compare your answers with your partner. 39

Mental Multiply 1

* Task A

Fill in each of the empty boxes to help you multiply each pair of numbers. In the first calculation you can see that the 42 has been split into 40 ones and 2 ones.

42 × 3

= 40 × 3 + 2 × 3 = 120 +

= 350 +

35 ×n 4s 73R×ea 6dy © Edf)Publ i c at i o ×f ×w p = p ×e +n • or+r evi e ur os so l y×•

= 120 + 20

w ww

* Task B

Try these sums using mental multiplication.

. te 143 × 2 =

m . u

= 60 + 18

ew i ev Pr

r o t = eB + s r e o p ok = u S d) 26 × 3 71 × 5

Teac he r

= 126

54 × 2

423 × 3 = o

c . che e r d) 231 o 512 × 6 = × t r s 4= super b)

* Task C: classPlayChallenge Fizz Buzz! The class stand in a circle. The first person (chosen by the teacher) says “one”, the Fizz Buzz

second person says “two” and so on. Whenever anyone has to say 3 or a multiple of three ( 6, 9, 12, etc.) they say Fizz instead. Whenever anyone has to say 5 or a multiple of 5 they must say Buzz instead. 15 and 30 will be Fizz Buzz. If someone says the wrong number or word, they are out and must sit down. The next person in line starts at “one” again.

Mental Mulitiply 2 Use the different mental strategies you’ve learnt to calculate each of the following.

2×3

21. 32 × 3

4×8

22. 43 × 2

5 × 11

Teac he r

r o e t s Bo r 7×6 24. 401 × 6 e p ok u 9 ×S 2 25. 52 × 4

23. 132 × 3

26. 17 × 3

5×9

27. 242 × 3

11 × 7

28. 623 × 4

7 × 12

29. 87 × 2

ew i ev Pr

13 × 10

•f orr evi ew pur posesonl y• 31. 432 × 6

12. 7 × 9

32. 514 × 7

w ww

13. 6 × 8

. t 9 ×e 6

m . u

11. 3 × 13

33. 83 × 4

14. 5 × 4

34. 97 × 5

15.

35. 352 × 8

16.

o c . c e r 7 × 10 h 36. 613 er o t s ×3 super

17. 15 × 10

37. 72 × 6

18. 261 × 10

38. 48 × 4

19. 485 × 10

39. 721 × 2

20. 1 238 × 10

40. 654 × 3 41

Mental Division

Task a

Sometimes it is easier to change a division question into a multiplication question. Fill in the empty boxes to change the division into a multiplication and then write the final answer. a. 40 ÷ 5 =

d. 36 ÷ 9 =

5 ×

= 40

9 ×

= 36

r o e t s Bo r e e. 132 ÷ 11 = o p u k =S 60 11 × = 132

So the answer is

b. 60 ÷ 12 =

So the answer is

c. 120 ÷ 10 =

f. 96 ÷ 8 =

= 120

10 ×

8 ×

So the answer is

= 96

So the answer is

ew i ev Pr

Teac he r

12 ×

So the answer is

42 ÷ 7

50 ÷ 5

= 42

w ww

7 ×

So the answer is

100

. te ÷ 5

27 ÷ 4

m . u

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

60 ÷ 20

48 ÷ 6

For this challenge you can use a calculator if you have one. ask c: Personal Challenge *• TInvestigate what happens to the numbers 23, 58 and • Investigate what happens to the numbers 58 000, 75

76 when you multiply them by 10, by 100, by 1000 and by 10 000. What do you notice? 42

000 and 3 600 when you divide them by 10, by 100, by 1000 and by 10 000. What do you notice?

Divide, Times, Take, Bring Down Look at this method of dividing numbers. It is called “Long Division”.

