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Year 3 Composition of non-unit fractions: addition and subtraction worksheet

“Building fractions piece by piece” is free to print, with no account. It is the first sheet in the Year 3 maths unit “Composition of non-unit fractions: addition and subtraction”, 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 31 to 33 of the year, 10 sheets in the unit.

Free sample · answers on the last page

Building fractions piece by piece

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

Today I can build a non-unit fraction by adding unit fractions one at a time.

A Look back3 min

  1. 1.

    Circle the fraction that is shaded.

    1/41/32/43/4
  2. 2.

    Half of 12 is

    12
  3. 3.

    How many halves make one whole?

B Watch me, then you4 min

Watch me

Each strip is 1/8.

1/8 + 1/8 + 1/8 = 3/8

Three strips are coloured, so the top number is 3.

Now you
  1. 1.

    1/8 + 1/8 = / 8

C Your turn6 min

Write each total. Use the bar of 5 equal strips to help you.

  1. 1.

    1/5 + 1/5 = / 5

  2. 2.

    1/5 + 1/5 + 1/5 = / 5

  3. 3.

    1/5 + 1/5 + 1/5 + 1/5 = / 5

  4. 4.

    1/5 + 1/5 + 1/5 + 1/5 + 1/5 = / 5

Say it out loud: What stays the same in every row, and what changes? What does the top number tell you?

D Spot the mistake3 min

Ben says: “The two shaded strips are not next to each other, so they can’t make 2/5.”
  1. 1.

    Is Ben right? Explain in one sentence.

E Think deeper4 min

  1. 1.

    Shade 4/6 of the bar so the shaded strips are not all next to each other. Then write the addition your bar shows.

How did it feel?

I can do it Nearly Not yet
StudyDen · Year 3 · Maths · Composition of non-unit fractions: addition and subtractionAnswers are on the grown-up page

For the grown-up

Building fractions piece by piece · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 1/4 If your child circles 3/4, they may be counting the unshaded strips. Ask how many strips are coloured in.

2. 6 If your child writes 2, they have divided the number by the wrong thing. Share 12 into 2 equal parts and count one part.

3. 2

B

1. 2 / 8 If your child writes 16, they added the bottom numbers. The bottom stays 8, so count the 1/8 pieces instead.

C

1. 2 / 5 If your child writes 10, they added the bottom numbers. The bottom stays 5, so count the 1/5 pieces instead.

2. 3 / 5

3. 4 / 5 If your child writes 20, they added the bottom numbers. The bottom stays 5, so count the 1/5 pieces instead.

4. 5 / 5

D

1. Look for: No, position does not matter; the equation is still 1/5 + 1/5 = 2/5 wherever the strips are. If your child agrees with Ben, ask whether the equation changes when the strips move. It does not, so the total stays 2/5.

E

1. Look for: Four strips shaded, not all side by side, with four lots of 1/6 added to make 4/6. If your child shades 4 strips in a row, ask them to move one strip apart. Does the total change? It is still 4/6.

Words to use

Say“Say the equation out loud, and point to each piece as you add it.”
Instead of“Tell them the answer straight away.”

After the sheet

Fold a sheet of paper into 5 equal parts. Colour one part at a time, and say the matching equation each time.

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:

  1. Building up to one whole(with a plan)
  2. Adding Same-Size Pieces(with a plan)
  3. Adding the top numbers(with a plan)
  4. Adding the same-named pieces(with a plan)
  5. Taking away fraction pieces(with a plan)
  6. Add and take away fractions(with a plan)
  7. Undoing Fraction Sums(with a plan)
  8. Taking fractions from one whole(with a plan)
  9. Swap the whole(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.

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