Cambridge Primary Mathematics Learner's Book 4_public

CAMBRIDGE PRIMARY

Mathematics
Learner’s Book
4

Emma Low

University Printing House, Cambridge , United Kingdom

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rd printing
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Introduction

is Learner’s Book is a supplementary resource that Teachers have access to an online tool that maps
consolidates and reinforces mathematical learning resources and links to materials o ered through
alongside the Cambridge Primary Mathematics Teacher’s the primary mathematics curriculum, NRICH and
Resource 4 (9781107692947). It provides introductory Cambridge Primary mathematics textbooks and
investigations (Let’s investigate) to encourage the e-books. ese resources include engaging online
application of mathematical knowledge, and numerous activities, best-practice guidance and examples of
questions and activities to develop problem-solving Cambridge Primary Maths in action.
skills.
Ideally, a session should be taught using the e Cambridge curriculum is dedicated to helping
appropriate Core activity in the Teacher’s Resource 4. schools develop learners who are con dent, responsible,
re ective, innovative and engaged. It is designed to
e associated content in the Learner’s Book 4 can give learners the skills to problem solve e ectively,
then be used for formative assessment at the end of a apply mathematical knowledge and develop a holistic
session, for homework, or used for support in learning understanding of the subject.
new vocabulary. ere is generally a double page
corresponding to each Core activity in the Teacher’s e Cambridge Primary Maths textbooks provide
Resource 4 printed book. e Core activity that the page best-in-class support for this problem-solving approach,
relates to is indicated at the bottom of the page. based on pedagogical practice found in successful
Hints and tips are provided throughout to support the schools across the world. e engaging NRICH online
learners. ey will appear as follows: resources help develop mathematical thinking and
problem-solving skills. To get involved visit www.cie.
Write a list of number org.uk/cambridgeprimarymaths
pairs to help you
e bene ts of being part of Cambridge Primary
Please note that the Learner’s Book on its own does Maths are:
not cover all of the Cambridge Primary mathematics • the opportunity to explore a maths curriculum
curriculum framework for Stage 4. You need to use it in
conjunction with the Teacher’s Resource 4 to ensure full founded on the values of the University of Cambridge
coverage. and best practice in schools
• access to an innovative package of online and print
is publication is part of the Cambridge resources that can help bring the Cambridge Primary
Primary Maths project. Cambridge Primary mathematics curriculum to life in the classroom.
Maths is an innovative combination of is series is arranged to ensure that the curriculum
curriculum and resources designed to is covered whilst allowing teachers to use a exible
support teachers and learners to succeed in primary approach. e Scheme of Work for Stage 4 has been
mathematics through best-practice international maths followed, though not in the same order and there will be
teaching and a problem-solving approach. some deviations. e components are:
Cambridge Primary Maths brings together the world- • Teacher’s Resource 4
class Cambridge Primary mathematics curriculum from ISBN: 9781107692947 (printed book and CD-ROM).
Cambridge International Examinations, high-quality • Learner’s Book 4
publishing from Cambridge University Press and ISBN: 9781107662698 (printed book)
expertise in engaging online enrichment materials for • Games Book 4
the mathematics curriculum from NRICH. ISBN: 9781107685420 (printed book and CD-ROM).
For associated NRICH activities, please visit the
Cambridge Primary Maths project at
www.cie.org.uk/cambridgeprimarymaths

Number

Reading, writing and partitioning numbers

Let’s investigate 18 7

Pablo has these digit cards.
He makes three-digit numbers with the cards.
Write down all the numbers he could make.

1 Write each red number in gures, words and expanded form.
(a) 1000 2000 3000 4000 5000 6000 7000 8000 9000

100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
123456789

(b) 1000 2000 3000 4000 5000 6000 7000 8000 9000

100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
123456789

2 Write each number in words. Vocabulary
(a) 2345 (b) 3030 (c) 2901

(d) 7777 (e) 2816 (f) 9109 digit: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are digits.

3 Write these numbers in gures. expanded form: 4567 ϭ 4000 ϩ 500 ϩ 60 ϩ 7
partition: breaking up a number into its
(a) nine thousand and nine parts.
(b) four thousand and forty In 830, the 3 has a

place value: the value value of 3 tens (30).
HTU
4 What is the value of 4 in of a digit determined 830
these numbers? by its position.

