Oxford International Primary Maths — Workbook 1

The whole first-year workbook in one page: all 12 units and 38 topics, from counting objects to reading a block graph. Every topic starts with a Discover picture, then works through three levels of practice. Tap the counters, type the answers, and everything you do is kept in this browser.

12 units · 38 topics 1156 exercises with answers Tap-and-count activities Picture glossary Progress tracker

How to use this workbook

Pick a unit from the list on the left. Every topic opens with a Discover panel that shows the idea with real things to look at and count, and then works through three levels: Practise with plenty of help, Practise more as the help is taken away, and Challenge for the children who are ready to think harder.

Children of this age work best beside an adult. Read the question aloud, let them tap the ten frames and counters on screen, then type the number together. Use Mark complete at the top of a topic to fill in the progress bar, and open the 🔑 Answers panel under each topic to check. Print gives you a clean worksheet with the answers hidden.

Oxford International Primary Maths is taught in English, so the lessons and exercises are in English. Everything typed stays on this device — nothing is uploaded.

12units, from counting to handling data

38topics, each at three levels

1156exercises, every one answered

5–6years — the first year of primary maths

Unit 1

Numbers and counting

Touch each thing once, say one number for each one, and the last number you say tells you how many there are. Then learn to read and write those numbers all the way to 20.

Number · 3 topics

Unit 1 · Topic 1

Counting objects

When you count, touch each thing once and say one number for each one. The last number you say is how many there are.

🐞 🐞 🐞 🐞 🐞

One, two, three, four, five. There are 5 ladybirds.

It helps to sort things first. Put all the red ones together, then all the blue ones, then count each pile. That way you never count the same one twice.

Count the ladybirds again, but start from the other end. Do you still get 5?

PractiseCount and write the number

Count each row. Write how many.
1. 🍎 🍎 🍎 🍎
2. ⭐ ⭐ ⭐ ⭐ ⭐ ⭐
3. 🐟 🐟 🐟
4. 🚗 🚗 🚗 🚗 🚗 🚗 🚗
Count the flowers. They are not in a line, so touch each one as you count.

🌸 🌼 🌸 🌼 🌸 🌼 🌸 🌼

There are flowers.
Tap the squares to fill the ten frame. Fill in 7, then write the number of empty squares.

Empty squares:
Count the two piles. Which pile has more?

🔵 🔵 🔵 🔵 🔵 🔵

and

🔴 🔴 🔴 🔴

There are more counters.

Practise moreNow on your own

Count each group of animals.
1. 🐑 🐑 🐑 🐑 🐑 🐑 🐑 🐑 🐑
2. 🐝 🐝
3. 🦆 🦆 🦆 🦆 🦆 🦆 🦆 🦆 🦆 🦆
4. 🐢 🐢 🐢 🐢 🐢 🐢 🐢 🐢
These buttons are mixed up. Count the buttons of each colour, then count them all.

🟡 🔵 🟡 🔴 🔵 🟡 🔴 🟡 🔵 🟡
1. Yellow
2. Blue
3. Red
4. Altogether
Count the dots in each ten frame.
1. First frame
2. Second frame
Count the fruit in the bowl, then answer.

🍓 🍌 🍓 🍇 🍓 🍌 🍓 🍇 🍓
1. How many strawberries?
2. How many bananas?
3. How many grapes?
4. How many pieces of fruit altogether?

ChallengeThink a bit harder

Rani counted this row and said "6". Sam counted the same row and said "7". Count it yourself and say who is right.

🐧 🐧 🐧 🐧 🐧 🐧 🐧

The answer is , so is right.

What mistake might the other child have made?
Fill the ten frame so that there are 3 empty squares. How many squares did you fill?

I filled squares.

Answers · 1A Counting objects

Practise

1a 4 b 6 c 3 d 7

2 8 flowers

3 7 filled, so 3 squares are empty.

4 6 blue and 4 red — there are more blue counters.

Practise more

1a 9 b 2 c 10 d 8

2 Yellow 5, blue 3, red 2, altogether 10.

3a 6 b 9

4 5 strawberries, 2 bananas, 2 grapes, 9 pieces altogether.

Challenge

1 There are 7 penguins, so Sam is right. Rani probably missed one out, or counted two of them with the same number. Touching each penguin once as you say the number stops both mistakes.

2 7 squares filled, because 7 and 3 make 10.

Unit 1 · Topic 2

Counting rhymes and actions

You can count things you cannot touch — claps, jumps, hops. You have to keep the count in your head, so say the numbers out loud as you go.

Counting rhymes help you learn the order of the numbers. In Five little ducks one duck swims away each time, so the numbers go backwards:

5→4→ 3→2→ 1→0

Counting forwards makes the number one bigger each time. Counting backwards makes it one smaller.

Clap while you count to 10. Now clap while you count back from 10. Which is harder?

PractiseSay it, then write it

Count forwards. Write the missing numbers.

123 5 7 9
Count backwards from 10. Write the missing numbers.

108 6 4 2
Five little ducks went swimming one day. Two swam away. How many are left?

🦆 🦆 🦆 🦆 🦆

ducks are left.
Answer these.
1. You clap 4 times, then 1 more. How many claps?
2. You jump 7 times, then 1 more. How many jumps?
3. Count on 1 from 9.
4. Count back 1 from 6.

Practise moreNow on your own

Write the next three numbers.
1. 6, 7, 8,
2. 11, 12, 13,
3. 9, 8, 7,
4. 20, 19, 18,
Ten green bottles hanging on the wall. Three accidentally fall. How many green bottles are hanging on the wall?

bottles.
Count on from the number given.
1. 3, then 2 more →
2. 8, then 2 more →
3. 14, then 3 more →
4. 16, then 4 more →
Count back from the number given.
1. 7, back 2 →
2. 12, back 3 →
3. 15, back 5 →
4. 20, back 4 →

ChallengeThink a bit harder

A rhyme starts with 5 monkeys. One falls off the bed each verse. After how many verses are there no monkeys left?

verses.

How do you know?
Bopha claps 6 times. Dara claps 2 more than Bopha. How many times does Dara clap?

claps.

Answers · 1B Counting rhymes and actions

Practise

1 4, 6, 8, 10

2 9, 7, 5, 3, 1

3 3 ducks

4a 5 b 8 c 10 d 5

Practise more

1a 9, 10, 11 b 14, 15, 16 c 6, 5, 4 d 17, 16, 15

2 7 bottles

3a 5 b 10 c 17 d 20

4a 5 b 9 c 10 d 16

Challenge

1 5 verses. One monkey goes each verse, so counting back 5, 4, 3, 2, 1, 0 takes five steps to reach 0.

2 8 claps — count on 2 from 6.

Unit 1 · Topic 3

Reading and writing numbers

Every number has a symbol you write and a word you say. Here are the numbers to 20:

12345 678910

1112131415 1617181920

A number tells you how many, so the symbol, the word and the set of things all match:

🐛🐛🐛🐛🐛🐛6 · six

Which numbers are the tricky ones to say? Most children find 11, 12, 13 and 15 the hardest.

PractiseMatch the number to the word

Write the number for each word.
1. three
2. seven
3. ten
4. five
Write the word for each number.
1. 2
2. 8
3. 4
4. 9
Count the worms and write the number.

🐛 🐛 🐛 🐛 🐛 🐛 🐛

worms — that is worms.
Which number is bigger? Circle it by typing it in the box.
1. 6 or 9 →
2. 12 or 8 →
3. 15 or 14 →
4. 20 or 11 →

Practise moreNow on your own

Write the number for each word.
1. eleven
2. fourteen
3. seventeen
4. twenty
Write the word for each number.
1. 13
2. 16
3. 12
4. 19
Each cushion has a number on it. Write the numbers in order, smallest first.

3725
Draw is not possible here, so write instead. How many counters would you need to match each number?
1. six → counters
2. fifteen → counters
3. eighteen → counters
4. ten → counters

ChallengeThink a bit harder

Sokha wrote the number thirteen like this: 31. What has she done wrong? Write thirteen correctly.

Thirteen is .

What went wrong?
I am thinking of a number. It is bigger than 14 and smaller than 16. What is my number?
Write every number from 10 to 20 that has a 1 as its first digit. How many are there?

There are of them.

Answers · 1C Reading and writing numbers

Practise

1a 3 b 7 c 10 d 5

2a two b eight c four d nine

3 7 worms — seven worms.

4a 9 b 12 c 15 d 20

Practise more

1a 11 b 14 c 17 d 20

2a thirteen b sixteen c twelve d nineteen

3 2, 3, 5, 7

4a 6 b 15 c 18 d 10

Challenge

1 Thirteen is 13. Sokha has written the digits the wrong way round. We say "thir-teen", which sounds like the 3 first, but thirteen means 1 ten and 3 ones, so the 1 is written first.

2 15

3 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 — that is 10 numbers. (20 starts with a 2.)

Unit 2

Exploring numbers

Numbers have neighbours. Find out which is more and which is less, what sits between two numbers, how tens and ones build a teen number, and how to put numbers in order.

Number · 4 topics

Unit 2 · Topic 1

More and less

To find out which set has more, line the things up and match them one to one. The set with something left over has more.

🍏 🍏 🍏 🍏 🍏
5

↔

🍊 🍊 🍊
3

5 is more than 3. 3 is less than 5. There are 2 more apples than oranges.

On the number track, one more is the next box along and one less is the box before.

45678

One less than 6 is 5. One more than 6 is 7.

Can two sets have neither more nor less? What do we call that?

PractiseMatch them up and compare

Count each set, then finish the sentences.

🐤 🐤 🐤 🐤 🐤 🐤 🐤

and

🐣 🐣 🐣 🐣
1. There are more .
2. There are less .
3. There are more 🐤 than 🐣.
Write one more than each number.
1. 3 →
2. 7 →
3. 9 →
4. 14 →
Write one less than each number.
1. 5 →
2. 8 →
3. 12 →
4. 20 →
There are 5 pencils in the red pot and 9 in the blue pot.
1. Which pot has more?
2. How many more?

Practise moreNow on your own

Write more or less in each gap.
1. 8 is than 5.
2. 4 is than 11.
3. 16 is than 13.
4. 9 is than 19.
Write one more and one less for each number.
1. One less · 10 · one more
2. One less · 15 · one more
3. One less · 18 · one more
4. One less · 1 · one more
Count the counters in each ten frame, then say which has more and by how many.
1. First frame
2. Second frame
3. The frame has more.
4. It has more.
Lyna has 12 stickers. Vanna has 2 less than Lyna. How many stickers does Vanna have?

stickers.

ChallengeThink a bit harder

I am one more than 9 and one less than 11. What number am I?
Two boxes hold the same number of cubes. Chan takes 3 cubes out of the first box. Which box has more now, and by how many?

The box has more.
Write three numbers that are all more than 6 but less than 12.

How many different numbers could you have chosen?

Answers · 2A More and less

Practise

1 7 and 4. a more 🐤 (chicks) b less 🐣 c 3 more.

2a 4 b 8 c 10 d 15

3a 4 b 7 c 11 d 19

4a the blue pot b 4 more

Practise more

1a more b less c more d less

2a 9, 11 b 14, 16 c 17, 19 d 0, 2

3 7 and 4; the first frame has more, by 3.

4 10 stickers

Challenge

1 10

2 The second box has 3 more, because the boxes started equal and 3 were taken from the first.

3 Any three of 7, 8, 9, 10, 11. There are 5 numbers to choose from.

Unit 2 · Topic 2

Between

A number is between two others when it comes after the first one and before the second one.

678

7 is between 6 and 8. It is one more than 6 and one less than 8.

Sometimes more than one number fits. Between 4 and 8 there are three numbers: 5, 6 and 7.

45678

Say the numbers out loud in order. The ones you say in the middle are the "between" numbers.

PractiseFind the middle number

Write the number that goes between.
1. 2 4
2. 7 9
3. 11 13
4. 18 20
Fill the gaps in the number track.

911 13 15
Write all the numbers between 5 and 9.
True or false? Tick the right box.
1. 6 is between 5 and 7. true false
2. 10 is between 12 and 14. true false

Practise moreNow on your own

Write the number that goes between.
1. 14 16
2. 0 2
3. 16 18
4. 12 14
Write all the numbers between each pair.
1. 10 and 14 →
2. 15 and 20 →
Fill the gaps.

34 78 10
Answer these.
1. How many numbers are between 3 and 7?
2. How many numbers are between 11 and 12?

ChallengeThink a bit harder

My number is between 12 and 16. It is not 13 and not 15. What is my number?
Ravi says "8 is between 9 and 7". Is he right? Explain.

Yes No

Answers · 2B Between

Practise

1a 3 b 8 c 12 d 19

2 10, 12, 14

3 6, 7, 8

4a true b false (10 comes before 12, not between 12 and 14)

Practise more

1a 15 b 1 c 17 d 13

2a 11, 12, 13 b 16, 17, 18, 19

3 5, 6, 9

4a 3 (they are 4, 5 and 6) b 0 — 11 and 12 are next-door neighbours, so no whole number fits between them.

Challenge

1 14 — the numbers between 12 and 16 are 13, 14 and 15, and two of them are ruled out.

2 Yes. 8 does sit between 7 and 9. Ravi has just said the two numbers in the other order, which does not change which number is in the middle.

Unit 2 · Topic 3

Tens and ones

When you have ten ones, join them into a tower of ten. Then the number is made of tens and ones.

That is 1 ten and 3 ones, which we write as 13.

Tens	Ones
1	3

In a teen number the first digit tells you the tens and the second digit tells you the ones.

Why does 13 have a 1 at the front when we say "thir-teen"?

PractiseBuild it, then write it

Count the dots. Write the tens and ones, then the number.

ten and ones makes .
Fill in the tens and ones.
1. 15 = ten and ones
2. 12 = ten and ones
3. 19 = ten and ones
4. 10 = ten and ones
Write the number.
1. 1 ten and 7 ones =
2. 1 ten and 4 ones =
3. 2 tens and 0 ones =
4. 1 ten and 8 ones =
Tap to fill 16 counters into the two ten frames.

Full frames: Ones left over:

Practise moreNow on your own

Complete the place value table.

Number Tens Ones

11

14

18

20
Write the number.
1. 1 ten 1 one =
2. 1 ten 6 ones =
3. 1 ten 9 ones =
4. 1 ten 5 ones =
Nita has 1 tower of ten cubes and 7 loose cubes. Ben has 13 cubes altogether.
1. How many cubes has Nita?
2. Who has more?
3. How many loose cubes would Ben have?
Which digit tells you the tens?
1. In 17 the tens digit is
2. In 17 the ones digit is
3. In 20 the tens digit is
4. In 20 the ones digit is

ChallengeThink a bit harder

Maly throws a dice and collects that many cubes each time. She throws 6, then 5, then 4. She makes towers of ten whenever she can.
1. How many cubes does she have altogether?
2. How many towers of ten?
3. How many cubes are left over?
A number has the same digit for tens and ones. It is smaller than 20. What is it?

