This work is for children who are able to use number properties

I am learning to solve multiplication problems using arrays and repeated addition.

2 x 8 = so 3 x 8 =

Draw arrays with to match the following multiplication expressions:

4 x 6 =3 x 5 =

Use arrays to help solve the following multiplication problems:

2 x 7 = so 3 x 7 = 5 x 4 = so 6 x 4 =

5 x 6 = so 6 x 7 = 10 x 4 = so 9 x 4 =

10 x 7 = so 9 x 7 = 6 x 3 = so 7 x 3 =

7 x 2 = so 6 x 2 = 3 x 8 = so 4 x 8 =

2 x 9 = so 3 x 9 = 5 x 3 = so 6 x 3 =

I am learning to solve division problems about sharing into equal sets.

Show how to share fifteen coins between five pirates.

How many do they each get? Write the number sentence for this

Solve these problems and write the number sentence for each.

Problem / Answer / Number Sentence
Fourteen coins shared between two pirates. How many do they each get?
Fifty coins shared between ten pirates. How many do they each get?
Twenty five coins shared between five pirates. How many do they each get?
Twelve coins shared between three pirates. How many do they each get?

Write and solve a story problem for this number sentence. 18 ÷ 2 =

I am learning to solve division problems about how many sets can be made.

Here are 20 biscuits to put into packets. You are going to put four biscuits into each packet. Colour the biscuits to put into each packet using a different colour for the different packets.

How many packets of biscuits could you make? Write the number sentence for this

Solve these problems and write the number sentence for each.

Problem /

Answer

/ Number Sentence
16 biscuits with 2 biscuits in each packet. How many packets can I make?
12 biscuits with 4 in each packet. How many packets can I make?
90 biscuits with 10 in each packet. How many packets can I make?
30 biscuits with 5 put into each packet. How many packets can I make?
18 biscuits with 3 put into each packet. How many packets can I make?

I am learning to work out my six, seven and eight times tables from my five times tables.

4 x 6 is the same as (4 x 5) + (4 x 1) = 20 + 4 = 24

Complete these number sentences.

6 x 6 is the same as () + () =

8 x 6 is the same as () + () =

6 x 7 is the same as () + () =

9 x 7 is the same as () + () =

7 x 8 is the same as () + () =

4 x 8 is the same as () + () =

12 x 7 is the same as () + () =

20 x 6 is the same as () + () =

100 x 8 is the same as() + () =

I am learning to multiply tens.

4 x 20

20 20 20 20

4 x 20 is the same as 4 x 2 tens. 4 x 2 = 8, so 4 x 20 = 80

Copy and complete these sentences.

3 x 30 is the same as x tensso 3 x 30 =

8 x 50 is the same as xso 8 x 50 =

2 x 40 is the same as 2 xso 2 x 40 =

6 x 60 is the same as xso 6 x 60 =

5 x 30 is the same as x so 5 x 30 =

4 x 70 is the same as xso 4 x 70 =

2 x 60 is the same as 2 xso 2 x 60 =

5 x 70 is the same as so 5 x 70 =

I am learning to multiply hundreds.

4 x 200

200 200 200 200

4 x 200 is the same as 4 x 2 hundreds 4 x 2 = 8, so 4 x 200 = 800

Copy and complete these sentences.

3 x 300 is the same as x so 3 x 300 =

8 x 500 is the same as xso 8 x 500 =

2 x 400 is the same as 2 xso 2 x 400 =

6 x 600 is the same as xso 6 x 600 =

5 x 300 is the same as x so 5 x 300 =

4 x 700 is the same as xso 4 x 700 =

2 x 600 is the same as 2 xso 2 x 600 =

5 x 700 is the same as xso 5 x 700 =

I am learning to solve multiplication problems by taking some off or putting some on (compensation)

6 x 10 = 60 so 6 x 9 = 60 – (6 x 1) = 54

Solve these problems by adding some on or taking some off.

4 x 10 = 40 so what is 4 x 9 = 4 x 11 =

6 x 5 = 30 so what is 6 x 4 = 6 x 6 =

9 x 10 = 90 so what is 9 x 8 = 9 x 12 =

5 x 20 = 100so what is 5 x 19 = 5 x 21 =

4 x 30 = 120 so what is 4 x 28 = 4 x 31 =

8 x 40 = 320 so what is8 x 38 = 8 x 42 =

7 x 50 =350so what is 7 x 49 = 7 x 52 =

9 x 100 = 900 so what is 9 x 99 = 9 x 101 =

3 x 70 = 210so what is 3 x 69 = 3 x 72 =

6 x 50 = 300 so what is6 x 49 = 6 x 51 =

7 x 200 = 1400so what is 7 x 198 = 7 x 202 =

6 x 1000 = 6000so what is 6 x 999 = 6 x 1002 =

I am learning to change the order of the numbers to make multiplication easier.

