Max Maths - Making Real-World Connections SB4 FULL

MAKING REAL-WORLD CONNECTIONS

maths a ×

MAKING REAL-WORLD CONNECTIONS M

STEPHANIE KING

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Contents

Finding new multiplication facts Multiplying and dividing by 10

How to Use This Book

Numbers and patterns Representing and describing 4-digit numbers Comparing and ordering numbers Place value Rounding numbers to the nearest 10 and 100 Counting patterns

67 Multiplying 2-digit numbers 71 Dividing 2-digit numbers 75

4 7

Data handling Collecting data Representing data Interpreting data

78 80 83 85

Fractions and decimals Representing, comparing and ordering fractions

Money and measures

18 20 24

90 Counting in fraction steps 94 Fractions of amounts and quantities 96 Representing and comparing decimal numbers 99 Counting in decimal steps 102 Numbers and patterns 104 Representing and describing whole numbers 106 Odd and even numbers 109 Factors and multiples 111 The four operations Working with addition 116 Working with subtraction 120 Multiplication table of 7 123 Multiplying and dividing by 100 125 Working with multiplication 127 Working with division 129 114

Money

Analogue clocks

Working with scales and measure The relationship between units of measurement

Addition and subtraction 32 The relationship between addition and subtraction 34 Strategies for mental addition and subtraction 37 Addition with 3-digit numbers 40 Subtraction with 3-digit numbers 43

Lines and shapes Points and lines Triangles, squares and rectangles Describing and drawing 3D shapes

46 48

10 Length, perimeter and area

Multiplication and division58 The relationship between multiplication and division 60

132 134 138 141

Length and distance

Perimeter

Area

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Contents

11 Shapes and angles

144 146 149 151 154 156

15 Numbers and patterns 194 More about whole numbers and decimal numbers 196 Patterns and sequences 199 Number groups 202 16 Calculating 204 Addition with 4-digit numbers 206 Subtraction with 4-digit numbers 208 Multiplication 211 Division with remainders 215 Puzzles and problems 217 17 Data handling 218 Collecting data 220 Representing data 223 Interpreting data 225 18 Shapes and direction 228 More about points and lines 230 Working with shapes and patterns 232 Position and direction 234

Angles Circles

3D shapes and nets

12 Capacity and mass Working with capacity

Working with mass 160 13 Fractions and decimals 164 Equivalent fractions 166 Mixed numbers and improper fractions 169 Adding and subtracting fractions 171 Representing, ordering and comparing decimals 175 Adding and subtracting decimals 177 14 Money and time 180 Digital clocks 182 Timetables and schedules 184 Calendars 187 Money totals, difference and change 190

iii

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How to Use This Book Welcome to Max Maths !

Positivity towards mathematics – the activities provide opportunities to explore mathematics through pattern, reasoning and in meaningful contexts. While developing proficiency, students experience an enjoyment in mathematics, and an appreciation of the beauty and power woven into its fabric. Max Maths is designed specifically to support the new OECS Learning Standards for Mathematics, and to provide regular engagement in all important mathematical processes. Look out for the icons that show: problem solving

The philosophy behind the design of Max Maths is to develop confident , curious , resourceful and proficient mathematicians. The Max Maths approach comprises a comprehensive set of resources that provide: Rich mathematical experiences – each activity uses a Concrete-Pictorial- Abstract (CPA) approach to enrich learning, and develop a visual and physical intuition for mathematical concepts. This means that abstract concepts and calculations are supported with visual representations and concrete materials such as cubes or counters to bring the mathematics to life through practical activities and visual prompts for discussion and understanding. Depth of understanding – the activities use a range of questioning techniques to enable students to develop skill and accuracy alongside a deep mathematical understanding of the concepts. Each year is organised to provide progression over time, with each revisit digging deeper into the skills and mathematical thinking.

reasoning

communicating

connecting

representing Opportunities to develop each

mathematical process are built into the main activities in the Student’s Books and are clearly signposted within the challenges provided in the Teacher’s Guides.

Winston

Jade

Letisha

Leon

Carl

Riana

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How To Use This Book

This student’s book provides a teaching resource to support whole-class teaching and is designed to be accompanied by a workbook for students to write and draw in, to create a record of their achievements. Each unit provides a double-page spread designed to be talked about, prompting students’ curiosity, communication, conjecture and challenge.

Unit 1 – Numbers to 10

1 Numbers to 10

KEY questions

KEY words

Which of these words can you use to describe what you see in the picture? Equal Same as Count Number

How many leaves? How many shells? How many cubes? How many counters? How do you know you have counted them all?

There are many different activity types, carefully ordered, to help students through their learning journey.