Answers · 2C Tens and ones

Practise

1 1 ten and 6 ones makes 16.

2a 1 ten, 5 ones b 1 ten, 2 ones c 1 ten, 9 ones d 1 ten, 0 ones

3a 17 b 14 c 20 d 18

4 1 full frame and 6 left over.

Practise more

1 11 → 1 ten 1 one; 14 → 1 ten 4 ones; 18 → 1 ten 8 ones; 20 → 2 tens 0 ones.

2a 11 b 16 c 19 d 15

3a 17 b Nita c 3 loose cubes

4a 1 b 7 c 2 d 0

Challenge

1 6 + 5 + 4 = 15 cubes, which makes 1 tower of ten with 5 left over.

2 11 — it has 1 ten and 1 one.

Unit 2 · Topic 4

Ordering numbers

To put numbers in order, find the smallest one first and write it down. Then find the smallest of the ones that are left, and keep going.

83116

Smallest first: 3, 6, 8, 11. Biggest first: 11, 8, 6, 3.

A number line helps, because numbers always get bigger as you move to the right.

The word "order" means the numbers follow a rule — always getting bigger, or always getting smaller.

PractiseSmallest first

Put these numbers in order, smallest first.

5297
Put these numbers in order, smallest first.

1461811
Put these numbers in order, biggest first.

31081
Answer these about the numbers 4, 15, 9 and 12.
1. Which is smallest?
2. Which is biggest?

Practise moreNow on your own

Order smallest first.
1. 13, 7, 20, 16 →
2. 2, 12, 9, 5, 17 →
Order biggest first.
1. 6, 19, 11, 3 →
2. 10, 4, 14, 8, 1 →
Four children ran a race. Order their numbers smallest to biggest, then answer.

125179

Which number is in the middle of the smallest and biggest? Either or .
Fill in the missing numbers so the track counts on in ones.

12 1517 19

ChallengeThink a bit harder

Use the digits 1 and 7 to make two different two-digit numbers. Write them in order, smallest first.
Three numbers are in order, smallest first: 8, ?, 14. Write two numbers that could go in the middle.
Sophea ordered these numbers and got 3, 7, 12, 9. Is she right? If not, write them correctly.

Right Wrong

Answers · 2D Ordering numbers

Practise

1 2, 5, 7, 9 2 6, 11, 14, 18 3 10, 8, 3, 1

4a 4 b 15

Practise more

1a 7, 13, 16, 20 b 2, 5, 9, 12, 17

2a 19, 11, 6, 3 b 14, 10, 8, 4, 1

3 5, 9, 12, 17. The two middle numbers are 9 and 12.

4 13, 14, 16, 18

Challenge

1 17 and 71 → in order: 17, 71.

2 Any two of 9, 10, 11, 12, 13.

3 Wrong. The correct order is 3, 7, 9, 12 — she put 12 before 9.

Unit 3

Number pairs

Two numbers that go together to make a total are called a number pair. Learn every pair for 6, 7, 8 and 9 — and then the most useful pairs of all, the pairs that make 10.

Number · 2 topics

Unit 3 · Topic 1

Number pairs for 6, 7, 8 and 9

Take 6 counters and split them into two groups. However you split them, the two numbers still make 6. Those two numbers are a number pair for 6.

🔴 🔴 🔴 🔴
4

and

🔵 🔵
2

4 and 2 make 6. We write it as 4 + 2 = 6.

Every pair for 6 is here:

0 and 6 · 1 and 5 · 2 and 4 · 3 and 3 · 4 and 2 · 5 and 1 · 6 and 0

Notice that 4 and 2 makes 6, and so does 2 and 4. You get a pair free every time you swap them round!

PractiseSplit the counters

These 7 counters are split into two groups. Write the pair.

🟠 🟠 🟠 🟠 🟠

and

🟣 🟣

+ = 7
Complete the number pairs for 6.
1. 5 + = 6
2. 3 + = 6
3. 1 + = 6
4. 0 + = 6
Complete the number pairs for 8.
1. 6 + = 8
2. 4 + = 8
3. 7 + = 8
4. 3 + = 8
Use the ten frame. Tap 5 squares, then count the empty ones to find the pair for 9.

5 + = 9 (careful — one square in the frame is not used)

Practise moreNow on your own

Complete the number pairs for 7.
1. 2 + = 7
2. 5 + = 7
3. + 4 = 7
4. + 6 = 7
Complete the number pairs for 9.
1. 8 + = 9
2. 6 + = 9
3. + 5 = 9
4. + 0 = 9
Write all the number pairs for 6, starting with 0 and 6.
1. 0 +
2. 1 +
3. 2 +
4. 3 +
5. 4 +
6. 5 +
7. 6 +
Nary has 8 shells. She puts some in her left hand and 3 in her right hand. How many are in her left hand?

shells.

ChallengeThink a bit harder

Which number pair for 8 uses the same number twice?

+ = 8

Can you do the same for 7? Yes No

Why?
There are 9 birds on a wall. Some fly to the tree. Write three different pairs that could show how many are left on the wall and how many are in the tree.
1. and
2. and
3. and

Answers · 3A Number pairs for 6, 7, 8 and 9

Practise

1 5 and 2; 5 + 2 = 7

2a 1 b 3 c 5 d 6

3a 2 b 4 c 1 d 5

4 5 + 4 = 9

Practise more

1a 5 b 2 c 3 d 1

2a 1 b 3 c 4 d 9

3 0 + 6, 1 + 5, 2 + 4, 3 + 3, 4 + 2, 5 + 1, 6 + 0

4 5 shells

Challenge

1 4 + 4 = 8. You cannot do the same for 7, because 7 is an odd number — it cannot be split into two equal whole groups. (3 + 3 is only 6 and 4 + 4 is already 8.)

2 Any three pairs that total 9: 0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5, 5 and 4, 6 and 3, 7 and 2, 8 and 1, 9 and 0.

Unit 3 · Topic 2

Number pairs for 10

The pairs that make 10 are the most useful pairs in maths. Learn them so well that you never have to work them out.

7 filled and 3 empty — so 7 + 3 = 10.

Here they all are:

0 + 10 · 1 + 9 · 2 + 8 · 3 + 7 · 4 + 6 · 5 + 5 · 6 + 4 · 7 + 3 · 8 + 2 · 9 + 1 · 10 + 0

Hold up ten fingers. Fold some down. The fingers left up and the fingers folded down are always a pair for 10.

PractiseFill the ten frame

Count the dots, then say how many more make 10.

+ = 10
Complete the pairs for 10.
1. 8 + = 10
2. 3 + = 10
3. 5 + = 10
4. 9 + = 10
Complete the pairs for 10.
1. + 4 = 10
2. + 7 = 10
3. + 2 = 10
4. + 10 = 10
Tap 6 squares in the ten frame, then answer.

Empty squares: So 6 + = 10.

Practise moreNow on your own

Write the missing number in each pair for 10.
1. 1 +
2. 6 +
3. 0 +
4. 4 +
5. 7 +
6. 2 +
Ten children are playing. Some are inside and the rest are outside. Complete the table.

Inside Outside

4

7

8

5
There are 10 eggs in a box. Some have been taken out. How many are left?
1. 3 taken out → left
2. 6 taken out → left
3. 9 taken out → left
4. 10 taken out → left
Which of these pairs make 10? Tick the ones that do.
1. 6 and 4 makes 10
2. 5 and 4 makes 10
3. 2 and 8 makes 10
4. 7 and 2 makes 10

Inside	Outside
4
7
	8
	5

ChallengeThink a bit harder

Use a pair for 10 to help you. 10 + 4 = 14, so what is 6 + 4 + 4?

Which two numbers did you add together first, and why?
Three numbers make 10. Two of them are 3 and 5. What is the third number?
Write three different ways to make 10 using three numbers.
1. + + = 10
2. + + = 10
3. + + = 10

Answers · 3B Number pairs for 10

Practise

1 6 + 4 = 10

2a 2 b 7 c 5 d 1

3a 6 b 3 c 8 d 0

4 4 empty, so 6 + 4 = 10.

Practise more

1a 9 b 4 c 10 d 6 e 3 f 8

2 4 → 6; 7 → 3; 2 → 8; 5 → 5

3a 7 b 4 c 1 d 0

4 Tick a (6 and 4) and c (2 and 8). 5 and 4 make 9; 7 and 2 make 9.

Challenge

1 14. Add 6 + 4 first because they are a pair for 10, then 10 + 4 = 14.

2 2, because 3 + 5 = 8 and 8 + 2 = 10.

3 Any three correct sums, for example 5 + 3 + 2, 4 + 4 + 2, 6 + 2 + 2, 1 + 2 + 7, 3 + 3 + 4.

Unit 4

Addition

Two ways to add. Push the sets together and count them all — or start at the bigger number and count on. The second way is quicker, and it is the one you will use for years.

Calculating · 2 topics

Unit 4 · Topic 1

Combining sets

When you put two sets together you add them. Push them together and count how many there are altogether.

🍪 🍪 🍪
3

🍪 🍪
2

3 and 2 altogether is 5. We write 3 + 2 = 5.

The + sign means "add". The = sign means "is the same as".

3 + 2 and 2 + 3 both make 5. Adding in either order gives the same total.

PractisePush them together and count

Count both sets, then find the total.

🐠 🐠 🐠 🐠

+

🐠 🐠 🐠

Altogether: fish.
Write the addition for each picture.
1. 🌰 🌰 and 🌰 🌰 🌰 🌰 🌰 → + =
2. 🎈 🎈 🎈 🎈 🎈 🎈 and 🎈 🎈 🎈 → + =
Work these out.
1. 2 + 3 =
2. 4 + 4 =
3. 5 + 2 =
4. 6 + 1 =
Tap 4 squares, then 3 more in the second frame, and find the total.

4 + 3 =

Practise moreNow on your own

Work these out.
1. 3 + 5 =
2. 6 + 2 =
3. 7 + 3 =
4. 5 + 5 =
5. 8 + 2 =
6. 4 + 0 =
Check that swapping the numbers gives the same total.
1. 2 + 7 = and 7 + 2 =
2. 1 + 8 = and 8 + 1 =
Solve these word problems.
1. Sita picks 5 mangoes and Chea picks 4. How many altogether?
2. There are 6 red cars and 3 blue cars in the car park. How many cars?
3. A plate has 7 rice cakes. Mum puts 2 more on. How many now?
Find the missing number.
1. 3 + = 8
2. 5 + = 9
3. + 4 = 10
4. + 6 = 7

ChallengeThink a bit harder

Add three sets: 2 + 3 + 4.

Total =

Which two did you add first?
Two numbers add to 9. One of them is double the other. What are the two numbers?

and
Dara says "7 + 2 is more than 2 + 7 because 7 comes first." Is Dara right? Explain.

Right Wrong

Answers · 4A Combining sets

Practise

1 4 and 3, altogether 7 fish.

2a 2 + 5 = 7 b 6 + 3 = 9

3a 5 b 8 c 7 d 7

4 4 + 3 = 7

Practise more

1a 8 b 8 c 10 d 10 e 10 f 4

2a 9 and 9 b 9 and 9 — swapping never changes the total.

3a 9 mangoes b 9 cars c 9 rice cakes

4a 5 b 4 c 6 d 1

Challenge

1 9. Any order works; many children add 2 + 4 = 6 first (or 3 + 4 = 7) and then add the third number.

2 3 and 6, because 6 is double 3 and 3 + 6 = 9.

3 Wrong. Both come to 9. The order you add in does not change the total — pushing the two sets together gives the same pile whichever one you start with.

Unit 4 · Topic 2

Counting on

You do not have to count both sets from the start. Hold the bigger number in your head and count on the smaller one.

For 8 + 3, start at 8 and count on three: 9, 10, 11.

So 8 + 3 = 11.

Why is it quicker to start at 8 and count on 3, than to start at 3 and count on 8?

PractiseStart big, count on

Count on to find the answer. Say the numbers out loud.
1. 6 + 2 → say 7, 8 →
2. 9 + 3 → say 10, 11, 12 →
3. 7 + 2 →
4. 10 + 4 →
Which number would you start at? Write the bigger number first, then the answer.
1. 3 + 9 → start at →
2. 2 + 11 → start at →
Fill in the number track as you count on 3 from 12.

12→ → →

So 12 + 3 =
Work these out by counting on.
1. 11 + 2 =
2. 14 + 3 =
3. 15 + 4 =
4. 16 + 3 =

Practise moreNow on your own

Work these out.
1. 8 + 4 =
2. 9 + 5 =
3. 13 + 4 =
4. 7 + 6 =
5. 12 + 5 =
6. 17 + 3 =
Add 1, 2 or 3 to each number.

Number +1 +2 +3

7

11

16
Solve these word problems by counting on.
1. There are 9 people on the bus. 4 more get on. How many now?
2. Mony has 13 marbles and wins 3 more. How many now?
3. A book has 15 pages read. Srey reads 5 more. How many pages read?
Find the missing number.
1. 9 + = 12
2. 14 + = 18
3. 8 + = 11
4. 16 + = 20

ChallengeThink a bit harder

Sokun works out 4 + 9 by starting at 4 and counting on 9. Nita starts at 9 and counts on 4. Both get 13. Whose way needs fewer counts, and why?

needs fewer.
Start at 6. Count on 4, then count on 3 more. Where do you finish?
I count on 5 from a number and land on 19. What number did I start on?

Answers · 4B Counting on

Practise

1a 8 b 12 c 9 d 14

2a start at 9 → 12 b start at 11 → 13

3 13, 14, 15; so 12 + 3 = 15.

4a 13 b 17 c 19 d 19

Practise more

1a 12 b 14 c 17 d 13 e 17 f 20

2 7 → 8, 9, 10; 11 → 12, 13, 14; 16 → 17, 18, 19.

3a 13 people b 16 marbles c 20 pages

4a 3 b 4 c 3 d 4

Challenge

1 Nita needs fewer. She counts on only 4 steps (10, 11, 12, 13) while Sokun counts 9 steps. Starting from the bigger number always means fewer counts, and fewer counts means fewer chances to make a mistake.

2 13 — 6 count on 4 is 10, then count on 3 more is 13.

3 14, because counting back 5 from 19 gives 14.

Unit 5

Subtraction and difference

Subtraction answers two different questions: how many are left when some go away, and how many more one set has than another. Both use the same − sign.

Calculating · 3 topics

Unit 5 · Topic 1

Taking away

When some things go away, you take away. Count what is left.

🍰 🍰 🍰 🍰 🍰 🍰 🍰

There were 7 cakes. 2 were eaten (the faded ones). 5 are left.

We write 7 − 2 = 5. The − sign means "take away".

Taking away makes the number smaller — unless you take away nothing at all.

