Number and Place Value

Ages 7–9

Number and

place value hun

dred

6

s te ns

10 9 8 7 20 6 9 5 1 4 18 7 3 1 6 30 2 1 9 5 2 1 41 28 1 7 3 2 1 6 40 2 2 1 9 5 1 3 1 42 38 2 7 3 3 6 50 22 3 2 9 5 1 4 2 43 48 3 7 3 4 60 23 46 3 9 5 1 5 4 3 4 58 4 7 3 5 70 24 56 4 9 5 1 6 5 4 68 54 7 3 6 5 80 2 66 5 9 5 1 7 6 5 78 64 7 3 7 6 6 90 2 7 6 9 5 61 88 47 8 7 7 3 7 00 68 2 1 8 7 9 5 71 89 48 9 8 7 3 69 2 8 1 10 3 9 8 5 1 8 49 5 9 3 2 3 29 9 1 9 5 ones

2 8

hund

reds

tens

ones

hund

reds

tens

Jamie Fraser

RIC-6029 5/5

ones

NUMBER AND PLACE VALUE (Ages 7–9)

Copyright Notice Blackline masters or copy masters are published and sold with a limited copyright. This copyright allows publishers to provide teachers and schools with a wide range of learning activities without copyright being breached. This limited copyright allows the purchaser to make sufficient copies for use within their own education institution. The copyright is not transferable, nor can it be onsold. Following these instructions is not essential but will ensure that you, as the purchaser, have evidence of legal ownership to the copyright if inspection occurs.

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For your added protection in the case of copyright inspection, please complete the form below. Retain this form, the complete original document and the invoice or receipt as proof of purchase.

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Published by Didax, Inc. 2005 Revised and reprinted under licence by R.I.C. Publications® 2006 Copyright© Jamie Fraser 2005 ISBN-10 1-74126-530-4 ISBN-13 978-1-74126-530-9 RIC–6029

This master may only be reproduced by the original purchaser for use with their class(es). The publisher prohibits the loaning or onselling of this master for the purposes of reproduction.

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It is strongly recommended that the class teacher checks all URLs before allowing students to access them.

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Foreword

Contents

Number and place value has been designed to provide students with hands-on investigations to develop a clear understanding of numbers and the place value system.

This resource provides teachers with:

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clear, step-by-step guidance through each lesson

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clear objectives

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activities broken down into an introduction, the lesson and the summary or conclusion to the lesson

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concise materials list for each lesson to aid with preparation

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appropriate grouping of the class to maximise learning

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activity cards suitable for learning centres or extended learning programs

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C.Publ i cat i ons assessment evaluation •andf o rr evi ew pur posesonl y• materials

answers, for ease of marking

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a collection of useful generic resources which can be photocopied and used where appropriate.

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Introduction Introduction ..................................................................................................................... ii Overview .......................................................................................................................... iii Getting started ..................................................................................................................iv Assessment ........................................................................................................................ vi Unit 1 Lesson 1: Sort of different ................................................................................................. 1 Lesson 2: Snap to it ........................................................................................................... 3 Lesson 3: Snap to it – 2 ....................................................................................................6 Lesson 4: How tall are you? ..............................................................................................9 Lesson 5: Race of the century ......................................................................................... 12 Assessment ....................................................................................................................... 14 Show what you know ...................................................................................................... 15 Activity cards ...................................................................................................................17 Unit 2 Lesson 1: Keep in balance ..............................................................................................18 Lesson 2: One and the same ...........................................................................................22 Lesson 3: Flat out ............................................................................................................ 24 Assessment ....................................................................................................................... 26 Activity cards ...................................................................................................................27 Unit 3 Lesson 1: Know your place .............................................................................................28 Lesson 2: Head count ...................................................................................................... 31 Lesson 3: Squeeze play.................................................................................................... 33 Lesson 4: Monkey in the middle ....................................................................................37 Lesson 5: Three in-a-row ................................................................................................ 43 Lesson 6: Puzzling ..........................................................................................................47 Lesson 7: Tetra hunt ....................................................................................................... 48 Assessment ....................................................................................................................... 52 Show what you know ...................................................................................................... 53 Activity cards ...................................................................................................................55 Unit 4 Lesson 1: Centiworms .....................................................................................................57 Lesson 2: See you tomARROW........................................................................................ 61 Lesson 3: Metre made .....................................................................................................64 Lesson 4: Squeeze the wash ............................................................................................67 Lesson 5: Lay it on the line.............................................................................................71 Assessment ....................................................................................................................... 75 Show what you know ...................................................................................................... 76 Activity cards ...................................................................................................................78 Mathmasters Mathmaster 1: Big idea icons .........................................................................................80 Mathmaster 2: Ten frames..............................................................................................81 Mathmaster 3: Number cards/tiles.................................................................................82 Mathmaster 4: Place value mat ..................................................................................... 84 Mathmaster 5: Place value cards ...................................................................................85 Mathmaster 6: Charts and grids .....................................................................................88 Mathmaster 7: Blank hundreds chart ............................................................................ 89 Mathmaster 8: Bingo card ..............................................................................................90 Mathmaster 9: Centiworms ............................................................................................91 Mathmaster 10: Number lines .......................................................................................92

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i

Introduction As adults, we have worked, played and experimented with numbers all our lives. Over this extended period, we have slowly internalised the underlying principles and patterns in our numeration system, building an intuition we call ‘number sense’. Children lack this experience.

The intent of this program is to provide children with hands-on investigations, along with appropriate time for reflection to discover the underlying principles that provide structure to our system of organising numbers. These principles described below are called the ‘Big ideas’ of number and place value throughout this resource.

THE ‘BIG TEN

IDEAS’

KNOW

POWER

The fact that we can build any number imaginable with only ten digits is incredibly powerful, efficient and beautiful. This is possible because the value of a digit is determined by its place in a number. What proves so wonderful for adults can be confusing for children. A child who is still developing a sense of the magnitude of ‘5’ as one more than ‘6’, two less than ‘7’, half of ‘ten’, the age of a friend etc. may find it hard to believe that 5 can also be 50 or 500.

Lessons reinforce the notion that a digit can have many different values, depending on where it is found in a number.

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Ours is a decimal numeration system. Many speculate that the convention is a result of our having ten fingers. Regardless of its origin, the number ‘ten’ as a base is strictly a convention, not a natural law, readily apparent to children.

Children see a variety of bases for counting in their lives: the base of 7 for counting weeks; the base of 12 and 60 in measuring time (seconds, minutes, hours, months) etc..…

They need time to learn that ten is the base we use for expressing numbers.

The lessons have been designed to provide visual evidence that our number system is organised around patterns of ten. When we count, we form new groups based on the number ten—ten units become one group of ten, ten groups of ten become one hundred and so on.

YOUR PLACE

SPEAK IN PATTERNS AND RELATIONSHIPS

There are patterns to the way our numbers are formed that provide order and predictability for children, but these patterns take time to be discovered and internalised. In this program, children play, explore, discover and manipulate the patterns inherent in our system to realise that numbers derive meaning from their context. The number 25 is 1 more than two dozen, a quarter of a dollar; two ten cents and five cents; five more than 20; 10 less than 35 etc. Each interpretation brings a different understanding of the meaning of 25.

These lessons explore the relationship and size of one number to another, as well as helping children build an intuition for ‘benchmark’ numbers such as 5, 10, 25, 50, 100 and 1000. These ‘benchmark’ numbers, once firmly internalised, help shed light on the relevance and meaning of other numbers in comparison.

SAME,

BUT DIFFERENT

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For adults, counting a group of items as a single object is not difficult. It does, however, present a difficult level of abstraction for children, whose initial concept of numbering is built through counting experiences, whereby one object is matched to a corresponding number name.

Understanding our numeration system demands that children be constantly mindful that ‘ten’ is simultaneously a single entity (1 ten) and ten separate units (10 ones), a concept that is often difficult for even the most proficient counters.

The first five lessons in Unit 1 focus on counting and the ‘tenfor-one’ regrouping structure we use to build numbers. These activities help children fully understand the embedded meaning in a number such as ‘56’, allowing them to see the 5 as fifty ones and five tens.

The first three lessons in Unit 2 reinforce the trading nature of our base ten system by asking children to represent numbers of the same value differently; for example: 48 is represented as 4 tens and 8 ones; 3 tens and 18 ones; 2 tens and 28 ones; 1 ten and 38 ones; 48 ones.

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NOTHING

IS SOMETHING

When children hear the number ‘four hundred and five’, there is no aural evidence of a zero in the number. It is only in writing the number that the zero plays a crucial role. Many children without a firm grasp of place value and zero as a place holder will write the number 4005, just as it sounds.

The third, fifth and sixth activities in Unit 3 provide children with opportunities to explore and discuss the role of zero as a place holder and to develop an understanding that a zero in the ten’s place and a zero in the thousand’s place communicate significantly different values, despite being zeroes.

Number and place value

Overview OVERARCHING

UNDERSTANDINGS

1. We use symbols to express ourselves (digits, numbers).

2. We have created patterning rules to organise number symbols.

3. Numbers are all around us and help explain our world.

Teaching to the ‘Big ideas’ Big idea

Activities

 Same, but different

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1.

2.

3.

4.

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Sort of different Snap to it Snap to it – 2 How tall are you?

Race of the century

1. Keep in balance 2. One and the same 3. Flat out

Activity cards

Observation: Throughout Performance tasks: Throughout Paper and pencil: Work-outs 1–3 Problem solving: Make a table, Act it out, page 14 Journals: Throughout Individual assessment: Page 14 End of unit: Show what you know (pages 15–16)

1. Jarring experience

Observation: Throughout Performance tasks: Throughout Paper and pencil: Work-outs 6–7 Problem solving: Make an organised list, page 26 Journals: Throughout Individual assessment: Page 26

1. The riddler

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 Ten power

Ongoing assessments

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 Nothing is something

Squeeze play Monkey in the middle Three in-a-row Puzzling Tetra hunt

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3.

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Centiworms See you tomARROW Metre made Squeeze the wash Lay it on the line

Paper and pencil: Work-outs 8–19 Problem solving: Use logical thinking, page 52 Journals: Throughout Individual assessment: Page 52 End of unit: Show what you know (pages 53–54)

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 Numbers speak in patterns and relationships

3.

4.

5.

6.

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Observation: Throughout Performance tasks: Throughout Paper and pencil: Work-outs 22–28 Problem solving: Draw a diagram, page 75 Journals: Throughout Individual assessment: Page 75 End of unit: Show what you know (pages 76–77)

1. No matter how you slice it

Embedded in the tasks

1. On your mark 2. Go between

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1. Know your place 2. Squeeze play 3. Monkey in the middle

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iii

Getting started While a full understanding of numeration and place value is built on the foundation of these ‘Big ideas’, it is important to note that the rationale for discussing each idea as an isolated concept is strictly to provide students with a schema to organise and reflect on their discoveries throughout the unit. The reality is that these ‘Big ideas’ are inextricably linked and interrelated principles that give rise to the full functioning and efficiency of our number system. If the students can, however, explain these ‘Big ideas’ and truly understand them conceptually, then they are well on their way to numeral fluency. Enjoy the journey.

HOW

IS THIS BOOK ORGANISED?

 ACTIVITIES: Each activity is intended to help you create an environment where students are invited to explore, think, invent, discuss and construct mathematical meaning for themselves. Not all students will follow the same path of exploration. This diversity is to be celebrated and shared.

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The format of each activity is clear and easy to follow. The design is intended to give you all that you need to support student learning. At the beginning of each lesson you will find the activity’s title, followed by the headings described below:

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Number and place value is designed to supplement or complement the resources currently used in the classroom to teach number and place value. Teachers may choose to use the entire book, or simply these activities that reinforce concepts that students are having difficulty understanding. The activities are intended to be engaging and relevant in multi-age settings, with students at different stages making discoveries at different levels of complexity.

Big ideas: Icons are used to identify which ‘Big ideas’ of number and place value are being explored in the lesson.

Larger icons indicate the primary focus of the lesson. Smaller icons indicate informal reinforcement of a ‘Big idea’.

Invitation to tune-in: Presents an appropriate wholeclass activity or discussion to help set the stage for students to work independently. Some introductions provide necessary definitions, others focus on explaining and modelling games, while others present a similar, but easier, problem that students solve together. Regardless of the format, the idea is to give students the appropriate tools and skills to solve the task in ‘Invitation to explore’.

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Materials: Identifies the game mats, mathmasters and manipulatives, as well as optional items required for the activity.

Invitation to practice: Reinforcement pages follow most activities. They are generally offered at two levels of difficulty (group 1 and group 2) to support multi-age groupings. These pages can be sent home, inviting parents to become a partner in their child’s education.

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A different view: Some lessons provide suggested activities that explore the same mathematical concept, but from a different perspective. Many of the activities will provide opportunities for enrichment or remediation.

In other cases, the activity will be changed to maintain student interest so that the concept can be revisited several times. iv

Invitation to explore: Presents games, investigations and problems to facilitate students’ discovery of the ‘Big ideas’ of number and place value. This philosophy supports the view that students learn by doing, communicating, reflecting and constructing their own mathematical meanings.

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Objective: States the particular mathematical concept that students will be exploring.

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Invitation to reflect: Provides ideas for a closing discussion where students share the thinking and reasoning behind their answers or game strategies that lead to specific discoveries.

Suggestions as to the introduction of the ‘Big ideas’ icons may also be found here.

Number and place value

Getting started

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 ACTIVITY CARDS: Each unit provides suggested activity cards that can be copied and used in a variety of ways: as wholeclass activities, as small-group investigations (particularly in combined-year settings), as individual assessment opportunities and as activities for the home.

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 PERFORMANCE ASSESSMENT THROUGH PROBLEM SOLVING: Each of the four units has a problem to reinforce the ‘Big idea’ of the unit and to formally teach specific problemsolving strategies within a problem-solving framework.

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‘Show what you know’ questions that can be used as pre- and post-tests, review and practice material or as portfolio pieces.