2 17 2

2 17 2 − 1 6

e r o t s B r 2 17 2 17 e o p o − − u k 2 17 S −

*Step 4: Bring down the 2. Repeat until you end up with zero. 8

*Step 2: 8 × 2 = 16 8

1 6 1 2

86 2 1 6 1 2 12 0

Try these division sums using the long division method. a

5 4 232 − 20

5 390

4 6 252

So 172 ÷ 2 is 86

ew i ev Pr

Teac he r

÷ × −

*Step 3: 17 − 6 = 1

*Step 1: 17 ÷ 2 = 8

3 84

w ww

. te

8 408

7 455

2 624

m . u

o c . che e r o t r s s per u h

4 304

7 441

Real Life Multiplication Answer each of these word problems and be sure to show how you got your answer. 1

Sally is making party bags for her friends to take home after her party. She puts 3 snake lollies in each bag and she has 27 friends coming to her party. How many snakes does she need altogether?

r o e t s Bo r e p ok u S 4

A new dress-up doll comes with 7 pairs of shoes and 32 dresses. How many different outfits can be made?

A bus can sit 4 people in each row. If there are 17 rows, how many people can have a seat on this bus?

Nick can type really fast. Each minute he can type 62 words. If he has been typing for 9 minutes, how many words has he typed?

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In a History multiple choice test you have 35 questions, each with 4 possible answers. How many possible answers are there in total?

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o c . che e r o t r shas only $10 and $20 upSamantha Matthew is making a rice dish s er 8

for some friends. It says he needs 2 cups of rice for 4 people. If he has 11 friends coming over, plus himself, how many cups of rice will he need? 44

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Seven friends decide to give $6 each to buy a present for their friend’s birthday. How much money do they have altogether?

notes in her purse. If she knows she has $440 in her purse and 8 $20 notes, how many $10 notes does she have?

Real Life Division Answer each of these word problems and be sure to show how you got your answer. 1

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A family needs to take 21 Litres of drinking water on a camping trip. How many 3 Litre bottles will they have to take to make sure 3 L they have enough?

Robert has 64 DVDs that he wants to put in his DVD shelves. If he can fit 16 DVDs on one shelf, how many shelves does he need?

Each week Craig’s parents give him $7 for doing his chores. How many weeks will he need to do chores to save up enough money to buy a $56 computer game?

Billy has lived in his new house for 126 days. How many weeks is this?

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Miss Thompson has 30 students in her Year 3 class. She wants to arrange the desks in groups of 5. How many groups does she need?

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Michaela needs to make 48 cupcakes. She only has one cupcake tray with 12 spaces for cupcakes. How many times does she need to use this tray?

o c . che e r o t r s r upe Nicole needs to write a 1 500 s word 126 people are waiting in line to 8

report for her science project. If she uses 6 pages to write her report, how many words were on each page?

ride the Ferris Wheel. If only 14 people can be on the ride each time, and all these people want two rides on the Ferris Wheel, then how many how many rides will it take to make all these people happy?

Teachers’ Notes

Fractions Cutting up the Cake

Students can be encouraged to draw and divide up their own rectangles in order to determine which fraction is the largest. With Task C it may be better to allow students some time to discuss amongst themselves the order of their fractions and you may like to intervene to keep them on the right track.

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

Colour the Fraction

While similar to many activities on shading fractions of areas, the rectangles in Task A and Task B are often not divided into enough slices or are divided into too many slices. The concept of similar fractions can be taught here. For example in Task A, when students shade 4/9 they will also find this is the same as 8/18 . You may like to provide students with grid paper to complete Task C.

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With this activity students will gain a sound understanding of the role of the numerator and the denominator in a fraction. Task C can be extended further by examining the pattern to be found in the number of equal pieces folded in the piece of paper each time.

Which is Larger?

Which of these are the same?

This is a useful way for students to explore the concept of equivalent fractions. Students can be encouraged to draw their own rectangles when working on Task B to further consolidate their learning. Task C can be a mini project and students may like to present their findings on a poster and perhaps present their findings to the class.

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o c . che e r o Fractions in Real t r s Life super

Students become aware through this activity that fractions aren’t only used to divide up areas but also to group and divide objects. Task C can be made more active by asking students to divide the class in half, or in quarters, or in thirds. Or it could be like a game of musical chairs, where if you have 21 students in your class and you ask them to divide into quarters, one person will “get out”.

