Year 3 Calculate the value of a part (fractions as operators) worksheet

“Building the whole” is free to print, with no account. It is the first sheet in the Year 3 maths unit “Calculate the value of a part (fractions as operators)”, for children aged 7 to 8, 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 28 to 29 of the year, 5 sheets in the unit.

Free sample · answers on the last page

Building the whole

Name: ____________ · Date: ____________
Year 3 · Maths · about 20 minutes
Answers are on the grown-up page

Today I can build a whole from one known part, using its fraction.

A Look back3 min

1.
3 rows of 4 counters make counters.
2.
5 groups of 2 make .
3.
Circle the fraction that shows the shaded part.
one-thirdone-quarterone-half

B Watch me, then you4 min

A 2 cm piece is one-third of a whole. Build the whole from the piece.

Watch me

One-third means the whole has 3 equal parts.

Each part is 2 cm.

2 + 2 + 2 = 6, so the whole is 6 cm.

Now you

1.
A 3 cm piece is one-quarter of a whole ribbon. The whole ribbon is cm.

C Your turn6 min

The bar shows the piece you already have. Fill in the other equal pieces, then write the length of the whole.

1.
A 4 cm piece is one-half of a whole. The whole is cm.
2.
A 4 cm piece is one-third of a whole. The whole is cm.
3.
A 6 cm piece is one-third of a whole. The whole is cm.
4.
A 5 cm piece is one-quarter of a whole. The whole is cm.

Say it out loud: What stayed the same in each row, and what changed? How many equal parts does the whole need each time?

D Spot the mistake3 min

Mia says: “The piece is 5 cm and it is one-third of the whole, so I need only 2 more pieces. The whole is 10 cm.”

1.
How long is the whole really? cm

E Think deeper4 min

A 4 cm piece is one-half of Whole A. The same 4 cm piece is one-quarter of Whole B. Work out how long Whole B is. Then tell your grown-up why Whole B is longer than Whole A.

1.
The 4 cm piece is one-quarter of Whole B. Whole B is cm long.

How did it feel?

I can do it Nearly Not yet

For the grown-up

Building the whole · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 12

2. 10

3. one-quarter If your child circles one-half, ask how many equal parts the shape has. Four equal parts means each part is one-quarter.

B

1. 12 If your child writes 6, they have counted only two pieces. A quarter needs four equal parts, so add four pieces of 3 cm.

C

1. 8 If your child writes 4, they have only the piece they were given. One-half needs a second equal piece, so 4 + 4 makes the whole.

2. 12 If your child writes 8, they have added only two pieces. One-third needs three equal parts, so add one more 4 cm piece.

3. 18

4. 20

D

1. 15 If your child writes 10, they have added only the two extra pieces, 5 + 5, and left out the piece already held. That piece is one of the three equal parts too. Three pieces of 5 cm make 15 cm.

E

1. 16 If your child writes 8, they have used the half-whole count of two pieces. A quarter needs four equal pieces, so 4 pieces of 4 cm make 16 cm.

Words to use

Say“Which piece do you already have? How many equal parts does the whole need?”

Instead of“Just tell them the answer.”

After the sheet

Line up three identical cups or books. Say one is one-third of the whole, then build the whole by putting all three in a line and measuring.

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 the whole from a part(with a plan)
Sharing sets into equal parts(with a plan)
Parts and wholes with division(with a plan)
Fractions as division(with a plan)

Every Year 3 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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