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Assessment The organising structure of Number and place value is detailed on page iii. The intent is to provide children with hands-on opportunities to build an understanding of the ‘Big ideas’ of number and place value. The assessment is designed to allow both the teacher and student to see how well these underlying principles and concepts are understood. Assessment opportunities present themselves often and in different forms throughout the unit:

 Teacher observation: Each lesson invites the teacher to stroll, participate and question students while they are engaged in the activities.

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 Paper and pencil: Practice sheets (Work-outs) that provide further insight into students’ understanding support most activities.

 Journals: The ‘Invitation to reflect’ questions can provide students with opportunities to write in their journals to share their discoveries and to explain their reasoning.  Performance-based: The lessons are performance-based—they demand students ‘learn on the fly’. In the context of the game or activity, they build knowledge which is extended and immediately applied to allow further understanding.

Suggested ongoing projects and end-of-unit assessments:  Have students build a class Big book, with answers to questions similar to these: • • • • •

How old will you be 1000 days from now?

How high is a stack of 1000 10c coins?

How long is a line of 1000 10c coins?

What time will it be 1000 seconds from now?

How heavy are 1000 10c coins?

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ASSESSMENT

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 Individual assessment: Additional questions are provided at the end of the unit that can only be answered if students understand the ‘Big idea’ of the unit.

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its rules?

 Imagine a world without numbers. Describe it.

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 Show what you know: Additional worksheets are provided that can be used as pre- and post-test tools.

 Activity cards: The activity cards can be used in student-teacher conferences to assess understanding.  Portfolios: The richness of the activities creates many opportunities for portfolio building.

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problem solving: Each unit has a fun, challenging problem that requires students to fully understand the ‘Big idea’ of the unit in order to solve the problem.

 Your friend walks into the classroom and sees the five ‘Big ideas’ icons. Write a letter to explain what each means.

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Number and place value

Sort of different – lesson plan

UNIT

1

INVITATION

BIG IDEAS:

TO TUNE-IN:

• Show the students 23 cubes. Ask: Someone once told me that whether I count a group of objects by 2s, 3s, 4s, 10s or any other number, the total will always be the same. Is that true? Students may need you to repeat or rephrase the question.

Encourage them to explain the reasons for their answers.

• Ask: Let’s test it out. I have some cubes here. Help me count them. We’ll start by counting by 2s: ( 2, 4, 6 … 20). As the students count, cluster the cubes into groups of 2. How many whole groups of 2 did we count? 11 How many leftover? 1 Record the count in a chart similar to the one below:

• Connecting cubes for each pair of students • Activity mat 1, page 2

Groups of

Whole groups

Leftovers

How many altogether?

2

11

1

23

3

7

2

23

4

5

10

2

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23

3

23

• Repeat the counting exercise with groupings of 3, 4 and 10 and record the results.

• Ask: Is it true that, no matter how I count the group of objects, the total will be the same? Yes

OBJECTIVE:

Students use different bases to count a collection of cubes. They begin to see the organisational efficiency of our base ten numeration system.

INVITATION

TO EXPLORE:

GROUPING:

PAIRS

Explain theP activity, different (Activity © R. I .

C. uSort bofl i cat i omatn1).s  In turn, each student in the pairing grabs as many cubes in his/her hands as possible.

The u cubesr are placed together in ao pile.n •f orr evi e wp p os es l y•  Students count the cubes by 2s and record the results on the first line of Chart 1.

ICON:

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Enlarge the five ‘Big ideas’ icons (Mathmaster 1, p. 80) and display them in the room.

Have students read them with you. Say: We will be spending the next few weeks making sense of these icons. Our first focus will be on ‘Ten power’. Everyone make a muscle. Wow! We have a powerful group. We are going to discover that our number system is also powerful.

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 Students continue counting according to the suggested groupings in Chart 1, then repeat Steps 1, 2 and 3 to complete Chart 2.

INVITATION

TO REFLECT:

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• Invite students to share some of their sorting results. Record them on a chart similar to the one below. Results will differ. Intentionally record multiple examples of groupings by 10 to reveal distinct patterns.

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Whole groups

Leftovers

How many altogether?

2

15

1

31

3

10

2

32

10

3

6

36

10

3

4

34

10

3

5

35

• Ask: Is there a pattern that occurs with the groups of ten that doesn’t with any other number? Yes. The number of whole groups combined with the leftovers matches the number of cubes altogether.

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1

Sort of different

UNIT

1

Partner 1, grab



Partner 2, grab



Place them together in a pile.

as many cubes

as you can.

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as you can.

Complete Chart 1.

Chart 1

Groups of

Whole groups

Leftovers

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ACTIVITY

How many altogether?

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Repeat steps 1, 2 and 3 and grab more cubes

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Groups of

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Leftovers

How many altogether?

2 3 10

2

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Number and place value

Activity mat 1

Snap to it – lesson plan

UNIT

1

INVITATION

BIG IDEAS:

TO TUNE-IN:

• Randomly place 34 cubes on an OHP. Turn on the OHP for 3 seconds. Ask: How many squares do you think are on the screen? Write your estimate. See Diagram 1.

• Organise the 34 cubes into tens and ones. Turn the OHP on for another three seconds. Ask: How many squares do you think are on the screen this time? Write your estimate.

See Diagram 2.

• Turn on the OHP once more. Ask: How many squares do you see on the projector? 34.

Explain that 34 cubes were on the projector both times that it was flashed on and off.

• Invite students to reflect back to see which of their estimates was closer to 34. Did you find one organisation of the cubes helped make guessing easier? Why? NVITATION TO EXPLORE

• Connecting cubes for each child, Activity mat 2, page 4 • Ten frame transparency (Mathmaster 2, p. 81) Diagram 1

GROUPING:

INDIVIDUAL

 Set a stopwatch or some other measuring device to record two minutes.  Tell students that you are going to snap together as many cubes as you can in two minutes. How many do you think I can snap together in that time? Answers will vary.  Set the timer and start snapping. Demonstrate that the cubes do not have to be snapped in one continuous sequence. Vary the length of the cube trains; e.g. one of 6, one of 8, another of 12.  When time is up, ask students to help you develop a strategy for determining how many cubes you snapped altogether. If a grouping strategy based on ten is not offered, introduce it with the ten frame.  Turn the ten frame (Mathmaster 2, p. 81) into a transparency for the OHP. Unlock the cubes you snapped and begin placing them on the ten frame from left to right and top to bottom. Have students call out the ascending count as you place each cube on the ten frame. One, two … five. What happens after five? Keep counting on the bottom row. Good. Keep counting with me. Six, seven … ten. What happens to the ten frame at ten? It’s full.  Demonstrate that when a ten frame is full, the ten cubes are reconnected to create a rod. See Diagram 3. Have the students cheer, Ten power.  Continue counting the remaining cubes until all of the cubes you snapped in two minutes are accounted for. How many cubes did you snap in two minutes?

Answers will vary.  Introduce the Snap to it activity (page 4) to the students.  Students will snap together as many cubes as they can in two minutes.  At the end of two minutes, students use the ten frame to calculate how many cubes they snapped together.  Remind students that when they fill the ten frame they reconnect the cubes and place each rod on the Tens track. When students regroup the ones to form a ten, have them cheer Ten power.

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MATERIALS

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Diagram 2

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Diagram 3

a full ten frame is reconnected to form a rod

OBJECTIVE:

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Students use ten frames to count how many cubes they can snap together in two minutes.

INVITATION

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TO PRACTICE:

Assign: Practice work-out 1, page 5

INVITATION

TO REFLECT:

• Have students share some of their totals.

• Ask: How did the ten frame help you organise your work?

• Ask: In the number 34, what does the 3 tell us? That there are three groups of ten in the number.

• Ask: How is 43 different from 34?

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Snap to it

UNIT

1

FRAME

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TEN

ACTIVITY

TRACK

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tens

ones in two minutes.

Number and place value

Activity mat 2

Snap to it

UNIT

1

PRACTICE

EXAMPLE RING

TEN

Ring groups of ten.

3

tens

ones

2

3

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Write the number of tens and ones in two different ways.

YOU

2

tens

TRY!

tens



ones

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tens

ones

tens

ones

tens

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tens ones

Work-out 1

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Snap to it – 2 – lesson plan INVITATION

TO TUNE-IN:

• Remind students of the Snap to it activity. Have them return to Activity mat 2, page 4.

• Say: I want you to connect enough cubes to be able to show the number of cubes you snapped in two minutes the other day.

• Remind students that each time they count ten cubes, they link them to form one rod.

• Ask the class to share their results.

INVITATION

GROUPING:

1

BIG IDEAS:

WHOLE CLASS

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TO EXPLORE:

 Have students work in groups of four to calculate the number of cubes they snapped altogether. They will already have a certain number of rods connected, but will need to join the remaining units into groups of ten.  Invite a representative from each group to bring you the group’s ten rods. Display them so they are visible to the class. Encourage a class count by tens: 10, 20, 30, 40, 50, 60, 70, 80 and so on, as you hold up each group of ten.  When you reach one hundred stop. How many cubes do we have now? One hundred How many tens do we have? Ten. I am going to put these ten cubes hundred. together in a bundle and secure them with an elastic band. How many are in a bundle? 100. See Diagram 1.  Continue to skip count from 100 until all the tens are accounted for: 110, 120, 130, 140, 160. We have 160 cubes counted already. Look around the class.

How many more cubes do you think are left to be counted?  Continue with the groups bringing their collection of unit cubes. Have them join them into ten rods, bring them to the front and continue to count by tens until no more tens are left to be counted.

ATERIALS:

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• Ask: I can’t believe how many cubes we snapped together the other day.

Your fingers must still be exhausted. Take a look around. I wonder how many cubes we snapped as a class? What do you think? Answers will vary.

• Today, I have an activity that requires cooperation from everyone. Your job, working as a class, is to find out how many cubes were snapped together in total.

Invite students to suggest a plan to solve the problem. If they present a workable solution, GO FOR IT. If not, perhaps the model below will help:

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UNIT

• Connecting cubes • Elastic bands Diagram 1

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INVITATION

TO REFLECT:

Students develop counting strategies to calculate how many cubes the whole class can snap together in two minutes.

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OBJECTIVE:

LANGUAGE

o c . che e r o t r s super

• Ask: How many tens do we have altogether? Answers will vary; for example: 82 • Ask: How many ones are left over? 6 • Ask: How many cubes did we snap together the other day? 826 • Write 826 on the board. What does the eight represent? 8 bundles, eight hundred, 800. What does the two represent? Two ten rods, twenty, 20. What does the 6 represent? Six cubes leftover, six, 66.

REMINDER

Each time students regroup ten ones for one rod or ten rods for a flat, encourage the cheer, Ten power.

INVITATION

TO PRACTICE:

Assign: Practice work-out 2, page 7 for Group 1 Assign: Practice work-out 3, page 8 for Group 2

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Number and place value

Make tens

UNIT

1

PRACTICE – GROUP 1

Circle groups of ten to make …



80.

(b)

120.

(c)

140.

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(a)

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50.

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Draw 22 cubes

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tens in 50 Work-out 2

Number and place value

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7

Snap to it – 2

UNIT

1

PRACTICE – GROUP 2

Our numbers are built on groups of ten: ‘Ten power’.

Hundreds

1000 one thousand = 10 hundreds

YOU

TRY!



Complete the table.

Tens

Ones

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10 one ten = 10 ones

1 one

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Thousands

Hundreds Tens ©Thousands R. I .

C.Pu bl i cat i on s Ones 56 •f orr evi ew pur posesonl y•6

385

3

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4230

3

What number is shown? (a)

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Hundreds Tens Ones

Hundreds Tens Ones

REFLECT 

8

John has $8.00. Mary has 80 10c coins. Who has more money?

Explain your thinking.

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Number and place value

Work-out 3

How tall are you? – lesson plan

UNIT

1

INVITATION

BIG IDEAS:

r o e t s Bo r e p o u k : S

• String, scissors • 20 connecting cubes for each pair of students • Activity Mat 3 for Group 1 • Activity Mat 4 for Group 2 • 5c coins

TO EXPLORE:

GROUPING:

PAIRS

Introduce and explain the investigation, How tall are you?

WHAT TO DO  Work with your partner to estimate how tall you are in cubes.  Have your partner measure your height in string. Cut the string to match your height.  Switch roles.  Work together to measure the length of string in cubes.  Be careful. You don’t have enough cubes to match the length of string. What will you do?

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10

20

remove all but the tenth cube

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INVITATION

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Students estimate, then measure their height in cubes.

If using 1-cm cubes, you may wish to replace the 10th and 20th cubes with a rod.

TO REFLECT:

• Ask students to share and compare. How tall are you in cubes?

• Ask: How did you figure out your height since you didn’t have enough cubes?

OBJECTIVE:

Note:

INVITATION

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Diagram 1

• Cut a string about 25 cm to use on an OHP. Hold it up for the class to see. How many cubes would it take to make a string this long? Answers will vary.

• Make a circle with the string on the projector. Have fewer cubes available than are needed to cover the circumference; example: 12 cubes. Begin to place cubes on the outside of the string. Have students count along with you. 1, 2, 3, 4 … 10. Stop! Did you just say ten? Yes. I’m afraid I’m not going to have enough cubes to cover the whole circle. I’m going to take nine cubes away and leave the tenth one exactly where it is. Continue counting. 11, 12, 13, … 20. Did I hear 20? Yes. I’m going to put another cube on the line at 20 and take the other cubes away. Finish filling in the perimeter of the circle. 21, 22, 23, 24, 25.

• Ask: How many cubes long is my string? 25 • Ask: What do the two cubes on the line tell you? Every time you counted to ten, you left a cube on the line. Each cube really means ten. Two cubes is really twenty. See Diagram 1.

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MATERIALS

TO TUNE-IN:

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

TO APPLY:

Assign: Activity mat 3, page 10 for Group 1 Assign: Activity mat 4, page 11 for Group 2

EXTENSION Ask: How long would the line be if all the snap cubes in the classrooms were lined up one after the other?