Unit 2 – Money and measures

Analogue clocks Let’s Recap

Let’s Practise

1 Estimate and measure. Which units of measurement will you use?

The clock shows that the time is half past three.

The mass of:

Estimate: Heavier than, lighter than or the same as one kilogram?

Measure

(a) 8 exercise books (b) Your shoe

The clock shows that the time is quarter past six.

(c)

A full pencil pot

Who do you agree with? Why? What do we need to know about when reading the time on an analogue clock? Let’s Learn Together 1 It takes the minute hand 5 minutes to move from one number to the next. It takes the minute hand 60 minutes to move all the way around the clock. There are 60 minutes in 1 hour.

(d) Your games bag

2 Work together in a small group to carry out this investigation

Does the tallest person have the longest stride?

Make estimates and think about the unit of measurement you will use. Record your measurements to the nearest whole unit. Make a table of your results. What does the information tell you? Can you answer the original question?

We can use what we know about counting in multiples of five to help us work with time.

60 minutes 0 minutes

55 minutes

5 minutes

50 minutes

10 minutes

Leon has only part of an old tape measure. Some of the numbers have rubbed off. He uses it to measure these objects in centimetres. What is the actual measurement of each object? Explain why. 28 40 42

15 minutes

45 minutes

40 minutes

20 minutes

35 minutes

25 minutes

30 minutes

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1 Numbers and patterns 1 Numbers and

KEY words

Which of these words can you use to describe what you see in the picture?

Thousand

Hundred(s)

Ten(s)

One(s)

Fifty

Twenty-five

Part

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Unit 1 – Numbers and patterns

KEY questions

The children need to collect 120 balls in total. What could they do? Is there more than one way for them to make a total of 120 balls? How many balls are there in total on the top shelf ?

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Representing and describing 4-digit numbers

Can you use beads to show how 10 tens and 10 ones make 1 hundred and 1 ten? Can you use blocks to show how 25 tens make 2 hundreds and 5 tens? What else can you show?

Use blocks to make 999.

What regrouping will you need to do when you represent the number that is one more than 999?

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Unit 1 – Numbers and patterns

1 We can represent and describe the number 1000 in different ways. 1000 is the first 4-digit number.

1000 is one more than 999 on a number line. 1000 is one less than 1001.

999 1000

1001

1000 is made of 10 hundreds, 100 tens or 1000 ones.

900

100

1000 is 900 plus 100.

1000

100 100 100 100 100

1000 is 500 + 500 or double 500.

100 100 100 100 100

We say and write the number as one thousand.

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Look at the numbers represented here.

1 Which numbers are represented here? Copy and complete. (a) There is

thousand and

hundreds.

The number is

We say and write the number as

(b)

There is

thousand,

hundreds,

tens

ones.

and

The number is

We say and write the number as

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Unit 1 – Numbers and patterns

2 Use blocks to represent these numbers. Talk about any patterns you notice. (a) 1352 (b) 1452 (c) 2452 (d) 2652 (e) 3652 (f ) 3642 3 Describe these numbers in different ways. What representations will you use? (a) 1999 (b) 1001 (c) 2000 (d) 1500 (e) 2501

Place value

1 Look at the numbers on the counters. What number do they represent in total?

100

10 1000

100

1000

100

1000

100

There are: 3 thousands

5 hundreds

3 tens

2 ones

The number is 3532 .

2 We can show the number on a place value chart.

The value of the first digit 3 is 3000 because it is in the thousands place. The value of the digit 5 is 500 because it is in the hundreds place. The value of the second digit 3 is 30 because it is in the tens place. The value of the digit 2 is 2 because it is in the ones place.

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We can expand the number 3532 to show the place value parts. 3532 = 3000 + 500 + 30 + 2 The total value is 3532.

1 What is the value of each digit in the number 4209? The digit is in the thousands place. Its value is

The digit

is in the hundreds place. Its value is

The digit

is in the tens place. Its value is

The digit

is in the ones place. Its value is

What number is represented here?

1000

100

1000

100

1000 1000

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Unit 1 – Numbers and patterns

Write the value of the digit that is circled. (a) 5 028 (b) 1 046

(d) 7 926

(e) 3 744

(f ) 8 516

3 Expand these numbers to show their place value parts. (a) 2345 (b) 3452 (d) 5324 (e) 4523

(f) 5432

Leon is thinking of a 4-digit odd number. Two digits are the same. The number has 12 hundreds altogether and 5 extra tens. What could the number be?

Riana has 9 blocks. What different numbers can she make between 6000 and 8000? Remember that blocks can be thousands, hundreds, tens or ones. Can you find all possibilities? Use blocks or counters to show your solutions.

