Worked example · English · Year 8
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
A secure Year 8 response, annotated so you can see which success criterion each part meets. It is also your answer key. Step 1: 81; 2024; 200 and 240; glass and other; 70. Step 2: 50%, 33.3%, 75%, 40%, then bottles 40%, wrappers 35%, all plastic 75%, cans 12.5%. Step 3: claims 1 and 5 supported, claim 3 partly supported, claims 2 and 4 not supported. Step 4: the 2025 bar is drawn 13 times as tall, but there are only 1.33 times as many bottles, a rise of 24 or 33.3%. Show this after pupils have tried the steps themselves.
(a) 81 plastic bottles were found in 2023.
(b) 2024, when 88 bottles were found. In 2023 there were only 81.
(c) 200 items in 2021 and 240 items in 2025.
(d) Glass (22 down to 18) and other litter (16 down to 12).
(e) The vertical axis starts at 70, not 0.
Every value is read exactly, and the pupil gives the figures that prove answers (b) and (d). Evidences criterion 1.
(a)
| Fraction | 1/2 | 1/3 | 3/4 | 2/5 |
|---|---|---|---|---|
| Percentage | 1 ÷ 2 × 100 = 50% | 1 ÷ 3 × 100 = 33.3% | 3 ÷ 4 × 100 = 75% | 2 ÷ 5 × 100 = 40% |
(b)
| Type of litter in 2025 | Number | Working | % of all 240 items |
|---|---|---|---|
| Plastic bottles | 96 | 96 ÷ 240 × 100 | 40% |
| Crisp and sweet wrappers | 84 | 84 ÷ 240 × 100 | 35% |
| All plastic (bottles + wrappers) | 96 + 84 = 180 | 180 ÷ 240 × 100 | 75% |
| Cans | 30 | 30 ÷ 240 × 100 | 12.5% |
The method is written out each time, so a mistake would be easy to find. The pupil notices that 40% is the same as 2/5 and 75% is the same as 3/4, which is exactly what Step 3 needs. Evidences criterion 2.
| Claim in the leaflet | Numbers and working | Verdict |
|---|---|---|
| 1. “Three quarters of the litter we find is plastic.” | 96 + 84 = 180 plastic items. 180 ÷ 240 × 100 = 75%, and 3/4 = 75%. | Supported |
| 2. “Most of it is plastic bottles.” | 96 ÷ 240 × 100 = 40%. “Most” means more than 50%, which would be more than 120 bottles. Bottles are the biggest single type, but they are less than half. | Not supported |
| 3. “Plastic bottles are ROCKETING!” | 72, 78, 81, 88, 96: the number went up every year. 96 − 72 = 24 more bottles. 24 ÷ 72 × 100 = 33.3%. A steady rise of a third, not a rocket. | Partly supported |
| 4. “The number of cans on our beach has DOUBLED since 2021.” | 20 in 2021, 30 in 2025. Double 20 is 40. 30 ÷ 20 = 1.5, so cans went up by half (50%). | Not supported |
| 5. “More than 1 in 3 of the things we pick up is a crisp or sweet wrapper.” | 84 ÷ 240 × 100 = 35%, and 1 in 3 = 33.3%. 35% is more than 33.3%. (It was 35% in 2021 too: 70 ÷ 200 × 100.) | Supported |
Every verdict rests on a figure from the table, with the working shown. The pupil defines “most” and “doubled” as numbers before judging them, and gives credit where the leaflet is right. Evidences criteria 2 and 3.
(a) The 2025 bar shows 96 − 70 = 26 bottles above the bottom of the axis. The 2021 bar shows 2. 26 ÷ 2 = 13, so the 2025 bar is drawn 13 times as tall as the 2021 bar.
(b) 96 ÷ 72 = 1.33, so there were about 1.33 times as many bottles, or a third more. The real rise is 96 − 72 = 24 bottles, and 24 ÷ 72 × 100 = 33.3%.
(c) Honest chart: axis from 0 to 100, 1 cm for every 10 bottles. The 2021 bar is 7.2 cm tall and the 2025 bar is 9.6 cm tall. The two bars look quite close in height.
(d) Because the axis starts at 70, the leaflet’s chart makes the rise look enormous, as if the number of bottles had shot up 13 times over. On an honest axis starting at 0 the 2025 bar is only a third taller, which shows a real but steady rise.
The pupil compares the height of the drawn bars with the real numbers and names the cause: the axis does not start at 0. The honest chart is drawn to an accurate scale. Evidences criteria 1 and 4.
(a) The leaflet uses numbers to make the litter problem seem bigger and more urgent than it really is. Some of its figures are accurate. “Three quarters of the litter we find is plastic” is true, because 180 of the 240 items in 2025 were plastic, which is exactly 75%. Starting with a true figure makes the reader trust the rest of the leaflet. However, the words around the numbers exaggerate. The metaphor “DROWNING” and the capital letters in “ROCKETING” and “DOUBLED” make the reader feel alarmed before they check the data. The data shows that cans went from 20 to 30, which is up by half, not double, and that bottles rose by 33.3%. The chart’s axis starts at 70, so the 2025 bar looks 13 times as tall as the 2021 bar. This persuades the reader to join the clean because the problem looks out of control.
(b) Claim 4 rewritten: “Cans on our beach are up by half since 2021, from 20 to 30. Help us stop them!” (18 words)
The paragraph links the numbers to the words around them, quotes the leaflet accurately, uses figures from the working as evidence, and explains the effect on the reader. It credits one true claim and exposes two misleading ones. The rewritten claim is true, uses exact figures and still ends with a call to action. Evidences criterion 5.
Items per volunteer: 2021, 200 ÷ 12 = 16.7; 2025, 240 ÷ 30 = 8.0. There were 2.5 times as many volunteers in 2025, searching the same 500 metres, so part of the rise could come from more people looking more carefully. Glass and “other” went down, and a leaflet that wants volunteers leaves out good news. An honest headline: “Three quarters of our beach litter is plastic” (8 words).