Number and place value

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9

Lay it on the line

UNIT

1

Estimate:

tens

Count:

(c)

Estimate:

tens

ones

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(b)

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Estimate:

Count:

ones

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(a)

How many centimetre cubes can you place on these lines?

ones

(d)

Estimate:

tens

ones

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APPLY – GROUP 1

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tens

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ones

Count:

Number and place value

tens

ones Activity mat 3

Numbers make cents

UNIT

1

APPLY – GROUP 2

Put the target on the floor. Drop a 5c coin five times onto the target. Write down where it lands each time.

What is your score? thousands

hundreds

tens

ones

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My score:

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Penny for your thoughts  Activity mat 4

What is the greatest number you could have scored? What is the least?

Number and place value

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11

Race of the century – lesson plan INVITATION

TO TUNE-IN:

INVITATION

1

BIG IDEAS:

r o e t s Bo r e p okM u S GROUPING:

TO EXPLORE:

PAIRS

HOW TO PLAY RACE OF THE CENTURY  Students place number tiles or cards face down.  The first player turns over a card or tile and places a matching number of cubes on the ten frame within the Race of the century game mat.  Players alternate turns. If a player gets 10 ones or more, he or she regroups 10 ones for one rod.  Players continue turning over tiles or cards, placing and regrouping until one player reaches 100.  Players clear their mats and play again.

ATERIALS:

• Centimetre connecting cubes • Number tiles or number cards (Mathmaster 3, pp.

82–83) • Game mat 1, page 13

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• Have the class place 6 cubes on the ten frame on the Race of the century mat. Have them place 7 more cubes on the ten frame. Ask: How many cubes do we have in the ones place? 13.

• Ask: What have we learned so far in this unit? When we have ten ones we regroup them to form one ten. Right. What’s our cheer? Ten power.

• Say: Exactly. Our numeration system is designed for regrouping (trading). When we have 10 units in the ones column, we regroup them for one unit of a higher value. In the example above, we regroup 10 ones for one rod, which represents a value of 10. We then place the rod in the ten’s place. We still have thirteen, but it is represented differently as one 10 and three ones.

• Repeat the above procedure with different trades until students are comfortable with the concept of regrouping or trading.

UNIT

OBJECTIVE:

Students randomly select numbers and add the results in an effort to be the first to reach 100.

TO REFLECT:

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INVITATION

• This game allows students to manipulate and play with the ten-for-one trade structure inherent in our number system. It may take many rounds before all the students can simultaneously consider 10 as one ten, and as ten ones, but they will have fun in the process.

• Ask: What happened each time you counted ten ones? We regrouped 10 ones for one ten.

• How many ones did you have to collect to win the game? 100.

• Revisit the ‘Big idea’ icon ‘Ten power’ (Mathmaster 1, p. 80). Ask students to explain it in their own words.

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INVITATION

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TO CONNECT:

A similar game can be played with 10c coins and $1 coins to reinforce the concept of regrouping with money, which is usually of interest to children.

LANGUAGE

REMINDER

Each time students regroup ten ones for one rod or ten rods for a flat, have them cheer, Ten power.

12

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Number and place value

The youngest person is Player 1.

Place the number tiles face down.

Player 1 turns over a number tile. Place the matching number of cubes on the ten frame.

Players take turns. If a player gets 10 or more, he/she regroups 10 ones for one rod.

Continue play until one player reaches 100.

Start:

Step 1:

Step 2:

Step 3:

Step 4:

TO PLAY

HUNDREDS ENS

eac T h er

Race of theT century

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HOW

1

UNIT

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Game mat 1

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Number and place value

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13

ONES

GAME

Assessment PERFORMANCE

ASSESSMENT THROUGH PROBLEM SOLVING:

BIG IDEA:

Grouping Individual Grouping: Strategy: Make a table, Act it out.

Strategy Materials: Base ten blocks or $10 notes and $1 coins.

Materials QUESTION:

Your dad has been napping on the lounge all week. You know that each time he does, a small amount of money slips out of his pocket and falls between the cushions. This week you checked the lounge every day. Strangely, you found exactly one $10 note and one $1 coin each time. How much money did you find this week?

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

SOLVE:

Try your plan • Act it out • Make a table

PLAN: Choose a strategy • Act it out • Make a table

Act it out

Make a table

After seven days, I found this many coins.

If not, try again.

$10

$1

$10

$1

$10

$1

$10

$1

7 tens = $70

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

tens

ones

1 1 1 1 1 1 1

1 1 1 1 1 1 1

7

7

7 ones = $7

o c . che e r o t r s super

COMMUNICATE: Explain your thinking using pictures, symbols and words.

INDIVIDUAL ASSESSMENT Materials: Cubes, ten frames (Mathmaster 2, p. 81)

14

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LOOK BACK

Task 2:

What is your answer

• I found seven $10 $10 $1 © R. I .

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P u b l i c a t i o n s notes and seven $10 $1 $1 coins, which is •f orr evi e w $1pur posesonl y $77. • $10

. te : (Question the answer) Did your plan work?

Task 1:

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Teac he r

UNDERSTAND: What do you know?

• Your dad napped each day this week.

• Each day that he did, a $10 note and a $1 coin slipped out of his pocket.

• There are seven days in a week.

What do you need to find out?

• How much money fell out of your dad’s pocket altogether?

Dump out 42 cubes. Allow students time to count or manipulate the cubes. Confirm that there are 42 cubes. Ask: How many ten frames will the 42 cubes fill?

Ask: How many children would it take to show 64 fingers?

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Number and place value

SHOW WHAT YOU KNOW • Group 1: Work-out 4, page 15 • Group 2: Work-out 5, page 16

SHOW 

WHAT YOU KNOW

– GROUP 1

How many marbles? tens

10



10

10

10

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How many black squares?

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10



10

How many toes?

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

10

tens

ones

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C.Publ i cat i ons Circle groups of ten. Write the number.

•f orr evi ew pur posesonl y•

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Circle 46.

Work-out 4

ones

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ones

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Number and place value

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15

SHOW 

WHAT YOU KNOW

– GROUP 2

What numbers do the blocks show? (b)

hundreds

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ones

hundreds

tens

ones

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(a)

Complete the chart.

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Cof. Pu i cat i ons number groups ofb tenl 100•f orr evi ew pur posesonl y•

number

160

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410 650

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o c . number c thousands hundreds tens e her r o t one hundred and eleven s super

Complete the chart.

six thousand, seven hundred

ones 1

0

five hundred and sixty-six two thousand and forty-two eight hundred and eight

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Number and place value

Work-out 5

Activity cards ACTIVITY

CARD

1–1

A

BIG IDEAS:

JARRING EXERCISE

MATERIALS:

A variety of jars containing different collections of items; for example: 10c coins, buttons, paper clips, cubes, ten frames for recording (Mathmaster 2, p. 81)

OBJECTIVE:

Students estimate the number of items in a jar. They then use ten frames and grouping strategies to confirm their estimate.

A

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

JARRING EXERCISE

C

C

C

AB AB CA B AB C C AB BC A B C AB A B CA

A

B

C

B

A

C

ACTIVITY

CARD

1–2

KEEP

PACE

MATERIALS: Cubes

BIG IDEAS:

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OBJECTIVE:

KEEP

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Jars filled with a variety of different items What to do:  Choose a jar of materials.  Estimate how many things are in the jar. Record your guess.  Use ten frames to help you count the actual number of things in the jar.  Do the activity again with a different jar.

Teac he r

MATERIALS:

The class estimates how many paces it will take to walk a certain distance.

PACE

MATERIALS:

Cubes

ACTIVITY

. t 1e –3

CARD

MATERIALS: OBJECTIVE:

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What to do:  Choose a distance to walk; e.g. around the school, down the hall and back, around the outside of the tennis court.  As you walk, count how many paces you take. Every time you count ten paces, put a cube in your pocket.  How many paces did you take?  Why might someone who walked the same distance have a different count?

o B c . ch e Base ten blocks, tene frames for recording (Mathmastero 2, p.r 81). t r s s r u e p Students use base ten blocks to build creatures. They then use CREATURE

COMFORTS

IG IDEAS:

ten frames to calculate the number of cubes in their creature.

CREATURE MATERIALS

COMFORTS

Base ten blocks, ten frames

What to do:  Use cubes and base ten materials to build a creature.  Use ten frames to calculate the value of your creature.

Number and place value

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17

Keep in balance – lesson plan INVITATION

2

TO TUNE-IN:

BIG IDEAS:

r o e t s Bo r e p okM u S GROUPING:

TO EXPLORE:

PAIRS

• Invite students to look at Activity mat 5, page 19. Make a copy of the same page for use on the overhead projector.

• Take time to model and explain the game, Keep in balance.

HOW TO PLAY KEEP IN BALANCE  Students work in pairs.  Each student builds a number, with base ten blocks on the left side of the balance.  Partners exchange scales.  Each balances his/her partner’s scale by matching the quantity, but with different base ten blocks. See example below:

ATERIALS:

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Teac he r

• Show the class a balance scale with three rods and seven cubes on one side of the balance.

• Say: I have a challenge for you. I know you can solve it, but you will have to think creatively.

• Ask: Who thinks they can balance this scale? Let students raise their hands in the air before adding; Oh, I almost forgot. You have to balance the scale without using three rods and seven cubes on the other side of the balance. Who wants to give it a try now?

• In time, perhaps with more direction and support, students will begin to balance the scale with the following equivalent representations: 2 rods and 17 cubes, 1 rod and 27 cubes, 0 rods and 37 cubes.

• Provide another example, if necessary.

INVITATION

UNIT

• Balance scale • Base ten blocks • Transparency of Activity mat 5, page 19

OBJECTIVE:

Students build scales that are © R. I .

C.Publ i cat i o ns balanced (equivalent), but have pans with different groupings of hundreds, and• ones.

•f orr evi ew pur poses ontens l y

INTRODUCE

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Player 2 Responds by building 46 with 3 tens and 16 ones

TO PRACTICE:

Assign Group 1: Practice workout 6, page 20 Assign Group 2: Practice workout 7, page 21

TO REFLECT:

• Ask: How did you know your scale was in balance? Answers will vary.

• Ask: How can something be the same, but different?

• Ask: Are there more ways to balance the number 56 or 78? Why? 78. There are more tens in the number that can be grouped as ones.

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INVITATION

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 Group 1 works only with rods and cubes and builds numbers that are 40 or less.

Group 2 works with flats, rods and cubes.

INVITATION

Introduce the ‘Big idea’, ‘Same but different’, by making a transparency of the icon on Mathmaster 1, page 80.

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Player 1 Builds 46 with four tens and 6 ones

ICON:

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Number and place value

Note: For two-digit numbers, the number of ways to make a number is one more than the value of the ten’s number.

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Right pan

ACTIVITY

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2

UNIT

Left pan

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Keep in balance

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Activity mat 5

Number and place value

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19

Keep in balance

UNIT

2



Use different'.

PRACTICE – GROUP 1

to balance the scales. Write your number. Remember, the scales need to be the 'same, but

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(a)

(b)

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Weigh in on the topic: 20

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Is 67 the same as 5 tens and 17 ones? Explain.

Number and place value

Work-out 6

Keep in balance

UNIT

2



Use 'same, but different'.

(b)

to balance the scales. Write your number. Remember, the scales need to be the

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

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(a)

PRACTICE – GROUP 2

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(d)

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(c)

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Weigh in on the topic: Work-out 7

Is 610 the same as 61 tens? Explain.

Number and place value

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21

One and the same – lesson plan INVITATION

TO TUNE-IN:

INVITATION

2

BIG IDEAS:

r o e t s Bo r e p okM u S GROUPING:

TO EXPLORE:

INDIVIDUAL

 Students spin the spinner and place a matching number of cubes on the ten frame within the place value chart.  Students spin five times, adding a matching number of cubes each time to the place value chart.  When ten or more cubes are collected, students regroup the ten ones for a rod.  At the end of five turns, students will have a number; for example: 32.  Students use the chart to represent their number in different ways.

Example: 3 tens and 2 left over 2 tens and 12 left over 1 ten and 22 left over 0 tens and 32 left over

ATERIALS:

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Teac he r

• Grab a handful of base ten cubes and place them on an OHP. Have students count with you to verify how many there are. Example: 1, 2, 3, 4, 5 … 34. How many cubes are on the projector? 34. Is everyone comfortable with that number? Yes. • Ask: In the last unit, we spent a lot of time counting and grouping. What did we learn about the trading rule for our base ten number system? When we count ten ones, we exchange them for one ten. When we count 10 tens, we exchange them for one hundred and so on.

• Ask: Let’s count the cubes on the OHP again, using the base ten grouping rule.

Before we do, how many tens are on the OHP now? None. How many ones are there? 34 I’m going to write that down like this: See Diagram 3.

• Say: Let’s count! 1, 2, 3 … 10. Let’s regroup: the ten ones become one ten.

What’s our new way of showing 34? One ten and 24 ones.

• Continue to count and record the remaining representations for 34. See Diagram 3.

UNIT

• Overhead projector • Base ten blocks • Activity mat 6, page 23 • Paper clip and pencil Diagram 1

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TO REFLECT:

TO EXTEND:

Throughout the unit, review ‘Same, but different’ by having students work with the following chart: Build

22

Diagram 3

tens

ones

0 1 2 3

34 24 14 4

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

• Ask: What do you think this activity tried to show? The same number can be shown a variety of ways.

• Ask: How many different ways were you able to show your number?

Answers will vary.

• Ask: How do you know you discovered all the possibilities? Answers will vary.

• Ask: What patterns do you see? When the ten goes up one the leftovers go down ten.

INVITATION

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INVITATION

Diagram 2

Same, but different

tens

ones

tens

ones

2

16

3

6

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Number 36

Number and place value

BJECTIVE:

Students sort a collection of cubes into groupings of tens and ones to see that a single quantity can be represented in different, but equivalent ways.

Note: Number tiles work very well for this activity in place of the spinner.

One and the same

UNIT

2



Spin.



ACTIVITY

Collect the number of cubes and place them on the ten frame.

PLACE

VALUE CHART

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Ones

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Tens

Use a pencil and a paper clip to make a spinner.

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Spin five times.



Each time, record your number in the chart below. Complete the chart showing the number as the ‘same, but different’.