(a) 6423 (b) 4623 (c) 3409 thousand: is a four-digit number that is
(d) 9040 (e) 1234 (f) 4321 10 times larger than a hundred.

Th H T U

1000

ϫ10

2
Unit 1A: Core activity 1.1 Reading, writing and partitioning numbers

5 Look at these number cards. 39 hundreds 390 tens
(a) Which cards have the same value as 3900?
(b) Which card has the smallest value? 39 tens
(c) What is 10 more than 390 tens?

6 Maria writes a number. It has the digit 4 in the hundreds
place and the digit 2 in the units place.
Which of these numbers could Maria have written?

5426 4652 4265 5462

7 What is the largest possible number that can be written
using the digits 3, 6, 3 and 4?

8 Which value is equal to 3 hundreds?

3 units 30 units 30 tens 300 tens

9 Find the missing numbers.

3000 is one hundred less than ?
5000 is one hundred more than ?
6500 is one thousand more than ?
980 is one hundred less than ?

10 Write the number that is 1 more than 9999.

11 Solve these number riddles. (b) I have four digits.

(a) I have four digits. My units digit and my
hundreds digit are the same.
I am more than 2500. I am less than 9000.
I am less than 3000. I am greater than 8000.
My hundreds digit is 6. My tens digit is 4.
My tens digit is one less My hundreds digit is two
than my hundreds digit. more than my tens digit.
My units digit is 0.
What number am I?
What number am I?

3

Ordering and rounding Vocabulary

Let’s investigate round to the nearest: to round to
Ahmed writes a list of four-digit whole the nearest hundred, look at the
numbers. The digits in each number add tens digit and if it is …HH TT UU
up to 3.
Ͻ 5, round down 88 ?? 00
He writes the numbers in order of size, ϭ 5 or Ͼ 5, round up
starting with the smallest.
Write down all the numbers that could H T U 830 to the nearest
be in Ahmed’s list. Make sure you write 8 3 0 hundred, is 800.
them in order of size.
H T U 48 to the nearest
4 8 ten, is 50.

Rounding numbers makes them
easier to use.

1 Write these numbers in order of size, starting with the smallest.

(a) 1066 1606 1660 1060 1666

(b) 9080 8990 9009 9090 8999

2 What is the number shown by an arrow on each number line?
(a) (b)

8000 9000 5500 6000

(c) (d)

7000 8000 5500 6000

3 Round these numbers to the nearest 100. (e) 885
(a) 1060 (b) 7225 (c) 4680 (d) 1007

4 Which of these numbers is closest to 1000?
1050 1039 1100 980 899

4
Unit 1A: Core activity 1.2 Ordering, comparing and rounding numbers

5 Here are some digit cards. 13 57

Use the cards to make three-digit
numbers greater than 500.
How many can you make?

6 Use the Ͻ and Ͼ signs to make these statements true.

(a) 505 ? 550 (b) 660 ? 606 (c) 989 ? 899

(d) 1234 ? 4321 (e) 1009 ? 1010 (f) 1001 ? 989

7 What number is halfway between 158 and 172? Ͼ is greater than
Ͻ is less than
158 ? 172

8 Find the numbers halfway between these pairs of numbers.

(a) 498 and 604 (b) 337 and 451 (c) 559 and 997

9 Here are four numbers: 3005 3006 3007 3009
Choose one number to make this number sentence correct.
3007 Ͻ ?

10 Which of these numbers is about the same size as the correct
answer to 480 ϩ 490?

100 500 400
1000 700 2000
11 Here are ve digits.

24569

Choose three of these digits to make the total as close
as possible to 1000.

300 ϩ ? ? ? ϭ ?

5

Multiplying and dividing by 10 and 100

Let’s investigate Th H T U
Use a calculator. Key in these numbers and signs.
5
5 ϫ 10 ϭ ϭ ϭ … Th H T U ϫ10

11 ϫ 100 ϭ ϭ ϭ … 50
12 500 Ϭ 10 ϭ ϭ ϭ … Th H T U ϫ10

500

What happens when you press the equals (ϭ) sign?
Try using different start numbers. Do you notice the same thing?