PractiseCross them off and count

The faded ones have gone. How many are left?
1. 🐦 🐦 🐦 🐦 🐦 🐦 6 − 2 =
2. 🍋 🍋 🍋 🍋 🍋 🍋 🍋 🍋 8 − 3 =
Work these out.
1. 5 − 1 =
2. 7 − 3 =
3. 9 − 4 =
4. 6 − 6 =
Tap 9 squares in the ten frame. Now imagine 4 of them going away.

9 − 4 =
Solve these.
1. There are 8 buns. 3 are eaten. How many are left?
2. 10 ducks are on the pond. 6 fly away. How many are left?

Practise moreNow on your own

Work these out.
1. 10 − 3 =
2. 8 − 5 =
3. 12 − 2 =
4. 9 − 0 =
5. 15 − 5 =
6. 7 − 7 =
Take 3 away from each number.

6→ 11→ 14→ 20→
Solve these word problems.
1. Rithy had 12 stickers and gave 4 to his sister. How many has he now?
2. A jug held 10 cups of water. 7 cups were poured out. How many are left?
3. There are 9 chairs. 5 children sit down. How many chairs are empty?
Find the missing number.
1. 8 − = 5
2. 10 − = 4
3. − 3 = 6
4. − 2 = 9

ChallengeThink a bit harder

Start with 10. Take away 2, then take away 3 more. How many are left?

What single subtraction gives the same answer? 10 −
Write two different subtractions that both have the answer 4.
1. − = 4
2. − = 4
Can 3 − 8 be done with counters? Explain what happens if you try.

Answers · 5A Taking away

Practise

1a 4 b 5

2a 4 b 4 c 5 d 0

3 5

4a 5 buns b 4 ducks

Practise more

1a 7 b 3 c 10 d 9 e 10 f 0

2 3, 8, 11, 17

3a 8 stickers b 3 cups c 4 chairs

4a 3 b 6 c 9 d 11

Challenge

1 5 left. The single subtraction is 10 − 5, because taking away 2 and then 3 is the same as taking away 5 altogether.

2 Any two, for example 6 − 2, 10 − 6, 9 − 5, 4 − 0.

3 No. You only have 3 counters, so once you have taken 3 away there are none left to take. You run out before you have taken 8. (Numbers below zero come later.)

Unit 5 · Topic 2

Counting back

Just as you can count on to add, you can count back to subtract. Start at the big number and hop backwards.

For 11 − 3, start at 11 and count back three: 10, 9, 8.

So 11 − 3 = 8.

Counting on moves you to the right. Which way does counting back move you?

PractiseHop backwards

Count back and write the numbers you say.
1. 9 − 3 → say , , → answer
2. 13 − 4 → say , , , → answer
Work these out by counting back.
1. 7 − 2 =
2. 12 − 3 =
3. 15 − 2 =
4. 18 − 4 =
Fill in the track as you count back 4 from 16.

16→ → → →
Take 1 away, then 2 away, then 3 away.
1. 10 − 1 =
2. 10 − 2 =
3. 10 − 3 =
4. 10 − 4 =

Practise moreNow on your own

Work these out.
1. 14 − 3 =
2. 17 − 5 =
3. 11 − 4 =
4. 20 − 3 =
5. 16 − 6 =
6. 19 − 5 =
Take away 2 from each number.

Start 13 16 11 20

Take 2
Solve these word problems.
1. 15 mangoes are in a basket. 4 are sold. How many are left?
2. A lift has 18 people. 5 get out. How many are still in the lift?
3. Chenda has 20 riel. She spends 6 riel. How much is left? riel
Which is quicker — counting back 2, or counting back 9? Work both out.
1. 12 − 2 =
2. 12 − 9 =

Start	13	16	11	20
Take 2

ChallengeThink a bit harder

I count back 3 and land on 9. What number did I start on?
Count back in twos from 20. Write the first six numbers you say.
For 12 − 9, Bopha counts back 9 hops. Vichea says "9 add 3 makes 12, so the answer is 3." Whose way is quicker? Explain.

is quicker.

Answers · 5B Counting back

Practise

1a 8, 7, 6 → 6 b 12, 11, 10, 9 → 9

2a 5 b 9 c 13 d 14

3 15, 14, 13, 12

4a 9 b 8 c 7 d 6

Practise more

1a 11 b 12 c 7 d 17 e 10 f 14

2 11, 14, 9, 18

3a 11 mangoes b 13 people c 14 riel

4a 10 b 3. Counting back 2 is much quicker — only two hops.

Challenge

1 12

2 18, 16, 14, 12, 10, 8

3 Vichea is quicker. Counting back 9 takes nine hops and it is easy to lose your place. Because 9 and 3 make 12, the gap between 9 and 12 is only 3 — so you can find the answer in one step instead of nine.

Unit 5 · Topic 3

Finding the difference

Sometimes nothing goes away — you just want to know how many more one set has than another. That is the difference.

Line the two sets up and match them one to one. The ones with no partner are the difference.

🟦 🟦 🟦 🟦 🟦 🟦 🟦
7

↔

🟨 🟨 🟨 🟨
4

Three blue squares have no partner, so the difference is 3. We write 7 − 4 = 3.

"How many more?" and "how many less?" both ask for the difference — and the answer is the same number.

PractiseMatch them up

Count each set, then find the difference.

🍏 🍏 🍏 🍏 🍏 🍏

↔

🍎 🍎 🍎

The difference is .
Find the difference between each pair.
1. 8 and 5 →
2. 10 and 6 →
3. 9 and 9 →
4. 12 and 7 →
There are 9 boys and 6 girls in a group.
1. How many more boys than girls?
2. How many fewer girls than boys?
Use the number line idea: count on from the smaller number to the bigger one. How many hops?
1. From 7 to 11 → hops
2. From 13 to 16 → hops

Practise moreNow on your own

Find the difference.
1. 15 and 11 →
2. 20 and 14 →
3. 6 and 13 →
4. 18 and 10 →
5. 4 and 12 →
6. 17 and 17 →
Two pots of pencils. The red pot has 5 pencils. The blue pot has 11.
1. Which pot has more?
2. How many more?
3. How many pencils would you move so both pots have the same?
Solve these word problems.
1. Sina is 8 years old. Her brother is 13. What is the difference in their ages? years
2. A red ribbon is 14 cm and a green one is 9 cm. How much longer is the red one? cm
3. Team A scored 7 goals and Team B scored 12. By how many did Team B win?
Fill in the missing number.
1. The difference between 9 and is 4. (bigger)
2. The difference between 15 and is 5. (smaller)

ChallengeThink a bit harder

The difference between two numbers is 3. One of them is 8. Write both numbers the other one could be.

or
Sok has 6 sweets. Dara has 10. Sok says "I need 4 more to have the same as Dara." Is Sok right? What else could they do so they have the same number each?

Right Wrong
Why does "taking away" and "finding the difference" both use the − sign?

Answers · 5C Finding the difference

Practise

1 6 and 3 — the difference is 3.

2a 3 b 4 c 0 d 5

3a 3 more boys b 3 fewer girls — the same number both ways.

4a 4 hops b 3 hops

Practise more

1a 4 b 6 c 7 d 8 e 8 f 0

2a the blue pot b 6 more c 3 pencils — moving 3 leaves 8 in each pot.

3a 5 years b 5 cm c by 5 goals

4a 13 b 10

Challenge

1 5 or 11 — the other number can be 3 below 8 or 3 above it.

2 Right — 6 + 4 = 10. They could also share fairly: put all 16 sweets together and give 8 each, or Dara could give Sok 2 so both have 8.

3 Both are asking about the gap between two numbers. Taking away asks what is left after some go, and difference asks how far apart two amounts are — in both cases you are working out the same gap, so the same sign is used.

Unit 6

Number patterns

Numbers have habits. Some split into two equal groups and some do not. Some are doubles. And once you know a double, the numbers either side of it come free.

Number · 3 topics

Unit 6 · Topic 2

Doubles and halves

To double a number, add it to itself. To halve a number, split it into two equal groups.

🟠 🟠 🟠 🟠
4

double →

🟠 🟠 🟠 🟠 🟠 🟠 🟠 🟠
8

Double 4 is 8, so half of 8 is 4. Doubling and halving undo each other.

The doubles you should know by heart:

1+1=2 · 2+2=4 · 3+3=6 · 4+4=8 · 5+5=10 · 6+6=12 · 7+7=14 · 8+8=16 · 9+9=18 · 10+10=20

Can you halve 7 and get a whole number? Try it with counters.

PractiseDouble it, halve it

Double each number.
1. Double 2 =
2. Double 5 =
3. Double 3 =
4. Double 6 =
Halve each number.
1. Half of 6 =
2. Half of 10 =
3. Half of 4 =
4. Half of 12 =
Fill in the doubles table.

Number 1 3 5 7

Double
Tap 4 squares in the first frame and 4 in the second. That shows double 4.

Double 4 =

Number	1	3	5	7
Double

Practise moreNow on your own

Double these.
1. Double 7 =
2. Double 8 =
3. Double 9 =
4. Double 10 =
Halve these.
1. Half of 14 =
2. Half of 16 =
3. Half of 18 =
4. Half of 20 =
Solve these word problems.
1. A spider has 8 legs. How many legs do 2 spiders have?
2. Mum shares 12 grapes equally between 2 children. How many each?
3. Sophea has 6 marbles. Kosal has double that. How many has Kosal?
Fill in the missing number.
1. Double = 10
2. Double = 16
3. Half of = 3
4. Half of = 9

ChallengeThink a bit harder

Look at all the doubles: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. What do you notice about them?
Which numbers below can be halved exactly? Tick them.
1. 9 can be halved
2. 12 can be halved
3. 15 can be halved
4. 18 can be halved
Double 3, then double the answer. What do you get? Is that the same as doubling 3 three times?

Double 3 = , doubled again =

Answers · 6B Doubles and halves

Practise

1a 4 b 10 c 6 d 12

2a 3 b 5 c 2 d 6

3 2, 6, 10, 14

4 8

Practise more

1a 14 b 16 c 18 d 20

2a 7 b 8 c 9 d 10

3a 16 legs b 6 grapes each c 12 marbles

4a 5 b 8 c 6 d 18

Challenge

1 Every double is an even number. That makes sense: a double is two equal groups, so every counter has a partner.

2 Tick 12 and 18. 9 and 15 are odd, so halving leaves one over.

3 Double 3 = 6, doubled again = 12. That is not the same as 3 + 3 + 3 = 9 — doubling twice multiplies by 4, not by 3.

Unit 6 · Topic 3

Near doubles

If you know a double, you get the sums either side of it for free. A near double is a double with one more or one less.

You know 5 + 5 = 10. So:

5 + 6 is one more than 10, which is 11.
5 + 4 is one less than 10, which is 9.

🟩 🟩 🟩 🟩 🟩
5

🟩 🟩 🟩 🟩 🟩 🟦
6

The blue one is the extra, so the total is 10 + 1 = 11.

When you see two numbers next to each other, like 6 + 7, think "double the smaller, add one".

PractiseUse the double you know

Use the double to find the near double.
1. 4 + 4 = , so 4 + 5 =
2. 6 + 6 = , so 6 + 7 =
3. 3 + 3 = , so 3 + 2 =
Work these out.
1. 2 + 3 =
2. 5 + 6 =
3. 7 + 8 =
4. 8 + 9 =
Which double helps you most? Write it, then the answer.
1. 6 + 5 → helper double → answer
2. 9 + 8 → helper double → answer
Work these out.
1. 4 + 3 =
2. 7 + 6 =
3. 9 + 10 =
4. 10 + 9 =

Practise moreNow on your own

Work these out.
1. 3 + 4 =
2. 5 + 4 =
3. 6 + 7 =
4. 8 + 7 =
5. 2 + 1 =
6. 9 + 10 =
Complete the sentence for each sum.
1. 7 + 8 is one more than double , so it is .
2. 6 + 5 is one less than double , so it is .
Solve these word problems.
1. Vanna has 7 shells and Rina has 8. How many altogether?
2. There are 9 red beads and 10 blue beads. How many beads?
Find the missing number.
1. 6 + = 13
2. 8 + = 15
3. + 5 = 9
4. + 4 = 7

ChallengeThink a bit harder

8 + 6 is a near-near double — the numbers are 2 apart. Use double 6 and then double 8 to check you get the same answer.

Double 6 = , add 2 →

Double 8 = , take 2 →
Two numbers next to each other add to 15. What are they?

and
Why can two numbers next to each other never add to an even number? Try a few and see.

Answers · 6C Near doubles

Practise

1a 8, 9 b 12, 13 c 6, 5

2a 5 b 11 c 15 d 17

3a double 5 (or double 6) → 11 b double 8 (or double 9) → 17

4a 7 b 13 c 19 d 19

Practise more

1a 7 b 9 c 13 d 15 e 3 f 19

2a double 7 → 15 b double 6 → 11

3a 15 shells b 19 beads

4a 7 b 7 c 4 d 3

Challenge

1 Double 6 = 12, add 2 → 14. Double 8 = 16, take 2 → 14. Both give 14.

2 7 and 8

3 Two numbers next to each other are always one odd and one even. An odd and an even added together always give an odd answer, so the total can never be even.

Unit 7

Counting and estimating

Put the numbers on a line and everything gets easier — jumping ten at a time, filling in the gaps, counting coins, and making a sensible guess before you count.

Number · 5 topics

Unit 7 · Topic 1

Number lines

A number line puts the numbers in order, evenly spaced. Numbers get bigger to the right and smaller to the left.

The dot is on 10. Numbers to its left are less than 10; numbers to its right are more than 10.

You can hop along a line to add or subtract. Hop right to add, hop left to subtract.

On this line the marks go up in twos. Where would 7 go?

PractiseRead the line

Fill in the missing numbers on this number line.

01 35 7 910
Use the line to answer.
1. Which number is just before 8?
2. Which number is just after 15?
3. Which number is 2 to the right of 6?
4. Which number is 3 to the left of 12?
Start at 5. Hop 4 to the right. Where do you land?

Start at 14. Hop 3 to the left. Where do you land?
This line goes up in twos. Fill the gaps.

02 610 14

Practise moreNow on your own

Fill the gaps on each line.
1. 1113 15
2. 15 1820
Where does each number sit? Write the number just before and just after.
1. · 9 ·
2. · 13 ·
3. · 17 ·
4. · 20 ·
Use hops to work these out.
1. Start 8, hop right 5 →
2. Start 16, hop left 4 →
3. Start 3, hop right 9 →
4. Start 20, hop left 7 →
Count in twos and fill the line.

1014 18

ChallengeThink a bit harder

A number line goes 0, 5, 10, 15, 20. Which numbers are missing between 5 and 10 if the line went up in ones?
I hop right 3, then left 5. I finish on 8. Where did I start?
On a line from 0 to 20, is 9 nearer to 0 or nearer to 20? How do you know?

Nearer to .

Answers · 7A Number lines

Practise

1 2, 4, 6, 8

2a 7 b 16 c 8 d 9

3 9; then 11

4 4, 8, 12

Practise more

1a 12, 14, 16 b 16, 17, 19

2a 8, 10 b 12, 14 c 16, 18 d 19, 21

3a 13 b 12 c 12 d 13

4 12, 16, 20

Challenge

1 6, 7, 8, 9

2 10 — hopping right 3 gives 13, then left 5 gives 8, so working backwards the start was 10.

