Worked example · Maths · Year 10
DCF: Data and computational thinking → Data and information literacy
A secure Year 10 response, annotated against the success criteria. The calculations have single right answers, so you can mark from this sheet: Graph A is 2 percentage points (3.2%) but looks 3 times as big; Graph B's bottle covers 4 times the area for 2 times the sales; Graph C's growth per year is 1.5, 3, 5, 15, 15; Graph D's slices add up to 120% and the Bus slice is 135° = 37.5%; Graph E is fair.
| Graph | Verdict | The trick | Evidence on the graph |
|---|---|---|---|
| A | Misleading | Bar chart with a cut-off axis. | The axis starts at 61, not 0. The 2023 bar is 1 gridline gap tall and the 2024 bar is 3, so a 2-point rise looks like the rate tripled. |
| B | Misleading | Picture scaled in two directions at once. | The 2024 bottle is twice as tall and twice as wide, so it covers four times the area for twice the sales. |
| C | Misleading | Uneven gaps on the time axis. | The six years are spaced equally but the gaps are 10, 5, 3, 1 and 1 years, so the line looks straight when growth was slow and then very fast. |
| D | Misleading | Pie chart of overlapping answers. | 45 + 38 + 30 + 7 = 120%. "Tick all that apply" means people are counted more than once, so the slices cannot be parts of one whole. It is also an online poll: anyone could vote, not only pupils. |
| E | Fair | None. | A line graph with the axis break drawn and the label saying "axis starts at 90". The headline says exactly what the line shows, a whole school year is shown, and the source is named. |
Names a different technique for each misleading graph, always points to something visible on the graph, and does not assume that every graph on the sheet is a trap. Evidences criteria 1 and 5.
(a) The 2023 bar goes from 61 to 62, one gap. The 2024 bar goes from 61 to 64, three gaps. So the 2024 bar is 3 times as tall, which suggests the rate has gone up by 200%.
(b) Real change: 64 − 62 = 2 percentage points. As a percentage increase on 2023: 2 ÷ 62 × 100 = 3.225… = 3.2%. So the picture exaggerates the increase more than 60 times over: 200% shown, 3.2% real.
Separates percentage points from percentage change, compares the real change with the one the picture suggests, and the redraw starts at zero with a headline that states the actual figures. Evidences criteria 2 and 4.
(a) 24,000 ÷ 12,000 = 2, so sales were multiplied by 2.
(b) The big bottle is 2 times as tall and 2 times as wide, so it covers 2 × 2 = 4 times the area. Your eye judges the amount of bottle, not just the height, so the advert looks as if sales quadrupled. Enlarging by a scale factor of 2 multiplies area by 2² = 4.
(c) Two bottles the same size as the 2023 one, side by side, so each bottle stands for 12,000. Or a simple bar chart starting at zero.
Uses the scale factor to explain the area effect instead of just saying "it looks bigger", and gives an honest alternative. Evidences criterion 3.
| From → to | Years | Members gained | Per year |
|---|---|---|---|
| 2004 → 2014 | 10 | 15 | 1.5 |
| 2014 → 2019 | 5 | 15 | 3 |
| 2019 → 2022 | 3 | 15 | 5 |
| 2022 → 2023 | 1 | 15 | 15 |
| 2023 → 2024 | 1 | 15 | 15 |
The line looks straight because every plotted step is exactly 15 members and every step is drawn the same width, even though one step covers 10 years and another covers 1. Growth was not steady at all: the club now gains ten times as many members a year as it did between 2004 and 2014.
Honest headline: "Slow growth for ten years, then membership took off" — or, with a number, "Club gained 30 members in the last two years, as many as in the fifteen years from 2004 to 2019."
Calculates a rate for each interval so the uneven spacing is proved, not just noticed, and the redraw to scale shows the curve the original hid. Evidences criteria 1, 2 and 4.
(a) 45 + 38 + 30 + 7 = 120%. The slices of a pie chart must add up to 100%, because together they are the whole.
(b) The Bus slice measures 135°. 135 ÷ 360 = 0.375, so the slice is 37.5% of the pie, while its label says 45%. Whoever made the chart shared the circle out in proportion to 120, so every slice is smaller than its label: the pie cannot show the numbers it claims to.
(c) Voters could tick every way they travel, so a pupil who gets the bus some days and a lift on others is counted twice. The 45% means "45% of voters sometimes take the bus", and those groups overlap. A bar chart with one bar per travel method, each out of 100%, would show this honestly. I would also want to know who voted: an online poll on a news page lets anyone vote, so the 400 votes may not be pupils at all.
Proves the chart is broken with a measurement, explains where the extra 20% comes from, and questions the sample as well as the chart. Evidences criteria 1 and 2.
Graph E is fair. On a bar chart the length of the bar is the value, so cutting the axis makes the lengths lie. On a line graph the point that matters is the change from month to month, and a school's attendance never gets anywhere near zero, so an axis from 0 to 100 would squash a real dip into a flat line. The graph also tells you the axis starts at 90, twice: in the label and with the zigzag break. The headline only says what the line shows. From September to December attendance fell 95.1 − 91.8 = 3.3 percentage points.
Knows why the zero rule applies to bars and not automatically to lines, and checks the labelling and the headline before giving a verdict. Evidences criterion 5.
Every question is tied to a trick it would catch, so the checklist is tested against the evidence rather than written from memory. Evidences criteria 1 and 5.