S1 Maths — Statistical Charts: Lesson Prep Guide for Tutors (pie angles, line-graph trends, misleading axis)

2026-11-14

Tutor lesson-prep guides · Secondary Maths

Pie charts go wrong on the angle, line graphs go wrong on a single point, bar charts go wrong on a dishonest axis. This lesson turns a class of 40 choosing four sports into 126, 90, 72 and 72 degrees, then adds a chart whose axis starts at 90 so students say for themselves that it looks three times bigger but is only 4% bigger.

Objectives — By the end students can: (1) turn 14, 10, 8 and 8 out of 40 into sectors of 126, 90, 72 and 72 degrees and state that the four angles total 360; (2) reverse a 54 degree sector back to 6 students using angle divided by 360 then times the total; (3) explain that an axis starting at 90 stretches 2 units and 6 units into a threefold look, when the true ratio of 96 to 92 is only 1.04.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Angles in a full turn	How many degrees do all sectors of a pie chart add up to?	360 degrees, not 100
Fraction multiplication	What is one quarter of 40?	10
Reading axes	What normally goes on each axis?	Categories or time across, quantity up

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Read the chart first	Show a pie chart and ask which sport is the most popular, with no numbers given	Answer from the sector size and give a reason
5-14 min	Working out an angle	Write 40 on the board, list each sport, and model 14 divided by 40 times 360 to get 126 degrees	Work out the 10-person sector to get 90 degrees
14-23 min	Four angles make 360	Add 126, 90, 72 and 72 together with the class	Get 360 and state that any other total means a slip
23-32 min	Line graphs show trend	Plot six months of library loans, 12, 18, 15, 24, 21 and 30, and ask for the range and the biggest monthly jump	Range 18, biggest jump 9, from 21 to 30
32-40 min	The axis illusion	Draw bars for 92 and 96 with the axis starting at 90, measuring 2 units and 6 units	Say it looks three times bigger while the data differs by about 4%
40-45 min	Exit check	Three quick questions: total degrees, reverse to people, axis judgement	Answer aloud; two misses are noted

03 Teaching script (read it out)

Scene 1: Act 1: a sector is a proportion of 360

“One thing to fix first: a full turn is 360 degrees, not 100. So the degrees for a category are its proportion times 360. Out of 40 students, 14 play football, and 14 out of 40 is 0.35, times 360 gives 126 degrees. Basketball is 10 out of 40, which is 0.25, so 90 degrees. Badminton and swimming are 8 each, so 72 degrees each. Add the four and you get 360; any other total means a figure was copied wrongly.”

Students repeat: proportion times 360, four sectors total 360

Scene 2: Act 2: going back divides by 360

“In reverse, if a paper gives you only a 54 degree sector and asks how many students, divide 54 by 360 to get 0.15, then times 40 to get 6. Going from angle back to people always starts with dividing by 360. And check: 54 degrees is less than 90, so the count must be less than 10, and 6 fits.”

Students repeat: angle back to people means divide by 360 first

Scene 3: Act 3: the axis can mislead

“Now the bar chart. This axis starts at 90. The bar for 92 is 2 units tall and the bar for 96 is 6 units tall, so it looks three times bigger. But 96 divided by 92 is 1.04, a difference of about four percent. So the first thing to read on a bar chart is where the axis starts, not how tall the bars are.”

Students repeat: bar height is not data ratio, check the axis start

04 Question types and worked steps

Type	Example	Steps	Answer
Angle of a sector	Out of 40 students, 14 chose football. What angle is that sector?	(1) Write the proportion 14/40 (2) multiply by 360 (3) give the unit, degrees (4) add all four sectors to check 360	14 / 40 x 360 = 126 degrees
Angle back to people	A sector is 54 degrees out of 40 students. How many is that?	(1) Divide 54 by 360 (2) get 0.15 (3) times 40 (4) the answer must be a whole number	54 / 360 x 40 = 6 students
Reading a line graph	Loans for six months are 12, 18, 15, 24, 21, 30. What is the biggest monthly jump?	(1) Subtract each pair (2) take the largest (3) name the two months (4) use the axis unit	30 – 21 = 9, from month five to month six
Spotting a misleading chart	Bars of 92 and 96 with the axis starting at 90: do bar heights and data keep the same ratio?	(1) Note the axis start (2) subtract to get bar heights (3) divide the raw values (4) state both ratios	Heights 3 to 1, data 1.04 to 1, so no

Sanity check (teach this): Reasonableness checks: the four sector angles must total 360, and 126 plus 90 plus 72 plus 72 does; the largest category must have the largest angle, and 126 beats 90 just as 14 beats 10; a reverse count must be a whole number, so 6 is fine and 6.7 means the total or the angle was misread; the biggest monthly jump must exceed any monthly fall, and 9 beats 3; with a non-zero axis the bar ratio overstates the data ratio, which is exactly the 3 to 1.04 gap here.

05 Independent practice (3 questions)

Question	Answer	What to watch
Out of 40 students, 8 chose badminton. What angle is that sector?	8 / 40 x 360 = 72 degrees	An answer of 20 means 100 was used as the full turn
A sector is 90 degrees out of 40 students. How many students?	90 / 360 x 40 = 10 students	Same direction as Act 2: divide by 360 first
Why does an axis starting at 90 make 96 look far bigger than 92?	The bars are 6 units and 2 units, so three times the height, while the data differ by 4 out of 92, about 4%	Both ratios, height and data, must be stated

06 Common mistakes and what to say

Mistake	Student writes	Say this
Using 100 for a full turn	“14 divided by 40 times 100 is 35 degrees.”	“35 is a percentage, not degrees. A full turn is 360 degrees, so multiply by 360 and you get 126.”
Multiplying when reversing	“54 degrees is 54 times 360, that is a lot of students.”	“Going back you divide. Angle over 360 gives the proportion, then times the total: 54 over 360 times 40 is 6.”
Reading a single point as a trend	“June had the most loans, so June had the biggest jump.”	“Most and biggest jump are different questions. A jump compares two neighbouring points, and 21 to 30 is the biggest at 9.”
Comparing bars without the axis	“The 96 bar is three times the 92 bar.”	“Three times is only the height, because the axis starts at 90. Divide the real numbers: 96 over 92 is 1.04, about four percent.”

07 Homework (paper, section and question numbers)

Redo Act 1: turn your class of 40 and four favourite sports into four sector angles that total 360 — Chapter practice, question 1
Find a bar chart in the news, note where its axis starts, and compute both the height ratio and the data ratio — Chapter practice, question 3
Record the temperature for six days, draw a line graph, and mark the day with the biggest rise — Chapter practice, question 2

08 Exit check (last 5 minutes)

Question	Answer	Decision
How many degrees in a full turn, and what must four sectors total?	360 degrees, and they must total 360	An answer of 100 means Act 1 again
A sector is 54 degrees out of 40 students. How many students?	54 / 360 x 40 = 6	Getting 6 without steps still means Act 2 again
With an axis starting at 90, how much bigger do 92 and 96 look, and how much bigger are they?	They look three times bigger but are about 1.04 times bigger	One of the two answers missing means Act 3 again

09 Tutor FAQ

Should students draw pie charts themselves?

In S1, drawing two sectors with a protractor is enough, say 126 and 90 degrees. More drawing wastes lesson time; the angle calculation is the point.

May they key 14 divided by 40 times 360 straight into a calculator?

Yes, but they write the expression first. Method marks come from the written line, not from the display.

Why teach a misleading axis when it is barely examined?

It is examined as interpretation, and it is the single most common way students are fooled by charts in the news.

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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.