Comparing and ordering numbers

1 We can use a number line to help compare numbers.

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Both numbers have 1 thousand and 6 more hundreds.

1639

1626 1628 1630 1632 1634 1636 1638 1640 1642

1639 is greater than 1628 so 1628 is smaller than 1639. We can show this with symbols as 1639 > 1628 and 1628 < 1639.

2 We can also use a place value chart to help compare numbers

2 2

2 1

5 5

3 4

Both numbers have 2 thousands so we must compare the hundreds. In 2325, the digit in the hundreds place is 3. In 2415, the digit in the hundreds place is 4.

4 hundreds is greater than 3 hundreds. 2415 is greater than 2325, so 2415 > 2325 What else can you say or show?

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Unit 1 – Numbers and patterns

We can use knowledge of the number line or place value to help order numbers. Let’s order these numbers from smallest to greatest.

2 3 3

0 4 2

8 9 7

0 9 3

Does your ordering match the number line? Explain how you know.

smallest to greatest 2080

3273 3499

We can also use symbols to show how we have ordered numbers. 2080 < 3273 < 3499 smallest greatest

Find the greater value.

7 8

9 0

9 1

9 3

thousand is greater than

thousand.

thousand is greater than

. So,

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2 Order these numbers from smallest to largest. 5398 4783 5411

is the smallest number because it only has

thousands.

is the largest number because it has

thousands and

hundreds.

So,

1 Find the smaller number. Show the numbers on a place value chart. (a) 986 and 1015 (b) 2135 and 2142 (c) 3672 and 3670 (d) 6873 and 7172

True or false? Correct any that are false. (a) 4301 > 4310 (b) 1034 < 1043 (c) 3104 > 3041 (d) 1034 < 431

3 Order each set of numbers from smallest to largest. (a) 6320, 648, 5922, 5292

(b) 4615, 1564, 1526, 4651

Which of these parcels is the heaviest? Order them from lightest to heaviest.

875 g

1025 g

Can you think of a mass that is heavier than 1175 g but lighter than 1250 g?

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Unit 1 – Numbers and patterns

Counting patterns

Start counting in multiples of ten: 10, 20, 30 … What is the 15th number that you will say? What is the 50th number you will say? What about the 100th number? Explain how you know. Now start counting in tens from 40: 40, 50, 60 …

1 Look at the counting patterns for multiples of 25 and multiples of 50. 0 25 50 75 100 125 150 175 200 225 250

100

150

200

250

There are two 25s in every 50 so the numbers in the count of 50 can also be found in the count of 25. 25 50 75 100 125 150 175 200 225 250 275 300 … The ones digits in the count of 25 also make a pattern with the digits 5 and 0. This means that the count of 25 has a pattern with even and odd numbers.

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2 Here is the start of the counting pattern for 100.

100

200

300

400

500

600

The numbers in the count of 100 are all even and have zero in both the tens and ones place. The number in 6th position in this count is 600. What will the number in 12th position be?

1 Count by 25s from these starting numbers. Write the next five numbers you say. (a) 50, , , , ,

(b) 75,

(d) , 250,

2 Carl counts backwards in multiples of 100 from 1500. (a) If 1400 is the first number that Carl says, what is the 5th number? (b) What is the 10th number he says? (c) Will the number 110 be in his count? Explain your answer.

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Unit 1 – Numbers and patterns

3 Look at the counting that the children are describing.

Both children stop counting when they reach 1000. Use these words to write about any patterns they should notice.

Letisha uses 100 g and 50 g weights to help find the mass of an object. Letisha first puts an odd number of 100 g weights on the balancing scales. Then she counts on in steps of 50 g to find the mass of the object. What could the mass of the object be if she uses 12 weights in total? Find all possibilities. Think about how you will communicate your solutions to others.

Rounding numbers to the nearest 10 and 100

Sort these numbers. 95 103 61 42 236 263 354 348 19

Round up to the nearest 10

Round down to the nearest 10

What do you notice about numbers that round up to the nearest 10? What do you notice about numbers that round down to the nearest 10?

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1 We can use rounding to help make estimates. 236 people buy tickets for the school play.

2 The number 236 is more than halfway between 230 and 240 on a number line so it rounds up to 240 to the nearest 10.

236

230

240

Numbers with digits 5, 6, 7, 8 or 9 in the ones position round up to the nearest 10. 3 The number 236 is less than halfway between 200 and 300 on a number line so it rounds down to 200 to the nearest 100.

236

200

300

Numbers with digits 0, 1, 2, 3 or 4 in the tens position round down to the nearest 100.

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Unit 1 – Numbers and patterns

1 Round 153 to the nearest 10 and then to the nearest 100. 153 is than halfway between and

to the nearest 10.