“Are these the same?” as it depends on an understanding of equivalent fractions. Students are to be encouraged to change each set of fractions to have the same denominator so as to make the task easier to visualize. You may like to explain the game of “Snap” for students who have never heard or seen the game played. Those students who are very confident with equivalent fractions will be able to play this game with some speed.

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This activity helps inform students that many 2D and 3D shapes can be sliced up into fractional amounts. Students may find it helpful to use a ruler for this task or to handle some tangible objects to assist them with their understanding of 3D objects. Task C can be set as a small homework task.

These eight problems may be set as individual tasks or small group work tasks. Asking each group to work on a selection of the problems and then explain how they did them to the class is a useful way for students to consolidate how they know what they know. It also serves as a useful way for students to communicate mathematically and for students to share their methods.

Cutting up the Cake Task a * 3 Toby serves his friends of a cake. This means he cuts the cake into 8 8

equal slices and served 3 slices to his friends. Fill in the following table:

3 8

How much cake has been served 4 7 1 6 12 10

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Write each of the following situations as a fraction.

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r o e t s B r e oo Number of equal slices p 8 u k S How many slices were served. 3

4 15

Natalie slices her lasagna into twelve equal pieces and serves 7 pieces to her family.

John divides his chocolate bar into 5 equal pieces and gives his brother 2 pieces.

eat?

John have?

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Kate divides her garden bed into 8 equal areas and plants herbs in the first three areas.

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Mr Williamson divides his students into 9 equal groups. Four of the groups are allowed to leave class early.

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What fraction of the garden bed has herbs planted?

What fraction of the class are not allowed to leave class early?

Task c: Personal Challenge * Take a piece of paper and fold it in half. How many equal pieces do you have?

Fold it in half again. Now how many equal pieces do you have? Fold it in half again. Now how many equal pieces do you have? Fold it in half as many times as you can. What’s the highest number of equal pieces you can have from folding the paper? 47

Colour the Fraction

* Task a

1 6

Look at each shaded diagram and write down the fraction that is shaded.

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* Task b

2 5

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Shade each of the following fractions on the diagrams:

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Task c: Challenge Your Partner * Create four of your own shaded grids (you may like to use grid paper) similar to those in Task B above.

See if your partner can give you the correct fraction for each of your grids. 48

Slice it up

* Task a

Slice up each of these shapes into the correct number of equal parts and shade the amount to be shared.

a) 2

b) 1

c) 2

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d) 3

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c) 3

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a) 5

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Task c: Personal Challenge * When you get home, look in your fridge and estimate each of these fractions.

• Estimate the fraction of milk left in the carton. • Estimate the fraction of soft drink left in the bottle. • Estimate the fraction of jam left in the jar. 49

Share Them

* Task a

How many does each person get if:

a) we share these among 5 people?

r o e t s Bo r e p o u we share these among 3 people? we share these amongk 6 people? S d)

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b) we share these among 4 people?

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c) 100 stickers amongst 20 people?

d) 450 plates amongst 75 people?

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Task c: class challenge * How many ways can you divide up your class into

equal small groups of students? Try to think of as many as possible. What fraction of students is in each group? 50

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many does each person get if we share: * Task b How © ReadyEdPubl i cat i ons a) 36 biscuits amongst 9 people? b) 60 balloons amongst 15 people? •f orr evi ew pur posesonl y•

Which is Larger?

* Look at the pairs of fractions below. Which is larger? Circle the correct answer. Task A

You may like to draw your own rectangles to help work this out. Look at the first example. a)

1 5

1 4

1 5

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1 3

1 9

1 is larger! 3

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1 = 3 1 = 4

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Task B Circle which pair of fractions are the same. © R e a d y E d P u b l i c a t i o n s * a b c 3 1 2 5 3 7 or or or or evi ew12pur p12oseson y• 5 4 •f 4r 5l

2 9

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2 6

Challenge * Task C: class Think of a fraction, any fraction, with a denominator of either 2, 4, 8, 16, 32 or 64. Write your fraction nice and large on a piece of A4 paper. Everyone in the class has to line up in order from the smallest fraction to the largest fraction. Be sure to help your classmates get the order right! 51

