At a glance. One lesson of about 60 minutes. Students see how an axis start changes a bar chart, choose a chart for seven situations, and criticise and redraw a misleading chart.
Calculator: no calculator. Nothing here needs one. Heights are differences and ratios of small numbers.
What students will learn
Know
- Pie for parts of one whole, line for change over time, histogram for grouped measurements, bar for separate groups or counts.
- A bar chart's value axis starts at 0.
- Scales must have equal steps for equal space.
Understand
- A chart can mislead without a wrong number on it.
- Heights compare distances above the axis start, not the values.
- The question and the type of data together decide the chart.
Do
- Choose a chart and justify it.
- Find how tall a bar looks against how large its value is.
- Say what is misleading and how to redraw it.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: matching charts to data types and computing bar heights (questions 1 to 3, 5 and 7).
- Criterion B. Investigating patterns: the axis figure. Ask students to find how the looks-times figure changes as the start rises, and to predict the value at a start of 80.
- Criterion C. Communicating: writing a short critique of a misleading chart and its fair redraw in full sentences (the what-if and the faded visitors example).
- Criterion D. Applying mathematics in real-life contexts: posters, newspaper charts and school results (the hook and worked examples).
The one thing to do with the figure
Ask for a prediction before the first slide. “Could the real values behind those bars be almost the same?” Then slide the start of the axis up and ask students to say when the chart starts to mislead.
In the second figure leave the chart hidden, ask for the chart, then move Show the chart to shown. Choose situation 5 and ask whether a bar chart would also work, so students see that the choice is about the question, not a single right answer.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook and the first figure on the start of the axis. |
| 10 min | Key idea; the second figure on choosing a chart. |
| 10 min | Worked example on reading minutes; students finish the faded visitors example in pairs. |
| 5 min | Question 1, the check. If many choose C or D, go back to the first figure. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 100; 60°; touch. |
|---|---|
| Worked example | 5 cm, 5.2 cm and 5.4 cm. |
| Faded example | 10 cm; 2 times, against a real ratio of 1.25. |
| 1. Why a bar looks too tall | B. A and C do not cause the exaggeration; D blames the numbers, which can all be correct. |
| 2. Choose a chart | B. Parts of one whole. A would also show amounts but not shares as clearly. |
| 3. How tall a bar looks | 2. 60 ÷ 30. |
| 4. Uneven scale | B. A and C invent rules; D picks the wrong fault. |
| 5. Honest bar height | 6. 60 ÷ 10. |
| 6. Judging a claim from a chart | B. A trusts the look; C and D give the wrong fault. |
| 7. Bar height above an axis start | 12. 92 − 80 = 12, at 1 cm a unit. |
| 8. Two charts of the same data | B. A treats printed numbers as the whole story; C values height; D refuses a comparison. |
| 9. How tall a bar looks against its value | C. A trusts the printed numbers; B reads the heights as the values; D uses the ratio of the values for how tall the bars look. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A, C or D in question 1 | Blamed width, chart type or the values. | Ask: if the axis started at 0, would the bars still look so different? |
| A, C or D in question 2 | Chose a chart by looks, not by the question. | Run the three questions: whole, time, grouped. |
| 1.5, 30 or 3 in question 3 | Gave the real ratio, the difference, or divided by the start. | Draw both bars and mark the axis start; measure from it. |
| A, C or D in question 4 | Missed the unequal steps behind equal gaps. | Write the gaps between labels as numbers: 1, 1, 2, 5. |
| 3 or 4.5 in question 5 | Used the rise, or halved. | Ask what one centimetre stands for, from 90 and 9 cm. |
| A, C or D in question 6 | Trusted the look of the bars. | Ask for the difference between the scores in numbers: 77 is 6 more than 71. |
| 4, 8 or 23 in question 7 | Gave the other bar, the difference, or divided. | Mark 80 on a number line and measure up from it. |
| A, C or D in question 8 | Treated the same numbers as the same picture. | Draw both charts for 92 and 97 and compare the gap. |
| A, B or D in question 9 | Trusted the printed numbers, read the bar heights as the values, or used the ratio of the values for how tall the bars look. | Draw the two bars from 40: how tall is each? Then compare 45 and 55 as values. |
Questions worth asking
- When is it acceptable for an axis not to start at 0? On a line graph when the axis is marked and the question is about change. Listen for “it is labelled”.
- Who might want a misleading chart, and why? Advertisers, politicians. Listen for purpose and for naming the feature.
- Could a pie chart ever mislead? Yes: too many sectors, or no totals. Listen for a reason.
- How can you check a chart before you believe it? Read the title, axes, scale and start. Listen for a short list.
Differentiation
A way in for anyone stuck
- Give a ready-drawn misleading chart and a matching honest one and ask students to say what changed.
- Provide a flow card: whole? time? grouped? Then the chart name.
- Use small differences students can see: 60, 63, 66 against an axis start of 58.
Stretch
- Question 7, then: the bar for 100 on the same chart. How tall? (20 cm.) How many times as tall as the 84 bar? (5 times.)
- Redraw a misleading chart from a newspaper or website, with a title, a labelled scale and a note on the axis start.
Students learning in English as an additional language
“Misleading” means giving a false idea. “Exaggerate” means to make something look bigger than it is. Say “starts at” with a finger on the axis.
| Word | Plain meaning | Example |
|---|---|---|
| misleading | giving a false idea, even if the numbers are right | a bar chart whose axis starts at 78 |
| exaggerate | make a difference look bigger than it is | bars that look three times as tall |
| axis start | the value where an axis begins | 0, or 78 |
| scale | the numbers and steps along an axis | 0, 50, 100 |
| uneven scale | equal gaps on the page for unequal steps | 1, 2, 3, 5, 10 evenly spaced |
| fair | showing the data as it is | bars that match the values |
Sentence starters for explaining aloud or in writing:
- The chart is misleading because …
- Starting the axis at … makes the difference look …
- A … fits this data because it is …
Two things not to say
“All charts lie.” Most charts are honest; the aim is to check, not to distrust everything.
“Always start at zero.” Bar charts should; a marked line graph may not.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- ChooseWhich chart fits the number of students in each of five clubs?
Bar chart. - ChooseWhich chart fits how a day of 24 hours is spent, as shares of the whole day?
Pie chart.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ContextA poster shows two bars for 70% and 75%, with the axis starting at 65. The bars are 5 and 10 units tall. How many times as tall does the second look, and what is the real ratio to one decimal place?
2 times; 75 ÷ 70 ≈ 1.07, which is 1.1 to one decimal place. - Earlier work (Unit 2, lesson 6)A value changes from 70 to 75. What is the percentage increase to one decimal place?
7.1%. 5 ÷ 70.
3Challenge
Reasoning, generalising and working backwards.
- ReasoningAn axis starts at 60. Bar A is 4 cm tall and bar B is 12 cm tall, with 1 cm per unit. What are the values, and how many times larger is B's value than A's?
64 and 72; 72 ÷ 64 is about 1.1 times, though B looks 3 times as tall. - Picture chartsA poster doubles the width and the height of a coin picture to show that savings doubled. How many times as big does the new coin look?
4 times: the area grows 2 × 2 = 4 times, though savings only doubled. Scale one direction only, or use bars.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
Both figures work with the keyboard (tab to a slider, then the arrow keys) and by touch. Under each one, “Show me the steps” gives the same states in words.
No device? Print one misleading chart and ask students to mark the axis start and redraw it on squared paper.