Year 6 Use knowledge of part-part-whole structure to solve additive problems worksheet

“Same whole, different parts” is free to print, with no account. It is the first sheet in the Year 6 maths unit “Use knowledge of part-part-whole structure to solve additive 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 1 to 2 of the year, 10 sheets in the unit.

Free sample · answers on the last page

Same whole, different parts

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

Today I can explain how different parts can make the same whole.

A Look back3 min

1.
6 + 4 + 3 =
2.
4 × 5 =
3.
50 − 20 =

B Watch me, then you4 min

This made-up rod set has no numbers on the rods. The key below only tells you how long each colour is, in cm: white 1, red 2, green 3, purple 4, yellow 5, black 7, brown 8, blue 9, orange 10.

Watch me

Orange is the whole. Brown and red are the parts.

Laid end to end, brown and red match orange exactly.

So orange is equivalent to brown + red.

Now you

1.
Blue and white laid end to end match one other rod exactly. Which rod is the whole? Circle it.
orangebluewhite

C Your turn6 min

Use the key from the last part. Each row changes one thing. Keep the orange rod as the whole.

1.
How many red rods fit exactly along one orange rod?
2.
How many yellow rods fit exactly along one orange rod?
3.
Brown rod plus which rod fits exactly along orange? Circle the colour that fits.
redpurpleblue
4.
Black rod plus which rod fits exactly along orange? Circle the colour that fits.
greenyellowpurple

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

D Spot the mistake3 min

Kit says: “Brown is 8 and red is 2, so brown and red make 9.”

1.
How long are brown and red together, in cm?

E Think deeper3 min

1.
Make a whole orange rod from three or more rods. Write it as an equation using + or ×. Explain how you know it fits.

How did it feel?

I can do it Nearly Not yet

For the grown-up

Same whole, different parts · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 13

2. 20 If your child writes 9, they added 4 and 5. Ask how many rows there are and how many are in each row.

3. 30 If your child writes 70, they added 50 and 20. Ask whether the missing part should be smaller than the whole.

B

1. orange If your child circles blue, ask which rod the other two fit along. The whole is the one the parts fit exactly along.

C

1. 5 If your child writes 2, they found how long one red rod is and stopped. Ask how many red rods it takes to reach the end of the orange rod.

2. 2 If your child writes 5, they used the yellow length instead of counting how many yellows fit. Ask: how many yellows reach the end?

3. red If your child circles purple, add the lengths: brown 8 and purple 4 make 12, which is too long. Try red.

4. green If your child circles yellow, black 7 and yellow 5 make 12, which is too long. Check the key for the rod that makes 3 more.

D

1. 10 cm If your child writes 9, they counted on by only 1 for the red rod. Say 8, then 9, then 10: red adds 2 more.

E

1. Look for: Three or more rods whose lengths add to 10, for example 2 × purple + red, with a reason such as adding the lengths.

Words to use

Say“What stays the same in every row? Which parts fit exactly along the whole?”

Instead of“Add up the lengths for them, or tell them which colour fits.”

After the sheet

Cut paper strips that match the lengths in the key, from 1 cm to 10 cm. Find two different ways to match the 10 cm strip, and write each as an equation.

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:

Equal, unequal or both?(with a plan)
Finding the missing part(with a plan)
Three parts, one whole(with a plan)
Stories that fit a bar(with a plan)
Bar models at work(with a plan)
Finding the missing part(with a plan)
Finding the missing part(with a plan)
Bar models from equations(with a plan)
Finding the missing part(with a plan)

Every Year 6 maths worksheet

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