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Year 6 Mean average worksheet

“Mean and equal sharing” is free to print, with no account. It is the first sheet in the Year 6 maths unit “Mean average”, 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 35 to 36 of the year, 5 sheets in the unit.

Free sample · answers on the last page

Mean and equal sharing

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

Today I can explain how the mean relates to sharing equally, and why the total stays the same.

A Look back3 min

  1. 1.

    6 + 9 + 5 =

    695
  2. 2.

    Share 18 stickers equally between 3 friends. Each friend gets .

    18
  3. 3.

    11 ÷ 2 =

    11

B Watch me, then you4 min

Ola, Sam, Priya and Kit each have some marbles. What is the mean number of marbles?

Watch me
Marbles each012345678OlaSamPriyaKit

Add the total: 2 + 6 + 4 + 8 = 20.

Share the total equally between 4 children: 20 ÷ 4 = 5.

The mean is 5. Each child would have 5 if they shared equally.

Now you
  1. 1.

    Mia, Zara and Noah have 3, 7 and 8 stickers. What is the mean number of stickers?

    Stickers each012345678MiaZaraNoah
Marbles after sharing012345678OlaSamPriyaKit

C Your turn6 min

  1. 1.

    Ali, Bea, Leo and Zara have these marbles. What is the mean?

    Marbles each012345678910AliBeaLeoZara
  2. 2.

    Now Zara has 10 marbles. What is the mean?

    Marbles each012345678910AliBeaLeoZara
  3. 3.

    Five children have these marbles. What is the mean?

    Marbles each012345678910AliBeaLeoZaraNoah
  4. 4.

    Five children each have 6 marbles on average. What is the total?

    Marbles each012345678910AliBeaLeoZaraNoah

Say it out loud: What stayed the same in each row, and what changed? Did the total change when the mean did?

D Spot the mistake3 min

Ruby says: “The mean of our four scores is 6, so the total of our four scores is 6.”
Scores012345678AyoLenaDevMia
  1. 1.

    What is the total of the four scores?

E Think deeper4 min

  1. 1.

    Ali, Bea, Leo and Zara have whole numbers of marbles. Their mean is 5.5. Write one set they could have. Then explain why 5.5 can be a mean even though no child has half a marble.

    Marbles each012345678910AliBeaLeoZara

How did it feel?

I can do it Nearly Not yet
StudyDen · Year 6 · Maths · Mean averageAnswers are on the grown-up page

For the grown-up

Mean and equal sharing · 2 minutes to read

Answers, and what a wrong one tells you

A

1. 20

2. 6 If your child writes 15, they took 3 away from 18 instead of sharing. Ask how many groups of 3 make 18.

3. 5.5

B

1. 6 If your child writes 18, they added the three numbers but did not divide by 3. The total is the first step, then divide.

C

1. 5 If your child writes 20, they stopped after adding the total. Divide the total by the four children.

2. 5.5 If your child writes 5, they used Zara's old 8 instead of 10. Check the bar for Zara again.

3. 6 If your child writes 7.5, they divided by 4 instead of 5. Count the bars: there are five children.

4. 30 If your child writes 11, they added 6 and 5. Each of the five children has 6, so the total is five lots of 6.

D

1. 24 If your child writes 6, they copied Ruby's mean. The total is all four scores added together: 5 + 7 + 4 + 8. There is no dividing this time.

E

1. Look for: Four whole numbers that total 22, and an explanation that the mean describes equal sharing rather than a real half marble. If your child's numbers do not total 22, add the four numbers and divide by 4 to check the mean.

Words to use

Say“What is the total first? Then how many children share it?”
Instead of“Tell them the answer is 5 and move on.”

After the sheet

Put 12 pasta pieces into 4 cups in any uneven way. Tip them into one pile, then share them equally between the cups and say the mean.

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. Counting the zeros(with a plan)
  2. How the mean changes(with a plan)
  3. Fair comparisons with the mean(with a plan)
  4. Is the mean fair?(with a plan)

Every Year 6 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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