Primary 5 Maths | Averages Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, four common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

An average is not just add them up and divide. The idea pupils need is that the total is being shared back out equally, which is why the answer always sits between the smallest and the largest value and can check itself.

Objectives — By the end of the lesson the pupil can: (1) state that the average equals the total divided by the count, and say why; (2) work back from an average and a count to the total; (3) self-check an answer by asking whether it sits between the smallest and largest value; (4) find one missing item when the average is known.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Column addition	adds 78, 85, 90 and 87	reaches 340 without copying a digit wrongly
Division with remainders	works out 340 divided by 4	gets 85 and knows what to do with a remainder
Reading a data table	says how many items the table holds	counts 4 values and skips the heading row

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0–6 min	Entry check	sets three quick items and watches each one	answers aloud and totals once
6–14 min	What an average is	pours four unequal cups into four equal ones	says the total is being shared out
14–24 min	The standard method	models 78, 85, 90, 87 step by step	repeats the steps once
24–34 min	Working back to the total	gives average 72 over five subjects	writes 72 times 5 equals 360
34–41 min	Independent practice	reads the questions only	works the three items alone
41–45 min	Exit check	collects and marks at once	says which step went wrong

03 Teaching script (read it out)

Scene 1: Act 1: An average shares the total back out

“Picture four cups of water at different heights. Nobody pours any away. We just pour between cups until all four are level. That level is the average of the original four. The total never changed, so the method has to be: add everything first, then divide by how many there are.”

In your own words, what is being shared out when we take an average?

Scene 2: Act 2: The commonest misconception — dividing by the wrong number

“The addition is rarely the problem. Dividing by the wrong number is. Four scores means divide by four, five subjects means divide by five, because you are making every share equal and the number of shares is the number of items. Some pupils divide by the gap between the highest and lowest, or by how many subjects they passed. Count the items first, then divide.”

If you have six numbers, what do you divide by?

Scene 3: Act 3: Check before you believe the answer

“An average can never be larger than the biggest value or smaller than the smallest. If four scores of 78, 85, 90 and 87 produce 60, you do not need to recompute: 60 is below 78, so it is wrong. One second of this check catches most careless errors.”

Can an average be larger than the biggest value? Why not?

04 Question types and worked steps

Type	Example	Steps	Answer
Find the average directly	average of 78, 85, 90, 87	add to 340, then 340 divided by 4	85
Work back to the total	five subjects averaging 72, find the total	72 times 5	360 marks
Find the missing item	five subjects average 80; four are 76, 88, 79, 85	80 times 5 minus 328	72 marks
Average after a new item joins	six people average 42 kg, one more at 48 kg	total 252 plus 48, then divide by 7	about 42.86 kg

Sanity check (teach this): Three checks: the average must sit between the smallest and the largest value; a total must be larger than the average unless there is only one item; and the unit in the answer must match the question, so kilograms stay kilograms.

05 Independent practice (3 questions)

Question	Answer	What to watch
Find the average of 68, 72, 80, 76 and 79.	75	whether the pupil adds first and divides by 5, not 4
Four subjects average 82; a fifth scores 92. What is the new average?	84 marks	whether the pupil uses 82 times 4 for the total instead of averaging 82 and 92
A pupil studies 1.2 hours a day on average. How many hours in seven days?	8.4 hours	whether the pupil sees that average times count gives the total

06 Common mistakes and what to say

Mistake	Student writes	Say this
Dividing by the wrong count	writes 340 divided by 5 equals 68	Four scores in the question means divide by four, not five.
Adding instead of multiplying	writes 72 plus 5 for a total	An average of 72 over five subjects is five lots of 72, so multiply.
Copying a digit wrongly	copies 85 as 58	Point at each number and read it aloud before you write.
Dropping the unit	answers 42.86 with no unit	Your answer has to say kilograms, not just a number.

07 Homework (paper, section and question numbers)

Primary 5 maths paper 1: data and graphs section — Section D, questions 1 to 5

08 Exit check (last 5 minutes)

Question	Answer	Decision
Find the average of 90, 85 and 95.	90	if wrong, reteach Act 1
Six tests average 60; five of them total 300. What is the sixth?	60 marks	if wrong, reteach working back to the total
Five people average 42 kg; a sixth weighs 30 kg. New average?	40 kg	if wrong, reteach the new-item case

09 Tutor FAQ

Where does this topic sit in the Primary 5 syllabus?

It belongs to data handling, taught alongside bar charts and line graphs. This guide spends 45 minutes on the calculation and the reverse cases.

Is 45 minutes enough?

Yes. The flow gives 24 minutes to explanation and modelling, 10 to independent practice and 4 to the exit check. If the entry check fails, repair addition first.

Is there a matching practice paper?

Yes. The homework links straight to the TutorZone Primary 5 maths paper, which carries answers for immediate checking.

Find a tutor — free Tutor Registration →

A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.

Practice papers　Paper 1 (basics)　·　Paper 2 (intermediate)　·　Paper 3 (challenge)　·　Paper 4 (error clinic)