Which of these are the same? Task A * Shade each of these fractions and decide if they are the same fraction. a)

1 3

and

1 2

and

3 4

1 2

and

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4 8

1 = 3 2 = 6

4 5

and

3 9

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The same! d)

2 6

and

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1 5 1 2 2 6

and

2 10

1 2

and

2 4

1 3

5 10

2 7

and

3 14

8 10

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and 50 100

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* Task c: Research Challenge

In small groups of 3 or 4 students, research “Equivalent Fractions”. Write a half page report on what Equivalent Fractions are and use pictures and diagrams to help explain what you mean. Make sure you give some examples of pairs of equivalent fractions. Present your report to the class.

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Fractions on a Line Task a * Divide this line into 8 equal sections. Place each of these fractions on the right spot on the line. 3

A: 8

B: 8

C: 2

D: 4

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r o e t s Bo r e Divide this line into 10 equalp sections. Place each of these fractions on the orightkspot on the line. u 4 1 9 3 11 S A: 10 B: 10 C: 5 D: 4 E: 12 * Task b

Draw a line and divide it into 9 equal sections so that you can place each of these fractions on the right spot on the line.

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1 A: 6

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Draw a line and divide it into 12 equal sections so that you can place each of these fractions on the right spot on the line. 5

A: 12

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C: 12

D: 4

E: 12

c: Small group challenge *In Task a group of 3 or 4 students you will make a pack of cards to use to play “Snap”.

Make up 20 cards, and on each card write a fraction that has a denominator of 2, 3, 4, 6, or 12. The numerator can be any number smaller than the denominator. It will be played like the normal game of “Snap”, but instead of having matching cards, you need matching fractions (fractions that are equivalent).

snap! 53

Fractions in Real Life Answer each of these word problems and be sure to show how you got your answer. a

Mrs Clarence has 30 desks in her classroom and she puts 5 desks in each group. Four groups of desks is what fraction?

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Lilly and Billy are sister and brother. Lilly says to Billy “Mum gave me 14 of the chocolate biscuits!” Billy says 2 to Lilly “Mum gave me 8 of the chocolate biscuits!” Mum says “I gave you both the same amount!”. Is Mum right? Why?

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George has 50 bricks and stacks them into groups of 10. Three groups of bricks is what fraction?

Billy says to Lilly “I swam in the pool 3 for 4 of an hour and you only swam 4 in the pool for 5 of an hour. I swam longer than you!” Is Billy right? Why?

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. te40 books into 8 Josie stacked her Timmy’s Mum says he can watch o cmany equal piles. How many books does of an hour of TV. How . c e represent? is Timmy allowed to watch? her minutess r o t super

5 8

3 5

Answers Numeration

f. Two thousand four hundred and fifty eight Task B a. Twelve thousand four hundred and fifty seven b. Thirty five thousand and one c. Sixty four thousand three hundred and five d. Eight thousand and forty two e. Twenty six thousand and eighty nine f. One hundred and ten thousand, three hundred and ninety five

Numbers in a Row, p11 Task A a. 1, 4, 6, 8, 9, 10, 12, 15, 19 b. 17, 19, 24, 33, 35, 42, 50, 63, 72, 91 c. 27, 72, 207, 270, 702, 720, 727 Task B a. 92, 88, 80, 57, 51, 45, 31, 30, 24, 17, 14 b. 960, 840, 810, 720, 630, 590, 420, 370, 340, 110 c. 872, 827, 782, 754, 745, 621, 612, 361, 351, 315 Place Value d. 423, 342, 321, 241, 234, 231, Numbers in Columns, p17 214, 213, 142, 123 Task A 302, 1204, 952, 3001, 12 367 Measuring Numbers, p12 457, 3 123, 92, 271, 15 235 Task A Task B Teacher to check a.3, b.0, c.5, d.2 Task b