3 Nearer to 0. It is 9 hops from 0 but 11 hops from 20, and 9 is less than 11.

Unit 7 · Topic 2

10 more or less

Adding 10 is a special jump. The ones digit stays the same and the tens digit goes up by one.

Number	Tens	Ones
4	0	4
14	1	4
24	2	4

4, 14, 24 — the 4 never changes. Each time we have added one more ten.

Taking 10 away works the same in reverse: 24 → 14 → 4.

On a hundred square, ten more is the square directly below and ten less is the square directly above.

PractiseJump a whole ten

Add 10 to each number.
1. 3 + 10 =
2. 7 + 10 =
3. 5 + 10 =
4. 9 + 10 =
Take 10 away from each number.
1. 12 − 10 =
2. 18 − 10 =
3. 15 − 10 =
4. 20 − 10 =
Fill in the table.

10 less Number 10 more

13

16

11
Count on in tens from 2.

2→ → →

Practise moreNow on your own

Work these out.
1. 6 + 10 =
2. 14 + 10 =
3. 25 − 10 =
4. 30 − 10 =
5. 21 + 10 =
6. 17 − 10 =
Count on in tens.

5

Count back in tens from 40.

40
Solve these word problems.
1. A box holds 10 pencils. Ratana has 1 box and 6 loose pencils. How many pencils?
2. There were 23 birds. 10 flew away. How many are left?
3. Sophy saves 10 riel a day. She already had 8 riel. How much after one day? riel
What has changed? Write 10 more or 10 less.
1. 7 → 17 is
2. 22 → 12 is
3. 19 → 29 is
4. 35 → 25 is

ChallengeThink a bit harder

I add 10, then add 10 again. I land on 26. Where did I start?
Look at 8, 18, 28, 38. What stays the same and what changes?
Is 10 more than 15 the same as 15 more than 10? Work both out.

10 more than 15 = 15 more than 10 =

Answers · 7B 10 more or less

Practise

1a 13 b 17 c 15 d 19

2a 2 b 8 c 5 d 10

3 3 · 13 · 23; 6 · 16 · 26; 1 · 11 · 21

4 12, 22, 32

Practise more

1a 16 b 24 c 15 d 20 e 31 f 7

2 15, 25, 35, 45; then 30, 20, 10, 0

3a 16 pencils b 13 birds c 18 riel

4a 10 more b 10 less c 10 more d 10 less

Challenge

1 6 — take 10 away twice from 26.

2 The ones digit stays 8 every time. The tens digit goes up by one each time, because each step adds one more ten.

3 Both are 25. Adding works in either order, so it does not matter which number you start from.

Unit 7 · Topic 3

Missing numbers

If a number is missing from a pattern, look at the numbers around it and work out the rule. Then use the rule to fill the gap.

46 1012

Each number is 2 more than the one before, so the missing number is 8.

In a sum, a missing number can be found by working backwards. For 7 + ? = 10, ask "what do I add to 7 to reach 10?" — count on: 8, 9, 10. That is 3 hops, so the answer is 3.

Is the pattern going up or going down? That is always the first thing to check.

PractiseFind the rule first

Fill the gaps. These patterns go up in ones.

79 11
Fill the gaps. These patterns go up in twos.

24 812
Fill the gaps. These patterns go down.

2018 16
Find the missing number in each sum.
1. 5 + = 9
2. 8 + = 12
3. 10 − = 6
4. 14 − = 11

Practise moreNow on your own

Fill the gaps and write the rule.
1. 510 20 rule:
2. 1816 12 rule:
Find the missing number.
1. 6 + = 11
2. + 7 = 13
3. 15 − = 9
4. − 4 = 8
5. 9 + = 17
6. 20 − = 13
Fill in the missing numbers on this piece of a hundred square.

11 13 14

22 24 25
Write the next two numbers in each pattern.
1. 3, 6, 9, ,
2. 20, 18, 16, ,

ChallengeThink a bit harder

Only the first and last numbers are given. Fill in the middle, counting on in equal steps.

4 12

The step is each time.
Sok fills a gap with 9 in this pattern: 3, 6, 9, 9, 15. Is he right? What should it be?

Right Wrong It should be .
Make your own pattern with one number missing. Write the rule underneath.

Rule:

Answers · 7C Missing numbers

Practise

1 8, 10, 12 2 6, 10 3 19, 17, 15

4a 4 b 4 c 4 d 3

Practise more

1a 15, 25 — the rule is "add 5" (counting in fives). b 14, 10 — the rule is "subtract 2" (counting back in twos).

2a 5 b 6 c 6 d 12 e 8 f 7

3 Top row 12 and 15; bottom row 21 and 23.

4a 12, 15 b 14, 12

Challenge

1 6, 8, 10 — the step is 2 each time.

2 Wrong. The pattern goes up in threes, so after 9 comes 12, then 15.

3 Teacher to check — any pattern with a clear rule and a correctly missing number.

Unit 7 · Topic 4

Money

Coins are worth different amounts. A big coin is not always worth more, so you have to read the number on it.

12510

To find the total, start with the biggest coin and count on.

1052

10 … count on 5 → 15 … count on 2 → 17.

Always start from the biggest coin. Counting 10, 15, 17 is much easier than 2, 7, 17.

PractiseCount the coins

How much is in each purse?
1. 521 total
2. 105 total
Work out the totals.
1. 5 + 2 =
2. 10 + 5 =
3. 10 + 2 + 1 =
4. 5 + 5 + 1 =
Which coins would you use? Write two coins that make each amount.
1. 7 → and
2. 12 → and
3. 15 → and
4. 3 → and
A sticker costs 6. You pay with a 10 coin. How much change?

Practise moreNow on your own

Find the total.
1. 10 + 10 =
2. 10 + 5 + 2 =
3. 5 + 5 + 5 =
4. 10 + 2 + 2 + 1 =
Which is more? Write the bigger amount.
1. Three 5 coins, or one 10 and one 2?
2. Two 2 coins, or one 5 coin?
Work out the change from a 20 coin.
1. Costs 15 → change
2. Costs 8 → change
3. Costs 12 → change
4. Costs 20 → change
Solve these shopping problems.
1. A pencil costs 4 and a rubber costs 3. How much for both?
2. Chan has 12. He buys a drink for 5. How much is left?
3. Two cakes cost 6 each. How much altogether?

ChallengeThink a bit harder

Make 11 using exactly three coins from 1, 2, 5 and 10. (You may use a coin more than once.)

+ + = 11
What is the smallest number of coins you need to make 17? Write them.

That is coins.
Sreyna says a 10 coin is worth more than five 2 coins because it is bigger. Is she right?

Right Wrong

Answers · 7D Money

Practise

1a 8 b 15

2a 7 b 15 c 13 d 11

3a 5 and 2 b 10 and 2 c 10 and 5 d 2 and 1

4 4 change

Practise more

1a 20 b 17 c 15 d 15

2a three 5 coins (15) beats 10 + 2 (12) b one 5 coin beats two 2 coins (4)

3a 5 b 12 c 8 d 0

4a 7 b 7 c 12

Challenge

1 5 + 5 + 1 = 11, or 10 + 1 + ... no (that is only two coins plus one), so also 2 + 2 + ... does not reach 11. The neat answer is 5 + 5 + 1.

2 10 + 5 + 2 = 17, which is 3 coins — fewer than any other way.

3 Wrong. Five 2 coins are worth 10 as well, so they are worth exactly the same. The size of a coin does not tell you its value — you have to read the number.

Unit 8

Multiplication and division

Two ways to split a pile fairly: share it out one at a time until it is gone, or make equal groups of the same size. Both are the beginning of division.

Calculating · 2 topics

Unit 8 · Topic 1

Sharing

To share fairly, deal the things out one at a time, like dealing cards — one for you, one for me, one for you, one for me.

Share 6 biscuits between 2 children:

🧒
🍪 🍪 🍪
3 each

and

🧒
🍪 🍪 🍪
3 each

Everyone gets the same number and nothing is left over. That is a fair share.

Sharing between 2 is the same as finding half. Share 10 between 2 and each gets 5 — and half of 10 is 5.

PractiseDeal them out

Share these fairly between 2 children.
1. 🍬 🍬 🍬 🍬 🍬 🍬 🍬 🍬 8 shared between 2 = each
2. 🍇 🍇 🍇 🍇 🍇 🍇 🍇 🍇 🍇 🍇 10 shared between 2 = each
Share fairly between 2.
1. 4 → each
2. 12 → each
3. 6 → each
4. 20 → each
Share fairly between 3.
1. 6 → each
2. 9 → each
3. 12 → each
4. 15 → each
12 sweets are shared between 4 children.
1. How many each?
2. How many are left over?

Practise moreNow on your own

Share fairly between 4.
1. 8 → each
2. 16 → each
3. 20 → each
4. 4 → each
Share fairly between 5.
1. 10 → each
2. 15 → each
3. 20 → each
4. 5 → each
Solve these sharing problems.
1. 18 crayons are shared between 3 children. How many each?
2. 14 fish are shared between 2 cats. How many each?
3. Mum shares 12 rambutans between 4 children. How many each?
Some sharing does not work out evenly. How many are left over?
1. 7 shared between 2 → each, left
2. 10 shared between 3 → each, left

ChallengeThink a bit harder

Vuth shares 12 marbles between 2 friends and says "6 each". Then he shares the same 12 between 4 friends. Does each friend get more or less now? How many?

— each.

Why does that happen?
I share some sweets between 3 children and they get 4 each, with none left. How many sweets were there?
Can 13 be shared fairly between 2 with none left over? Explain.

Yes No

Answers · 8A Sharing

Practise

1a 4 each b 5 each

2a 2 b 6 c 3 d 10

3a 2 b 3 c 4 d 5

4a 3 each b 0 left over

Practise more

1a 2 b 4 c 5 d 1

2a 2 b 3 c 4 d 1

3a 6 crayons b 7 fish c 3 rambutans

4a 3 each, 1 left b 3 each, 1 left

Challenge

1 Less — 3 each. The same 12 marbles have to stretch between twice as many friends, so each share is half the size.

2 12 sweets, because 4 + 4 + 4 = 12.

3 No. 13 is an odd number, so dealing one at a time leaves 6 each with 1 left over.

Unit 8 · Topic 2

Grouping

Grouping is different from sharing. This time you know how big each group is, and you want to know how many groups you can make.

How many groups of 2 can you make from 10 socks?

🧦🧦 🧦🧦 🧦🧦 🧦🧦 🧦🧦

That makes 5 groups of 2.

Counting the groups is the same as counting in twos: 2, 4, 6, 8, 10 — five numbers, five groups.

Sharing 10 between 2 gives 5 each. Grouping 10 into 2s gives 5 groups. Why is the answer the same?

PractiseMake equal groups

How many groups of 2?
1. 🥚🥚 🥚🥚 🥚🥚 6 in groups of 2 = groups
2. 🌰🌰 🌰🌰 🌰🌰 🌰🌰 8 in groups of 2 = groups
How many groups can you make?
1. 10 in 5s →
2. 12 in 3s →
3. 15 in 5s →
4. 8 in 4s →
Count in twos to fill the line, then say how many groups of 2 make 12.

26 10

Groups of 2 in 12:
Count in fives. How many fives make 20?

5

fives make 20.

Practise moreNow on your own

How many groups?
1. 16 in 4s →
2. 18 in 2s →
3. 20 in 5s →
4. 9 in 3s →
5. 20 in 10s →
6. 14 in 2s →
Fill in the counting patterns.
1. Twos: 2, 4, 6, , ,
2. Fives: 5, 10, ,
3. Tens: 10, , ,
Solve these grouping problems.
1. Eggs go in boxes of 6. How many boxes for 12 eggs?
2. Each child needs 2 shoes. How many children can wear 14 shoes?
3. Flowers are tied in bunches of 5. How many bunches from 20 flowers?
Some do not group evenly. How many full groups, and how many left over?
1. 11 in 2s → groups, left
2. 17 in 5s → groups, left

ChallengeThink a bit harder

12 counters can be put into equal groups in several ways. Complete the table.

Group size 2 3 4 6

How many groups

What do you notice as the groups get bigger?
I make 4 groups of 5. How many do I have altogether?
Why can 15 be put into groups of 5 but not into groups of 2 without one left over?

Group size	2	3	4	6
How many groups

Answers · 8B Grouping

Practise

1a 3 groups b 4 groups

2a 2 b 4 c 3 d 2

3 4, 8, 12; there are 6 groups of 2 in 12.

4 10, 15, 20; 4 fives make 20.

Practise more

1a 4 b 9 c 4 d 3 e 2 f 7

2a 8, 10, 12 b 15, 20 c 20, 30, 40

3a 2 boxes b 7 children c 4 bunches

4a 5 groups, 1 left b 3 groups, 2 left

Challenge

1 6, 4, 3, 2. As the groups get bigger, the number of groups gets smaller — the same 12 counters are just packed differently.

2 20, because 5 + 5 + 5 + 5 = 20.

3 15 is made of exactly three 5s, so groups of 5 come out even. But 15 is an odd number, and groups of 2 always use up an even amount — so one is always left behind.

Unit 9

Measures

Longer, shorter, heavier, lighter, full, empty. Before you ever use a ruler you learn to compare two things directly — and to say clearly which is which.

Measures · 3 topics

Unit 9 · Topic 1

Length and weight

To compare two lengths, line them up at the same starting point. Then you can see which is longer and which is shorter.

📏 ━━━━━━━━ longer

✏️ ━━━━ shorter

You can measure with everyday things instead of a ruler. A pencil might be 6 cubes long. These are called non-standard units.

For weight, hold one thing in each hand. The heavier one pulls your hand down. The lighter one feels easy to hold.

A big thing is not always the heavier one. A balloon is big but very light; a stone is small but heavy.

PractiseCompare two things

Write longer or shorter.
1. A bus is than a bicycle.
2. A pencil is than a metre ruler.
3. Your arm is than your finger.
Write heavier or lighter.
1. A watermelon is than a grape.
2. A feather is than a brick.
3. An empty bag is than a full bag.
These ribbons are measured in cubes. Which is longest?

Ribbon Red Blue Green

Cubes 7 4 9
1. Longest:
2. Shortest:
3. How many cubes longer is green than blue?
Order these lengths, shortest first: 8 cubes, 3 cubes, 11 cubes, 6 cubes.

Ribbon	Red	Blue	Green
Cubes	7	4	9

Practise moreNow on your own

Choose the right word: tall, short, heavy or light.
1. A tree is .
2. A leaf is .
3. An elephant is .
4. A baby is (compared to an adult).
Three pencils are 5, 9 and 7 cubes long.
1. Which is the longest? cubes
2. What is the difference between the longest and shortest? cubes
3. Put them in order, longest first: , ,
True or false?
1. The biggest thing is always the heaviest. true false
2. If you line two sticks up at one end, you can see which is longer. true false
A table is 12 hand-spans long and a desk is 8 hand-spans.
1. Which is longer?
2. By how many hand-spans?