1 Calculate. (b) 40 Ϭ 10 (c) 3600 Ϭ 100 ϫ100
(a) 67 ϫ 10 (e) 350 Ϭ 10 (f) 35 ϫ 100 Ϭ100
(d) 415 ϫ 10 (h) 4700 Ϭ 10 (i) 3900 Ϭ 100
(g) 4100 Ϭ 100

2 What is the missing number? 5400 Ϭ ? ? ϭ 100

3 Write the missing digits. (b) 461 ? Ϭ 10 ϭ ? 61
(d) 31 ? ϫ 10 ϭ ? ? 60
(a) ? ? ? ϫ 10 ϭ 2320
(c) 34 ? 0 Ϭ 10 ϭ ? ? 6

4 Write the missing numbers. (b) 307 ϫ ? ϭ 3070
(d) 3400 Ϭ ? ϭ 34
(a) ? Ϭ 10 ϭ 54
(c) ? ϫ 100 ϭ 6000

5 Here are four number cards. C eigahtnhdunfdtyred
D ve hundred
A fty-eight B ve hundred and eight
and eighty

Write down the letter of the card that is the answer to:

(a) 85 ϫ 10 (b) 5800 Ϭ 10 (c) 5800 Ϭ 100

(d) 8500 Ϭ 10 (e) 580 Ϭ 10 (f) 5080 Ϭ 10

6
Unit 1A: Core activity 1.3 Multiplying and dividing by 10 and 100

6 Calculate. (b) 64 m ϭ ? cm 10 mm ϭ 1 cm
(a) 3800 cm ϭ ? m (d) ? mm ϭ 67 cm 100 cm ϭ 1 m
(c) 500 mm ϭ ? cm

7 Copy the diagrams below. Write down the missing numbers.
(a) (b)

ϫ10 Ϭ10

6 1400

ϫ100 ? Ϭ100 ?

? ϫ10 ? Ϭ10

(c) (d)

ϫ10 Ϭ10

32 8000

ϫ100 ? Ϭ100 ?

? ϫ10 ? Ϭ10

8 Here is a number calculation. 15 ϫ 10 ϭ 150

Write two different division calculations that use the same numbers.

9 A packet contains 500 grams of gerbil food.
Aysha feeds her gerbil 10 grams of food each day.
How many days does the packet of food last?

10 Here are three signs ϫ Ϭ ϭ

Use these signs to make each calculation below correct.
There may be more than one answer.

(a) 60 ? 6 ? 10 (b) 10 ? 15 ? 150 (c) 450 ? 10 ? 45

11 Write the missing numbers. 4500 Ϭ10 ? Ϭ10 ?
13 ϫ10 ? ϫ10 ?

7

Addition (1) Vocabulary

Let’s investigate Some words that
we use for addition:
Make a route through the grid from Start to Finish.You add, addition, plus,
can move horizontally or vertically. Add up the numbers increase, sum, total,
on your route. Find the route that gives the lowest total. altogether.

4 8 2 Finish Questions that ask
9 1 46 us to add: How many
8 5 52 are there altogether?
2 4 38 What is the total
Start 1 79 number of …?

For example, 2 ϩ 8 ϩ 5 ϩ 1 ϩ 9 ϩ 4 ϩ 8 ϩ 2 ϭ 34

1 Choose a method to solve these addition problems. Use complements
to 10 and 20 to
(a) 5 ϩ 8 ϩ 5 ϩ 3 ϭ ? (b) 4 ϩ 19 ϩ 12 ϩ 1 ϭ ? help you.These
are also called
(c) 1 ϩ 11 ϩ 9 ϩ 4 ϭ ? (d) 4 ϩ 17 ϩ 2 ϩ 3 ϭ ? 'number pairs' to
10 and 20.
(e) 13 ϩ 2 ϩ 1 ϩ 5 ϭ ? (f) 3 ϩ 14 ϩ 9 ϩ 3 ϭ ?

Explain to your partner why you chose that method. If you think
your partner could choose a better method, tell them why.

2 Copy the addition number sentences below.Then copy the list
of numbers on the right. Draw arrows to complete the number
sentences.The rst one has been done for you.

76 ϩ 52 ϭ 168

28 ϩ 34 ϭ 85

65 ϩ 89 ϭ 128

94 ϩ 22 ϭ 154

17 ϩ 68 ϭ 104

43 ϩ 52 ϭ 95

91 ϩ 77 ϭ 62

40 ϩ 64 ϭ 116

8
Unit 1A: Core activity 2.1 Addition (1)

3 Throw hoops over the cones to make the totals in the stars.
All four hoops must land on a cone.
There can be more than one hoop on a cone.