Colour to show 3 x 4 Colour to show 4 x 3

Complete these sentences:

9 x 2 is the same as 4 x 8 is the same as

5 x 7 is the same as 16 x 8 is the same as

Circle which one you would find easier to solve then work it out.

5 x 9 or 9 x 5 The answer is ______7 x 2 or 2 x 7 The answer is ______

100 x 8 or 8 x 100 The answer is _____ 99 x 7 or 7 x 99 The answer is _____

6 x 50 or 50 x 6 The answer is ______2 x 140 or 140 x 2The answer is _____

Now solve these multiplication problems, changing the order of the numbers if you think it would make the problem easier.

Problem / The order of numbers I prefer / Answer
999 x 3
4 x 52
2343 x 2
11 x 32

I am learning to solve division problems using repeated addition and multiplication facts I know.

1. Draw the jumps and find the answer to:

18 ÷ 3 = 18 ÷ 6 = 18 ÷ 2 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

2.Draw the jumps using an empty number line to solve these problems:

30 ÷ 3 = 30 ÷ 5 = 30 ÷ 6 =

0 30

3. Solve these equations using repeated addition & multiplication facts you know.

15 ÷ 3 = 16 ÷ 4 = 45 ÷ 5 = 49 ÷ 7 =

70 ÷ 10 = 35 ÷ 7 = 48 ÷ 8 =54 ÷ 6 =

42 ÷ 6 = 28 ÷ 4 = 32 ÷ 8 =21 ÷ 3 =

36 ÷ 6 = 21 ÷ 7 = 24 ÷ 8 =36 ÷ 9 =

I am learning to solve division problems using multiplication

Eggs come in packets if 6. I need 48 eggs. How many packets do I need?

x 6 = 48

Colour 48 eggs to show how many packets

of 6 you will need.

You will need packets.

Henry is working out how to share 36 lollies among his 9 friends. How many lollies should he give each friend? Record this problem as 2 equations.

and x =

Re-write these division problems as a multiplication problem, then solve them.

45 ÷ 5 = as 5 x = 45 44 ÷ 4 = as 4 x = 44

42 ÷ 6 = as 6 x = 42 54 ÷ 6 = as 6 x = 54

24 ÷ 3 = as 3 x = 24 63 ÷ 9 = as 9 x = 63

32 ÷ 8 = as 36 ÷ 9 = as

18 ÷ 3 = as 72 ÷ 9 = as

24÷ 6 = as 35 ÷ 7 = as

I am learning to solve multiplication problems using doubling and halving

Colour the faces to show 6 x 4 Colour the faces to show 3 x 8

6 x 4 = 3 x 8 =

Can you use this idea of doubling one number and halving the other to make these multiplication problems easier?

3 x 16 is the same as x so 3 x 16 =

24 x 3 is the same as x so 24 x 3 =

3 x 18 is the same as x so 3 x 18 =

14 x 50 is the same as x so 14 x 50 =

6 482 x 5 is the same as x so 6482 x 5 =

86 x 50 is the same as x so 86 x 50 =

I am learning to solve multiplication problems using a variety of mental strategies

Look at how the following children solved this problem.

Each loaf of bread has 38 slices.

There are eight loaves. How many slices

of bread are there altogether?

Karen did /

Shifa did

/

Kalama did

8 x 30 is 240.
8 x 8 is 64.
So the answer is 240 + 64 which is 304. / 8 x 40 is 320, but as there are only 38 slices and not 40 I have to take off 2 x 8 which is 16.
So 320 – 16 = 304 / If there were 10 loaves that would be 10 x 38 – 380. But as there are only 8 loaves I have to take off 2 x 38 = 76, so the answer is 304

Write how you think each child would solve the following problem.

Leonardo was selling his paintings for $48 each.

He sold 9 of them. How much money did he make altogether?

Karen would do / Shifa would do / Kalama would do

Choose which way you think would be easiest to solve these problems in your head.

7 x 26 = 3 x 99 = 5 x 68 =

I am learning to solve division problems using how many times one number will go into another

Sue had 96 sweets that were wrapped in packets of 6.

How many packets of sweets did she have? ______

To make this problem easier, think how many packets she would have if the sweets were wrapped in packets of 2. (i.e. divide 96 by 2). Then because that would provide 3 times as many packets, you will need to divide the total by 3.

So 96  6 (96  2)  3 48  3 16

Jill has 72 lollies wrapped in packets of 4. How many packets does she have?

If the lollies were wrapped in packets of 8 there would be 9 packets as 72  8 = 9 . So to find packets of 4, what would you need to do? Use the diagram below to help.

