Cover lesson · Maths · Year 10 · Intermediate

Misleading graphs in the media

DCF: Data and computational thinking → Data and information literacy

Name: Class: Date:

Cover teacher — you need no subject knowledge and no computers

Print: this sheet, one per pupil, and the stimulus sheet "Five graphs, five headlines", one between two, in colour if possible. Pupils need a calculator, a ruler and, for Step 5, a protractor. If there are no protractors, give pupils the angle (135°) and let them do the rest.

Run: 5 min look at all five graphs without writing · 10 min Step 1, spot the trick · 10 min Step 2, Graph A in numbers and redraw · 6 min Step 3 · 7 min Step 4 · 7 min Step 5 · 5 min Step 6 · 5 min Step 7, the checklist.

Collect: this sheet. All answers are on the worked example sheet. Two to check: Graph A's real increase is 2 percentage points, or 3.2%, although the bar looks three times as tall; and Graph E is the fair one — pupils who call it misleading have over-learned the rule.

What you are doing

A graph can be accurate in every number and still leave you believing something false. You are going to find the trick in each of five graphs, measure how big a false impression each one creates, redraw one honestly, and then write a checklist you can use on any graph you meet online. Careful: not every graph on the sheet is misleading.

Step 1 — spot the trick

Graph	Fair or misleading?	The trick, in a few words	The evidence you can see on the graph
A
B
C
D
E

Step 2 — Graph A in numbers

(a) Count gridlines from the bottom of the axis. How many times as tall as the 2023 bar is the 2024 bar?

(b) What is the real change, in percentage points? And as a percentage increase on the 2023 figure, to 1 decimal place? Show your working.

(c) Redraw Graph A with the axis starting at zero, and give it an honest headline.

Step 3 — Graph B, the bottles

(a) By what number were sales multiplied from 2023 to 2024?

(b) Measure the two bottles. The big bottle is how many times as tall, and how many times as wide? So how many times as much area does it cover on the page?

(c) What should the advert have drawn instead?

Step 4 — Graph C, the swimming club

From → to	Years	Members gained	Members gained per year
2004 → 2014
2014 → 2019
2019 → 2022
2022 → 2023
2023 → 2024

Why does the line look straight? Write a headline that matches what really happened.

Step 5 — Graph D, the pie chart

(a) Add up the four percentages. What should the slices of a pie chart always add up to?

(b) Use a protractor to measure the angle of the Bus slice. What percentage of the whole pie is that slice really? (A full turn is 360°.)

(c) Explain why the percentages add up to more than 100, and say what kind of chart should have been used.

Step 6 — Graph E, the attendance line

Graph E's axis does not start at zero either. Is it misleading? Use the headline, the axis label and the type of graph in your answer. Then work out the fall from September to December in percentage points.

Step 7 — your graph checklist

Write five questions anyone should ask before they believe or share a graph. Each question should catch at least one of the tricks on the stimulus sheet.

Step by step

5 min — Look at all five graphs. Read the headline, then the axes, then the source line.
10 min — Step 1: fair or misleading, the trick and the evidence.
10 min — Step 2: the real change in Graph A, and the honest redraw.
6 min — Step 3: the bottles and area.
7 min — Step 4: growth per year for the swimming club.
7 min — Step 5: the pie chart that adds up to too much.
5 min — Step 6: decide whether Graph E is fair.
5 min — Step 7: your five-question checklist.

Success criteria

I can name the technique that makes a graph misleading and point to the evidence on the graph itself.
I can calculate the real change, in percentage points and as a percentage, and compare it with the change the picture suggests.
I can explain why doubling the height and width of a picture makes it look four times as big.
I can redraw a misleading graph honestly and write a headline that matches the data.
I can recognise a fair graph, including a line graph whose axis clearly does not start at zero.

If you finish early

Redraw Graph C on the back of this sheet with the years to scale, so that a gap of 10 years is ten times as wide as a gap of 1 year. What shape is the line now?
If the smoothie advert had drawn solid 3D bottles, twice as tall, wide and deep, how many times bigger would the 2024 bottle look?
If you have a computer: the UK government publishes its own rules for charts (Government Analysis Function, "Data visualisation: charts"). Find what it says about starting a bar chart's axis at zero, and about line charts.