Check your total is correct by adding together your
numbers using two different methods.

22 7 31
12 8 13

50 5 27

4 Number sentence stories
Kasim thought up a story for the number sentence

63 ϩ 56 ϭ 119. 63 people
Write a story for each of these number sentences: visited our art
16 ϩ 8 ϩ 4 ϭ 28 show on Monday and
5 ϩ 4 ϩ 6 ϩ 5 ϭ 20 56 visited on Tuesday.
49 ϩ 37 ϭ 86 So 119 people visited
our art show

altogether.

9

Subtraction (1) Vocabulary

Let’s investigate Some words that we use for
Break the four-digit code to open the subtraction: subtract, subtraction,
treasure chest. take, take away, minus, decrease,
fewer, leave, difference.
65 Ϫ 58 ϭ (a)
Questions that ask us to subtract:
41 Ϫ 2 (b) ϭ 12
How many are left?
86 Ϫ 79 ϭ (c) How many are left over?
How many more is ? than ? ?
67 Ϫ (d) 8 ϭ 39 How many fewer is ? than ? ?
How much more is ? than ? ?
(a) (b) (c) (d) How much less is ? than ? ?

Sarah used the ‘counting back’ method to calculate 74 Ϫ 13.

13 is a small number. 1 Solve 62 – 11 using
I will take away 10 then the ‘counting back’
3 more.The answer is 61. method.

Ϫ1 Ϫ1 Ϫ1 Ϫ10

61 62 63 64 74

Tim used ‘ nding the difference’ to calculate 81 Ϫ 76.

76 is quite close to 81. 2 Solve 62 – 58 by
I will count up to find the ‘ nding the difference’
between the two
difference between numbers.
the numbers.

The answer is 5.

ϩ1 ϩ1 ϩ1 ϩ1 ϩ1

10 76 77 78 79 80 81

Unit 1A: Core activity 2.2 Subtraction (1)

3 Choose a method to solve these subtraction problems.

(a) 45 Ϫ 43 ϭ ? (b) 92 Ϫ 14 ϭ ? (c) 36 Ϫ 29 ϭ ?

(d) 89 Ϫ 5 ϭ ? (e) 52 Ϫ 34 ϭ ? (f) 42 Ϫ 18 ϭ ?

(g) 77 Ϫ 68 ϭ ? (h) 39 Ϫ 35 ϭ ?

Explain to your partner why you used your chosen methods.
If you think your partner could choose a better method, tell them why.

4 Fred leaves his house with 99 cents and walks to the shop.
He needs 15 cents to buy a snack. But Fred has a hole in his pocket!
Each time he passes a , Fred loses that amount of money from his
pocket.This map shows all the possible routes from his home to the shop.

Find Fred a route to the shop so that he will still have enough money
to buy his snack when he gets there.

37 11 24
27
29 18
15
34 23
20
9

5 Number sentence stories

Hayley thought up a story for 86 Ϫ 49 ϭ 37.

Write a story for each of these number sentences.

35 Ϫ 7 ϭ 28 A shop had 86
77 Ϫ 68 ϭ 9 loaves of bread.They sold
95 Ϫ 35 ϭ 60 49 loaves, so 37 were left.

11

Partitioning to add and subtract

Let’s investigate 545 238 86 228 Vocabulary
Find five pairs of numbers 96 791 355 601
that add up to 900. 672 109 589 437 partition: breaking up
One has been done for you. 463 322 814 465 a number into parts.
For example,
672 ϩ 228 ϭ 900 608 ϭ 600 ϩ 8.

900 is a multiple of 10. Look for two numbers that add to make a
multiple of 10. We can do this by looking for number pairs to 10 in the
units digits.Then choose a method to add the two numbers together.

For example, 67 2 ϩ 22 8 ...

Partitioning to add

423 ϩ 589 ϭ ?

400 ϩ 20 ϩ 3 add 500 ϩ 80 ϩ 9

400 ϩ 500 ϭ 900
20 ϩ 80 ϭ 100
3 ϩ 9 ϭ 12

Therefore, 423 ϩ 589 ϭ 1012

1 Partition each number into hundreds, tens and ones.
Then calculate each answer.
(a) 482 ϩ 213 ϭ ?
(b) 237 ϩ 149 ϭ ?
(c) 821 ϩ 546 ϭ ?
(d) 271 ϩ 649 ϭ ?
(e) 362 ϩ 841 ϭ ?
(f) 598 ϩ 613 ϭ ?

