Year 6 Solving problems with two unknowns worksheet

“Two lengths, one clue” is free to print, with no account. It is the first sheet in the Year 6 maths unit “Solving problems with two unknowns”, 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 32 to 34 of the year, 10 sheets in the unit.

Free sample · answers on the last page

Two lengths, one clue

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

Today I can work out two unknown lengths from their total and the difference between them.

A Look back3 min

1.
A number plus 7 makes 19. The number is
2.
4 × = 36
3.
58 52. Which sign goes in the box?

B Watch me, then you4 min

Two ribbons together are 15 cm. One ribbon is 3 cm longer than the other. How long is each ribbon?

Watch me

Take the extra 3 cm off the total: 15 − 3 = 12.

Share 12 equally: 12 ÷ 2 = 6. That is the shorter ribbon.

Add the extra 3 cm back on: 6 + 3 = 9. The ribbons are 6 cm and 9 cm.

Now you

1.
Two ropes make 20 m. One rope is 4 m longer than the other. The shorter rope is m.

C Your turn6 min

Each rope pair makes 10 m in total. Only the gap changes.

1.
Two ropes make 10 m. One is 2 m longer than the other. The longer rope is m.
2.
Two ropes make 10 m. One is 4 m longer than the other. The longer rope is m.
3.
Two ropes make 10 m. One is 6 m longer than the other. The longer rope is m.
4.
Two ropes make 10 m. One is 8 m longer than the other. The longer rope is m.

Say it out loud: As the gap between the ropes grows, what happens to the longer rope? What happens to the shorter one?

D Spot the mistake3 min

Sam says: “Two ropes make 10 m, and one is 2 m longer. So the longer rope is 12 m.”

1.
How long is the longer rope really? m

E Think deeper4 min

1.
Two ropes make 12 m in total. One is longer than the other. Both ropes are whole metres. Write every possible length for the shorter rope.

How did it feel?

I can do it Nearly Not yet

For the grown-up

Two lengths, one clue · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 12 If your child writes 26, they added 7 to 19. Ask: is the missing part the whole, or one piece of it?

2. 9

3. >

B

1. 8 If your child writes 16, they took the gap off the total and stopped. Take the gap off first, then share what is left into two equal parts.

C

1. 6 If your child writes 8, they took the gap off the total: 10 − 2 = 8. Now share the 8 into two equal parts: 4 and 4. Add the 2 m gap back on to the longer one: 4 + 2 = 6.

2. 7 If your child writes 3, that is the shorter rope. Add the 4 m gap back on to find the longer one: 3 + 4 = 7.

3. 8 If your child writes 2, that is the shorter rope. Add the 6 m gap back on to find the longer one: 2 + 6 = 8.

4. 9 If your child writes 1, that is the shorter rope. Add the 8 m gap back on to find the longer one: 1 + 8 = 9.

D

1. 6 If your child writes 12, they added the gap to the total. The longer rope is one part of the 10 m, so it must be less than 10 m. Share the total first, then add the gap to one part.

E

1. 1, 2, 3, 4 or 5 m. The pairs are 1 and 11, 2 and 10, 3 and 9, 4 and 8, 5 and 7. If your child writes 6, they made two equal ropes. One rope must be longer, so the shorter rope is less than 6 m. Check each pair adds to 12.

Words to use

Say“What is the total? What is the gap? Share the total first, then adjust.”

Instead of“Guess pairs of numbers until one seems to work.”

After the sheet

Lay two strips of paper end to end to make 10 cm. Make one strip 2 cm longer than the other, then measure to check.

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:

Two bars, two unknowns(with a plan)
Only one pair fits(with a plan)
Two bills, one price(with a plan)
Lining up bars(with a plan)
One bar, two unknowns(with a plan)
Two unknowns, two bundles(with a plan)
Have I found them all?(with a plan)
Keeping the balance(with a plan)
One, several or infinite answers(with a plan)

Every Year 6 maths worksheet

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