So 72  4 = because 72  8 x

Use this idea of adjusting the divisor to help solve these division problems. The first one is done for you.

Problem / Adjusted problem / Answer / Problem / Adjusted problem / Answer
72  4 / (72  8) x 2 / 18 / 81  3
64  4 / 48  3
96  6 / 108  6
63  3 / 96  4
140  5 / 170  5

I am learning to solve division problems that have remainders

Solve these problems and make up a story to match each problem.

Problem / Answer / Word Story
17 ÷ 5 = / 3 r 2 / 17 children who wanted to play soccer. There are 5 people in each team. How many teams were there and how many children would have to be reserves?
34 ÷ 6 =
84 ÷ 9 =
47 ÷ 3 =
35 ÷ 4 =
51 ÷ 6 =

I am learning to solve division problems that have remainders

Remainders can be expressed as what is “left over” or as fractions or as decimals.

E.g. 52 ÷ 5 could be expressed as either: 10 r2 or 10 2/5 or 10.4

Solve these word problems, by thinking about the problem as a number sentence and choosing how best to describe the remainder. The first one is done for you.

Word Story / Number Sentence / Answer
Harry has 49 stamps. He needs 6 stamps to post each parcel. How many parcels can he post? How many stamps will he have left? / 49 ÷ 6 = 8r1 / 8 parcels and
1 stamp left
Silke can wash a car in 7 minutes at the fundraising carwash. How many cars can she wash every hour?
Tino has used 22 metres of rope to make 4 skipping ropes. Each one is the same length. How long is each skipping rope?
Charlie’s chocolates come in boxes of 8. He has 39 chocolates to put into boxes. How many boxes can he fill?
Coach Bernice needs 7 people to make each netball team. She has 50 players. How many teams can she make? How many players will be reserves?
Rangi ran 9 lengths of the court in 83 seconds. What was his average time per length in seconds?
Peter has $29. Pens cost $3 each. How many pens could Peter buy? How much money will he have left over?
Fleur had $67 to spend on fair ground rides. Each ride costs $9. How many rides could she go on? How much money will she have left?

I am learning to solve division problems by changing them to simpler problems that have the same answer.

48  12 is the same as  6 is the same as  3

Complete the following number sentences:

72  8 is the same as is the same as =

96  12 is the same as is the same as =

160  16 is the same as is the same as =

105  15 is the same as =

Solve the following problems by proportionally adjusting each number to make the question easier. The first one is done for you.

Problem Answer

140  28 70  14 35  7 5

408  24

324  36

324  27

I am learning to multiply multi-digit whole numbers

Write the multiplication expression which is shown on the large array below.

Complete the following diagrams of the arrays to help solve these multi-digit multiplication problems. The first one is completed for you as an example.

Problem / Cross Product Table / Addition of products / Answer
23 x 38 / 203
30 600 90
8 160 24 / 600 + 90 + 160 + 24 / 874
37 x 25
82 x 37
49 x 26
58 x 63

Now write and solve 10 more multi-digit problems of your own,

I am learning to decide if a number is divisible by nine or three

1. Are these numbers divisible by 9.? Write Yes or No and explain why.

Problem / Yes or No / Explanation / Problem / Yes or No / Explanation
167 / No / 1 + 6 + 7 = 14 / 828
475 / 367
285 / 342
5688 / 6047
2106 / 9639

2. The following numbers are all divisible by nine but one digit is missing. Complete the missing digit to make the numbers work. There may be more than answer.

4___3 60______29 8___2 ___73 59___

126___ 5___8 20___7 ___057 937___ 2___81

3. What will be the remainder when these numbers are divided by 9?

remainder is remainder is remainder is

265 594 797

remainder is remainder is remainder is

8256 2054 6248

4. Sort the following numbers onto the venn diagram below to show which numbers are divisible by 9, 3, both or

neither.

430 491 273

264 366 298

1638 2836 3954

9370 4386 4946

12,476 93570

80,856

I am learning to solve multiplication and division problems using factors of factors

2 x 2 x 2 x 2 x 2 x 2 x

= 4 x 3 = 8 x 3

Complete the following multiplication sentences using factors of factors:

18 x 3 is the same as 2 x x 318 x 6 is the same as 3 x x 6

4 x 24 is the same as 4 x 4 x 27 x 5 is the same as 3 x x 5

36 x 12 is the same as 36 x 3 x 23 x 18 is the same as 23 x 2 x

15 x 48 is the same as x x 4835 x 61 is the same as x x 61

79 x 72 is the same as 79 x x x =

Now try these division problems using factors of factors:

480  32 = 480    = ______

1035  45 = 1035    = ______

1224  24 = 1224     = ______

684  54 = 648     = ______

Show how you would solve this problem:

832  64 =

Marie Hirst, Numeracy Facilitator