ChallengeThink a bit harder

Dara measures the table with his hand and gets 12 spans. His teacher measures the same table and gets 8 spans. Who has made a mistake?

Dara The teacher Neither
Ribbon A is longer than ribbon B. Ribbon B is longer than ribbon C. Which ribbon is the shortest?
Why is it better for the whole class to measure with the same cubes rather than with their own hands?

Answers · 9A Length and weight

Practise

1a longer b shorter c longer

2a heavier b lighter c lighter

3a green b blue c 5 cubes

4 3, 6, 8, 11

Practise more

1a tall b light c heavy d short

2a 9 cubes b 4 cubes c 9, 7, 5

3a false — a balloon is big and light b true

4a the table b 4 hand-spans

Challenge

1 Neither. The teacher's hand is bigger, so fewer of her spans fit along the same table. Both measured correctly — they just used different-sized units.

2 Ribbon C. A is longer than B, and B is longer than C, so C must be shortest of all.

3 Because everyone's hands are a different size, so the same table gives different answers. Cubes are all identical, so everyone gets the same measurement and the results can be compared.

Unit 9 · Topic 2

Estimating capacity

Capacity is how much a container holds. A container can be full, empty, or somewhere in between — half full, nearly full, nearly empty.

🥛
full

🥛
half full

To compare two containers, fill one with cups of water and count the cups. The container that takes more cups holds more.

A tall thin container can hold less than a short wide one, so you have to test it — you cannot always tell by looking.

Which holds more: a tall thin glass or a wide short bowl? How could you find out for certain?

PractiseFull, empty or in between

Write full, empty or half full.
1. A glass with nothing in it is .
2. A glass filled right to the top is .
3. A glass filled to the middle is .
These containers were filled with cups of water.

Container Jug Bottle Cup

Cups of water 8 5 1
1. Which holds the most?
2. Which holds the least?
3. How many more cups does the jug hold than the bottle?
Which would hold more? Write the answer.
1. A bucket or a spoon?
2. A bath or a mug?
A jug holds 10 cups. 4 cups are poured out. How many are left in the jug?

cups.

Container	Jug	Bottle	Cup
Cups of water	8	5	1

Practise moreNow on your own

Order these containers, most first: 6 cups, 12 cups, 2 cups, 9 cups.
Estimate. Is each a sensible guess? Write yes or no.
1. A teaspoon holds about 20 cups
2. A water bottle holds about 3 cups
3. A bath holds about 2 cups
4. A bucket holds about 10 cups
Two jugs. The red jug holds 7 cups and the blue jug holds 11 cups.
1. Which holds more?
2. How many more cups?
3. How many cups do the two jugs hold altogether?
A bottle holds 8 cups. It is half full. How many cups are in it?

cups.

ChallengeThink a bit harder

A tall thin bottle and a short wide bowl both hold exactly 6 cups. Sok says the tall one must hold more because it is taller. Is he right? Explain.

Right Wrong
A jug holds 12 cups. How many cups would fill it half full? And a quarter full?

Half full: cups. Quarter full: cups.
You have a 5-cup jug and a 3-cup jug, both full. How many cups altogether? If you pour 2 cups away, how many are left?

Altogether , left .

Answers · 9B Estimating capacity

Practise

1a empty b full c half full

2a the jug b the cup c 3 more cups

3a a bucket b a bath

4 6 cups

Practise more

1 12, 9, 6, 2

2a no b yes c no d yes

3a the blue jug b 4 more c 18 cups

4 4 cups

Challenge

1 Wrong. They hold the same — 6 cups each. The bowl is wider, which makes up for being shorter. Height alone does not tell you the capacity, which is why you have to fill and count.

2 Half full is 6 cups; a quarter full is 3 cups.

3 8 cups altogether, and 6 left after pouring 2 away.

Unit 9 · Topic 3

Comparing and describing

When you compare two things you use words like bigger, longer, heavier.

When you compare three or more, you use the -est words: biggest, longest, heaviest.

Two things	Three or more
long → longer	the longest
heavy → heavier	the heaviest
short → shorter	the shortest

"Taller" needs two things to compare. "Tallest" means it beats all the others.

PractiseChoose the right word

Write the missing word.
1. A snake is than a worm. (long)
2. Of all three boxes, the red one is the . (heavy)
3. A mouse is than a cat. (small)
Three towers are 6, 10 and 4 cubes tall.
1. Which is tallest? cubes
2. Which is shortest? cubes
3. What is the difference between them?
Order from lightest to heaviest: a book, a feather, a car.
1. 1st (lightest)
2. 2nd
3. 3rd (heaviest)
Write true or false.
1. A lorry is heavier than a bicycle.
2. A pin is longer than a pencil.

Practise moreNow on your own

Four children measured their height in cubes: Sina 42, Rith 39, Mony 45, Kanha 40.
1. Who is tallest?
2. Who is shortest?
3. Order them, shortest first:
Complete each sentence with the -er or -est word.
1. This is the pencil of all five. (short)
2. My bag is than yours. (heavy)
3. She is the in the class. (tall)
4. This box is than that one. (big)
Three ropes: 15 cubes, 8 cubes and 11 cubes.
1. How much longer is the longest than the shortest? cubes
2. Which rope is in the middle? cubes
Write a sentence comparing two things in your classroom.

ChallengeThink a bit harder

Ana is taller than Bo. Chan is taller than Ana. Put all three in order, tallest first.

, ,
Can something be both the longest and the lightest? Give an example if you think so.

Yes No
Why can you not say "this is the tallest" when you are only holding one thing?

Answers · 9C Comparing and describing

Practise

1a longer b heaviest c smaller

2a 10 cubes b 4 cubes c 6

3 feather, book, car

4a true b false

Practise more

1a Mony b Rith c Rith (39), Kanha (40), Sina (42), Mony (45)

2a shortest b heavier c tallest d bigger

3a 7 cubes b 11 cubes

4 Teacher to check — any sensible comparison using an -er word.

Challenge

1 Chan, Ana, Bo.

2 Yes. A long piece of string or a feather can be the longest thing on the table and still weigh the least. Length and weight are different things.

3 Because "tallest" compares it with other things. With only one object there is nothing to beat, so the word has no meaning until you have at least three to compare.

Unit 10

Shapes

Flat shapes and solid shapes, the mirror lines that cut them in half, and the words that say exactly where something is and which way it turned.

Shape & space · 4 topics

10A

Unit 10 · Topic 1

2D shapes

2D shapes are flat. You can draw them on paper. We name them by counting their sides and corners.

circle
0 sides

triangle
3 sides

square
4 equal sides

rectangle
4 sides

pentagon
5 sides

hexagon
6 sides

A square is a special rectangle — all four of its sides are the same length.

A shape has 3 sides. How many corners does it have? Is that true for every shape?

PractiseCount the sides

How many sides does each shape have?
1. triangle
2. square
3. hexagon
4. pentagon
Name the shape.
1. It is round with no corners.
2. It has 3 sides and 3 corners.
3. It has 4 sides that are all the same length.
4. It has 6 sides.
How many corners does each shape have?
1. rectangle
2. triangle
3. circle
4. pentagon
Which everyday things are these shapes? Write one for each.
1. circle →
2. rectangle →

Practise moreNow on your own

Fill in the table.

Shape Sides Corners

triangle

square

pentagon

hexagon
True or false?
1. Every square is a rectangle. true false
2. Every rectangle is a square. true false
3. A circle has one straight side. true false
A shape has the same number of sides as corners. Write the number of corners for a shape with:
1. 4 sides →
2. 5 sides →
3. 6 sides →
4. 8 sides →
Sort these shapes: circle, square, triangle, rectangle, hexagon. Which have 4 sides?

ChallengeThink a bit harder

Two triangles are put together along a whole side. What shape can they make? Name one.
I have more sides than a square but fewer than a hexagon. What shape am I?
Sopheak says a shape with 4 sides must be a square. Draw or describe a shape that shows he is wrong.

Answers · 10A 2D shapes

Practise

1a 3 b 4 c 6 d 5

2a circle b triangle c square d hexagon

3a 4 b 3 c 0 d 5

4 Teacher to check — for example a plate or a coin (circle), a door or a book (rectangle).

Practise more

1 triangle 3 and 3; square 4 and 4; pentagon 5 and 5; hexagon 6 and 6.

2a true b false c false (its edge is curved)

3a 4 b 5 c 6 d 8

4 square and rectangle

Challenge

1 A square, a rectangle or a bigger triangle, depending on the triangles used. Any one of those is correct.

2 A pentagon (5 sides).

3 Any long thin rectangle shows he is wrong — it has 4 sides but its sides are not all equal, so it is not a square.

10B

Unit 10 · Topic 2

3D shapes

3D shapes are solid. You can pick them up. They have faces (the flat parts), edges and corners.

🎲 cube 📦 cuboid ⚽ sphere 🥫 cylinder 🍦 cone

Shape	What it is like
cube	6 square faces, like a dice
cuboid	6 rectangle faces, like a box
sphere	perfectly round, like a ball
cylinder	two circle faces and a curved side, like a tin
cone	a circle face and a point, like an ice-cream cone

Shapes that roll have a curved surface. Shapes that stack have flat faces. A cylinder can do both!

PractiseName the solid

Name the 3D shape.
1. A dice is a .
2. A ball is a .
3. A tin of food is a .
4. A cereal box is a .
How many faces?
1. cube
2. cuboid
3. cylinder (flat faces)
4. sphere (flat faces)
Will it roll or will it stack? Write roll or stack.
1. sphere
2. cube
3. cuboid
4. cone
What shape are the faces of a cube?

Practise moreNow on your own

Match each solid to an everyday object. Write your answer.
1. cylinder →
2. cone →
3. sphere →
4. cube →
True or false?
1. A cube has 6 faces and they are all squares. true false
2. A sphere has flat faces. true false
3. A cylinder has two circle faces. true false
A cube has 6 faces, 12 edges and 8 corners. Answer these.
1. How many faces on 2 cubes?
2. How many corners on 2 cubes?
Which 2D shape do you see if you look at the flat end of a cylinder?

ChallengeThink a bit harder

A cylinder can roll and stack. Explain how both can be true.
I have 6 faces. They are not all squares. What am I?
Which is the odd one out — cube, cuboid, sphere? Give a reason.

Answers · 10B 3D shapes

Practise

1a cube b sphere c cylinder d cuboid

2a 6 b 6 c 2 d 0

3a roll b stack c stack d roll

4 squares

Practise more

1 Teacher to check — for example a tin or a candle (cylinder), a party hat (cone), a ball or an orange (sphere), a dice or a sugar cube (cube).

2a true b false c true

3a 12 faces b 16 corners

4 a circle

Challenge

1 It depends which way up it is. Lying on its curved side it rolls; stood on one of its flat circle faces it sits still and you can stack another one on top.

2 A cuboid — 6 faces, but rectangles rather than squares.

3 The sphere, because it is the only one with no flat faces and no corners — it is the only one that cannot be stacked. (A child who says "cube, because the other two can have rectangle faces" has also reasoned well.)

10C

Unit 10 · Topic 3

Symmetry

A shape has symmetry if you can fold it in half and the two halves match exactly. The fold is called a line of symmetry.

rectangle

triangle

circle

A square has 4 lines of symmetry. A circle has so many you cannot count them — every line through the middle works.

Some shapes have no lines of symmetry at all.

Is the letter A symmetrical? What about the letter R?

PractiseFold it in half

Does it have a line of symmetry? Write yes or no.
1. square
2. circle
3. the letter A
4. the letter J
How many lines of symmetry?
1. square
2. rectangle
3. the letter H
4. the letter T
Which of these letters are symmetrical? Tick them.
1. M symmetrical
2. P symmetrical
3. O symmetrical
4. S symmetrical
Name one thing in nature that is symmetrical.

Practise moreNow on your own

Write how many lines of symmetry.
1. equilateral triangle
2. hexagon (regular)
3. the letter X
4. the letter F
True or false?
1. Every shape has a line of symmetry. true false
2. A butterfly's wings are symmetrical. true false
A shape is folded along its line of symmetry and one half has 3 dots on it. How many dots does the whole shape have?
Write two letters of the alphabet with exactly one line of symmetry.

and

ChallengeThink a bit harder

Why does a circle have more lines of symmetry than a square?
A rectangle has 2 lines of symmetry, but a square has 4. Both have 4 sides. Why the difference?
Chenda says the letter S is symmetrical because it looks the same upside down. Is a line of symmetry the same as turning it round? Explain.

Answers · 10C Symmetry

Practise

1a yes b yes c yes d no

2a 4 b 2 c 2 d 1

3 Tick M and O. P and S have none.

4 Teacher to check — a butterfly, a leaf, a face, a flower.

Practise more

1a 3 b 6 c 2 d 0

2a false b true

3 6 dots — the other half must match exactly.

4 Any two of A, B, C, D, E, M, T, U, V, W, Y.

Challenge

1 A circle looks exactly the same all the way round, so any line through the centre folds it into matching halves. A square only matches on four particular folds — the two through the middle of opposite sides and the two diagonals.

2 A square's sides are all equal, so the diagonal folds match up too. In a rectangle the long and short sides are different, so folding along a diagonal does not make the halves match.

3 No, they are different. A line of symmetry means folding gives matching halves. S does not fold into matching halves — it only looks the same after a turn. That is called rotational symmetry, which Chenda has spotted but has given the wrong name.

10D

Unit 10 · Topic 4

Position and movement

Position words say where something is: on, under, in, next to, between, in front of, behind, above, below, left, right.

🐱📦the cat is next to the box

📦🐱the cat is on the right

Movement words say how something turns: a whole turn brings you back to the start, a half turn points you the opposite way, and a quarter turn is a corner turn — clockwise or anticlockwise.

Stand up and make a half turn. You are now facing the opposite way. Two half turns bring you back.

PractiseSay where it is

Choose the best position word.
1. The book is the table. (on / under)
2. The cat is the chair. (under / above)
3. Bopha stands Dara and Sina. (between / behind)
Answer about your own classroom.
1. What is above you?
2. What is next to you?
Which turn is it?
1. Facing north, then facing south = a turn.
2. Facing north, then facing east = a turn.
You face the door. You make a whole turn. What are you facing now?

Practise moreNow on your own

Three children stand in a line: Sina, then Rith, then Mony.
1. Who is between the other two?
2. Who is in front of Rith?
3. Who is behind Rith?
Write left or right.
1. You write with your hand (most people).
2. In 🐶 🐰, the rabbit is on the .
How many quarter turns make each of these?
1. a half turn
2. a whole turn
3. a quarter turn
A robot faces up. It makes a quarter turn clockwise, then another quarter turn clockwise. Which way does it face now?