153 rounds

than halfway between

and

153 is

to the nearest 100.

153 rounds

Round these numbers as shown. Number Round to the nearest 10

Round to the nearest 100

(a)

(b)

403

(c)

655

Look at these measurements.

Which of the measurements round to: (a) 450 cm to the nearest 10 cm? (b) 400 cm to the nearest 100cm? (c) 500 cm to the nearest 100 cm?

Can you think of some other measurements that will round in this way?

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2 2 Money and measures

KEY words

Dollar Cent Hour Minute Metre Centimetre Kilogram Gram Litre Millilitre Which of these words can you use to describe what you see in the picture?

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Unit 2 – Money and measures

KEY questions

How much more will it cost to buy 2 kilograms of apples than 2 boxes of 12 eggs? What can you buy for $100? What can you not buy for $100? How much more will you need to buy the scooter?

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Money

Here are the Eastern Caribbean notes and coins that you have worked with so far.

Think about some items that cost about the same as each note or coin.

Look at the part-whole relationships shown here.

75 cents

21 dollars

Sketch your own bar models to show other part-whole relationships for 75 cents and $21.

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Unit 2 – Money and measures

The Eastern Caribbean currency also includes a $100 note. $100 (hundred dollars) is equal to two $50 notes. $100 is equal to five $20 notes. $100 is equal to ten $10 notes.

2 Is the amount of money in each purse the same?

$50, $20, $20 and $10 is $100 in total. $20, $20, $20, $20, $10, $5 and $5 is $100 in total.

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Look at the prices of these items. 500g cheese $29 loaf of bread $3 2 litres of pop $5 8 Mbps internet (month) $120 Pair of jeans $195 Microwave oven $339 32” flat screen TV $1000

We need ten $100 notes to buy the flat screen TV.

$0 $100 $200 $300 $400 $500 $600 $700 $800 $900 $1000

Use counting to help find the totals. (a)

(b)

(c)

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Unit 2 – Money and measures

2 A monthly ticket for public transport costs $89. Winston’s aunt pays for a ticket with the exact amount of money. What notes and coins can she use? Find at least three different possibilities.

TICKET $89

3 Use the price list of items from ‘Let’s Learn Together’.

Choose the best estimate for: (a) One year of internet use (b) Two microwaves ovens (c) Three loaves of bread and 1 kg of cheese

Less than $1000 More than $1000 Less than $700 More than $700

Less than $70 More than $70

Use the internet to find prices of items that you can buy for the amounts represented in each shaded part of the number line:

$0 $100 $200 $300 $400 $500 $600 $700 $800 $900 $1000

Design a price list for your 7 items in a computer package. Use the prices of your items to create estimating problems that are similar to the ones you solved in question 3. Swap with a friend.

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Analogue clocks

Who do you agree with? Why? What do we need to know about when reading the time on an analogue clock?

1 It takes the minute hand 5 minutes to move from one number to the next. It takes the minute hand 60 minutes to move all the way around the clock. There are 60 minutes in 1 hour.

60 minutes 0 minutes

55 minutes

5 minutes

50 minutes

10 minutes

15 minutes

45 minutes

40 minutes

20 minutes

35 minutes

25 minutes

30 minutes

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Unit 2 – Money and measures

Look at these clocks. What is the time?

The minute hand has moved two steps of 5 minutes around the clock. 10 minutes have passed since 3 o’clock. The time is ten minutes past three (10 minutes past 3). We can also say ten past three or 10 past 3. The hour hand has moved past 3 to show that the time is now later than 3 o’clock.

The minute hand has moved five steps of 5 minutes around the clock. 25 minutes have passed since 3 o’clock. The time is twenty-five minutes past three (25 minutes past 3). The hour hand has moved nearly halfway between 3 and 4. The minute hand has moved eight steps of 5 minutes around the clock.

40 minutes have passed since 3 o’clock. There are 20 minutes to go until 4 o’clock. The time is twenty minutes to four (20 minutes to 4). The hour hand is moving closer to 4.

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1 What time is it? What will the time be 5 minutes later?

steps

The minute hand has moved

of 5 minutes around the clock. minutes have passed since o’clock.

The time is

Five minutes later the time will be

What times do the clocks show? (a) (b)

(c)

2 Draw hands on clock faces to show these times. Think carefully about the position of the minute hand and the hour hand. (a) (b) (c)

1 _ 4 to 9

20 past 6

20 to 6

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Unit 2 – Money and measures

The minute hands have fallen off these clocks. What could the times be? Describe where the minute hand will be positioned each time. Make up a similar problem for a friend to solve.