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How Many Hundreds Are There? p8 Task A 431 = CCCC + XXX 688 = CCCCCC + XXXXXXXX 199 = C + XXXXXXXXX 912 = CCCCCCCCC + X Task B 275 = CC + XXXXXXX 587 = CCCCC + XXXXXXX 398 = CCC + XXXXXXXXX 765 = CCCCCCC + XXXXXX

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How Many Tens Are There? p7 Task A 24 = XX + IIII 17 = X + IIIIIII 85 = XXXXXXXX + IIIII 92 = XXXXXXXXX + II 52 = XXXXX + II 76 = XXXXXXX + IIIIII Task B 7 = IIIIIII 32 = XXX + II 46 = XXXX + IIIIII 71 = XXXXXXX + I

34 - Thirty four 1203 - One thousand two hundred and three

tod check © ReadTeacher yE Publ i ca t i ons How Many Are There? p18 Task A Large Numbers, p13 •f orr evi e w p u r p o s e s o n87l y• a. 23, 104, Task A 1

124

1243

350

7028

702

7028

4389

438

4389

13437 13

134

1343 13437

Words to Numbers, p10 Task A a.17, b.45, c.106, d.89, e.723, f.90, g.413 Task B 72 - Seventy two 301 - Three hundred and one 512 - Five hundred and twelve

Numbers to Words, p14 Task A a. Fifty seven b. Two hundred and eighty two c. One thousand and fifteen d. Eight hundred and twenty three e. Seven hundred and sixteen

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Task B a. 2455, 2545, 2554, 3278, 3287, 6023, 6302, 9580, 10420 b. 10267, 10627, 11351, 11531, 12368, 13268, 15921, 19521 c. 56712, 57126, 67215, 67512, 75126, 75621, 76215, 76512

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b. 40, 23, 87 c. 1, 4, 23 Task b a. 6, 17, 125 b. 5, 38, 68 c. 3, 10, 8, 45

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Numbers in Cubes and Colour, p9 Task A 83 has 8 completely coloured MSB blocks plus 3 individual cubes of the 9th block. 57 has 5 full rows or columns coloured plus 7 individual cubes of the 6th row or column Task B 462 = 4, 6, 2 63 = 0, 6, 3 897 = 8, 9, 7 374 = 3, 7, 4

Describing the Number, p19 Task A 5 tens 324 ones, 3 hundreds 85 tens, 8 hundreds 2351 ones, 2 thousands 724 tens, 72 hundreds Task b 72 ones, 7 tens 634 ones, 63 tens, 6 hundreds 215 ones, 21 tens, 2 hundreds 2310 ones, 231 tens, 23 hundreds, 2 thousands

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Different Groupings, p20 Task A a. 9 hundreds plus 23 ones 55

b. 20 tens plus 3 ones 2 hundreds plus 3 ones c. 1 thousand plus 36 tens plus 2 ones 13 hundreds plus 62 ones 136 tens plus 2 ones d. 30 hundreds plus 67 ones 3 thousands plus 6 tens plus 7 ones 306 tens plus 7 ones Task b a. 2 groupings b. 4 groupings c. 4 groupings d. 6 groupings

Grouping Numbers for Addition, 22 45+23 6X+8I = 68 72+15 7X+1X+2I+5I = 8X+7I=87 65+27 6X+2X+5I+7I=8X+12I=9X+2I=92 48+39 4X+3X+8I+9I=7X+17I=8X+7I=87 82+95 8X+9X+2I+5I=17X+7I=177 214+35 1X+3X+4I+5I=24X+9I=2C+4X+9I=249

Mental Strategy 1a, p28 a. 32 + 20+7 =52+7= 59 b. 82 + 10+7 =92+7= 99 c. 53 + 30+4 = 83+4=87 d. 87 – 20-1 =67-1= 66 e. 66 – 10-4 =56-4 = 52 f. 65 + 30+3=95+3= 98 g. 78 – 20 – 5=58 -5 = 53 h. 95 – 70 – 3=25 - 3 = 22 i. 79 j. 82 k. 57

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What’s the Number? p21 Task A a.125, b.327, c.2543, d.42, e.367, f.7812 Task b a.56, b.43, c.5, d.230, 4, e.4, 6