ChallengeThink a bit harder

A robot faces right. It makes 3 quarter turns clockwise. Which way is it facing?
Is one quarter turn clockwise the same as three quarter turns anticlockwise? Try it and explain.

Same Different
Sina is to the left of Rith. Rith is to the left of Mony. Who is furthest right?

Answers · 10D Position and movement

Practise

1a on b under c between

2 Teacher to check — for example the ceiling or a fan above; a desk or a friend next to you.

3a half b quarter

4 The door again — a whole turn brings you back to where you started.

Practise more

1a Rith b Sina c Mony

2a right b right

3a 2 b 4 c 1

4 Down — two quarter turns make a half turn.

Challenge

1 Up. Starting facing right: one quarter turn clockwise faces down, two faces left, three faces up.

2 Same. Both end up facing the same way. Turning one quarter one way is the same as going the long way round — three quarters — in the other direction, because four quarter turns make a whole turn.

3 Mony.

Unit 12

Handling data

Once you have collected some information, a picture makes it easy to read. Build block graphs and pictograms, then sort things into rings and boxes.

Handling data · 4 topics

12A

Unit 12 · Topic 1

Block graphs

A block graph uses one block for each thing you counted. Stack the blocks and the tallest tower wins.

Favourite fruit in a class of 12:

🍌 5

🍎 4

🍇 2

🍊 1

Bananas have the most blocks, so bananas are the most popular. Oranges have the fewest.

Every block must be the same size, or the graph tells a lie.

PractiseRead the towers

This block graph shows how children travel to school.

🚶 walk

🚲 bike

🚌 bus

🚗 car
1. How many walk?
2. How many come by bus?
3. How many come by bike?
4. How many come by car?
Use the same graph.
1. Which way is most popular?
2. Which way is least popular?
3. How many children altogether?
How many more children walk than come by car?
Which two ways together are used by 7 children?

and

Practise moreNow on your own

This block graph shows pets in a class.

🐕 dog

🐈 cat

🐟 fish

🐦 bird
1. How many dogs?
2. How many cats?
3. How many birds?
4. How many pets altogether?
Use the pet graph.
1. How many more dogs than fish?
2. How many fewer birds than cats?
3. Which pet has exactly 3?
A class counted their favourite colours: red 6, blue 8, green 3, yellow 5. Answer without drawing.
1. Which colour would have the tallest tower?
2. Which would have the shortest?
3. How many children altogether?
4. How many more chose blue than green?
Why must all the blocks be the same size?

ChallengeThink a bit harder

In the pet graph, two more children join and both have cats. How many cats now? Does cat become the most popular?

Cats: . Most popular? Yes No
A block graph has 4 towers and 20 blocks in total. If three towers have 6, 5 and 4 blocks, how many are in the fourth?
Can a block graph have a tower with no blocks at all? What would that mean?

Answers · 12A Block graphs

Practise

1a 6 b 4 c 3 d 2

2a walking b car c 15 children

3 4 more

4 bike (3) and bus (4) — together 7.

Practise more

1a 7 b 5 c 2 d 17

2a 4 more b 3 fewer c fish

3a blue b green c 22 d 5 more

4 If the blocks were different sizes, a short tower of big blocks could look taller than a tall tower of small ones. Equal blocks mean the height always tells you the number.

Challenge

1 7 cats. No — dogs also have 7, so they are now equal most popular.

2 5 blocks, because 6 + 5 + 4 = 15 and 20 − 15 = 5.

3 Yes. An empty tower means nobody chose that one — the answer is zero. It is still worth showing, because it tells you the choice was offered and nobody picked it.

12B

Unit 12 · Topic 2

Pictograms, lists and tables

A pictogram uses a small picture for each thing counted. A key tells you what one picture is worth.

Monday⭐ ⭐ ⭐

Tuesday⭐ ⭐ ⭐ ⭐ ⭐

Wednesday⭐ ⭐

Key: ⭐ = 1 star earned

A table puts the same information into rows and columns, which is tidier when there are a lot of numbers.

Day	Stars
Monday	3
Tuesday	5
Wednesday	2

Always read the key first. If one picture stands for 2 things, three pictures mean six!

PractiseRead the pictures

This pictogram shows fruit sold at a stall.

Mango🥭 🥭 🥭 🥭

Banana🍌 🍌 🍌 🍌 🍌 🍌

Papaya🍈 🍈

Key: one picture = 1 fruit
1. How many mangoes?
2. How many bananas?
3. How many papayas?
4. How many fruit altogether?
Use the fruit pictogram.
1. Which fruit sold the most?
2. How many more bananas than papayas?
Read this table.

Game Children

Football 9

Skipping 6

Tag 4
1. How many play football?
2. How many play tag?
3. Which game is most popular?
4. How many children altogether?
How many more children play football than skipping?

Game	Children
Football	9
Skipping	6
Tag	4

Practise moreNow on your own

This pictogram has a different key. Read it carefully.

Class 1😀 😀 😀

Class 2😀 😀 😀 😀

Class 3😀 😀

Key: 😀 = 2 children
1. How many children in Class 1?
2. How many in Class 2?
3. How many in Class 3?
4. How many altogether?
Complete the table from this list of weather: sunny, rainy, sunny, sunny, cloudy, rainy, sunny.

Weather Sunny Rainy Cloudy

Days

How many days altogether?
Use your weather table.
1. Which weather happened most?
2. How many more sunny days than rainy?
Why is a key important on a pictogram?

Weather	Sunny	Rainy	Cloudy
Days

ChallengeThink a bit harder

On a pictogram where 😀 = 2 children, how would you show 5 children?
Sina drew a pictogram with 4 pictures in a row and said "that means 4". Rith drew 4 pictures and said "that means 8". Can they both be right?

Yes No
Would you use a list or a table to record what 30 children ate for lunch? Why?

Answers · 12B Pictograms, lists and tables

Practise

1a 4 b 6 c 2 d 12

2a banana b 4 more

3a 9 b 4 c football d 19

4 3 more

Practise more

1a 6 b 8 c 4 d 18 — remember each face is worth 2.

2 Sunny 4, rainy 2, cloudy 1; 7 days altogether.

3a sunny b 2 more

4 Without the key you do not know what one picture is worth. Four pictures could mean 4, or 8, or 40 — the key is the only thing that tells you.

Challenge

1 Draw two whole faces (worth 4) and then half a face for the last child.

2 Yes, if their keys are different. Sina's key must be "1 picture = 1 child" and Rith's "1 picture = 2 children". Neither is wrong — you just have to read the key.

3 A table. A list of 30 separate answers is hard to count and easy to lose your place in. A table groups the same answers together so you can see the totals at a glance.

12C

Unit 12 · Topic 3

Venn diagrams

A Venn diagram sorts things into rings. Things that belong to both groups go in the overlap in the middle. Things that belong to neither stay outside the rings.

RedRound

🟥 🚩

🍎 🔴

⚽ 🟡

The apple is red and round, so it goes in the middle. The football is round but not red. The flag is red but not round.

Always check the middle first — those are the things that belong to both.

PractiseWhere does it go?

This Venn diagram sorts animals.

Can flyHas feathers

🦇 🦋

🦅 🦜

🐧
1. How many can fly AND have feathers?
2. How many can fly but have no feathers?
3. How many have feathers but cannot fly?
4. How many animals altogether?
Where would you put each animal? Write left, middle or right.
1. An owl (flies, feathers)
2. A bee (flies, no feathers)
3. An ostrich (feathers, no flying)
Numbers 1 to 10 are sorted into "even" and "bigger than 5".
1. Which numbers go in the middle (even AND bigger than 5)?
2. Which numbers go outside both rings?
What does the overlap in a Venn diagram mean?

Practise moreNow on your own

A class is sorted by "wears glasses" and "has a pet". 4 children wear glasses only, 3 do both, 8 have a pet only, and 5 do neither.
1. How many wear glasses in total?
2. How many have a pet in total?
3. How many children in the class?
4. How many do NOT have a pet?
Sort the numbers 1 to 12 into "odd" and "bigger than 8".
1. Odd only:
2. Both (odd and bigger than 8):
3. Bigger than 8 only:
True or false?
1. Something in the overlap belongs to both groups. true false
2. Everything must go inside one of the rings. true false
Think of two groups you could sort your classmates into. Write them.

ChallengeThink a bit harder

A Venn diagram sorts shapes into "has 4 sides" and "is red". Where would a red triangle go?
Could the overlap of a Venn diagram ever be empty? Give an example of two groups where nothing would go in the middle.
7 children like mango, 6 like banana and 3 like both. How many children are there in total (if everyone likes at least one)?

Answers · 12C Venn diagrams

Practise

1a 2 b 2 c 1 d 5

2a middle b left c right

3a 6, 8, 10 b 1, 3, 5 (odd and not bigger than 5)

4 It means the things there belong to both groups at the same time.

Practise more

1a 7 (4 + 3) b 11 (8 + 3) c 20 d 9 (4 glasses-only + 5 neither)

2a 1, 3, 5, 7 b 9, 11 c 10, 12

3a true b false — things belonging to neither group sit outside both rings.

4 Teacher to check — for example "has a brother" and "walks to school".

Challenge

1 In the red ring only, not in the overlap — a triangle has 3 sides, so it fails the "4 sides" test.

2 Yes. If the two groups can never both be true — such as "odd numbers" and "even numbers" — then nothing can go in the middle and the overlap stays empty.

3 10 children. 7 + 6 = 13, but the 3 who like both have been counted twice, so 13 − 3 = 10.

12D

Unit 12 · Topic 4

Carroll diagrams

A Carroll diagram sorts things into boxes. Each heading has an opposite — so every single thing has exactly one box it belongs in, and nothing is left outside.

	Red	Not red
Round	🍎 🔴	⚽ 🟡
Not round	🚩 🟥	📗 🟩

The apple is red and round. The book is not red and not round. Every object fits somewhere.

In a Venn diagram some things sit outside the rings. Why does that never happen in a Carroll diagram?

PractiseFind the right box

This Carroll diagram sorts numbers 1 to 10.

Even Not even

Less than 6 2, 4 1, 3, 5

Not less than 6 6, 8, 10 7, 9
1. How many numbers are even and less than 6?
2. How many are odd and 6 or more?
3. How many numbers altogether?
Which box does each number go in? Write the row and column.
1. 4 →
2. 9 →
Complete this Carroll diagram for shapes.

Has straight sides No straight sides

4 corners

Not 4 corners

Use these: square, circle, triangle. (One box will be empty.)
Why does every heading need an opposite?

	Even	Not even
Less than 6	2, 4	1, 3, 5
Not less than 6	6, 8, 10	7, 9

Practise moreNow on your own

A class is sorted like this.

Boy Girl

Walks to school 5 7

Does not walk 4 3
1. How many boys walk?
2. How many girls altogether?
3. How many children walk?
4. How many children in the class?
Use the same diagram.
1. How many boys are there in total?
2. How many children do not walk?
3. Are there more boys or more girls?
Sort the numbers 1 to 12 into this diagram. Write the numbers for each box.

Bigger than 6 Not bigger than 6

Even

Odd
What is the difference between a Venn diagram and a Carroll diagram?

	Boy	Girl
Walks to school	5	7
Does not walk	4	3

ChallengeThink a bit harder

In a Carroll diagram of 20 children, 12 are boys and 9 wear glasses. 5 boys wear glasses. How many girls do NOT wear glasses?
Can a box in a Carroll diagram be empty? What would that tell you?

Yes No
Design your own Carroll diagram for the fruit in a bowl. Write your two headings and their opposites.

Answers · 12D Carroll diagrams

Practise

1a 2 b 2 c 10

2a even and less than 6 b not even (odd) and not less than 6

3 4 corners + straight sides → square. Not 4 corners + straight sides → triangle. Not 4 corners + no straight sides → circle. The box for "4 corners, no straight sides" is empty.

4 So that every single thing fits in exactly one box — nothing is left out and nothing fits in two places.

Practise more

1a 5 b 10 c 12 d 19

2a 9 boys b 7 children c more girls (10 against 9)

3 Even and bigger than 6: 8, 10, 12. Even and not bigger than 6: 2, 4, 6. Odd and bigger than 6: 7, 9, 11. Odd and not bigger than 6: 1, 3, 5.

4 A Venn diagram uses rings that overlap, and anything belonging to neither group sits outside them. A Carroll diagram uses boxes with opposite headings, so every single thing has exactly one box and nothing sits outside.

Challenge

1 4 girls. There are 8 girls (20 − 12), and 4 girls wear glasses (9 − 5), so 8 − 4 = 4 do not.

2 Yes. An empty box means nothing has that combination — for example no shape can have 4 corners and no straight sides. That is useful information, not a mistake.

3 Teacher to check — for example "yellow / not yellow" against "round / not round".

Reference

Picture glossary

Every maths word in this workbook, in plain language, with an example you can picture. Type a word in the box to find it quickly.

All 12 units

A B C D E F G H L M N O P Q R S T V W

No words match that search. Try a shorter word.

A

add: To put two or more amounts together to find how many there are altogether.3 + 2 = 5

afternoon: The part of the day between midday and the evening.

altogether: The total when everything has been counted or added.

anticlockwise: Turning the opposite way to the hands of a clock.

B

between: A number that comes after one number and before another.7 is between 6 and 8.

block graph: A graph that uses one block for each thing counted. The tallest tower has the most.

C

capacity: How much a container can hold.This jug holds 8 cups.

Carroll diagram: A sorting diagram made of boxes. Every heading has an opposite, so everything fits in exactly one box.

circle: A round flat shape with no straight sides and no corners.

clockwise: Turning the same way as the hands of a clock.

compare: To look at two or more things and say how they are different — bigger, longer, heavier.

cone: A solid shape with one circle face and a point, like an ice-cream cone.

corner: The point where two sides of a shape meet. Also called a vertex.

count back: To say the numbers in reverse order. Counting back is a way to subtract.11 − 3: say 10, 9, 8.

count on: To start at one number and keep counting forwards. Counting on is a way to add.8 + 3: say 9, 10, 11.

cube: A solid shape with 6 square faces, like a dice.

cuboid: A solid shape with 6 rectangle faces, like a box.

cylinder: A solid shape with two circle faces and a curved side, like a tin.

D

day: One of the seven named parts of a week, from Monday to Sunday.

difference: How much bigger one number is than another. Match the two sets up and count the ones left over.The difference between 7 and 4 is 3.

digit: One of the symbols 0 to 9 used to write numbers.13 is written with the digits 1 and 3.

double: To add a number to itself.Double 4 is 8.

E

edge: The line where two faces of a solid shape meet.

empty: With nothing inside.

estimate: A sensible guess made before counting or measuring. It should be close, but does not have to be exact.

even: A number that splits into two equal groups with none left over. Even numbers end in 0, 2, 4, 6 or 8.

F

face: A flat surface on a solid shape.A cube has 6 faces.

fewer: Not as many. The opposite of more.

full: Holding as much as it possibly can.