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(a)

Activity mat 6

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Words

Number sentence

o c 40. +2 chetens left over e r o t r tens left over s super 4

2

(b)

tens

left over

(c)

tens

left over

(d)

tens

left over

(e)

tens

left over

Number and place value

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23

Flat out – lesson plan INVITATION

UNIT

2

TO TUNE-IN:

• Place 4 rods and 6 cubes on the OHP. See Diagram 1. Ask: What number do we have?

46 46.

• Ask: Think about our earlier work. Is there another way we can show 46? Answers will vary.

• Model exchanges of rods for cubes until all possible representations of 46 have been shown. Each time you complete an exchange, ask the class to confirm that the total is still 46. See Diagram 2. Remember to reinforce the language, ‘Same, but different’, with each representation.

INVITATION

r o e t s Bo r e : p okM u S GROUPING:

TO EXPLORE

PAIRS

ATERIALS:

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• Ask students if they remember playing Race of the century? Today we are going to play a similar game, but instead of racing to see who is the first to build a hundred, we will race to see who is the first to remove 100 cubes from their place value mat.

• Invite a volunteer to help you model the game.

• Encourage students to cheer: ‘Same, but different’ each time they exchange a flat for 10 rods and a rod for 10 ones.

HOW TO PLAY FLAT OUT  Students place number tiles or number cards face down.  Students place a hundred flat in the hundreds section of their gameboard.  The first player turns over a card or tile and exchanges a flat for 10 rods. One rod is then exchanged for 10 cubes. Remove the amount of cubes that matches the number on the card or tile from the gameboard.  Player 2 has a turn.  Players alternate turns, choosing a tile or number card and removing cubes until one player has removed all the cubes from the mat.  To win, an exact number must be selected from the number cards or tiles. For instance, if a player has three cubes remaining on the gameboard, a three must be selected to win.  Players clear their mats and play again.

Teac he r

BIG IDEAS:

• Base ten blocks • Number tiles or number cards (Mathmaster 3,pp.

82–83) • Game mat 2, page 25 Diagram 1

© R. I .

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TO REFLECT

ones

4 3 2 1 0

6 16 26 36 46

o c . che O e r o r st super

• Have students share some of the results of their games.

• Ask: What does the first move in every game require? A flat exchanged for ten rods then one rod exchanged for ten cubes.

• Ask: Did anyone develop a short cut during the game? Sometimes, I wouldn’t fully complete a 10 for one trade. For example, if I had four cubes in the one’s place and I rolled a six, I would still make a trade, but instead of putting ten cubes in the one’s place I would only add four because I knew that 14 – 6 was going to be 8.

• Ask: What does ‘Same, but different’ mean to you?

24

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INVITATION

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Diagram 2

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Number and place value

BJECTIVE:

Students deconstruct numbers as they race to see who can be the first to remove 100 cubes from their place value mat.

A

DIFFERENT VIEW

A simpler version can be played; students race to remove 50 cubes.

Number and place value

Players take turns.

Continue play until one player has taken all cubes from his/her gameboard. To win, the final number card selected must match the number of cubes on the gameboard exactly.

Step 4:

Player 1 turns over a number tile and exchanges the flat for ten rods. One rod is then exchanged for ten ones. Then take away the number of cubes that matches the amount on the number tile.

Step 2:

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o c . che e r o t r s super

Step 3:

Place the number tiles face down. Place a hundred flat in the hundreds section of your gameboard.

The oldest person is Player 1.

TO PLAY

HUNDREDS

. te

Step 1:

Start:

HOW

2

UNIT ENS

eac T h er

Flat out T

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Game mat 1

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25

ONES

GAME

Assessment PERFORMANCE

ASSESSMENT THROUGH PROBLEM SOLVING:

Grouping Individual Grouping: Strategy: Make an organised list.

Strategy Materials: $10 notes and $1 coins; or base ten blocks.

Materials QUESTION:

Matthew counted his money. He has 52 $1 coins and 25 $10 notes. It costs $48 to buy his favourite game.

How many different ways can Matthew put his money together to buy the game?

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

Try your plan • Make an organised list

1.

$48

PLAN: Choose a strategy: • Make an organised list

$10 note

$1 coin

0

48

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Teac he r

UNDERSTAND: What do you know?

• Matthew wants to buy a game.

• He has $10 notes and $1 coins.

• The game costs $48 to buy.

What do you need to find out?

• How many different ways can Matthew put his money together to buy the game?

SOLVE:

BIG IDEA:

What is your answer?

There are five different ways to put the money together.

2. $48 38 © R. I .

C.P1ubl i cat i ons 3. $48 2 28 •f orr ev e wp r p18osesonl y• $48 3u 4.i 5.

$48

LOOK BACK: (Question the answer) Did your plan work?

If not, try again.

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o c . che e r o t r s s Provide students with base ten blocks and r u e p ask them to design different configurations Task 2:

for the number 28. The blocks must lie flat and can’t be stacked on one another. Many designs are possible. Some are shown here: 2 tens and 8 ones

26

8 COMMUNICATE: Explain your thinking using pictures, symbols and words.

INDIVIDUAL ASSESSMENT Materials: Base ten blocks, 10 x 10 cm grid (Mathmaster 6, p. 88) Task 1:

4

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1 ten and 18 ones

Give students a 10 x 10 cm grid (Mathmaster 6, p. 88). Ask: How many different ways can you fill this grid using flats, rods and cubes? 1 flat and 0 rods and 0 ones, 0 flats and 9 rods and 10 ones, 0 flats and 8 rods and 20 ones, 0 flats and 7 rods and 30 ones, 0 flats and 6 rods and 40 ones, 0 flats and 5 rods and 50 ones, 0 flats and 4 rods and 60 ones, 0 flats and 3 rods and 70 ones, 0 flats and 2 rods and 80 ones, 0 flats and 1 rod and 90 ones, 0 flats and 0 rods and 100 ones.

Number and place value

Activity cards ACTIVITY

CARD

MATERIALS:

2–1

THE

BIG IDEAS:

RIDDLER

• Base ten blocks • Pencil and recording paper

OBJECTIVE: What to do:

Answer the three riddles below:

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Teac he r



r o e t s Bo r e p ok u S Students solve three riddles involving base ten blocks. They then create their own riddles for other class members to solve.

s.

26 block h it w 4 ke 4 I can ma ?

Can you

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16 block h it w 3 ke 13 I can ma ?

Can you

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

Make up your own riddle. Write the riddle on one side of a sheet of paper. Write the answer on the back of the sheet.



The riddle can now be shared with other students in the class.

Number and place value

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27

Know your place – lesson plan INVITATION

TO TUNE-IN:

INVITATION

3

BIG IDEAS:

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Teac he r

• Say ‘126’ out loud. Invite the class to build the hundreds tens ones number with base ten blocks on their place value mat. In earlier lessons, you were allowed to build numbers in many different ways. This time, I want you to build the number using the least number of blocks possible. Have a volunteer share a solution.

• Now build 216. Ask: How are the two numbers alike and how are they different? As students explore this question, they will realise that both numbers, while composed of the same digits, have very different values. The power of place value, with only 10 digits (0–9), is that we can create any number imaginable. This is possible because our system gives digits a different value depending on their place in a number.

• Continue calling numbers for students to build. Discuss the value of individual digits in the number; for example: What is the value of the 6 in 368? 6 tens or 60.

UNIT

MATERIALS:

GROUPING: PAIRS

TO EXPLORE:

Distribute game mats (Mathmaster 4, p. 84). Provide each pair of students with 10 number tiles or number cards (0–9). Introduce the game, Know your place.

HOW TO PLAY KNOW YOUR PLACE  Player 1 chooses a tile or card and selects an equal number of flats, rods or cubes to place in the hundreds, tens or ones place on the gameboard. Once the blocks have been placed on the gameboard, they cannot be changed.  Players alternate turns until each player has placed a number in all three or four places, depending on level of development, on the game board.  Players compare the two three-digit/four-digit numbers.  The player with the greater number wins.  Players clear their mats and play again to see who can build the lower number.

• Base ten blocks • Place value mat • Mathmaster 4, page 84 • Number cards (Mathmaster 3, pp. 82–83) or number tiles (0–9)

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TO REFLECT:

o c . che e r o t r s super

• Say: In the first version of the game, when you were trying to build the greatest number, where should smaller digits be placed? In the one’s column. Where should greater numbers be placed? Preferably, in the hundred’s place. What strategy are you using to compare numbers to find the game’s winner? Look first at the hundred’s/thousand’s digit. The number with the larger digit is greater. If the digits are the same, compare the digits in the ten’s place. The number with the greater ten’s digit is the winner.

INVITATION

TO PRACTICE:

Assign Group 1: Practice work-out 8, page 29 Assign Group 2: Practice work-out 9, page 30

28

In an attempt to build the greatest number possible, students play a game in which they randomly select digits from a pile of cards or tiles. Group 1 play to 999.

Group 2 play to 9999.

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INVITATION

BJECTIVE

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Number and place value

Note:

After each turn, students return the number card or tile to its respective deck or pile.

Get the number ‘write’

UNIT

3

PRACTICE – GROUP 1

LET’S SEE Use

hundreds tens ones

and

.

Show how many hundreds, tens and ones there are, then write the number.

You try!

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hundreds



tens

ones

tens

ones

hundreds

tens

ones

1

2

6

hundreds

number

126

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hundreds

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hundreds

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hundreds

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hundreds

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o number c . che e r o t rup s er tens s ones hundreds tens

ones

ones

number

Think!

What does the 6 stand for in each number?

Work-out 8

642

Number and place value

436

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29

Get the number ‘write’

UNIT

3

PRACTICE – GROUP 2

LET’S SEE Use

thousands hundreds tens ones

and

.

Show how many thousands, hundreds, tens and ones there are, then write the number. thousands

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hundreds

tens

thousands hundreds

ones

1

You try!



thousands

tens

ones

6

number 1126

thousands hundreds

tens

ones

number

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hundreds

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hundreds

2

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ones

thousands hundreds

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ones

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ones

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hundreds

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ones

thousands hundreds

tens

ones

number

Think!

What does the 5 stand for in each number? 2051 30

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2615

Number and place value

5328

8592 Work-out 9

Head count – lesson plan

UNIT

3

INVITATION

BIG IDEAS:

• Ask: When I retire, I think I would like to become a magician, but I still need lots of practice. Who would like to volunteer to help me? Select a volunteer.

• Ask the volunteer to write a two-digit number on a sticky note. The number can’t have both digits the same. Have the student hand it to you without revealing the number; for example, the volunteer selects 86.

• Stick the number on your forehead and roam the classroom so that all can see the number. Encourage students to not tell you the number.

• Begin to guess the number. Is it 43? No. I forgot to mention. You have to tell me more than just ‘yes’ or ‘no’. If my guess has one of the correct digits in the number, and it is in the right place, you have to tell me ‘hot’ on my Head count recording sheet. If my guess has a correct digit, but in the wrong place, you have to give me a ‘warm’ on my Head count recording sheet. If I don’t have anything right, tell me ‘cold’. Now score 43 for me. Cold.

• Say: Okay, a slow start, but at least I know that there is no 4 and no 3 in the number. Right? Right.

HEAD COUNT RECORDING SHEET • Ask: Is my number 82? Hot. Interesting, now I know that the number has 86 SECRET NUMBER either an 8 in the ten’s place or a 2 in Round Guess Score the one’s place. I’m not sure which it tens ones is though.

1.

• Ask: Is the number 24? Cold.

Cold So the 2. ‘hot’ in round 2 couldn’t have been for the 2, so I know that the ten’s digit 3. has to be the 8. I’m getting closer.

4.

• Continue to guess and model your 5. thinking as you progress through the game and guess the number.

• Play another round to make sure students understand the game.

• Sticky notes • Pencils • Head count game mat 3, page 32

OBJECTIVE:

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Teac he r

MATERIALS

TO TUNE-IN:

INTRODUCE

ICON:

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Give students a chance to view the ‘Know your place’ icon (page 80). Ask them to share their understanding of its meaning.

A

. te:

DIFFERENT VIEW

INVITATION

TO EXPLORE:

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Students place a mystery number on their forehead and play a game similar to Mastermind® to deepen their understanding of place value.

GROUPING:

PAIRS

o c . che e r o t r s super

Change the game so that the person choosing the number provides clues that help the ‘guesser’ identify the number.

Challenge students to think of ways to present information so that the partner can guess the number with only one clue.

Example: It is one more than 22; or it is five less than 30; or it is between 43 and 45.

PLAY HEAD COUNT  Distribute sticky notes to each pair of students and a Head count (Game mat 3, p. 32) to each individual.  Invite students to play Head count.

INVITATION

TO REFLECT:

• Two factors will influence the students’ success in this game: the quality of their questions and how they use information gathered from earlier questions to inform future ones. These skills will only improve if students are encouraged to share their strategies and thinking • Ask: Did you develop any effective strategies while playing?

Number and place value

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31

Head count

UNIT

3

HOW

GAME

TO PLAY

Start:

The person with the longer hair is Player 1.

Step 1:

Player 1 picks a two-digit number (the digits have to be different) and writes it on a sticky note.

Step 2:

Player 2 sticks the sticky note on his/her forehead and begins to guess the number. (Don’t let Player 2 see the number.)

Step 3:

Player 1 lets Player 2 know how close his/her guess is by giving the following scoring clues:  ‘Hot’

One digit in the right place.

=

One of the digits is in the number, but in the wrong place.

 ‘Cold’

=

Neither of the two digits is in the number.

 ‘Warm, warm’

=

Both digits are in the number, but in the wrong place.

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=

 ‘Warm’

Step 4:

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Players switch roles. The player to find the secret number with the least amount of guesses wins.

HEAD

COUNT RECORDING SHEET

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Round

1.

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9.

10.

DIGITS 0123456789 32

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Number and place value

Game mat 3

Squeeze play – lesson plan

UNIT

3

BIG IDEAS:

INVITATION

• Write the digits 4, 7 and 8 on the board and ask the class to name the different numbers that can be made using each of these digits once. There are 6 possibilities: 478, 487, 784, 748, 847, 874.

• Ask: What are the greatest and least numbers that can be created? Greatest number is 874, least number is 478. How did you know?

