Primary 6 Maths | Averages And Charts Lesson-Prep Guide (for Tutors) | Mean, Pie-chart Angles And Chart Traps

Primary 6 Maths | Averages and Charts Lesson-Prep Guide (for tutors) | Mean, pie-chart angles and chart traps

2026-11-11

Tutor lesson-prep guides · Primary Maths

Pupils can add and divide, yet freeze when a new value joins the group. This lesson puts the mean back on the total, which can be worked backwards, then turns charts into evidence that has to be judged.

Objectives — Pupils can: (1) find a mean as total divided by count and work back from a mean to a total; (2) explain that a value above the mean raises it and one below lowers it; (3) read the key of a bar or line graph before reading the bars; (4) convert pie-chart percentages into degrees and people, and name three common chart traps.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Division	What is 336 divided by 4?	84, exactly
Percentages	What fraction is 25%?	One quarter
Everyday meaning of average	What does “two bowls of rice each on average” mean?	The total shared out, not that everyone ate exactly two

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Two opening questions	Ask for the mean of 78, 85, 90 and 83; then ask whether “you scored 84” is true, and let pupils argue	Give an answer and a reason
6-16 min	Mean = total / count	Write 336 / 4 = 84 and stress dividing by the number of scores, not the highest score	Copy the total line
16-24 min	One new value	Five scores average 80 (total 400); add 92 and write (400 + 92) / 6 = 82, then ask why it rose	Say “because 92 is above 80” and recompute
24-32 min	Working back to a total	Six scores average 82, so the total is 82 x 6 = 492; five of them total 400, so the sixth is 92	Work back and check
32-40 min	Three kinds of chart	Bar: read what one square stands for; line: describe the trend; pie: 360 degrees for 100%, so 1% is 3.6 degrees	State the key and the whole for each chart
40-45 min	Exit check	Three quick questions; whichever is missed becomes the first item next lesson	Answer orally

03 Teaching script (read it out)

Scene 1: A mean is what sharing would give

The mean is not a score everyone got; it is what each would get if all had the same. Add first, then share.

336 shared among 4 is 84 each

Scene 2: New values pull the mean

Anything above the old mean raises it, anything below lowers it, and the count dilutes the change.

400 plus 92 is 492, over 6 gives 82, only two marks up

Scene 3: Read the key before the bars

One square for 5 people and one square for 50 look identical but differ tenfold.

Check the vertical axis label first

Scene 4: A pie chart is an angle problem

The full circle is 360 degrees for 100%, so 1% is 3.6 degrees and 25% is a right angle.

Draw 25% as a right angle

04 Question types and worked steps

Type	Example	Steps	Answer
Find the mean	Four dictation scores: 78, 85, 90, 83. What is the mean?	(1) Add to get 336; (2) divide by 4; (3) 84 marks	84 marks
Work back to a total	Six pupils average 82 marks and five of them total 400. What did the sixth score?	(1) 82 x 6 = 492; (2) 492 – 400 = 92; (3) 92 marks	92 marks
Convert a pie slice	In a pie chart of 200 pupils, 25% chose football. What angle, and how many pupils?	(1) 25 x 3.6 = 90 degrees; (2) 200 x 25% = 50 pupils	90 degrees, 50 pupils

Sanity check (teach this): Check three things afterwards: the mean must sit between the smallest and largest value (84 is between 78 and 90); after adding a value above the old mean the new mean must rise but stay below that value (82 sits between 80 and 92); all pie-chart angles must add to 360 degrees and all percentages to 100%.

05 Independent practice (3 questions)

Question	Answer	What to watch
Five pupils average 76 marks; a sixth scores 94. What is the new mean?	Total 380 plus 94 is 474, over 6 gives 79, above the old mean but below 94	Check the four scores are added before dividing
A pie chart shows 40% travel by bus. What angle is that?	40 x 3.6 = 144 degrees, larger than a right angle	Check the multiply by 3.6 is written
One square stands for 5 people and a bar is 6 squares tall. How many people if one square stood for 50?	30 people; then 300, so always read the axis	Check the axis key is read first

06 Common mistakes and what to say

Mistake	Student writes	Say this
Treating the mean as everyone’s score	“The mean is 84, so everyone got 84.”	The mean is what sharing would give; list the four scores to show the spread
Dividing by the wrong number	“336 divided by 90, roughly…”	Always divide by the count of values, and circle that count first
Using a percentage as an angle	“25% means 25 degrees.”	Multiply by 3.6: 25% is 90 degrees; write the line 25 x 3.6
Ignoring where the axis starts	“This bar is twice as tall, so twice as many people.”	Check whether the axis starts at zero; if not, say the gap is exaggerated

07 Homework (paper, section and question numbers)

Primary 6 maths test paper, Part A, statistics question 4 — Part A, Q4
Primary 6 maths test paper, Part B, pie-chart question 9 — Part B, Q9
Primary maths chapter index (pick a related chapter) — Chapter index

08 Exit check (last 5 minutes)

Question	Answer	Decision
Scores of 70, 80, 90 and 88: what is the mean?	82 (total 328, divided by 4)	If wrong, redo “add first, then divide” and write the total
Five pupils average 60 and a 90 joins. Does the mean rise, and roughly to what?	It rises, to about 65 (390 over 6)	If they only say “rise”, make them finish the line
What angle is 10% of a pie chart?	36 degrees	If they say 10 degrees, rewrite 10 x 3.6

09 Tutor FAQ

Which year is this for?

Written for Primary 6; Primary 5 can do the mean and bar charts and leave pie-chart angles.

Must pupils memorise 3.6?

No. Let them derive it from 360 divided by 100 once and it sticks.

Is there a matching worksheet?

Parts A and B of the Primary 6 maths test paper both carry statistics questions, cited in the homework box.

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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.