12 Unit 1A: Core activity 2.3 Partitioning to add and subtract

Partitioning to subtract

623 Ϫ 238 ϭ ?

500 ϩ 110 ϩ 13 Ϫ 200 ϩ 30 ϩ 8

500 Ϫ 200 ϭ 300

110 Ϫ 30 ϭ 80

13 Ϫ 8 ϭ5

Therefore, 623 Ϫ 238 ϭ 385

2 Partition each number into hundreds, tens and ones.
Then calculate each answer.

(a) 628 Ϫ 405 ϭ ?

(b) 972 Ϫ 813 ϭ ?

(c) 716 Ϫ 246 ϭ ? If we partition 623 to 600 ϩ 20 ϩ 3,
(d) 609 Ϫ 388 ϭ ? then later we will have to calculate
(e) 981 Ϫ 458 ϭ ? 20 Ϫ 30 and 3 Ϫ 8. So, we partition it to
(f) 560 Ϫ 308 ϭ ? 500 ϩ 110 ϩ 13.

(g) 612 Ϫ 237 ϭ ?

(h) 507 Ϫ 239 ϭ ?

3 Choose a method to solve each of these problems.
Explain why you used your chosen methods.

(a) I bought a television for $438 and the delivery charge was $48.
How much did I pay altogether?

(b) A sea journey is 657 km. So far the ship has travelled 239 km.
How much further does the ship have to travel?

(c) I bought 350 beads. I used 124 beads to make jewellery
for my friends.
How many beads do I have left?

(d) My tree grew 68 cm one year, then 57 cm the next year,
and 72 cm the year after that.
How much has it grown in total over the 3 years?

13

Learning multiplication facts Vocabulary

Let’s investigate multiple: a number
Try to learn multiplication facts for the 2ϫ, 3ϫ, 4ϫ, that can be divided
5ϫ, 6ϫ, 9ϫ and 10ϫ tables so you can remember exactly by another
them quickly. For example: number is a multiple of
that number. Start at 0
ϫ2 multiples are even numbers and count up in steps
of the same size and
ϫ5 multiples end in 0 or 5 you will nd numbers
that are multiples of
ϫ10 multiples end in 0. the step size.

1 Use a blank ϫ 1 2 3 4 5 6 7 8 9 10 ϩ2 ϩ2 ϩ2 ϩ2 ϩ2
multiplication 1 R OW
square like the 2 0 1 2 3 4 5 6 7 8 9 10
one here to look 3C
for patterns. 4O So the multiples of 2
5L are 2, 4, 6, 8, 10, 12 …
6U
7M The multiples of 3 are
8N 3, 6, 9, 12 …
9
10

(a) Write the 1× table across the rst row and down the rst column.
The table is symmetrical so the answers in the rst column will be
the same as the answers in the rst row:
1 ϫ 2 ϭ 2 (row) and 2 ϫ 1 ϭ 2 (column)

(b) Repeat for other times tables such as the 2ϫ, 5ϫ and 10ϫ tables.

(c) Look at the blank squares.Think about how you could ll them in.

You could use:
Counting on or repeated addition.You already have the rst two
multiples of 3 (3 and 6) so keep adding 3 to give you 9, 12, 15.

Using existing answers.You already have answers for the 2ϫ table,
so multiply each answer by 2 to give you the 4ϫ table.
Then multiply the answers to the 4ϫ table by two to get the 8ϫ table.

Complete the rest of the multiplication grid.

14 Unit 1A: Core activity 3.1 Learning and using multiplication facts

2 Look at the spider diagrams for the 2ϫ table.
Copy the diagrams and ll in the missing boxes.

(a) (b)

14 ?
12
6? ?

??? 2ϫ2 7ϫ2 9ϫ2

18 ? 2 ? 16 ? 10ϫ2 2 4ϫ2 ?

??? 3ϫ2 8ϫ2 6ϫ2

20 4 ? ?

8?

Work with a partner to create spider diagrams for other times tables.