• Repeat, using the digits 0, 2 and 6. What numbers can you build now? 602, 620, 260, 206 206. Discuss that, for the purposes of today, 026 and 062 are not permissible.

• Ask: What does the zero in the number represent? The zero is a place holder. It tells us that there are no ones, tens or hundreds and so on, in the number. While nothing is always nothing, a zero communicates very different information, depending on its placement in a number: the zero in 403 is very different from the 0 in 4032.

Teac he r

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

• Base ten blocks • On track (Game mat 4, p. 44) • Number cards or number tiles (0–9) (Mathmaster 3, pp. 82–83) or use the spinner • Pencil and paper clip

INVITATION

TO EXPLORE:

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MATERIALS

TO TUNE-IN:

GROUPING:

PAIRS

• Distribute On track Game mat (page ON TRACK S 34) to each pair of students. Model how Group 1 place 10 a 10 in Start to label the On track mat. Group 1 place a 10 in the Start square and 100 square and 100 in Finish square. Group 2 place a in the Finish square. Group 2 put a 100 100 in Start square and 1000 in 100 in the Start square and a 1000 in the Finish square.

F Finish square.

• Demonstrate how to play Squeeze play.

HOW TO PLAY SQUEEZE PLAY  The first player chooses two (Group 1) or three (Group 2) number tiles or cards and makes a number. For example, if digits two and six are chosen, the first player can choose to make the numbers 26 or 62.  Player 1 decides where to write the chosen number on his or her On track gameboard.  Players alternate turns and record their results on separate On track gameboards.  If a player cannot place either of the possible numbers in a remaining square, nothing is recorded.  The first player to complete a gameboard, so that it is filled with numbers in ascending order from least to greatest, is the winner.

TART

BJECTIVE

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Students play a game in which they select digits from a pile of cards or tiles and arrange them on a number track to build numbers. The winner is the first player to fill the On track game mat with numbers in order from least to greatest.

LANGUAGE

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REMINDER

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Revisit icon ‘Know your place’ (Mathmaster 1, p. 79). Ask: What is it that allows two different numbers to be made with two digits? Place value.

INVITATION

INISH

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TO PRACTICE:

Assign Group 1: Practice Workout 10, page 35 Assign Group 2: Practice Workout 11, page 36

NVITATION TO REFLECT

• This game allows students to play with the concept of place value. We shouldn’t assume that because they can count and write numbers, they understand the underlying meaning of the symbols. This game, by asking students to strategically place numbers on the gameboard in order from least to greatest, gives them an opportunity to develop a feel for the relative magnitude of number, compare numbers, see relationships, and build a variety of skills commonly referred to as number sense.

• Ask: How did you decide where to put your numbers?

• Ask: If you made the number 97, would you put it near the beginning or the end of the track?

• Ask: What would you do differently next time?

Number and place value

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33

The child with the shortest name is Player 1.

Player 1 chooses number tiles and makes a number. Decide where to write the number on your gameboard.

Players take turns. If a number can’t be placed on the gameboard, miss a turn. The first player to complete the gameboard, so it is filled with numbers from least to greatest, is the winner.

Step 1:

Step 2:

TO PLAY

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Start:

HOW

3

UNIT

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Number and place value

Use a pencil and a paper clip to make a spinner.

Teac he r

On track

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Game mat 4

GAME

Mystery number

UNIT

3



Use the clues. Circle the mystery number in the box. Use

(a) I have: 7 tens

(b) I have:

724

274

247

472

4 tens

208

0 tens

280

802 820

2 hundreds

(c) I have:

8 ones

8 ones

(d) I have: 843

3 tens 438 4 ones

348

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to help.

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2 hundreds 4 ones

PRACTICE – GROUP 1

433

434

334

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2 ones



Use numerals below. (a) 2, 6, 5

Work-out 10

(f) I have: 4 hundreds

824 842 248 482

0 ones

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(e) I have:

470

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407

704

740

to show the different three-digit numbers that can be made using the (b) 8, 7, 5

Number and place value

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Mystery number

UNIT

3

Use the clues. Circle the mystery number in the box.

(a) I have:

(b) I have:

7348

4 thousands

4738

8 ones

8734

0 tens

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3 tens 7 hundreds

6802

Teac he r 0 hundreds

(d) I have: 4024 2044 2404 4204

2 thousands

7 ones 4 tens 1 thousand

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7413

4731

1347

1473

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(e) I have:

(f) I have:

6 tens

8 thousands 2 hundreds

8 tens

6482

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4 ones

36

2860

6 thousands

(c) I have:



6208

2 hundreds

8 ones

4 tens

2806

2846

4 thousands

2486

6 hundreds

8264

. te

2 ones

4628

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

PRACTICE – GROUP 2

6824

8426

4682

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What are the least and greatestc numbers that you can make with the four digits? e her r o t s super 9 6 4 1 2 8 3 7 (a) (b) least

least

greatest

greatest

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Number and place value

Work-out 11

Monkey in the middle – lesson plan

UNIT

3

BIG IDEAS:

INVITATION

TO TUNE-IN:

r o e t s Bo r e p ok u : S I NVITATION TO EXPLORE

MATERIALS:

• Place value cards (Mathmaster 5, pp. 85–87).

For Group 1, use the sets 1–9 and 10–90. Use 1–9, 10–90 and 100–900 for Group 2.

• Game mat 5, page 38

GROUPING:

TEAMS OF THREE

• Group students in teams of three. Provide each team with a set of place value cards and a game mat (page 38) for each child.

• Invite students to join you in a demonstration game of Monkey in the middle.

HOW TO PLAY MONKEY IN THE MIDDLE  Players lay the place value cards into three piles (Group 2) or two piles (Group 1).

One pile for the hundreds (Group 2 only), one pile for the tens and one pile for the ones.  Each of the three students chooses a place value card 3 0 0 369 from each pile and builds a number. For example: 6 0 9 Player 1, a Group 2 member, turns over a 300, a 60 and a 9, using the cards to build the number 369. Each player is careful to keep his/her number hidden from the other two people in the group.  The students examine their numbers and guess whether it is the least, middle or greatest of the three numbers made.  Students record their guess on the Number guess (Game mat 5, p. 38).  Students play ten rounds. The person with the most points after ten rounds is the winner.

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• Say: Today we are going to be number builders. It’s an important job. Here’s how we do it.

• Show students how to use the place value cards to build numbers; for example: Together, we are going to build the number 473. How do you think we might do it? Choose the card showing 400, place it down first, then find the 70 card and place it over the two zeros on the 400. Finally, find the 3 and place it over the zero in 70.

• Say: Let’s build some numbers … rapid fire. 67, 34, 88, 45, 378, 494, 202. After each number has been made, write it in words for children to see. Sixty-seven, thirtyfour, eighty-eight, forty-five … two hundred and two.

OBJECTIVE:

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Students use place value cards to make a hidden two-digit number (Group 1) or three-digit number (Group 2). They then guess whether their number is the least, middle or greatest of the three numbers made within their grouping.

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Note: How to Score

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Players score one point if they guess the right position for their number. For example: Player 1 makes the number 369, while the other players make the numbers 486 and 523. Player 1 guesses his/her number to be the middle number. It is not. It is the least number. His/her score is 0 points.

INVITATION

TO REFLECT:

• Ask: Which place value card had the greater influence on your guess? The hundreds (Group 2). The tens (Group 1).

• Ask: Was it possible to build a number with zero as a place-holder? No. • Revisit the ‘Big idea’ icon, ‘Know your place’ (Mathmaster 1, p. 79). Discuss its meaning with the class.

INVITATION

TO PRACTICE:

Assign Group 1: Practice work-outs 12 and 13, pages 39–40 Assign Group 2: Practice work-outs 14 and 15, pages 41–42

Number and place value

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37

Monkey in the middle

UNIT

3

HOW

GAME

TO PLAY

The oldest person is Player 1.

Step 1:

Turn over place value cards; for example:

Step 2:

Keep the cards hidden from the other two players in your group.

Step 3:

Make your number; for example:

Step 4:

Decide whether you think your number is the least, middle or greatest number of the three numbers made in your group.

Step 5:

Record your guess.

Teac he r

Start:

300

60

9

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

6

9

Score one point if you guess the right position for your number. For example: You make the number 369, your partners make the numbers 486 and 523. You guess your number to be the middle number.

It is not. It is the smallest number. You score 0 points.

Step 7:

Play 10 rounds. The player with the most points wins.

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Step 6:

© R. I .

C Publ i cat i ons N. •f orr e vi ew p ur pos esonl yPoints • Round Least Middle Greatest UMBER GUESS

369

486

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1.

2.

3.

4.

5.

6.

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523

0

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Example

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7.

8.

9.

10.

38

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Number and place value

Game mat 5

Build the number – 1

UNIT

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 30 40 50 60 70 80 90

fifteen sixteen seventeen eighteen nineteen twenty thirty forty fifty sixty seventy eighty ninety

You can use these to write other numbers: 56 is fifty-six.

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

Use place value cards



one two three four five six seven eight nine ten eleven twelve thirteen fourteen

30 6

to complete the chart.

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3

PRACTICE – GROUP 1

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ones

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6

(a)

(b)

(c)

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tens

5

3

sixty-three

0

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Write the number

7

o c . che e r o t ones r s super ones 4

forty-eight

(d)

(e)

Work-out 12

tens

ones

3

0 9

tens

ones

3

4

Number and place value

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Build the number – 2

UNIT

3



Use place value cards

30 6

(c)

(d)

eighteen

11

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0 6

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40

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0 8

Teac he r

(a)

to build the number. Complete the chart.

1

18

PRACTICE – GROUP 1

nineteen

o c . che e r o t r s super

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fourteen

Number and place value

Work-out 13

Build the number – 1

UNIT

3

one

10

ten

19

nineteen 100 one hundred

2

two

11

eleven

20

twenty

200 two hundred

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three

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twelve

30

thirty

300 three hundred

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four

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thirteen

40

forty

400 four hundred

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five

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fourteen

50

fifty

500 five hundred

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six

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fifteen

60

sixty

600 six hundred

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seven

16

sixteen

70

seventy

700 seven hundred

8

eight

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seventeen

80

eighty

800 eight hundred

9

nine

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eighteen

90

ninety

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Use place value cards



1

300 60

9

to complete the chart.

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Teac he r

You can use these to write other numbers: 356 is three hundred and fifty-six.

PRACTICE – GROUP 2

900 nine hundred

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C.P ub i cat i ons Use words Build thel number •f orr ev i ew pur s sonl y• 3p 0o 0e hundreds tens ones Write the number

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(b)

(c)

(d)

Work-out 14

hundreds

3

6

tens

ones

3

0 6

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0

0

2

0

three hundred and thirty-six

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3

1 . te o hundreds tens ones c . che e r o t r s six hundred and eighty-four super hundreds

tens

ones

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9

7

hundreds

tens

ones

8

0

2

Number and place value

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Build the number – 2

UNIT

3

Use place value cards

300 40 6

to build the number. Complete the chart.

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56

(b)

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(a)

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fifty-six

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PRACTICE – GROUP 2

o c . che e r o t r s super 6

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Number and place value

Work-out 15

Three in-a-row – lesson plan

UNIT

3

BIG IDEAS:

TO TUNE-IN:

• Ask the class to look at the Hundreds of possibilities chart. Allow them a few minutes to carefully examine it to find patterns of interest to them. Review the distinction between columns and rows on the chart.

• Ask: What patterns do you see? Answers will vary. Try to elicit the following discoveries: all the numbers in a column share the same ones digit; numbers increase by one when you move right one square and decrease by one when you move left one square; numbers increase by 10 when you move down one square and they decrease by 10 when you move up one square.

• Give students a starting number and ask them to find a new number; for example: Find the number 14 on your chart. What number is two squares below it? 34. Find 14 again. What number is three squares to the left of it? 11.

• Continue to introduce numbers, until students are comfortable locating them on the hundred chart.

• As a possible extension, have the class use the terms ‘east’, ‘west’, ‘north’ and ‘south’ to describe the movements on the board to improve their direction and mapping skills.

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

• Coloured counters • Hundreds of possibilities Game mat 6, page 44

INVITATION

OBJECTIVE:

Students move paper clips on a number line to build two-digit numbers, which are then covered on a hundred chart. The first player to cover three squares in a row horizontally, vertically or diagonally is the winner.

TO EXPLORE:

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Teac he r

MATERIALS

INVITATION

GROUPING: PAIRS

Explain Three in-a-row as described below.

HOW TO PLAY THREE IN-A-ROW  Players place two paperclips on any two numbers on the On track grid. They then decide which number will represent tens and which will represent ones (Example: a player places a paperclip on the 4 and the 3, then decides whether to form the number 34 or 43). He or she then 0 1 2 3 4 5 6 7 8 9 covers the number on the Hundreds of possibilities chart; for example: the player chooses 43.  The next player must move one paperclip, but only one. He/she places the digits to create a two-digit number and covers that square on the Hundreds of possibilities chart. Note: Both paperclips can be placed on the same number to create a double.  Play continues until one player has placed three coloured counters in a row— horizontally, vertically or diagonally.  A modification of the game uses two different coloured paperclips, one to select the tens digit and the other for the ones.

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91 92 93 94 95 96 97 98 99 100

NVITATION TO REFLECT

0

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9

• Ask: What strategies did you use while playing the game?

• Ask: Did you notice any patterns?

• Revisit ‘Big idea’ icon, ‘Know your place’ (Mathmaster 1, p. 80). Invite students to make a journal entry to explain its meaning.

INVITATION

TO PRACTICE:

Assign Group 1: Practice work-out 16, page 45 Assign Group 2: Practice work-out 17, page 46 Number and place value

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43

Hundreds of possibilities

UNIT

3

HOW

GAME

TO PLAY

The person with the shortest name is Player 1.

Step 1:

Player 1 places two paperclips on the ‘On track’. Decide on the number it will make; for example, your paperclips are on 3 and 9. You can make 39 or 93. Use a counter to cover the number on the ‘Hundred chart’.

Step 2:

Player 2 has his/her turn. Player 2 can only move one paperclip to make a new number.

Step 3:

Players take turns until one player has placed three counters in a row (diagonally, vertically or horizontally).

