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Year 4 Apply the distributive law to multiplication worksheet

“Spotting the shared number” is free to print, with no account. It is the first sheet in the Year 4 maths unit “Apply the distributive law to multiplication”, for children aged 8 to 9, 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. Week 17 of the year, 5 sheets in the unit.

Free sample · answers on the last page

Spotting the shared number

Name: ____________ · Date: ____________
Year 4 · Maths · about 20 minutes
Answers are on the grown-up page

Today I can spot a shared factor in two multiplications and add the other factors before I multiply.

A Look back3 min

  1. 1.

    Count the dots. 4 rows of 6 is

  2. 2.

    7 × 5 =

  3. 3.

    Turn 3 × 6 round. 6 × 3 =

B Watch me, then you4 min

Ola has bags with 6 apples in each bag. She has 4 bags, then 2 more bags. How many apples are there?

Empty wooden crates stacked beside a farm shop door
Watch me

4 bags of 6 and 2 bags of 6. The 6 is the shared factor.

Add the other factors: 4 + 2 = 6 bags.

Then 6 × 6 = 36 apples.

Now you
  1. 1.

    Sam has 5 boxes with 4 pencils in each, and 3 more boxes with 4 in each. How many pencils in all?

C Your turn6 min

  1. 1.

    2 × 5 + 3 × 5 =

  2. 2.

    4 × 5 + 3 × 5 =

  3. 3.

    4 × 6 + 3 × 6 =

  4. 4.

    6 × 4 + 6 × 3 =

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

D Spot the mistake3 min

Kit says: “3 × 4 + 3 × 5 is the same as 3 × 4 × 5, so the answer is 60.”
  1. 1.

    What is 3 × 4 + 3 × 5?

E Think deeper4 min

  1. 1.

    Here is 6 × 8. Write it as two multiplications added together, with 6 in both, so the total is still 48.

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StudyDen · Year 4 · Maths · Apply the distributive law to multiplicationAnswers are on the grown-up page

For the grown-up

Spotting the shared number · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 24

2. 35

3. 18

B

1. 32 If your child writes 240, they multiplied all four numbers. Add the 5 and the 3 first, then multiply by the shared 4.

C

1. 25 If your child writes 150, they multiplied every number. Add the 2 and the 3 first, then multiply by the shared 5.

2. 35

3. 42

4. 42

D

1. 27 Kit got 60 by multiplying all three numbers, 3 × 4 × 5. Add the 4 and the 5 first, which makes 9, then multiply by the shared 3 to get 27.

E

1. Look for: Two multiplications using 6 as the shared factor, whose other factors add to 8, such as 6 × 3 + 6 × 5 or 6 × 1 + 6 × 7. If your child uses two different shared numbers, ask which number appears in both parts. Then check that the other factors add to 8.

Words to use

Say“Which number is shared? Add the other two numbers first, then multiply.”
Instead of“Multiply all the numbers together to get the answer.”

After the sheet

Set out 2 cups with 5 buttons in each and 3 cups with 5 buttons in each. Push the cups together, count the cups, then multiply by 5.

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:

  1. Taking away groups(with a plan)
  2. Splitting to multiply(with a plan)
  3. Splitting bigger multiplications(with a plan)
  4. Splitting to solve problems(with a plan)

Every Year 4 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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