Year 5 Understand and use the concept of factorisation (square and prime numbers) worksheet

“Factors and arrays” is free to print, with no account. It is the first sheet in the Year 5 maths unit “Understand and use the concept of factorisation (square and prime numbers)”, for children aged 9 to 10, and takes about 20 minutes.

Print it on A4. The child's pages come first; the answers, and what each wrong answer tells you, are on the grown-up page that follows. Week 23 of the year, 5 sheets in the unit.

Free sample · answers on the last page

Factors and arrays

Name: ____________ · Date: ____________
Year 5 · Maths · about 20 minutes
Answers are on the grown-up page

Today I can find factors by making equal rows and using multiplication facts.

A Look back3 min

1.
4 × 6 =
2.
28 ÷ 4 =
3.
6, 12, 18,

B Watch me, then you4 min

Watch me

12 tiles are in 3 rows of 4.

3 × 4 = 12, so 3 and 4 are factors of 12.

Every row is the same length, so this is a proper array.

Now you

1.
15 tiles are arranged in 3 equal rows. How many tiles are in each row?

C Your turn5 min

Each row has the same number of tiles. Fill in the missing number.

1.
2 × = 8
2.
2 × = 12
3.
3 × = 18
4.
4 × = 32

Say it out loud: How did the equal rows help you find each missing factor?

D Spot the mistake3 min

Kit says: “10 tiles make 3 equal rows with 0 left over, so 3 is a factor of 10.”

1.
Put 10 tiles into 3 equal rows, making the rows as long as you can. How many tiles are left over?

E Think deeper4 min

Every row needs an equal count of tiles. Write every number of rows you could use for 24 tiles.

1.
Possible numbers of rows for 24 tiles:

How did it feel?

I can do it Nearly Not yet

For the grown-up

Factors and arrays · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 24

2. 7

3. 24

B

1. 5

C

1. 4 If your child writes 16, they doubled 8 instead of sharing it between 2 rows. Ask: how many tiles would 2 rows of 8 be?

2. 6 If your child writes 24, they multiplied 12 by 2. The 2 rows are already there, so ask them to share 12 between them.

3. 6

4. 8 If your child writes 28, they took 4 away from 32. Ask how many tiles go in each of the 4 equal rows.

D

1. 1 If your child writes 4, they made rows of 2. Rows of 3 still fit, so ask them to make 3 equal rows of 3 and count what is left.

E

1. 1, 2, 3, 4, 6, 8, 12, 24 If a number is missing, ask your child to test each number in turn. Does it divide 24 with nothing left over?

Words to use

Say“Make every row the same length first, then count the rows and columns.”

Instead of“Tell them the factors straight away.”

After the sheet

Use 12 dried pasta pieces or buttons. Make every equal-row arrangement you can, and say the multiplication for each one.

Tick what your child got right in StudyDen. Anything missed comes back in a later Look back box, so there's no need to redo the sheet.

The rest of this unit

4 more sheets come with a StudyDen plan, in teaching order:

Finding every factor in order(with a plan)
Square numbers and factors(with a plan)
Prime or composite?(with a plan)
Building blocks of numbers(with a plan)

Every Year 5 maths worksheet

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