Note: Double numbers can be made by placing both paperclips on the same number.

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

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Start:

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o c . e 73 c 74 75 76 77 78 79 80 her r o st super On track

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4

5

Number and place value

Game mat 6

Hundreds of possibilities

UNIT

3

PRACTICE – GROUP 1

Your friend has spilled jam on your hundreds chart. What are the missing numbers?

5 6 7 8 r o e t s Bo r e p o u 18 S13 14 15 16 17 k

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. te 73 74 75 76 77 78 o 79 c . c e88 89 82 83 h 84 85 86 87 r e o r st super 92

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Missing numbers:

Work-out 16

Number and place value

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Hundreds of possibilities

UNIT

3

PRACTICE – GROUP 2

Your friend has spilled jam on your 200s chart. What are the missing numbers?

206 207 208 209 r o e t s Bo r e p o u 213 214 215 216 217 218 k 219 S 203

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o c . c e 284 285 286 287 288 289 her r o st super 294

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Missing numbers:

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Number and place value

Work-out 17

Puzzling – lesson plan

UNIT

3

BIG IDEAS:

TO TUNE-IN:

• Say: We are going to play another game that involves the hundreds chart. It is a little different today, since we are starting with a blank chart.

• Hand out a copy of Mathmaster 7 (page 89) to each pair of students.

• Guide students to fill the four corners and the 50 on the hundreds chart.

• Turn over a place value card from a one’s pile and a 1 10 place value card from a ten’s pile; for example: a 6 and a 40. Ask: What number can I build with these cards?

50 46 Great. Now here’s the tricky part. Where would 46. you place this number on your hundreds chart?

Have a volunteer indicate the number’s location on your overhead transparency.

• Continue building numbers. Have volunteers place the numbers on the blank chart.

• Coloured markers, one per student, each a different colour • Blank hundreds chart (Mathmaster 7, p. 89) • Number cards (Mathmaster 3, pp. 82–83) 2 of each digit 0–9 per student • Envelopes and scissors • For the teacher: overhead transparencies of Mathmaster 7, Mathmaster 5, pages 85–87

INVITATION

TO EXPLORE:

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Teac he r

MATERIALS

INVITATION

GROUPING: PAIRS

Hand out a copy of Mathmaster 5 and 20 number cards or tiles (2 each of digits 0-9) to each of the students. Have students label the four corners and the 50 on the chart.

Model and explain the game Puzzling.

HOW TO PLAY PUZZLING  Player 1 selects three number tiles. With these 7 1 10 11 12 16 tiles he or she creates two two-digit numbers; for 23 26 27 example: Player 1 selects a 4, 6 and a 3 and 36 37 31 32 33 34 chooses to build the number 36 and 46.

44 45 46 50 56 57  Player 1 fills these numbers in their appropriate 66 67 68 69 location on the hundreds chart.

79  Player 2 repeats the same steps.

88 97 91 100  Players alternate turns until one player has Player 1 wins running north completed a path from one side of the hundreds chart to the other. A completed path can travel top to to south. Player 2 has a good bottom (north/south) or left to right (west/east). A path, but is blocked running west to east. completed path may also include squares that share only a common corner.  Once the game is over, players complete the hundreds chart.  Using scissors, the team cuts the hundreds chart into seven to ten pieces (students cut on the lines only).  Playing groups write a group name on the back of each piece.  Players place the pieces in an envelope and put their group name on the envelope.  Players exchange puzzles and solve them.

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OBJECTIVE:

Students fill in a blank hundreds chart in an attempt to be the first to form a continuous path from one side to the other.

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Note:

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1. The four corners and the 50 are ‘free’ spaces that can be used for both player’s path.

2. Students can use 0s to form the numbers 1 to 9.

Example: 05 is 5.

IDEA: The envelopes of unsolved puzzles can be used as an activity centre.

INVITATION

TO REFLECT:

• Ask: How can you get a 4, when choosing two digits? You have to turn over a zero.

• Say: We have explored three ‘big ideas’ relating to place value. Invite students to describe them. Introduce the ‘big idea’, ‘Nothing is something’ (Mathmaster 1, p. 79). What does ‘Nothing is something’ mean to you?

INVITATION

TO PRACTICE:

Students can exchange puzzles.

Number and place value

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Tetra hunt – lesson plan INVITATION

UNIT

3

TO TUNE-IN:

INVITATION

BIG IDEAS:

r o e t s Bo M r e p ok u S: GROUPING:

TO EXPLORE

PAIRS

Introduce and explain the game, Tetra hunt.

HOW TO PLAY TETRA HUNT  Each player selects two of his/her tetrominoes and places them on the Tetra hunt chart.  Players keep their gameboards hidden from each other during the game.  Players take turns guessing the location of 1 2 3 4 5 6 7 8 9 10 each other’s tetrominoes (Player 1: Does 11 12 13 14 15 16 17 18 19 20 one of your tetrominoes cover number 21 22 23 24 25 26 27 28 29 30 18? Player 2: No. Player 2: Does one of 31 32 33 34 35 36 37 38 39 40 your tetrominoes cover number 54?

41 42 43 44 45 46 47 48 49 50 Player 1: Yes.) 51 52 53 54 55 56 57 58 59 60  Players should use their own Tetra hunt 61 62 63 64 65 66 67 68 69 70 chart to keep track of their guesses.

71 72 73 74 75 76 77 78 79 80  The first player to find all of the numbers 81 82 83 84 85 86 87 88 89 90 that his or her partner’s tetrominoes cover 91 92 93 94 95 96 97 98 99 100 (eight in total) is the winner.

ATERIALS:

• Tetra hunt Game mat 7, page 49 • 2 cm connecting cubes

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Teac he r

• Connect four cubes together in a straight line and tell students that this is a ‘tetromino’. Explain that any shape that has four congruent squares, with one full side of each square touching at least one full side of another square, is called a tetromino.

• Tell students to find all the other tetrominoes that can be made with four connecting cubes. Remind them that if a shape can be flipped (reflected) or turned (rotated) to be ‘congruent’ (have the same size and shape, but not necessarily the same position, as another figure) with another shape, it is not different.

• Explain that some people use letters of the alphabet to describe tetrominoes (e.g. I, L, 0, T, Z).

OBJECTIVE:

This is a modified game of Battleship™. Students build five tetrominoes with connecting cubes. They hide two of the shapes on the Tetra hunt chart.

Students call out numbers on the Tetra hunt chart in search of their partner’s tetrominoes. The first to locate both hidden shapes is the winner.

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INVITATION

. te

TO REFLECT:

o c . che e r o t r s super

• Ask: What strategies, if any, did you use to play Tetra hunt?

INVITATION

TO APPLY:

:

Assign Group 1: Practice work-out 18, page 50 Assign Group 2: Practice work-out 19, page 51

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Number and place value

Tetra hunt

UNIT

3

HOW

GAME

TO PLAY

Step 1:

Each player chooses two tetrominoes. Place them on the chart below. Keep your chart hidden from the other player.

Step 2:

Players take turns to guess the position of each other’s tetrominoes.

Step 3:

Keep track of your guesses with or on your own chart. The first player to find all the numbers covered by his/her partner’s tetrominoes is the winner.

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On track 0 Game mat 7

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Number and place value

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Tetra hunt

UNIT

3



Fill in the missing numbers from the 100 chart.

(a)

(b)

(c)

(d)

r o e t s Bo r e p ok u S 31

(g)

(h)

30

41

(j)

47

74

(k)

26

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83

(i)

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Teac he r

75

(e)

PRACTICE – GROUP 1

(l)

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(a)

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Place these numbers where they belong on the chart.

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(d) eighty-three

fifty-six

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(e) sixty-four

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(c)

4 tens 8 ones

(f)

3 tens 9 ones

40

65

Number and place value

Work-out 18

Tetra hunt

UNIT

3

PRACTICE – GROUP 2

Fill in the missing numbers from the 200 chart.

(a)

(c) 183

(b)

(e)

r o e t s Bo r e p ok u S 113

(f) 138

(g)

120

(i)

(h)

160

106

(j)

(k)

159

182

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Place these numbers where they belong on the chart.

(a)

(d)

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

194

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115

(d)

136

(b) (c) . te o c 145 122 . c e her r o t s super one hundred and twentythree

one hundred and ninety-nine

(e)

one hundred 123 and forty-three

200

Work-out 19

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Number and place value

1 hundred 6 tens 4 ones

(f) one hundred and seventyseven

176

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Assessment PERFORMANCE

ASSESSMENT THROUGH PROBLEM SOLVING:

Grouping Individual Grouping: Strategy: Use logical thinking Strategy Materials: Number tiles or number cards (Mathmaster 3).

Materials ACTIVITY:

BIG IDEA:

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

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Teac he r

Margot lost the combination to her diary. Just in case this ever happened, she had previously hidden clues under the bed. Here are the clues:  The three digits that make up the combination are 4, 3 and 1.  The number in the hundreds place is less than two.  The cover of the diary is blue.  The 1 and the 4 are not next to each other.

Help Margot figure out her combination.

PLAN: Choose a strategy UNDERSTAND: What do you know?

• Use logical thinking • The combination of the diary is made up of the digits 4, 3 and 1.

• The number in the hundred’s place is less than two.

• The cover of the diary is blue.

• The 1 and the 4 are not next to each other.

What do you need to find out?

• The combination to Margot’s diary.

© R. I .

C.Publ i cat i ons Try your plan •f orr evi ew pur posesonl y• • The first clue tells us what digits make up the combination 4, 3 and 1.

• • •

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The second clue tells us that the 1 has to be in the hundred’s place.

The third clue does not give us any useful information.

The fourth clue tells us that the 1 and 4 can’t be beside one another.

Since the 1 is in the hundreds place, the 4 must be in the ones place.

The only place leftover for the three is in the tens place.

What is your answer The combination is 134.

hundreds

tens

ones

tens

ones

1 hundreds

m . u

SOLVE:

1

hundreds

tens

4

ones

3 . te o c : (Question the answer) C : Use pictures, symbols and words to explain . c e your answers.

Did your plan work? If not,h try again. r er o st super

LOOK BACK

INDIVIDUAL ASSESSMENT Materials: 5 $1 coins and 5 10c coins, place value cards (Mathmaster 5, pp. 85–87), base ten blocks.

Task 1: Write in symbols and in words a variety of three-digit numbers; for example: 346, 489, 722 …

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1

OMMUNICATE

Have students build the numbers with place value cards and base ten blocks.

Task 2: Tate has 7 coins. She has one more $1 coin than she has 10c coins. How much money does she have? $4.30.

Number and place value

SHOW WHAT YOU KNOW Group 1: Work-out 20, page 53 Group 2: Work-out 21, page 54

SHOW

WHAT YOU KNOW

– GROUP 1:

 Use base ten blocks (a) 436

. Build the number. (b) 323

(c) 486

(d) 672

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

 What numbers can you make with these digits?

(b) 8, 0, 5

 Use place value cards

3 0

6

to complete the chart.

Write the number tens

(a)

Build the number

Use words

ones

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5

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35

42

76

Work-out 20

Number and place value

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SHOW WHAT YOU KNOW – GROUP 2: Use base ten blocks

. Build the number.

(a) 3029 

(b) 4653

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What is the value of 8 in each number?

(d) 783

(e) 806

(f) 8201

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Write each number.

(a) three hundred and sixty

(b) 800 + 60 + 5

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Fill in the missing numbers from the 200s chart. ch e r er o t s s r u e p (a) (b) (c) (c) four thousand, three hundred and six



(c)

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(b)

(a) 308



(d) 400 + 1000

83

123

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(d) 6003

Write the numbers shown by the base ten blocks. (a)



(c) 2891

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Number and place value

Activity cards ACTIVITY

CARD

3–1

BIG IDEAS:

BINGO

MATERIALS:

Blank Bingo cards (Mathmaster 8, p. 90), place value cards (Mathmaster 5, pp. 85–87) or spinners, coloured counters.

OBJECTIVE:

Players fill their Bingo cards with self-selected two-digit numbers (Group 1) and three-digit numbers (Group 2). They then turn over place value cards to build numbers. If the number created matches a number on a player’s card, it is covered with a coloured counter.

BINGO MATERIALS:

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

Blank Bingo cards, place value cards or spinners, coloured counters What to do:

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 Fill your Bingo card with two-digit numbers (Group 1) or three-digit (Group 2).  Turn the place value cards face down.

 Turn over 1 ten’s place value card and 1 one’s place value card (and a hundreds card for Group 2). Build a number.  If the number built matches a number on your card, cover it with a counter.

 The first player to cover a row of five numbers horizontally, vertically or diagonally wins.

© R. I .

C.Publ i cat i ons •f o evi ew pu posesonl y•BIG IDEAS: 3 –r 2r Wr  Play again. This time, Group 1 uses the three-digit cards, while Group 2 uses just the oneand two-digit cards.

ACTIVITY

CARD

AR

MATERIALS: Number cards, four each of digits 0–9 (Mathmaster 3, pp. 82–83).

Players turn over two cards and make the largest two-digit number possible. Players compare their numbers. The person with the larger number wins all the cards. The first player to acquire all forty cards is the winner.

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WAR

MATERIALS:

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40 number cards or number tiles, four each of digits 0–9 c e her r o What to do: t s super  Shuffle the number cards and deal 20 cards to each player. 

Players turn over two cards and make the greatest two-digit number possible.



The player with the greatest number wins all the cards in the round.



In the case of a tie, each player turns over one more card. The player with the greater number wins.



Continue play until one player has all 40 cards.



Play again. This time turn over three cards to make three-digit numbers.

Number and place value

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55

Activity cards ACTIVITY

CARD

3–3

WIPE

BIG IDEAS:

OUT

MATERIALS: Calculator OBJECTIVE: WIPE

Students play Wipe-out on a calculator.

OUT

MATERIALS:

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Calculator

What to do:

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 Enter 2413 on a calculator.  Change the four to a zero by making only one calculator operation (–400).  Complete the chart to the right.  Make your own Wipe out chart for a partner to solve.

