Primary 6 maths · Data & graphs · About 12 minutes
Recover a total or number of items from an average
Recover a total or number of items from an average
Start the interactive lesson →Practise: Missing-total mission
What you will learn
- Recover a total or number of items from an average
- Find the total from an average and the number of items
- Find the number of items from a total and an average
- Find a missing value when the average is known
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
The average of 5 numbers is 8. What is their total?
What does an average of 8 tell us?
An average of 8 means…
each of the 5 numbers counts as 8 once levelled
Picture 5 equal parts, each worth 8.
Rebuild the total by multiplying.
8 × 5
What is the total?
40
So the total is 40.
total = 8 × 5 = 40
Check by going back the other way.
40 ÷ 5 = 8 ✓
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
- turn “average × number of items = total” around in any direction
- find a total from an average
- find how many items there were
- find a missing value when the average is known
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
- Interpret average as total divided by number of itemsInterpret average as total divided by number of items · About 12 minutes