Work with a partner. Take it in turns to choose one of the times shown here. 1 _ 2 past 11 20 minutes past 4 10 minutes to 5 1 _ 4 to 2 Quarter past one Roll a 1–6 dice to find the number of 5-minute jumps to count on and count back from your chosen time. Say: ‘… minutes earlier than … is … and … minutes later than is… ’. Your partner checks on a clock face. Score a point for each correct new time you give. 25 past 7 five past nine twenty to eight Score an extra point if you can say how much earlier or later the time is using fractions of an hour e.g. ‘Half an hour later than … is … ’ or ‘Quarter of an hour earlier than … is … ’. Who has the most points after you each have five turns?

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Working with scales and measure

Talk about different objects that you would not measure using these units of measurement. Explain why. What would you do instead?

1 We use scales to help us measure accurately. What is the same and what is different about the scales shown here? Think about the value of the marks you can see.

500

400

300

450 50

200

400

100

350

150

(g) 250 300 200

100

0cm1 2 3 4 5 6 7 8 9 101112131415

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Unit 2 – Money and measures

1 Estimate and measure. Which units of measurement will you use?

The mass of:

Estimate: Heavier than, lighter than or the same as one kilogram?

Measure

(a) 8 exercise books (b) Your shoe

(c)

A full pencil pot

(d) Your games bag

2 Work together in a small group to carry out this investigation

Does the tallest person have the longest stride?

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The relationship between units of measurement

When we work with both large and small measurements, it is important to know the relationship between them.

We can use the bar model to help convert between units of measurement. 100 cm 100 cm 100 cm 3 metres

1 Work in a small group to compare capacities. Find some containers that hold 1 litre of water and others that hold 1000 millilitres of water. Now try 2 litres and 2000 millilitres. What do you notice? What statement can you make? 2 Now work together to compare masses. Find objects that have a mass of 1 kilogram and others that have a mass of 1000 grams.

Now try masses of 2 kilograms and 2000 grams. What do you notice? What statement can you make this time?

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Unit 2 – Money and measures

Complete these.

1 metre (m) =

centimetres (cm)

metres (m)

1 kilometre (km) =

1 litre (l) =

millilitres (ml)

grams (g)

1 kilogram (kg) =

1 Sketch bar models to show how to convert these measurements. (a) 4 kilograms = grams

(b) 6 kilometres =

metres

centimetres

(d) 2 litres =

millilitres

Solve these problems. (a) Jade measures out 2 kg of soil and 3000 g of sand. How many more grams of sand does she have than soil? (b) Leon uses 5 m of string for his kite and another 200 cm of string for his model. How many centimetres of string has he used in total?

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Addition and subtraction

KEY words

Which of these words can you use to describe what you see in the picture?

Add

Subtract Estimate

Hundred

Tens

Ones

Inverse

Regroup

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Unit 3 – Addition and subtraction

KEY questions

In how many ways can you pick three flags to represent the number 378? What different additions and subtractions can you make up?

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The relationship between addition and subtraction

We can use part-whole relationships to think about addition and subtraction. Talk to your partner about how you can use the bar model to show that:

100

75 + 25 = 100 25 + 75 = 100

100 − 25 = 75 100 − 75 = 25

Leon has nine shells in his bucket. He collects some more shells from a rock pool and puts them in his bucket.

Use cubes and counters to act out what happens with the shells in Leon’s bucket. Find different ways to make the story true. What do you notice about the number of shells in the bucket at the start of the story and the number in the bucket at the end of the story? Can you explain why?

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Unit 3 – Addition and subtraction

1 Addition and subtraction are inverse operations so they ‘undo’ each other. Look at this number line.

9 10

11 12 13 14 15

–5

2 We can use the inverse to help solve missing number problems. Bar models are helpful too. + 10 = 25 − 30 = 20

3 We can use the inverse to check our calculations by ‘undoing’ each one.

38 + 20 = 58

45 = 12 = 34

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1 Use the inverse to check these calculations. (a) 85 − 52 = 32 is because

(b) 35 + 43 = 78 is

because

−

What is the missing number?

= 95

60 +

We can use the inverse to help us. It is easier to use the subtraction − = than 95 − = 60. The missing number is .

1 Write two addition sentences and two subtraction sentences each time. (a) 150 50 200 (b) 5 15 20 2 Use the inverse to check these calculations. Correct any that are wrong. Write down the inverse calculations you use each time.