OUT

OPERATIONS

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Number and place value

Centiworms – lesson plan

UNIT

4

INVITATION

BIG IDEAS:

• Say: We are going to be playing with some new friends this week: Centiworms.

I would like to first introduce you to Slippy2, the smallest of all the centiworms.

Hand a copy of Slippy2 to all students along with a copy of Activity mat 7, page 59.

• Say: Centiworms have an interesting habitat; they live in number cocoons on the hundreds chart. Let’s find out where Slippy2 and all his friends live.

• Place Slippy2 on the OHP. Where does Slippy2 live? On the two. That’s right. Slippy2 and his friends live in every second number. To find them we will have to count by twos.

• Say: Help me find the rest of Slippy2’s friends. Colour the number two and shift Slippy2 to reveal the next centiworms home: number 4.

• Continue to find the hidden homes. Encourage students to say with you: 2, 4, 6, 8, 10, 12, 14, 16 … Have them place a coloured counter on each home on their hundreds chart. Ask: What is the next number? How do you know? 18. Possible answers: 18 is the next even number; you keep colouring under the numbers already done, in a vertical line; or you skip every other number. Ask students to make predictions: Do you think a centiworm lives in 26? Yes. In 47? No. In 100? Yes. • Demonstrate how to use the pattern tracker to record the pattern.

HUNDREDS CHART PATTERN TRACKER SLIPPY2

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• Centiworms (Mathmaster 9, p. 91) • Pattern tracker (Activity mat 7, p. 59) • Overhead transparency of pattern tracker • Coloured markers

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one hundred.

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A different view:

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This activity works well with a metre stick in place of the hundreds chart.

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C.Publ i cat i ons Students use centiworms to •f orr evi ew pur posesonl y• explore number patterns to OBJECTIVE:

0

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• Ask: How is the 3s pattern on the 100 chart the same and how is it different from the 2s? You colour the 6, 12, 18 … on both; you colour an odd number, an even number and then an odd number and so on; the numbers fall in a horizontal line, not vertical.

Number and place value

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Centiworms – lesson plan continued INVITATION

GROUPING: THREES

TO EXPLORE:

UNIT

4

• Give each group a different centiworm (Mathmaster 9, p. 91).

• Introduce the Centiworms activity.

CENTIWORMS  Invite students to use the chart on Activity mat 7 (page 59) to get to know their centiworms.  Ask them to predict where their centiworms live on the hundreds chart.  Working in their groups, students find and record the homes of their centiworms.  Students who finish early can be asked to find the homes of another centiworm.

TO REFLECT

• Post the completed patterns around the room. Ask students to be centiworm detectives and invite them to take 15 minutes to browse the walls looking for interesting patterns and shape formations.

• Ask: Are there any numbers that seem to show up in more than one pattern? 24, 30, 36, 40, 48 and 80 show up on five different charts. 60, 72, 90 show up on six different charts.

• Ask: Are there any numbers that never or rarely show up? Prime numbers do not show up.

• Ask: How many Slippy2 worms live on a hundred chart? 50. How many Octo worms live on a hundred chart? 12 etc. …

• Spend additional time PATTERN TRACKER exploring the patterns in OCTO the numbers themselves, circling the core pattern.

0 8 For example: counting by 1 6 8s creates an 8, 6, 4, 2, 0 2 4 repeating pattern in the 3 2 ones place.

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INVITATION

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INVITATION

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TO PRACTICE:

Practice work-out 22, page 60

INTRODUCE

ICON:

Connect students’ discoveries of patterns to the ‘Big Idea’ icon: ‘Numbers speak in patterns and relationships’ (Mathmaster 1, p. 80).

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Number and place value

Centiworms

UNIT

4

ACTIVITY

CENTIWORM

LENGTH

ON

100S

Slippy2

2 squares

Trio

3 squares

Quadi Pent Hex

Octo

Nona

4 squares 5 squares 6 squares 7 squares

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CHART

8 squares 9 squares

Deci

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Number and place value

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Number patterns

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Use a hundred chart to fill in the blanks. (a) Count by 2s. Fill in the blanks.

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Use a hundred chart to find how many pencils.

(a) 3 jars of

(b) 3 jars of

pencils 60

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(c) 3 jars of

pencils Number and place value

pencils Work-out 22

See you tomARROW – lesson plan

UNIT

4

INVITATION

BIG IDEAS:

MATERIALS:

• Distribute one copy of See you tomARROW Game mat 8 (page 62) to each pair of students. Hand out 12 coloured cubes to each pair of students.

• Ask: Find number 18 on your chart. What number is two squares below it? 38.

Find 18 again. What number is three squares to the left? 15.

• Explain to the students that you are going to teach them a special maths code to describe movements on a 100s chart. Display the following chart and review the command of each arrow. See Diagram 1.

1 2 3 4 5 6 7 8 9 10 • Provide students with a number of different codes. 11 12 13 14 15 16 17 18 19 20 Start with one-step arrow codes and progress until 21 22 23 24 25 26 27 28 29 30 they are comfortable with three-step codes; for 31 32 33 34 35 36 37 38 39 40 example: 24 .

41 42 43 44 45 46 47 48 49 50 Model the process by placing 51 52 53 54 55 56 57 58 59 60 an ‘X’ on the starting square: 24. Place a cube 61 62 63 64 65 66 67 68 69 70 24 on 24 and then move 71 72 73 74 75 76 77 78 79 80 the cube to match 81 82 83 84 85 86 87 88 89 90 the commands of 91 92 93 94 95 96 97 98 99 100 the arrows: down 2, right one (+10, +10, +1 = 45).

Diagram 1

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

•Coloured 1-cm cubes • See you tomARROW Game mat 8, page 62 • Overhead transparency hundreds chart (Mathmaster 6, p. 88) • Two game pieces

Teac he r

TO TUNE-IN:

© R. I .

C.Publ i ca t i ons G : I : Model for students howr top playo Sees youe tomARROW. tomARROW •f orr evi ew pu son l y• H S ARROW

18 = 8 move up one square: subtract 10

18 = 17 move left one square: subtract 1

18 = 28 move down one square: add 10

18 = 40 move right 2 and down 2: add 2 then add 20

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OBJECTIVE:

Students use arrow patterns to explore the base ten relationship of our number system.

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Note: Some games may take too long for all 12 cubes to be captured.

You may wish to impose a time limit.

INVITATION

ROUPING PAIRS

NVITATION TO EXPLORE

OW TO PLAY

EE YOU TOM

 Each student selects six numbers upon which to place cubes. When finished, there should be 12 cubes covering 12 numbers on the chart.  Player 1 takes a game piece and places it on any number not already covered by a cube. Player 2 does the same.  Player 1 spins the arrow spinner and moves his/her game piece to match the command. If Player 1 lands on a number square with a cube, he or she captures the cube.  Players alternate turns until all cubes have been captured.  The player with the greatest number of cubes wins.  It is possible that a player won’t be able to move; for example, the player sits on a number in the 90s and spins a . In such cases the player loses a turn.

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18 = 19 move right one square: add 1

o c . che e r o t r s super

TO PRACTICE:

Practice work-out 23, page 63

INVITATION

TO REFLECT:

• Ask: How is a hundred chart like base ten blocks? Each row is made up of ten squares just like a rod is made up of 10 cubes. A full row and part of the next is the same as one rod and a collection of ones.

• Ask: What number comes after 48? 49. What arrow would show that?

• Ask: What number is 10 less than 63? 53. What arrow would show that?

• Ask: Imagine starting at 43 and ending at 32. What arrows could lead to the change? Answers will vary? Example: .

Number and place value

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61

See you tomARROW

UNIT

4

HOW

GAME

Use a pencil and a paperclip to make a spinner.

TO PLAY

Each player places six cubes each on the hundred chart.

Step 2:

Player 1 and Player 2 each place a game piece on any open square.

Step 3:

Player 1, spin the spinner. Move your game piece to match the spinner.

ARROW

SPINNER

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

Step 4:

If you land on the square with a cube, you capture the cube.

Step 5:

Player 1 and Player 2 take turns until all 12 cubes are captured.

Step 6:

The player with the most cubes wins.

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Number and place value

40

Game mat 8

See you tomARROW

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HUNDRED CHART

Use a hundred chart to fill in the blanks. 

What number comes before:

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PRACTICE

©R .

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C.Publ i cat i ons(d) 33? (b) 86? (c) 54?

•f orr evi ew pur posesonl y• What number comes after: (a) 19?

(a) 37?

(a) 61?







49?

(c)

72?

58?

(c)

22?

(d)

What number is 10 more than:

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16?

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o c (a) (b) 65? (c) 99? (d) 17? . ch e r o t r Fill in the missing number. e s super What number is 10 less than:

(a) 44

(b) 65

(c) 26

(d) 72

(e) 58

(f)

80

Fill in the missing arrows. (a) 39

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Work-out 23

50

Number and place value

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63

Metre made – lesson plan INVITATION

TO TUNE-IN:

• Provide each pair of students with a metre stick, or have them lay ten base ten rods lengthwise to form one metre.

• Ask students to share any observations they have about the metre stick. There are numbers 1 to 100 on it. Ten rods equal one metre.

UNIT

BIG IDEAS:

4

r o e t M s B r e oo p u k S

ATERIALS:

INVITATION

GROUPING:

TO EXPLORE:

TEAMS OF THREE

After modelling the game Metre made, hand out one base ten rod or a Deci centiworm and invite the class to play.

HOW TO PLAY METRE MADE  Each player places a game piece (coloured cube) on the number 50 on the metre stick. If students are using base ten rods as their gameboard, it will help to have the rods labelled as shown:

• Metre stick for each pair of students • 1 Deci centiworm (Mathmaster 9, p. 91) or a base ten rod for each student • Coloured cube as a game piece for each student • Metre made game Mat 9, page 65 • Pencil and paperclip

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• Ask a volunteer to help you model the game Metre made.

© R. I .

C.Publ i cat i ons O :  Player 1 spins the• spinner andr moves his/her cube to matchp theu command.

For s f o r e vi ew r po es onl y• Students add and subtract example: Player 1 spins the command –10 and moves the game piece to 40.

BJECTIVE

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INVITATION

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TO REFLECT:

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• Invite students to examine the icon, ‘Numbers speak in patterns and relationships’ (Mathmaster 1, p. 80).

• Ask: What patterns do you notice when you add or subtract multiples of 10?

• Ask: How is it like adding ones? How is it different?

• Ask: What does the zero in the number tell you?

INVITATION

multiples of ten in an attempt to build a metre.

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 Players spin ten times, recording their results each time on the Metre mat.  The player who is closest to one metre at the end of 10 rounds is the winner.  A game ends if a player reaches the end of the ruler before the full ten rounds.

TO PRACTICE:

Practice work-out 24, page 66

Note:

Be sure to explain to students that the ending number in one round becomes the starting number in the next round.

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Number and place value

Metre made

UNIT

4

METRE

GAME

SPINNER

Use a pencil and a paperclip to make a spinner.

HOW

TO PLAY

Step 1:

Each player places his/her game piece on the number 50 on the metre stick.

Teac he r

The person with the largest shoes is Player 1.

Step 2:

Player 1 spins the spinner and moves his/her game piece to match.

Step 3:

Players take turns to spin 10 times each. Record results in the chart below as you go.

–20 METRE

MAT

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Start:

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Number and place value

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Metre made

UNIT

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THINK

SPINNER

Complete the chart.

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Finish from top to bottom by counting by 10s. (a)

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Last number:

Last number:

How many tens are in one thousand?

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Number and place value

Work-out 24

Squeeze the wash – lesson plan

UNIT

4

INVITATION

BIG IDEAS:

• Display a ‘washing line’ in front of the class, showing the following multiples of ten: • Pick up a place value card; for example: 30. Who would like to place the number 30 where it belongs on the number line? Provide a clothes peg. When the number is placed on the line ask the students if they are satisfied with the number’s placement.

Encourage them to explain their reasoning.

• Continue selecting and placing numbers on the line until all multiples of ten from 10–100 have been properly positioned.

• Ask: Where do you think 110 would belong? 200? 1000?

• Next, introduce > and < as symbols to compare the relative size of numbers.

• Attach a ‘less than’ sign between the number 10 and 20 and a ‘greater’ than sign before the 100.

• Ask: I am thinking of a mystery number on this line.

Who would like to take a guess?

Is it greater than 40? Yes. I am going to move the ‘less than’ sign to fall between the 40 and 50 to reflect that wonderful guess. Whose next?

• Guessing continues until the secret number is discovered.

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

• Place value cards (Mathmaster 5, pp. 85–87) set 10–90 and 100 • String to build a washing line • 12 clothes pegs • Squeeze the wash Game mat 10, page 68 • Pencil and paperclip

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MATERIALS

TO TUNE-IN:

IC. :t © R. I .

Publ i ca i ons G : O : • Distribute Squeeze the wash game mat 10, page 68. Group 1 play Washing line 1 • f o r r e v i e w2. Group pu r p os s nl y• and 2 play Washing linee 3 and 4. o Students use the symbols < NVITATION TO EXPLORE

ROUPING PAIRS

BJECTIVE

TO PRACTICE:

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INVITATION

Group 1: Practice work-out 25, page 69

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• Review with children how to play Squeeze the wash.

HOW TO PLAY SQUEEZE THE WASH  Player 1 chooses a mystery number that falls on Washing line 1 and keeps it a secret from Player 2; for example: 36.  Player 2 spins the spinner twice to create a two-digit number. For example: Player 2 spins a 4 and a 2 and makes the number 24 (the number 42 could also have been made).  Player 2 asks: Is your number 24? Player 1 answers: No. My number is greater than 24.  Player 2 then draws a < ‘less than’ sign between 24 and 25 to help guide the next guess.  Player 2 continues to guess until the mystery number is discovered. The number of guesses required to find the number is the player’s score for the round—the fewer the better.  Players switch roles and continue to play on Washing line 2.

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and > to compare and order numbers on a number line.

o c . che e r o t r s super Students often confuse the

Group 2: Practice work-out 26, page 70 Watch for:

symbols > and <. Perhaps the ‘hungry crocodile’ analogy can help. Introduce the notion that the crocodile always eats the greater number.