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Task a a. 29 b. 40, 10 c. 39, 42 d. 118, 118 e. 480, 50 f. 900, 900 Task b b. 53 – 36 = 4 + 10 + 3 = 17 c. 87 – 28 = 2 + 50 + 7 = 59 d. 72 – 47 = 3 + 20 + 2 = 25

Strategy 1b, p29 © ReadyEdMental bl i c at i o s a.P 510u + 100+20 =610+20= 630n b. 678 – 100-20-3 =578-20-3=558-3= 555 •f orr evi ew pc.u r p ose onl y• 473 +200+10+5 =s 673+10+5=683+5= 688

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Addition and Subtraction

Mental Strategy 2, p30 Task A a. 7 + 10 + 6 = 17 + 6 = 23 b. 2 + 10 + 5 = 12 + 5 = 17 c. 3 + 20 + 2 = 23 + 2 = 25 d. 5 + 40 + 3 = 45 + 3 = 48 Task b a. 20 + 100 + 20 = 120 + 20 = 140 b. 10 + 400 + 70 = 410 + 70 = 480 c. 55 + 200 + 31 = 255 + 51 = 286 d. 16 + 300 + 32 = 316 + 32 = 348

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Estimation, p24 Task A b. 32 + 11 = 30 + 10 = 40 c. 79 – 19 = 80 – 20 = 60 d. 151 + 39 = 150 + 40 = 190 e. 289 – 32 = 290 – 30 = 260 f. 531 – 49 = 530 – 50 = 480 Task b a. 60 b. 60 c. 380 d. 800

Add or Subtract, p27

d.795 – 300-40-2 =495-40-2=455-2= 453 e.998 – 400-50-2 =598-50-2=548-2= 546 f.821 + 200+30+7=1021+30+7=1051+7 = 1058 g. 546 – 400-20-3= 146-20-3=126-3 = 123 h. 742 + 400+30+5=1142+30+5=1172+5 = 1177

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Grouping Numbers for Subtraction, 23 76-32 4X+4I=44 85-21 8X-2X+5I-1I=6X+4I=64 234-51 23X-5X+4I-1I=18X+3I=183 758-46 75X-4X+8I-6I=71X+2I=712 53-25 5X-2X+3I-5I=2X+13I-5I=2X+8I=28 451-67 45X-6X+1I-7I=38X+11I-7I=38X+4I=384

Mental Mania 1, p31 1.56 21.28 2.98 22.118 3.61 23.83 4.64 24.18

25.137 26.100 27.35 28.18 29.37 30.117 31.78 32.95 33.85 34.29 35.32 36.40 37.116 38.38 39.46 40.15

Task A 1. 44 – 12 = 32 years old 2. 20 -7 = 13 layers 3. 50 – 23 = $27 4. 356 – 125 = 231 pages Task b 1. 75 – 11 – 22 – 32 = $10 2. 195 – 80 = 115 seconds 3. 187 – 125 = 62, so 63 points 4. 25 000 – 13 500 = 11 500 MB

a. 143 × 2 = 286 b. 423 × 3 = 1269 c. 512 × 6 = 3072 d. 231 × 4 = 924 Mental Multiply 2, p41 1.6 21.63 2.32 22.86 3.55 23.396 4.42 24.2406 5.18 25.208 6.130 26.51 7.45 27.726 8.77 28.2492 9.84 29.174 10.24 30.470 11.39 31.2592 12.63 32.3598 13.48 33.332 14.20 34.485 15.54 35.2816 16.70 36.1839 17.150 37.432 18.2610 38.192 19.4850 39.1442 20.12380 40.1962

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Mental Mania 2, p32 1.164 21.660 2.348 22.1298 3.557 23.908 4.582 24.729 5.734 25.1174 6.361 26.518 7.469 27.594 8.222 28.183 9.997 29.134 10.602 30.217 11.597 31.1355 12.123 32.284 13.797 33.636 14.334 34.867 15.887 35.993 16.697 36.148 17.623 37.1264 18.432 38.237 19.1189 39.917 20.112 40.587 Real Life Addition, p33 Task A 1. 25 + 32 = $57 2. 5423 + 2374 = 7797 ml 3. 742 + 595 = 1337 units 4. 175 + 279 = 454 km Task b 1. 8 + 32 + 12 = 52 years old 2. 24 + 31 + 29 = 84 students 3. 230 + 157 + 75 = $462 4. 435 + 240 + 562 = 1237 words