(a) 72 + 19 = 93 (d) 100 − 47 = 52

(b) 42 − 25 = 17 (e) 32 + 39 = 71

Find the missing numbers. (a) − 200 = 95 (b)

+ 65 = 80

= 34

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Unit 3 – Addition and subtraction

Strategies for mental addition and subtraction

We can use different strategies to help us add. 55 + 43 = 50 + 5 + 40 + 3 = 90 + 8 = 98 What is the same and what is different about each method? Use subtraction to check the calculation. What strategy will you choose? 55 +40 +3 95 98

1 We can use number facts to help solve addition problems. 42 + 43 75 + 29 10 + 90

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We can solve 75 + 29 in a different way. The number 29 is one less than 30.

We can use a number line to find 75 + 30 and then make the answer one less because we have added one too much. So, 75 + 29 = 104.

+30

–1

104 105

3 We can also use number facts to help solve subtraction problems. 102 − 45 112 − 19 80 − 50

4 We can solve 112 − 19 in a different way.

The number 19 is one less than 20. We can use a number line to find 112 − 20 and then make the answer one more because we have subtracted one too much. So, 112 − 19 = 93

–20

92 93

112

1 Try these additions. What strategy will you use each time? (a) 36 + 37 (b) 89 + 24 (c) 80 + 90 (d) 65 + 29 (e) 54 + 35

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Unit 3 – Addition and subtraction

2 Try these subtractions. What strategy will you use each time?

(a) 99 − 35 (d) 105 − 17

(b) 84 − 42 (e) 83 − 78

Carl adds two numbers. He adds the tens first. There are 12 tens in total. He add the ones next. There are 9 ones in total. What could Carl’s addition be? Find at least five different solutions.

The children are discussing these addition calculations. 12 + 67 22 + 73 29 + 85

67 + 12 73 + 22 85 + 29

What do you think? What do you notice about the answers to the calculations in the two boxes? Think about how you will represent and communicate your findings to others.

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Addition with 3-digit numbers

1 Look at the different methods used to complete the addition 355 + 132. Why is 400 + 100 = 500 a useful estimate?

+100

355 + 132 = 300 + 50 + 5 + 100 + 30 + 2 = 400 + 80 + 7 = 487

+30 +20

487

355

455 485 What is the same and what is different about the methods? What calculation can you use to check?

355 + 132 = 355 + 100 + 30 + 2 = 455 + 30 + 2 = 485 + 2 = 487

2 We can also solve additions using the written column method.

We start by adding the ones: 5 ones + 2 ones = 7 ones 5 tens + 3 tens = 8 tens 3 hundreds + 1 hundred = 4 hundreds

H T O 3 5 5 + 1 3 2 4 8 7

H T

Which method did you prefer for this calculation? Why?

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Unit 3 – Addition and subtraction

3 What is different about the addition 365 + 138? Look at what happens when the 5 ones and 8 ones are added.

We start by adding the ones: 5 ones + 8 ones = 13 ones 6 tens + 3 tens = 9 tens 3 hundreds + 1 hundred = 4 hundreds +

We can regroup to make another ten, so 13 ones is 1 ten and 3 ones.

H T O 3 5 5 + 1 3 8 4 9 3 1

(a) Estimate the answer to 678 + 217. 678 rounds to

to the nearest 100

678

217

to the nearest 100

217 rounds to

(b) Complete the calculation using the two different methods. 678 + 217 = 600 + + + + +

H T O 6 7 8

+ 2

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1 Copy and complete. What method will you use each time? Remember to make and estimate first and check your answers. (a) 356 + 237 (b) 428 + 356 (c) 645 + 149 (d) 708 + 251 (e) 256 + 337 (f) 456 + 328 (g) 649 + 145 (h) 758 + 201 What do you notice? Discuss why this has happened.

2 Which is the most likely answer to 396 + 195?

Copy and complete: The most likely answer is

because

The cost of a child’s bicycle is $439. The cost of an adult’s bicycle is $246 more. What is the cost of the adult’s bicycle? $

Work with a partner. Arrange the numbers in the puzzle so that the value in a circle is the total of the two pentagons that it joins.

887 252 600

416 348 955

791 539 668

Now make up a similar puzzle for others to solve.

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Unit 3 – Addition and subtraction

Subtraction with 3-digit numbers

1 We can complete the subtraction 689 − 336 using different methods. Will the actual answer be more or less than the estimate 700 − 300 = 400? 689 − 336 = 600 − 300 = 300 80 − 30 = 50 9 − 6 = 3 300 + 50 + 3 = 353 353 –300 –6 –30 689 389

359 What is the same and what is different about the methods? What calculation can you use to check?

689 − 336 = 689 − 300 − 30 − 6 = 389 − 30 − 6 = 359 − 6 = 353

2 We can also solve subtractions using the written column method.

We start by subtracting the ones: 9 ones − 6 ones = 3 ones 8 tens − 3 tens = 5 tens 6 hundreds − 3 hundreds = 3 hundreds

T O

H T O 6 8 9 − 3 3 6 3 5 3

– 3

Which method did you prefer for this calculation? Why?