The open mouth is always facing the greater number.

INVITATION

TO REFLECT:

• Ask: Can you compare the numbers 546, 293 and 186 just by looking at the tens?

• Ask: Which is greater, the 8 in 781 or the 9 in 649?

Number and place value

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Squeeze the wash

UNIT

4

GAME Use a pencil and a paperclip to make a spinner.

HOW

TO PLAY

Start:

The person with the shortest socks is Player 1.

Step 1:

Player 1 chooses a mystery number from the washing line. Keep it a secret.

Step 2:

Player 2 spins the spinner twice to make a two-digit number. Ask Player 1 if the number is the mystery number. Player 2 says ‘yes’ if it is, then the players swap turns. If the answer is ‘no’, Player 2 states whether it is less than or greater than the mystery number.

Teac he r

I spun a 4 and a 2. Is your number 24?

24 is less than the mystery number

No. My number is greater than 24.

Mystery number

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Player 2 records a < or > on the washing line. Continue until the mystery number is discovered.

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Number and place value

Game mat 10

Squeeze the wash

UNIT

4

Complete the number line. Fill in the

36

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

38

39

41

43

44 45

(b) What number is after 46? (c) What number is between 43 and 45? (d) What number is halfway between 40 and 50?

49

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Use the number line. Write < or > in the

(a) 38

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47

Use the number line.

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46

40

(e) 40

44

(b)

Work-out 25

62

48

50

(f)

45

41

39

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Write the numbers in order from the least to the greatest. (a)

(c)

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

PRACTICE – GROUP 1

93

6

72

Number and place value

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Squeeze the wash

UNIT

4



Complete the number line. Fill in the

85 86 

87

Use the number line.

PRACTICE – GROUP 2

.

89 90

92 93 94

95

97 98 99

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

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Teac he r

(a) What number is before 91? (b) What number is after 86?

(c) What number is between 92 and 94? (d) What number is halfway between 90 and 100?

Use the number line. Write < or > in the

(a) 87

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92

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(e) 92

89

Order the numbers in order from least to the greatest. (a)

(b)

70

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Number and place value

Work-out 26

Lay it on the line – lesson plan

UNIT

4

INVITATION

BIG IDEAS:

MATERIALS:

• Use a Bingo card (Mathmaster 8, p. 90) to create the following overhead transparency.

• Turn over two number cards; for example: 6 and 5. What numbers can I create with these two digits? 56 or 65. Exactly, I am going to make my number 56 and place it here on my Bingo card. What else might I have done with the digits? You could have made the number 65 and placed it beside the 64 in the row 64–81.

• Ask: Which game that we have played before does this remind you of? Squeeze play.

• Ask: Are there are any two digits that you can turn over that make it impossible to make a move in the first round. Yes, 4 and 6, 2 and 8, 1 and 1, 1 and 0, and 0 and 0.

11 29 47 64 82

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

OBJECTIVE:

INVITATION

TO EXPLORE:

11 29 47 64 82

free

28 46 63 81 99

free

28 46 63 81 99

56

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• Transparency of Bingo Card (Mathmaster 8, p. 90) • Number cards (0–9) or number tiles • Lay it on the line Game mat 11, page 72

Teac he r

TO TUNE-IN:

GROUPING:

PAIRS

• Hand out one copy of Lay it on the line Game mat 11 (page 72) to each pair of students, along with two sets of number cards (0–9) or number tiles.

• Explain how to play Lay it on the line.

HOW TO PLAY LAY IT ON THE LINE  Each student chooses a crayon, pen or pencil of a different colour.  Students spread the cards or tiles face down.  Player 1 selects two number cards—example 6 and 5—and builds a two-digit number: 65 or 56. Player 1 returns the cards to the pile.  Player 1 decides where on the Bingo board to write his/her number. Once placed, it can’t be erased. The numbers in a row must move left to right, least to greatest.  Players alternate turns until the Bingo card is filled. The player with the most squares wins.  If a player can’t make a number to fit the card, he or she misses their turn.

INVITATION

TO PRACTICE:

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Assign Group 1: Practice workout 27, page 73 Assign Group 2: Practice work-

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Students review place value concepts and continue to order and compare two-digit numbers.

o c . line. The first to get three inc e her r o row, horizontally, vertically or t s super diagonally is the winner.

A different view:

INVITATION

TO REFLECT:

• Ask: Is this game skill or luck?

• Ask: Is it possible to have a tie in this game? Yes. • Ask: Did you notice any number combinations that allowed for only one number to be made? Yes, 1 and 8, 2 and 9, 3 and 6, 4 and 7, all same-digit combinations.

Note:

The ‘free’ space can have two numbers written in it—one for each student.

Number and place value

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Lay it on the line

UNIT

4

B

I

N

G

O

11

28

29

46

47

Free

63

64

81

r o e t s Bo r e p ok u S 82

99

HOW

TO PLAY

The person with the most buttons on his/her shirt is Player 1.

Step 1:

Player 1 turns over two number cards and builds a number.

For example, 4 and 5 (I will make the number 54). 5 4

Step 2:

Player 1 writes the number on the Bingo card. The numbers in each row must be in order from least to greatest.

Step 3:

Player 2 takes a turn.

Step 4:

Keep taking turns until the Bingo card is full.

Step 5:

The player who fills in the most squares wins.

Step 6:

If you can’t make a number fit, you miss a turn.

I turned over a 4 and a 5. I think I’ll make the number 54.

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Start:

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28

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64

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82

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Number and place value

Game mat 11

Lay it on the line

UNIT

4



PRACTICE – GROUP 1

Use the number line to answer the questions.

70

71

72

73

74

75

76

77

78

79

80

81

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

82

83

84

(a) Circle the number that comes before 75.

(c) Draw a box around the number that comes before 72.

Match the number to the letter on the number line.

A

10 93

C

D

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100

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Look at the number and answer the question.

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(b) Underline the number that comes between 78 and 80.

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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



Work-out 27

Order the numbers from least to greatest.

Number and place value

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73

Lay it on the line

UNIT

4

PRACTICE – GROUP 2

Sport speed 190 km/h

Fastest squash ball

Roy Buckland

233 km/h

Fastest bowl

Shoaib Akhtar

161 km/h

Fastest tennis serve

Andy Roddick

246 km/h

Teac he r

Bobby Hull

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

(a) Place the speeds on the number line.

160

170

180

190

200

210

220

230

(c)

250

Compare, write < or > in the circle .

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(a)

100

300 + 20 + 6

(b) 2000 + 300 + 6

400 + 30

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

240

© R. I .

C.Publ i cat i ons Is the squash ball speed closer to 230 or 240?

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(b) Is the fastest bowl closer to 160 or 170?



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Fastest slap shot

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300

8000 + 600 + 30 + 5

(d) 400 + 80 + 9

500

400 + 90 + 9

1000

(b)

105

74

106

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110

111

Number and place value

Work-out 28

Assessment PERFORMANCE

ASSESSMENT THROUGH PROBLEM SOLVING:

BIG IDEA:

Grouping Individual Grouping: Strategy: Draw a diagram Strategy Materials: Hundreds chart (Mathmaster 6, p. 88).

Materials ACTIVITY:

Slippy2 spent the day visiting his friends on the hundred chart. He started at Milly’s apartment. She lives at number 36. He took the elevator up two floors (rows) to Frank’s apartment. Then he travelled down four floors to see Jimmy. Finally, he went down another two floors to see Marlene. Where do Slippy2’s friends live?

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

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16

25

26

35

36

45

46

Milly

55

56

65

66

75

76

© R. I .

C.Publ i cat i ons What is your answer Milly lives at apartment •f orr evi ew pur posesonl y • number 36.

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Try your plan  Slippy leaves Milly’s and goes up two floors to see Frank. Frank lives at 16.  Slippy then goes down four floors to visit Jimmy.

Jimmy lives at 56.  Slippy then visits Marlene, who lives two floors below Jimmy. Marlene lives at 76.

LOOK BACK: (Question the answer) Did your plan work? If not, try again.

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6

16

Frank

26 36

Milly

46 56

Jimmy

66 76 86

Marlene

Frank lives at 16.

Jimmy lives at 56.

Marlene lives at 76.

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SOLVE:

15

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UNDERSTAND: What do you know?

PLAN: • Slippy2 is visiting friends.

Choose a strategy • He starts at Milly’s apartment. She lives at number 36. • Draw a diagram • Frank lives two floors above Milly.

• Jimmy lives four floors below Frank.

• Marlene lives two floors below Jimmy.

What do you need to find out?

• The apartment number of each of Slippy2’s friends.

COMMUNICATE: Use pictures, symbols and/or words to communicate your answers.

o c . che e r o t r s super

INDIVIDUAL ASSESSMENT Materials: Blank number lines

Task 2: Fill in the first and last square

(Mathmaster 10, p. 92), blank hundred chart (Mathmaster 7, p. 89), coloured cubes.

Task 1: Partially fill in a blank number line. Place cubes on the line where numbers have not been labelled. Have students write the corresponding number on the line. Ask: What number comes before ? What number comes ten after ? What number comes between ?

of the hundred chart. Place cubes on the chart. Have students replace the cube with a number. Ask: What number comes before ? What number comes ten after ? What number comes between ? The chart can be a 100 chart, a 200 chart or a 1000 chart, depending on the level ability of the individual.

Number and place value

SHOW WHAT YOU KNOW Group 1: Work-out 29, page 76 Group 2: Work-out 30, page 77

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75

SHOW

WHAT YOU KNOW:

GROUP 1

 Count by 2s. Fill in the blanks.

36,

,

,

,

,

,

,

.

 Count by 5s. Fill in the blanks.

65,

,

r o e t s Bo r e p 9 7 3 ok 8 7 0 u S ,

,

,

,

,

.

 Write the least and greatest numbers possible using the digits.

8

6

(b)

least

greatest

least

least

greatest

greatest

 Fill in the missing number. (a) 84

(b) 61

(c)

74

 Write these letters on the number line.

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25 30 35  What number is 10 more?

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(a) 43?

40

45

50

(b) 35?

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(c)

55

60

65

48?

(d)

 Finish from top to bottom by counting ten.

(a)

Start. Count by 10s.

Start. Count by 10s.

(c)

Start. Count by 10s.

57

94

58

67

77

91

69

97

87

91

22

30

47

304

373

107

103

207

102

32

20

96

104

117

125

302

182

42

142

66

667

127

251

198

202

52

357

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

75

89?

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Last number: 76

70

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9

(c)

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(a)

804

408

704

312

733

723

182

906

51

282

713

401

607

12

703

414

261

683

693

536

472

Last number: Number and place value

Last number: Work-out 29

SHOW

WHAT YOU KNOW:

GROUP 2

 Look for patterns. Write the four next numbers.

(a) 345, 355, 365, 375,

,

,

,

.

(b) 425, 430, 435, 440,

,

,

,

.

(c) 440, 450, 460, 470,

,

,

,

.

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3

6

4

2

(b)

1

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 Write the least and greatest numbers possible using the digits.

4

8

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C.Publ i cat i ons (a) 340, 860, 210, , , .

•f orr ev i ew, pur posesonl y• (b) 965, 2010, 323, , .

 List the numbers from least to greatest.

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,

.

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(c) 4563, 5471, 3021,

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(b) 163

(c)

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 Estimate where to place these letters on the number lines. (a)

A = 323

100

(b)

1000 Work-out 30

B = 150

C = 750

500

A = 6073

146

B = 3450

D = 879

1000

C = 7500

5000 Number and place value

D = 4960

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77

Activity cards ACTIVITY

3–1

CARD

ON

BIG IDEAS:

YOUR MARK

MATERIALS:

Number cards, two each of digits 0–9 (Mathmaster 3, pp. 82-83), Self-made recording sheet similar to the one on the card below, calculator, hundred chart (optional).

OBJECTIVE:

Students build two-digit numbers, which become targets. Students guess whether the target will be hit as they skip-count on a calculator.

ON

YOUR MARK

r o e t s Bo r e p ok u S Skip-counting on a calculator:

MATERIALS:

Teac he r

WHAT

Keys to use:

Press these keys to skip-count by any number.

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Number cards, make a recording sheet like the one below, calculator.

Let’s try 4s:

TO DO

 Make your own recording chart.  Player 1: turn over two number cards and build a two-digit number. This is your target.



Play five times. The player with the most accurate guesses wins.

Example Round 1 Round 2

 Turn over another number card. This is your skipcounting number.

44s © R. I .

C.Publ i cat i on 6 •f orr evi ew pur posesno onl y•

Target number  Will you hit your target number when you skip-count by Skip count by your second number?

Hit target guess  Record your guess. Use your calculator to find out.

3–2

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ACTIVITY

CARD

NO

MATTER HOW YOU SLICE IT

MATERIALS: Base ten blocks, including a one thousand cube.

OBJECTIVE:

NO

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o c . che e r o t r s super

Students explore the relationship between the base ten blocks to determine how many units, rods and flats it would take to build one thousand.

MATTER HOW YOU SLICE IT

MATERIALS:

Base ten blocks What to do: Answer these questions.

78

1

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points

 Player 2: Your turn.

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Number and place value

BIG IDEAS:

Activity cards ACTIVITY

CARD

3–1

GO

BIG IDEAS:

BETWEEN

MATERIALS:

Number cards or number tiles, two each of digits 0–9 (Mathmaster 3, pp. 82-83); self-made recording sheets similar to the card below.

OBJECTIVE:

Students build two numbers with the same three number cards or tiles. They then select three more cards or tiles in an attempt to build a number that falls between the first two numbers.

GO

BETWEEN

MATERIALS:

TO DO

 Make your recording card.

I can make

 Player 1: Turn over three number cards or tiles.

Build the least and greatest numbers and record them on the ‘I can make’ chart. Return the cards or tiles to the pile.  Turn over three more tiles. Build a three-digit number. Score a point if it falls between your least and greatest numbers.

My numbers 1st pick Example: 3, 6, 4  

2nd pick 5, 9, 6,

Least 345

Between

Greatest

Score

569

643

1 point

© R. I .

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Number cards or number tiles, two each of digits 0–9; self-made recording sheets similar to the card below.

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Number and place value

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