Primary 6 maths · Data & graphs · About 12 minutes
Interpret average as total divided by number of items
Interpret average as total divided by number of items
Start the interactive lesson →Practise: Average detectives
What you will learn
- Interpret average as total divided by number of items
- Read an average as the total shared equally
- Find the average of a small set of numbers
- Explain why an average need not be one of the numbers
Models used: counters, sharing, bar models, number sentences, stories.
Before you start
Make the shares fair
Three children have 2, 4 and 6 counters. The shares are unequal.
The three trays belong to three children. Moving counters between trays keeps the total the same.
Three children have 2, 4 and 6 counters. The shares are unequal.
We are redistributing the same total. Giving one counter away means another tray must receive that counter.
The three trays belong to three children. Moving counters between trays keeps the total the same.
Move one counter from the largest share to the smallest. No counters are added or lost.
We are redistributing the same total. Giving one counter away means another tray must receive that counter.
The three trays belong to three children. Moving counters between trays keeps the total the same.
Move one more. All three shares now have 4.
12 ÷ 3 = 4
The average describes the fair share of the original total. It need not be an amount anyone had at the start.
The three trays belong to three children. Moving counters between trays keeps the total the same.
Four is the average: the amount each would have if the same total were shared equally.
average × number of shares = total
The average describes the fair share of the original total. It need not be an amount anyone had at the start.
Why do we divide by how many there are?
Because the total is being split into one equal share per item. Four shelves means four equal shares, so we divide by 4. If there were six shelves, the same 12 books would level out lower, at 2 each — the number of shares is what decides the size of each share.
Worked example
Find the average of 7, 3, 8 and 6.
First find the total.
7 + 3 + 8 + 6
What is the total?
24
Count how many numbers there are.
How many numbers?
4
Share the total equally between them.
24 ÷ 4
So the average is 6.
24 ÷ 4 = 6
Check: four 6s rebuild the total.
6 × 4 = 24 ✓
Common mistakes to discuss
- Adding the numbers and stopping. The sum is only the first step. The average shares that total equally between the items, so divide by how many there are.
- Thinking the average must be one of the numbers. Levelling the amounts can land between them: 4 and 7 level out at 5.5, which is in neither box.
- Dividing by the wrong number. Divide by how many items there are, not by one of the values. Count the items first.
Check your understanding
- share a total equally to find the average
- work out the average of three to five numbers
- read an average from a bar model
- say why an average can sit between the numbers
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
Try this lesson →Related Primary 6 lessons
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