Year 6 Use equivalence and compensation to simplify and solve subtraction problems worksheet

“Same gap, moved along” is free to print, with no account. It is the first sheet in the Year 6 maths unit “Use equivalence and compensation to simplify and solve subtraction problems”, 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. Weeks 5 to 6 of the year, 10 sheets in the unit.

Free sample · answers on the last page

Same gap, moved along

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

Today I can explain that a difference stays the same when both numbers change by the same amount.

A Look back3 min

1.
90 − 40 =
2.
93 39
3.
There are 4 rows of 5 counters. 8 counters are taken away. How many are left?

B Watch me, then you4 min

Watch me

34 − 19 = 15.

Add 1 to both numbers: 35 − 20.

The gap is still 15, so 35 − 20 = 15.

Now you

1.
42 − 27 = . Add 3 to both numbers first.

C Your turn5 min

1.
30 − 10 =
2.
35 − 15 =
3.
40 − 20 =
4.
45 − 25 =

Say it out loud: What changed in each row, and what stayed the same?

D Spot the mistake3 min

Jo knows 60 − 20 = 40. Jo says: “61 − 21 is 39, because both numbers went up, so the gap shrinks.”

1.
What is 61 − 21?

E Think deeper4 min

1.
Two numbers have a difference of 45. Both go up by 300. Write the new difference and say why.

How did it feel?

I can do it Nearly Not yet

For the grown-up

Same gap, moved along · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 50

2. >

3. 12

B

1. 15

C

1. 20 If your child writes 40, they added 10 to 30. Ask whether the gap between the two numbers is bigger or smaller than 30.

2. 20 If your child writes 25, they took 10 from 35 instead of 15. Ask: which number is being taken away?

3. 20

4. 20 If your child writes 25, they took 20 from 45 instead of 25. Ask which number was taken away, then count the gap on a ruler.

D

1. 40 If your child writes 39, they took 22 from 61. Both numbers rose by 1, so the gap stays at 40.

E

1. Look for: 45, and a reason such as both numbers moved by the same amount, so the gap is unchanged

Words to use

Say“Which number moved, and how far did both of them move?”

Instead of“Work out both sums the long way and compare the answers.”

After the sheet

Lay two pencils on a table a fixed gap apart, slide both the same distance, and check the gap has not changed.

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

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

Smarter subtraction(with a plan)
Same gap, missing number(with a plan)
Changing the start number(with a plan)
Hidden facts in big subtractions(with a plan)
Adjust the first number(with a plan)
Adjusting the subtrahend(with a plan)
Changing what we take away(with a plan)
Subtraction: Opposite Moves(with a plan)
Keep the gap the same(with a plan)

Every Year 6 maths worksheet

The worksheets plan opens a printable sheet for every lesson in Years 1 to 6, each with its answers on a separate page for you. It costs £6.99 a month or £59 a year for the whole family, with no free trial.

The full StudyDen plan adds the lessons themselves, marked as your child works, with the worksheets included. It is 7 days free, then £29.99 a month.

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