Year 6 Using equivalence to calculate worksheet

“Same product, new shape” is free to print, with no account. It is the first sheet in the Year 6 maths unit “Using equivalence to calculate”, for children aged 10 to 11, 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 15 of the year, 5 sheets in the unit.

Free sample · answers on the last page

Same product, new shape

Name: ____________ · Date: ____________
Year 6 · Maths · about 20 minutes
Answers are on the grown-up page

Today I can explain why the product stays the same when one factor is doubled and the other is halved.

A Look back3 min

1.
34 ÷ 10 =
2.
5 × 4 =
3.
7 × 10 =

B Watch me, then you4 min

Sam sets out 6 rows of 5 stickers. He wants fewer rows. Does the total change?

Watch me

Sam has 6 rows of 5, which is 30 stickers.

Halve the 6 rows to 3, and double the 5 to 10.

3 rows of 10 is also 30 stickers, so the total stays the same.

Now you

1.
8 × 5 = 4 ×

C Your turn5 min

Double or halve one factor, and do the opposite to the other. You may need to do this more than once. Then find the missing number.

1.
5 × 12 = 10 ×
2.
5 × 12 = 20 ×
3.
5 × 12 = 2.5 ×
4.
16 × 25 = 8 ×

Say it out loud: Which factor did you halve, and which did you double, in each row? What stayed the same?

D Spot the mistake2 min

Ama says: “Doubling both 6 and 5 gives 12 × 10, and that is still 30.”

1.
What is 12 × 10?

E Think deeper4 min

This rectangle has 4 rows of 6, so 4 × 6 = 24.

1.
Use doubling and halving to write a different multiplication that equals 4 × 6. Then explain in one sentence why the product is still 24.

How did it feel?

I can do it Nearly Not yet

For the grown-up

Same product, new shape · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 3.4

2. 20

3. 70

B

1. 10 If your child writes 2, they divided the 8 by 4 instead of finding what times 4 makes 40. Halve the 8 to 4, then double the 5 to 10.

C

1. 6

2. 3 If your child writes 60, they copied the product. The box needs the other factor, so think what times 20 makes 60.

3. 24 If your child writes 6, they halved the 12 instead of doubling it. The 5 was halved to 2.5, so the 12 must double to 24.

4. 50

D

1. 120 If your child writes 22, they added 12 and 10. Doubling both factors makes the product four times as big, not the same. Only one factor should double and the other halve.

E

1. Look for: A pair such as 2 × 12 or 8 × 3 where one factor is doubled and the other halved, plus a sentence saying the product stays 24 because the number of squares does not change.

Words to use

Say“Which factor did you change, and what did you do to the other one?”

Instead of“Double both numbers to make them bigger, then check the answer.”

After the sheet

Lay 12 dried beans in 2 rows of 6, then in 4 rows of 3. Count each time and say why the total does not change.

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:

Scaling factors to match(with a plan)
Scaling one factor(with a plan)
Same answer, bigger numbers(with a plan)
Same answer, bigger numbers(with a plan)

Every Year 6 maths worksheet

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