Real Life Addition and Subtraction, p35 1. 1200 – 865 = 335 words 2. 2200 + 3100 + 2750 = 8050 g 3. 186 – 55 = 131 cm 4. 245 + 223 = 468 195 + 264 = 459 Sam and Emily 5. 18433 – 125 – 62 = 18246 places 6. 40320 – 280 = 40 040 ways 7. 1000 – 123 – 340 – 238 = 299 pieces 8. 16000 – 8200 – 4300 – 245 = 3255 MB

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5.66 6.22 7.59 8.8 9.79 10.89 11.25 12.74 13.55 14.55 15.64 16.99 17.32 18.79 19.61 20.78

Task b a.12,10 b.240,24 c.50,10 d.12, 12 e.3, 333 f.10, 10

a.8, b.5, c.12, d.4, e.12, f.12 Task b a.6, b.10, c.7, d.20, e.3, f.8

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Multiplication or Division? p38 Task A a.2 b.2,2 c.4,24 d.4,12 e.3,10 f.9,9

Divide, Times, Take, Bring Down, p43 a. 58 b. 42 c. 28 d. 78 e. 65 f. 312 g. 51 h. 76 i. 63

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Real Life Subtraction, p34

Changing the Order, p39 Task A a.8 b.2,6 c.1 d.4,7 e.2,10 f.9,2 Task b T, F, T, F, F, T Mental Multiply 1, p40 Task A b.50 × 2 + 4×2 =100+8= 108 c.20 × 3+6×3= 60+18 = 78 d.70 × 5+1×5 =350+5= 355 e.70 × 6+3×6=420+18 = 438 f.30 × 4+5×4=120+20 = 140 Task b

Real Life Multiplication, p44 1. 7 × 6 = $42 2. 27 × 3 = 81 snake lollies 3. 7 × 32 = 224 outfits 4. 17 × 4 = 68 people 5. 62 × 9 = 558 words 6. 35 × 4 = 140 answers 57

7. 3 × 2 = 6 cups of rice 8. 28 $10 notes

b. 1/4 c. 1/3 d. 1/10 e. 1/2 f. 1/6 Task b a. 3/4 b. 7/12 c. 5/5 d. 4/6 e. 5/8 f. 2/6

Real Life Division, p45 1. 48 ÷ 12 = 4 times 2. 30 ÷ 5 = 6 groups 3. 21 ÷ 3 = 7 bottles 4. 64 ÷ 16 = 4 shelves 5. 56 ÷ 7 = 8 weeks 6. 126 ÷ 7 = 18 weeks 7. 1500 ÷ 6 = 250 words 8. 18 rides

Fractions

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Task b a. 7/12 b. 3/5 c. 3/8 d. 5/9

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Colour the Fraction, p48 Task a Teacher to check Task B a. 4/8 b. 6/16 c. 1/3 d. 3/8 e. 6/16 f. 6/20 Slice it up, p49 Task a Teacher to check Task b Teacher to check

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Share Them, p50 Task a a.2, b.3, c.3, d.4 Task b a.4, b.4, c.5, d.6 Which is Larger? p51 Task a a. 1/3 58

Teacher to check Task b Teacher to check

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Cutting up the cake, p47 Task a Number of 8 12 10 6 15 equal slices

Which of these are the same? p52 Task a b. Not the same c. Same d. Not the same e. Same f. Same Task b a.1/5 and 2/10 b.1/2 and 2/4 d.1/2 and 5/10 f.8/10, and 16/20 h.25/50 and 50/100

Fractions in Real Life, p54 a. 3/5 b. 4/6 c. Yes, ¼ = 2/8 d. No, ¾ < 4/5 e. 25 books f. 36 minutes

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