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3 What is different about the subtraction 686 − 339? Look at what we need to do so we can subtract 9 ones.

H T O 6 8 6 − 3 3 9 3 4 7 7 1

T O

16 ones − 9 ones = 7 ones 7 tens − 3 tens = 4 tens 6 hundreds − 3 hundreds = 3 hundreds

(a) Estimate the answer to 594 − 427. 594 rounds to

to the nearest 100

427

594

to the nearest 100

427 rounds to

−

(b) Complete the calculation using the two different methods. 594 − 427 =

H T O 5 9 4

−

− 4

−

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Unit 3 – Addition and subtraction

1 Copy and complete. What method will you use each time? Remember to make and estimate first and check your answers. (a) 856 − 423 (b) 685 − 359 (c) 773 − 254 (d) 500 − 230 (e) 956 − 523 (f) 985 − 659 (g) 673 − 154 (h) 800 − 530 What do you notice? Discuss why this has happened. 2 The mass of a cabbage is 852 g. The mass of an onion is 418 g lighter. What is the mass of the onion?

Look at Winston’s subtraction. Explain the mistake he has made. What do you need to tell Winston about subtracting?

H 8 3 5

T 5 1 4

O 3 8 5

–

Use all the digit cards each time to make different subtractions.

H T O

−

How many answers can you find that are greater than 250 but less than 450?

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Lines and shapes

KEY words

Which of these words can you use to describe what you see in the picture?

Straight

Curve

Face

Vertex

Edge

Angle

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Unit 4 – lines and shapes

KEY questions

Can you name all the solid (3D) shapes? What are the shapes of their faces?

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Points and lines

Straight lines go on forever in either direction. Draw line AB. Line segments are part of a line and have a start

point and an end point. Draw line segment CD.

Measure the length of each line segment. Order the lengths from longest to shortest. E

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Unit 4 – lines and shapes

A point is a location. It has no size. We use a dot to mark a point. We use a letter to label a point. Here are three points: point A, point B and point C. A

2 A ray has a start point but goes on forever in the other direction. E F

This is ray EF. It has a start point E but goes on forever in direction F.

1 Copy and complete to name each of these.

XY is a

because it

either direction. We name it

because it has a

point but

EF is a

in the other direction. We name it

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Name each of these: (a) (b)

(c)

(d)

3 Draw the following line segments. Remember to label them. Try to draw them in different directions e.g. diagonal, vertical or horizontal. (a) AB CD EF GH JK Line segment

Length

8 cm 16 cm 6 cm 7 cm 12 cm

(b) How much longer is line segment CD than line segment GH? (c) Line segment JK is double the length of line segment EF. Which other two line segments share the same relationship?

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Unit 4 – lines and shapes

Triangles, squares and rectangles

Use a ruler. Draw four different triangles. Make sure that the bases of your triangles are not all horizontal.

Knowing about the different properties of shapes can help us identify them and classify them.

1 All triangles have three straight sides and three angles.

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2 All squares have four equal straight sides and four right angles.

3 All rectangles having four straight sides and four right angles.

4 All squares and rectangles are symmetrical.

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Unit 4 – lines and shapes

Write three sentences each time: (a) What is the same and what is different about a triangle and a square? (b) What is the same and what is different about a square and a rectangle?

2 Use an elastic band to make this triangle on a geoboard.

(a) Change the position of one of the vertices to make a different triangle. Talk about the similarities and differences. (b) Can you now make a rectangle by changing no more than two corners? (c) How many corners do you need to change to make a square? 3 Letisha has some different triangles, squares and rectangles. How can she sort them into these boxes? Sketch the shapes for each box.

Two pairs of opposite sides

Symmetrical

Straight sides

Right angles

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4 Carl draws the first four squares in a pattern of eight squares.

Use grid paper to copy and then complete the pattern of eight squares.

Cross - curricular

This picture is made up of three rectangles and three squares. Can you see them?

Use a computer drawing program to make a copy of the picture. Can you now design your own pattern for a friend to copy?

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Unit 4 – lines and shapes

Describing and drawing 3D shapes

Solid shapes are three-dimensional (3D). We can pick them up. Here is a cube and a cuboid. 12 edges

6 faces

8 vertices

Both the cube and cuboid have the same number of faces, edges and vertices. What is different about the shape of their faces and the length of their edges?

1 Let’s look at the similarities and differences between these shapes.

cylinder

sphere

cone

All the shapes have curved faces. The cylinder has two flat circular faces but the cone only has one. The cylinder has two curved edges but the cone has one. Can you think why? The sphere does not have any flat circular faces or curved edges.