3 Look at the numbers in the two circles. 35
Find pairs of numbers in the rst circle that 64
multiply together to give an answer from
inside the second circle. 2

Find as many pairs of numbers as possible. 12
Record both multiplications for each pair.
For example: 5 ϫ 4 ϭ 20 and 4 ϫ 5 ϭ 20

Work with a partner. Draw two circles each. 15 24
Choose ve numbers from 1 to 9 to write in one circle. 20
Swap circles and work out the answers to write in the
second circle.
Ask your partner to check your work.

15

Using multiplication facts Vocabulary

Let’s investigate expression: numbers and signs
What number goes in the circle to complete grouped to show how much
the puzzle? something is. For example,
4 ϩ 2 is an expression for 6,
2 and 3 ϫ 5 is an expression
14 for 15.

1 24 3 product: the answer you get
when you multiply numbers.
6?
4 3 ϫ 5 ϭ 15 product

1 Sanjiv has a collection of toy cars. inverse: signs that ‘undo’ each
other. Multiply and divide are
inverse signs, for example,

ϫ5

7 35

Ϭ5

Which expressions can he use to nd the total number of toy cars?

5ϫ3 3ϫ5 3ϩ3ϩ3 5ϫ5ϫ5

2 Which two number sentences have the same answer?

2ϫ8ϭ ? 2ϫ9ϭ ? 3ϫ7ϭ ? 4ϫ4ϭ ?

3 Use multiplication facts to help you answer these questions.
(a) Sara buys 3 bunches of bananas.
There are 6 bananas in each bunch.
How many bananas does Sara buy altogether?
(b) Ahmed paints 4 rows of animals. He paints 8 animals in each row.
What is the total number of animals Ahmed paints?
(c) Fatima has 5 packets of beads. Each packet contains 8 beads.
How many beads has Fatima got?

16 Unit 1A: Core activity 3.1 Learning and using multiplication facts

4 Use each of the digits 3, 5, 7 and 0 to complete these statements.
You can only use each digit once.
? ? is a multiple of 5 greater than 50.
? ? is a multiple of 10 less than 50.

5 Hugo is thinking of a number.
He says:‘My number is a multiple of 2 and a multiple of 3.
My number is greater than 10.’
What is the smallest number Hugo could be thinking of?

6 Which numbers on the grid are multiples of 5?

61 62 63 64 65

69 70 71 72 73

77 78 79 80 81

7 Parveen has some number cards.

(a) She says:‘If I multiply the number on my card by 5 the answer is 45.’
What number is on her card?

(b) She chooses a different card and says:
‘If I divide the number on this card by 4 the answer is 6.’
What number is on her card?

(c) Write some similar puzzles for your partner to try.

8 Find the missing numbers.

(a) 4 ϫ 5 ϭ ? (b) 5 ϫ ? ϭ 45 (c) ? ϫ 3 ϭ 27

9 Look at this list of numbers. Which ones are multiples of 3?
23 12 21 27 26 9
28 22 15 17 18
Look at your answers. Explain to your partner what you notice about them.

17

Investigating patterns

Work through these investigations with a partner.
1 These triangles are made from sticks.

Pattern number Number of sticks
1 3
2 6
3 9

pattern 1 pattern 2 pattern 3

(a) How many sticks would be needed to make pattern 7?
(b) How many sticks would be needed to make pattern 17?
(c) Which pattern could be made from 33 sticks?

2 These squares are made from sticks.

Pattern number Number of sticks
1 4
2 8
3
12

pattern 1 pattern 2 pattern 3

(a) How many sticks would be needed to make pattern 9?
(b) How many sticks would be needed to make pattern 15?
(c) Which pattern could be made from 48 sticks? How do you know?

Explain to your partner how you worked out the answer.

18 Unit 1A: Core activity 3.1 Learning and using multiplication facts

3 Look at these stair patterns.

pattern 1 pattern 2 pattern 3
It takes 2 steps It takes 4 steps It takes 6 steps
to go up and down. to go up and down. to go up and down.

(a) How many steps would it take to go up and down the
8th pattern of stairs?

(b) How do you know?
Explain your method to your partner.

(c) How many steps would it take to go up and down the
10th pattern of stairs?

(d) How many steps would it take to go up and down the
100th pattern of stairs?

4 Look at these squares made on a pinboard.

square 1 square 2 square 3
It touches 4 pins. It touches 8 pins. It touches 12 pins.

(a) How many pins should the 7th square touch?
(b) Explain to your partner how to work out the answer

without drawing a diagram.

What have you noticed in all these investigations?

What has your partner noticed?

19