G

group: To put things into equal-sized sets and count how many sets you make.10 socks in groups of 2 makes 5 groups.

H

half: One of two equal parts.Half of 10 is 5.

half past: Thirty minutes after the hour. The long hand points to the 6.

heavy: Hard to lift. The opposite of light.

hexagon: A flat shape with 6 straight sides and 6 corners.

hour: A length of time. There are 24 hours in a day, and the short hand on a clock shows the hour.

L

length: How long something is from end to end.

less: Not as much or not as many. The opposite of more.

light: Easy to lift. The opposite of heavy.

line of symmetry: A fold line that cuts a shape into two matching halves.

M

measure: To find out how long, how heavy or how much something is.

minute: A short length of time. The long hand on a clock shows the minutes.

month: One of the 12 parts of a year.

more: A larger amount or number. The opposite of less.

morning: The part of the day from waking up until midday.

N

near double: A sum where the two numbers are only one apart, so a double helps you.6 + 7 is one more than double 6, so it is 13.

number line: A line with numbers marked in order, evenly spaced. You can hop along it to add or subtract.

number pair: Two numbers that add together to make a total.4 and 6 are a number pair for 10.

O

o'clock: An exact hour, when the long hand points to the 12.

odd: A number that cannot be split into two equal groups — one is always left over. Odd numbers end in 1, 3, 5, 7 or 9.

one to one: Touching each thing once and saying one number for each one.

order: To arrange numbers or things from smallest to biggest, or biggest to smallest.

ones: The single units in a number. In 13 there are 3 ones.

P

pattern: Numbers or shapes that follow a rule and repeat.2, 4, 6, 8 — the rule is "add 2".

pentagon: A flat shape with 5 straight sides and 5 corners.

pictogram: A graph that uses a small picture for each thing counted. The key tells you what one picture is worth.

position: Where something is — on, under, in, next to, between, above, below.

Q

quarter turn: A corner turn. Four quarter turns make a whole turn.

R

rectangle: A flat shape with 4 straight sides and 4 corners. Opposite sides are the same length.

S

share: To deal things out one at a time so that everyone gets the same amount.6 shared between 2 is 3 each.

side: One of the straight lines that make the edge of a flat shape.

sort: To put things into groups that belong together.

sphere: A perfectly round solid shape, like a ball.

square: A flat shape with 4 straight sides that are all the same length, and 4 corners.

subtract: To take away, or to find the difference between two numbers.7 − 2 = 5

symmetry: When a shape can be folded so that both halves match exactly.

T

table: Information set out in rows and columns so it is easy to read.

take away: To remove some things and count how many are left.

ten frame: A grid of 10 squares. Filling it helps you see how a number sits next to 10.

tens: Groups of ten in a number. In 13 there is 1 ten.

total: The whole amount when everything is added together.

triangle: A flat shape with 3 straight sides and 3 corners.

V

Venn diagram: A sorting diagram made of rings. Things belonging to both groups go in the overlap; things belonging to neither sit outside.

W

week: Seven days, from Monday to Sunday.

weekend: Saturday and Sunday.

weight: How heavy something is.

whole turn: A full circle that brings you back to face the way you started.

Reference

All answers

Every answer in the workbook, unit by unit, so an adult can check a whole session at once. Each topic also has its own 🔑 Answers panel.

38 topics

Unit 1 · Numbers and counting

Answers · 1A Counting objects

Practise

1a 4 b 6 c 3 d 7

2 8 flowers

3 7 filled, so 3 squares are empty.

4 6 blue and 4 red — there are more blue counters.

Practise more

1a 9 b 2 c 10 d 8

2 Yellow 5, blue 3, red 2, altogether 10.

3a 6 b 9

4 5 strawberries, 2 bananas, 2 grapes, 9 pieces altogether.

Challenge

1 There are 7 penguins, so Sam is right. Rani probably missed one out, or counted two of them with the same number. Touching each penguin once as you say the number stops both mistakes.

2 7 squares filled, because 7 and 3 make 10.

Answers · 1B Counting rhymes and actions

Practise

1 4, 6, 8, 10

2 9, 7, 5, 3, 1

3 3 ducks

4a 5 b 8 c 10 d 5

Practise more

1a 9, 10, 11 b 14, 15, 16 c 6, 5, 4 d 17, 16, 15

2 7 bottles

3a 5 b 10 c 17 d 20

4a 5 b 9 c 10 d 16

Challenge

1 5 verses. One monkey goes each verse, so counting back 5, 4, 3, 2, 1, 0 takes five steps to reach 0.

2 8 claps — count on 2 from 6.

Answers · 1C Reading and writing numbers

Practise

1a 3 b 7 c 10 d 5

2a two b eight c four d nine

3 7 worms — seven worms.

4a 9 b 12 c 15 d 20

Practise more

1a 11 b 14 c 17 d 20

2a thirteen b sixteen c twelve d nineteen

3 2, 3, 5, 7

4a 6 b 15 c 18 d 10

Challenge

1 Thirteen is 13. Sokha has written the digits the wrong way round. We say "thir-teen", which sounds like the 3 first, but thirteen means 1 ten and 3 ones, so the 1 is written first.

2 15

3 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 — that is 10 numbers. (20 starts with a 2.)

Unit 2 · Exploring numbers

Answers · 2A More and less

Practise

1 7 and 4. a more 🐤 (chicks) b less 🐣 c 3 more.

2a 4 b 8 c 10 d 15

3a 4 b 7 c 11 d 19

4a the blue pot b 4 more

Practise more

1a more b less c more d less

2a 9, 11 b 14, 16 c 17, 19 d 0, 2

3 7 and 4; the first frame has more, by 3.

4 10 stickers

Challenge

1 10

2 The second box has 3 more, because the boxes started equal and 3 were taken from the first.

3 Any three of 7, 8, 9, 10, 11. There are 5 numbers to choose from.

Answers · 2B Between

Practise

1a 3 b 8 c 12 d 19

2 10, 12, 14

3 6, 7, 8

4a true b false (10 comes before 12, not between 12 and 14)

Practise more

1a 15 b 1 c 17 d 13

2a 11, 12, 13 b 16, 17, 18, 19

3 5, 6, 9

4a 3 (they are 4, 5 and 6) b 0 — 11 and 12 are next-door neighbours, so no whole number fits between them.

Challenge

1 14 — the numbers between 12 and 16 are 13, 14 and 15, and two of them are ruled out.

2 Yes. 8 does sit between 7 and 9. Ravi has just said the two numbers in the other order, which does not change which number is in the middle.

Answers · 2C Tens and ones

Practise

1 1 ten and 6 ones makes 16.

2a 1 ten, 5 ones b 1 ten, 2 ones c 1 ten, 9 ones d 1 ten, 0 ones

3a 17 b 14 c 20 d 18

4 1 full frame and 6 left over.

Practise more

1 11 → 1 ten 1 one; 14 → 1 ten 4 ones; 18 → 1 ten 8 ones; 20 → 2 tens 0 ones.

2a 11 b 16 c 19 d 15

3a 17 b Nita c 3 loose cubes

4a 1 b 7 c 2 d 0

Challenge

1 6 + 5 + 4 = 15 cubes, which makes 1 tower of ten with 5 left over.

2 11 — it has 1 ten and 1 one.

Answers · 2D Ordering numbers

Practise

1 2, 5, 7, 9 2 6, 11, 14, 18 3 10, 8, 3, 1

4a 4 b 15

Practise more

1a 7, 13, 16, 20 b 2, 5, 9, 12, 17

2a 19, 11, 6, 3 b 14, 10, 8, 4, 1

3 5, 9, 12, 17. The two middle numbers are 9 and 12.

4 13, 14, 16, 18

Challenge

1 17 and 71 → in order: 17, 71.

2 Any two of 9, 10, 11, 12, 13.

3 Wrong. The correct order is 3, 7, 9, 12 — she put 12 before 9.

Unit 3 · Number pairs

Answers · 3A Number pairs for 6, 7, 8 and 9

Practise

1 5 and 2; 5 + 2 = 7

2a 1 b 3 c 5 d 6

3a 2 b 4 c 1 d 5

4 5 + 4 = 9

Practise more

1a 5 b 2 c 3 d 1

2a 1 b 3 c 4 d 9

3 0 + 6, 1 + 5, 2 + 4, 3 + 3, 4 + 2, 5 + 1, 6 + 0

4 5 shells

Challenge

1 4 + 4 = 8. You cannot do the same for 7, because 7 is an odd number — it cannot be split into two equal whole groups. (3 + 3 is only 6 and 4 + 4 is already 8.)

2 Any three pairs that total 9: 0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5, 5 and 4, 6 and 3, 7 and 2, 8 and 1, 9 and 0.

Answers · 3B Number pairs for 10

Practise

1 6 + 4 = 10

2a 2 b 7 c 5 d 1

3a 6 b 3 c 8 d 0

4 4 empty, so 6 + 4 = 10.

Practise more

1a 9 b 4 c 10 d 6 e 3 f 8

2 4 → 6; 7 → 3; 2 → 8; 5 → 5

3a 7 b 4 c 1 d 0

4 Tick a (6 and 4) and c (2 and 8). 5 and 4 make 9; 7 and 2 make 9.

Challenge

1 14. Add 6 + 4 first because they are a pair for 10, then 10 + 4 = 14.

2 2, because 3 + 5 = 8 and 8 + 2 = 10.

3 Any three correct sums, for example 5 + 3 + 2, 4 + 4 + 2, 6 + 2 + 2, 1 + 2 + 7, 3 + 3 + 4.

Unit 4 · Addition

Answers · 4A Combining sets

Practise

1 4 and 3, altogether 7 fish.

2a 2 + 5 = 7 b 6 + 3 = 9

3a 5 b 8 c 7 d 7

4 4 + 3 = 7

Practise more

1a 8 b 8 c 10 d 10 e 10 f 4

2a 9 and 9 b 9 and 9 — swapping never changes the total.

3a 9 mangoes b 9 cars c 9 rice cakes

4a 5 b 4 c 6 d 1

Challenge

1 9. Any order works; many children add 2 + 4 = 6 first (or 3 + 4 = 7) and then add the third number.

2 3 and 6, because 6 is double 3 and 3 + 6 = 9.

3 Wrong. Both come to 9. The order you add in does not change the total — pushing the two sets together gives the same pile whichever one you start with.

Answers · 4B Counting on

Practise

1a 8 b 12 c 9 d 14

2a start at 9 → 12 b start at 11 → 13

3 13, 14, 15; so 12 + 3 = 15.

4a 13 b 17 c 19 d 19

Practise more

1a 12 b 14 c 17 d 13 e 17 f 20

2 7 → 8, 9, 10; 11 → 12, 13, 14; 16 → 17, 18, 19.

3a 13 people b 16 marbles c 20 pages

4a 3 b 4 c 3 d 4

Challenge

2 13 — 6 count on 4 is 10, then count on 3 more is 13.

3 14, because counting back 5 from 19 gives 14.

Unit 5 · Subtraction and difference

Answers · 5A Taking away

Practise

1a 4 b 5

2a 4 b 4 c 5 d 0

3 5

4a 5 buns b 4 ducks

Practise more

1a 7 b 3 c 10 d 9 e 10 f 0

2 3, 8, 11, 17

3a 8 stickers b 3 cups c 4 chairs

4a 3 b 6 c 9 d 11

Challenge

1 5 left. The single subtraction is 10 − 5, because taking away 2 and then 3 is the same as taking away 5 altogether.

2 Any two, for example 6 − 2, 10 − 6, 9 − 5, 4 − 0.

3 No. You only have 3 counters, so once you have taken 3 away there are none left to take. You run out before you have taken 8. (Numbers below zero come later.)

Answers · 5B Counting back

Practise

1a 8, 7, 6 → 6 b 12, 11, 10, 9 → 9

2a 5 b 9 c 13 d 14

3 15, 14, 13, 12

4a 9 b 8 c 7 d 6

Practise more

1a 11 b 12 c 7 d 17 e 10 f 14

2 11, 14, 9, 18

3a 11 mangoes b 13 people c 14 riel

4a 10 b 3. Counting back 2 is much quicker — only two hops.

Challenge

1 12

2 18, 16, 14, 12, 10, 8

Answers · 5C Finding the difference

Practise

1 6 and 3 — the difference is 3.

2a 3 b 4 c 0 d 5

3a 3 more boys b 3 fewer girls — the same number both ways.

4a 4 hops b 3 hops

Practise more

1a 4 b 6 c 7 d 8 e 8 f 0

2a the blue pot b 6 more c 3 pencils — moving 3 leaves 8 in each pot.

3a 5 years b 5 cm c by 5 goals

4a 13 b 10

Challenge

1 5 or 11 — the other number can be 3 below 8 or 3 above it.

2 Right — 6 + 4 = 10. They could also share fairly: put all 16 sweets together and give 8 each, or Dara could give Sok 2 so both have 8.

Unit 6 · Number patterns

Answers · 6A Even and odd

Practise

1a even b odd

2a even b odd c even d odd

3 4, 8, 12, 16, 20

4 5, 9, 13, 17

Practise more

1 Tick 10, 16 and 20.

2 Even: 14, 16, 18. Odd: 13, 15, 17.

3a yes b no c yes d no — even numbers share equally between two, odd numbers leave one over.

4a even b odd c even d odd

Challenge

1 10, 10, 16 — the answer is always even. Two sets that both pair up neatly still pair up neatly when pushed together.

2 8, 8, 14 — the answer is always even too. This surprises most children. Each odd number has one counter left over, and the two leftovers pair up with each other.

3 15 or 17 — both are odd and both lie between 14 and 18.

Answers · 6B Doubles and halves

Practise

1a 4 b 10 c 6 d 12

2a 3 b 5 c 2 d 6

3 2, 6, 10, 14

4 8

Practise more

1a 14 b 16 c 18 d 20

2a 7 b 8 c 9 d 10

3a 16 legs b 6 grapes each c 12 marbles

4a 5 b 8 c 6 d 18

Challenge

1 Every double is an even number. That makes sense: a double is two equal groups, so every counter has a partner.

2 Tick 12 and 18. 9 and 15 are odd, so halving leaves one over.

3 Double 3 = 6, doubled again = 12. That is not the same as 3 + 3 + 3 = 9 — doubling twice multiplies by 4, not by 3.

Answers · 6C Near doubles

Practise

1a 8, 9 b 12, 13 c 6, 5

2a 5 b 11 c 15 d 17

3a double 5 (or double 6) → 11 b double 8 (or double 9) → 17

4a 7 b 13 c 19 d 19

Practise more

1a 7 b 9 c 13 d 15 e 3 f 19

2a double 7 → 15 b double 6 → 11

3a 15 shells b 19 beads

4a 7 b 7 c 4 d 3

Challenge

1 Double 6 = 12, add 2 → 14. Double 8 = 16, take 2 → 14. Both give 14.

2 7 and 8

3 Two numbers next to each other are always one odd and one even. An odd and an even added together always give an odd answer, so the total can never be even.