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2 We can make two-dimensional drawings of three-dimensional shapes.

Step 1

Step 2

Step 3

1 What information is missing from the table?

Number of flat faces

How many curved faces

Number of straight edges

Number of curved edges

Number of vertices

Shape

Cube Cuboid

Sphere

Cylinder Square-based pyramid

What is the shape? (a) one curved face, a flat circular face, a curved edge, an apex (b) 12 edges, 8 vertices and 6 rectangular faces.

2 Jade chooses three solid shapes. She can count 8 flat faces in total. Which shapes could they be? Find four different solutions.

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Unit 4 – lines and shapes

Copy and complete the table.

How many curved faces?

How many faces are rectangles

How many faces are circles?

Shape

Sphere Cuboid Cone Cylinder Triangular prism

Work with a partner. Use grid paper. Draw two different-sized cubes and cuboids. Measure and label the length of the edges. Now try making a model of one of your shapes. You can use paper straws or lolly sticks.

Leon has sketched a cone. How can you use his idea to help sketch a cylinder?

Step 1

Step 2

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Multiplication and division

KEY words

Which of these words can you use to describe what you see in the picture?

Multiply

Divide

Double

Half

Array

Equal

Group

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Unit 5 – Multiplication and division

KEY questions

How does the picture show multiplication and division? What different multiplication and division problems can you make up?

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The relationship between multiplication and division

We can use an array to think about multiplication and division. Talk to your partner about how you can use the array to show that: 4 × 6 = 24 24 ÷ 6 = 4

6 × 4 = 24

24 ÷ 4 = 6

Riana has some 10 cent coins. Uncle gives her more 10 cent coins so she now has double the amount of money.

Use coins to act out what happens with Riana’s money. Find different ways to make the story true. What do you notice about the amount of money Riana had at the start of the story and the amount of money she has at the end of the story? Can you explain why?

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Unit 5 – Multiplication and division

1 Multiplication and division are inverse operations so they ‘undo’ each other. Look at this number line.

5 10 15 20

2 We can use the inverse to help solve missing number problems. Bar models are helpful too. 6 × = 30 ÷ 3 = 6

? ? ? ? ? ? 30

3 We can use the inverse to check our calculations by ‘undoing’ each one.

6 = 9

11 x 4 = 44

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1 Use the inverse to check these calculations. (a) 8 × 4 = 32 is because

(b) 42 ÷ 6 = 6 is

because

What is the missing number? ÷ 5 = 8

8 8 8 8 8 ?

groups of

are equal to the missing number.

, so the missing number is

1 Describe the relationships between the circled numbers each time. Use the words ‘times as large as’ and ‘time as small as’.

30 6 12 18 24 36 42

20 4 8 12 16

What is the missing number? 6 × = 60

? ? ? ? ? ? ?

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Unit 5 – Multiplication and division

3 Use the inverse to check these calculations. Correct any that are wrong. Write down the inverse calculations you use each time.

(a) 9 × 3 = 28 (d) 56 ÷ 2 = 23

(b) 42 ÷ 6 = 7 (e) 12 × 3 = 38

Make up some puzzles like this for a friend to solve.

Finding new multiplication facts

Winston uses cubes to show the relationship between the multiplication tables of 2 and 4.

How do you think he can use the cubes to show the relationship between the multiplication tables of 4 and 8?

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We can use the multiplication facts we know to help find new facts.

There are 2 fours in every eight.

× 1 2 3 4 5 6 7 8

1 × 8 = 8

1×4=4 1

2 × 8 = 16

2×4=8 2

3 × 8 = 24

3×4=12 3

4 × 8 = 32

4×4=16 4

5 × 8 = 40

5×4=20 5

There are twice as many counters in 1 row of 8 than in 1 row of 4. So, 1 × 8 is double 1 × 4

There are 3 threes in every nine.

×123456789

1 × 9 = 9

1×3=3 1

2 × 9 = 18

2×3=6 2

3 × 9 = 27

3×3=9 3

4 × 9 = 36

4×3=12 4

5 × 9 = 45

5×3=15 5

There are three times as many counters in 1 row of 9 than in 1 row of 3. So, 1 × 9 is triple 1 × 3

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Unit 5 – Multiplication and division

1 How many cubes will we need to make the following towers? (a) (b)

Use squared paper. Shade squares to show the multiplication tables of 4 and 8.

1 x 4 = 4

1 x 8 = 8

Go up to 10 rows. Talk about any patterns you notice.

2 Now complete the multiplication table of 8 up to 10 × 8 and 8 × 10: 1 × 8 = 2 × 8 =

8 × 1 =

8 × 2 =

…

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