Unit 7 · Counting and estimating

Answers · 7A Number lines

Practise

1 2, 4, 6, 8

2a 7 b 16 c 8 d 9

3 9; then 11

4 4, 8, 12

Practise more

1a 12, 14, 16 b 16, 17, 19

2a 8, 10 b 12, 14 c 16, 18 d 19, 21

3a 13 b 12 c 12 d 13

4 12, 16, 20

Challenge

1 6, 7, 8, 9

2 10 — hopping right 3 gives 13, then left 5 gives 8, so working backwards the start was 10.

3 Nearer to 0. It is 9 hops from 0 but 11 hops from 20, and 9 is less than 11.

Answers · 7B 10 more or less

Practise

1a 13 b 17 c 15 d 19

2a 2 b 8 c 5 d 10

3 3 · 13 · 23; 6 · 16 · 26; 1 · 11 · 21

4 12, 22, 32

Practise more

1a 16 b 24 c 15 d 20 e 31 f 7

2 15, 25, 35, 45; then 30, 20, 10, 0

3a 16 pencils b 13 birds c 18 riel

4a 10 more b 10 less c 10 more d 10 less

Challenge

1 6 — take 10 away twice from 26.

2 The ones digit stays 8 every time. The tens digit goes up by one each time, because each step adds one more ten.

3 Both are 25. Adding works in either order, so it does not matter which number you start from.

Answers · 7C Missing numbers

Practise

1 8, 10, 12 2 6, 10 3 19, 17, 15

4a 4 b 4 c 4 d 3

Practise more

1a 15, 25 — the rule is "add 5" (counting in fives). b 14, 10 — the rule is "subtract 2" (counting back in twos).

2a 5 b 6 c 6 d 12 e 8 f 7

3 Top row 12 and 15; bottom row 21 and 23.

4a 12, 15 b 14, 12

Challenge

1 6, 8, 10 — the step is 2 each time.

2 Wrong. The pattern goes up in threes, so after 9 comes 12, then 15.

3 Teacher to check — any pattern with a clear rule and a correctly missing number.

Answers · 7D Money

Practise

1a 8 b 15

2a 7 b 15 c 13 d 11

3a 5 and 2 b 10 and 2 c 10 and 5 d 2 and 1

4 4 change

Practise more

1a 20 b 17 c 15 d 15

2a three 5 coins (15) beats 10 + 2 (12) b one 5 coin beats two 2 coins (4)

3a 5 b 12 c 8 d 0

4a 7 b 7 c 12

Challenge

1 5 + 5 + 1 = 11, or 10 + 1 + ... no (that is only two coins plus one), so also 2 + 2 + ... does not reach 11. The neat answer is 5 + 5 + 1.

2 10 + 5 + 2 = 17, which is 3 coins — fewer than any other way.

3 Wrong. Five 2 coins are worth 10 as well, so they are worth exactly the same. The size of a coin does not tell you its value — you have to read the number.

Answers · 7E Estimating

Practise

1 Estimate — teacher to check. Exact count 12.

2 Estimate — teacher to check. Exact count 7.

3a about 30 b about 4

4a 20 b 10

Practise more

1 Count 15. An estimate within about 5 is a good one at this stage.

2a yes b no c yes d no (a car has 4)

3a 10 b 20 c 10 d 20

4 Tick 3 sweets and 95 sweets — both are a long way from 20. 18 and 21 are close to 20, so neither is surprising.

Challenge

1 Sina was better. She was out by 2; Rith was out by 18.

2 An estimate tells you roughly what to expect, so if your count comes out wildly different you know to check it again. It is a way of catching your own mistakes — and sometimes a good estimate is all you need.

Unit 8 · Multiplication and division

Answers · 8A Sharing

Practise

1a 4 each b 5 each

2a 2 b 6 c 3 d 10

3a 2 b 3 c 4 d 5

4a 3 each b 0 left over

Practise more

1a 2 b 4 c 5 d 1

2a 2 b 3 c 4 d 1

3a 6 crayons b 7 fish c 3 rambutans

4a 3 each, 1 left b 3 each, 1 left

Challenge

1 Less — 3 each. The same 12 marbles have to stretch between twice as many friends, so each share is half the size.

2 12 sweets, because 4 + 4 + 4 = 12.

3 No. 13 is an odd number, so dealing one at a time leaves 6 each with 1 left over.

Answers · 8B Grouping

Practise

1a 3 groups b 4 groups

2a 2 b 4 c 3 d 2

3 4, 8, 12; there are 6 groups of 2 in 12.

4 10, 15, 20; 4 fives make 20.

Practise more

1a 4 b 9 c 4 d 3 e 2 f 7

2a 8, 10, 12 b 15, 20 c 20, 30, 40

3a 2 boxes b 7 children c 4 bunches

4a 5 groups, 1 left b 3 groups, 2 left

Challenge

1 6, 4, 3, 2. As the groups get bigger, the number of groups gets smaller — the same 12 counters are just packed differently.

2 20, because 5 + 5 + 5 + 5 = 20.

3 15 is made of exactly three 5s, so groups of 5 come out even. But 15 is an odd number, and groups of 2 always use up an even amount — so one is always left behind.

Unit 9 · Measures

Answers · 9A Length and weight

Practise

1a longer b shorter c longer

2a heavier b lighter c lighter

3a green b blue c 5 cubes

4 3, 6, 8, 11

Practise more

1a tall b light c heavy d short

2a 9 cubes b 4 cubes c 9, 7, 5

3a false — a balloon is big and light b true

4a the table b 4 hand-spans

Challenge

1 Neither. The teacher's hand is bigger, so fewer of her spans fit along the same table. Both measured correctly — they just used different-sized units.

2 Ribbon C. A is longer than B, and B is longer than C, so C must be shortest of all.

3 Because everyone's hands are a different size, so the same table gives different answers. Cubes are all identical, so everyone gets the same measurement and the results can be compared.

Answers · 9B Estimating capacity

Practise

1a empty b full c half full

2a the jug b the cup c 3 more cups

3a a bucket b a bath

4 6 cups

Practise more

1 12, 9, 6, 2

2a no b yes c no d yes

3a the blue jug b 4 more c 18 cups

4 4 cups

Challenge

1 Wrong. They hold the same — 6 cups each. The bowl is wider, which makes up for being shorter. Height alone does not tell you the capacity, which is why you have to fill and count.

2 Half full is 6 cups; a quarter full is 3 cups.

3 8 cups altogether, and 6 left after pouring 2 away.

Answers · 9C Comparing and describing

Practise

1a longer b heaviest c smaller

2a 10 cubes b 4 cubes c 6

3 feather, book, car

4a true b false

Practise more

1a Mony b Rith c Rith (39), Kanha (40), Sina (42), Mony (45)

2a shortest b heavier c tallest d bigger

3a 7 cubes b 11 cubes

4 Teacher to check — any sensible comparison using an -er word.

Challenge

1 Chan, Ana, Bo.

2 Yes. A long piece of string or a feather can be the longest thing on the table and still weigh the least. Length and weight are different things.

3 Because "tallest" compares it with other things. With only one object there is nothing to beat, so the word has no meaning until you have at least three to compare.

Unit 10 · Shapes

Answers · 10A 2D shapes

Practise

1a 3 b 4 c 6 d 5

2a circle b triangle c square d hexagon

3a 4 b 3 c 0 d 5

4 Teacher to check — for example a plate or a coin (circle), a door or a book (rectangle).

Practise more

1 triangle 3 and 3; square 4 and 4; pentagon 5 and 5; hexagon 6 and 6.

2a true b false c false (its edge is curved)

3a 4 b 5 c 6 d 8

4 square and rectangle

Challenge

1 A square, a rectangle or a bigger triangle, depending on the triangles used. Any one of those is correct.

2 A pentagon (5 sides).

3 Any long thin rectangle shows he is wrong — it has 4 sides but its sides are not all equal, so it is not a square.

Answers · 10B 3D shapes

Practise

1a cube b sphere c cylinder d cuboid

2a 6 b 6 c 2 d 0

3a roll b stack c stack d roll

4 squares

Practise more

1 Teacher to check — for example a tin or a candle (cylinder), a party hat (cone), a ball or an orange (sphere), a dice or a sugar cube (cube).

2a true b false c true

3a 12 faces b 16 corners

4 a circle

Challenge

1 It depends which way up it is. Lying on its curved side it rolls; stood on one of its flat circle faces it sits still and you can stack another one on top.

2 A cuboid — 6 faces, but rectangles rather than squares.

Answers · 10C Symmetry

Practise

1a yes b yes c yes d no

2a 4 b 2 c 2 d 1

3 Tick M and O. P and S have none.

4 Teacher to check — a butterfly, a leaf, a face, a flower.

Practise more

1a 3 b 6 c 2 d 0

2a false b true

3 6 dots — the other half must match exactly.

4 Any two of A, B, C, D, E, M, T, U, V, W, Y.

Challenge

2 A square's sides are all equal, so the diagonal folds match up too. In a rectangle the long and short sides are different, so folding along a diagonal does not make the halves match.

Answers · 10D Position and movement

Practise

1a on b under c between

2 Teacher to check — for example the ceiling or a fan above; a desk or a friend next to you.

3a half b quarter

4 The door again — a whole turn brings you back to where you started.

Practise more

1a Rith b Sina c Mony

2a right b right

3a 2 b 4 c 1

4 Down — two quarter turns make a half turn.

Challenge

1 Up. Starting facing right: one quarter turn clockwise faces down, two faces left, three faces up.

3 Mony.

Unit 11 · Time

Answers · 11A Ordering events

Practise

1 Eat 3, Mix 1, Bake 2.

2 Shoes 2, Get out of bed 1, Arrive 4, Walk 3.

3a short b long c short d long

4a morning b night

Practise more

1 Blooms 5, Plant 1, Shoot 3, Water 2, Leaves 4.

2a yesterday b tomorrow c today

3a B b A c B d A

4 Teacher to check.

Challenge

1 Breakfast comes in the morning and dinner in the evening, so the order is backwards. It should be "I eat breakfast, then I eat dinner, then I go to bed."

2 Yes. For example you can listen to music while you walk, or the sun can shine while it rains. Events do not have to happen one after another.

Answers · 11B Days of the week

Practise

1a Tuesday b Friday c Sunday

2a 7 b 2 c 5 d 12

3a Wednesday b Monday c Saturday d Thursday

4a Thursday b Sunday

Practise more

1 Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

2a Tuesday b Thursday c Friday d Sunday

3a true b false

4 2 times

Challenge

1 Friday again. There are 7 days in a week, so after exactly 7 days you have gone right round the week and landed on the same day.

2 Wednesday.

3 Right — 7 + 7 = 14. Three weeks is 21 days.

Answers · 11C Telling the time

Practise

1a Clock A is 6 o'clock b Clock B is 9 o'clock

2a 12 b 5

3 6

4a 8 o'clock b half past 4

Practise more

1a Clock C shows half past 4 b Clock D shows 1 o'clock

2a long hand 12, short hand 9 b long hand 6, short hand between 6 and 7

3a 4 b 8 c 12 d 3

4 4 hours

Challenge

1 Right. At half past 3 the short hand has travelled halfway from the 3 towards the 4, so it does look "nearly on the 4". The long hand on the 6 tells you it is half past, and the hour is the number the short hand has just passed — the 3.

2 1 o'clock — after 12 the hours start again at 1.

3 The long hand goes all the way round in one hour, but the short hand only moves from one number to the next in that same hour. The short hand has to travel round just once while the long hand goes round twelve times.

Unit 12 · Handling data

Answers · 12A Block graphs

Practise

1a 6 b 4 c 3 d 2

2a walking b car c 15 children

3 4 more

4 bike (3) and bus (4) — together 7.

Practise more

1a 7 b 5 c 2 d 17

2a 4 more b 3 fewer c fish

3a blue b green c 22 d 5 more

4 If the blocks were different sizes, a short tower of big blocks could look taller than a tall tower of small ones. Equal blocks mean the height always tells you the number.

Challenge

1 7 cats. No — dogs also have 7, so they are now equal most popular.

2 5 blocks, because 6 + 5 + 4 = 15 and 20 − 15 = 5.

3 Yes. An empty tower means nobody chose that one — the answer is zero. It is still worth showing, because it tells you the choice was offered and nobody picked it.

Answers · 12B Pictograms, lists and tables

Practise

1a 4 b 6 c 2 d 12

2a banana b 4 more

3a 9 b 4 c football d 19

4 3 more

Practise more

1a 6 b 8 c 4 d 18 — remember each face is worth 2.

2 Sunny 4, rainy 2, cloudy 1; 7 days altogether.

3a sunny b 2 more

4 Without the key you do not know what one picture is worth. Four pictures could mean 4, or 8, or 40 — the key is the only thing that tells you.

Challenge

1 Draw two whole faces (worth 4) and then half a face for the last child.

2 Yes, if their keys are different. Sina's key must be "1 picture = 1 child" and Rith's "1 picture = 2 children". Neither is wrong — you just have to read the key.

3 A table. A list of 30 separate answers is hard to count and easy to lose your place in. A table groups the same answers together so you can see the totals at a glance.

Answers · 12C Venn diagrams

Practise

1a 2 b 2 c 1 d 5

2a middle b left c right

3a 6, 8, 10 b 1, 3, 5 (odd and not bigger than 5)

4 It means the things there belong to both groups at the same time.

Practise more

1a 7 (4 + 3) b 11 (8 + 3) c 20 d 9 (4 glasses-only + 5 neither)

2a 1, 3, 5, 7 b 9, 11 c 10, 12

3a true b false — things belonging to neither group sit outside both rings.

4 Teacher to check — for example "has a brother" and "walks to school".

Challenge

1 In the red ring only, not in the overlap — a triangle has 3 sides, so it fails the "4 sides" test.

2 Yes. If the two groups can never both be true — such as "odd numbers" and "even numbers" — then nothing can go in the middle and the overlap stays empty.

3 10 children. 7 + 6 = 13, but the 3 who like both have been counted twice, so 13 − 3 = 10.

Answers · 12D Carroll diagrams

Practise

1a 2 b 2 c 10

2a even and less than 6 b not even (odd) and not less than 6

4 So that every single thing fits in exactly one box — nothing is left out and nothing fits in two places.

Practise more

1a 5 b 10 c 12 d 19

2a 9 boys b 7 children c more girls (10 against 9)

3 Even and bigger than 6: 8, 10, 12. Even and not bigger than 6: 2, 4, 6. Odd and bigger than 6: 7, 9, 11. Odd and not bigger than 6: 1, 3, 5.

Challenge

1 4 girls. There are 8 girls (20 − 12), and 4 girls wear glasses (9 − 5), so 8 − 4 = 4 do not.

2 Yes. An empty box means nothing has that combination — for example no shape can have 4 corners and no straight sides. That is useful information, not a mistake.

3 Teacher to check — for example "yellow / not yellow" against "round / not round".