Worked example · PE · Year 10
DCF: Data and computational thinking → Problem-solving and modelling
A complete, secure Year 10 response, annotated so you can see which success criterion each part meets. It is also the answer key. The four errors are D3, E4, G5 and D6. The two traps: Priya’s sprints look aerobic by heart rate but are a creatine phosphate session, and Mari’s 107 bpm is just inside her aerobic zone once her typed-in maximum is fixed. All percentages are heart rate ÷ corrected MHR × 100, to one decimal place.
| Column | Input, process or output? | What it does |
|---|---|---|
| B (Age) | Input | Typed in. Everything else is worked out from it. |
| C (Resting HR) | Input | Typed in, but no formula uses it. |
| D (Max HR) | Process and output | Takes the age away from 220 to estimate maximum heart rate. E, F and G all use this answer. |
| E, F and G | Processes giving outputs | Multiply MHR by 0.6, 0.8 and 0.9 to give the aerobic threshold, the anaerobic threshold and the top of the anaerobic zone. |
Column C, resting heart rate, is never used.
Every column is named as input, process or output, with its purpose. Spotting that D is both an output and the input to E, F and G shows how the parts connect. Evidences criterion 1.
| Cell | What is wrong | Correct formula | Correct value | Also fixes |
|---|---|---|---|---|
| D3 | Adds the age instead of taking it away, so Owain’s MHR is 237. | =220-B3 | 203 | E3 = 122, F3 = 162, G3 = 183 |
| E4 | Multiplies by 0.06 (6%) instead of 0.6 (60%), so the threshold shows 12. | =D4*0.6 | 124 | Nothing else: E4 is not used by other cells. |
| G5 | Points at D4 (Priya’s MHR, 206) instead of D5 (Dafydd’s, 207). | =D5*0.9 | 186 | Nothing else. |
| D6 | 180 has been typed over the formula. Mari is 42, so it should be 220 − 42. | =220-B6 | 178 | E6 = 107, F6 = 142, G6 = 160 |
G5 (185 instead of 186) and D6 (180 instead of 178) look believable. Nobody would notice them by eye, so they get trusted and used. A value of 237 or 12 is obviously wrong, so someone would check it. The D6 error also hides: if Mari has a birthday, the typed 180 will not change, but a formula would.
Each error is located, explained, corrected as a formula and as a value, and its knock-on effect is traced. The explanation of why believable errors are dangerous is the key idea. Evidences criterion 2.
| Name | Age | Max HR | 60% | 80% | 90% |
|---|---|---|---|---|---|
| Elin | 18 | 220 − 18 = 202 | 202 × 0.6 = 121.2, so 121 | 202 × 0.8 = 161.6, so 162 | 202 × 0.9 = 181.8, so 182 |
| Gareth | 44 | 220 − 44 = 176 | 176 × 0.6 = 105.6, so 106 | 176 × 0.8 = 140.8, so 141 | 176 × 0.9 = 158.4, so 158 |
The model is run by hand exactly as the correct formulas would run it, with working shown and consistent rounding. Evidences criterion 1.
| Athlete | HR ÷ MHR × 100 | Zone | Energy system | Reason |
|---|---|---|---|---|
| Nia | 150 ÷ 204 = 73.5% | Aerobic zone | Aerobic | 40 minutes at a pace where she could still talk: long duration, moderate intensity. |
| Owain | 174 ÷ 203 = 85.7% | Anaerobic zone | Lactic acid | High intensity, and each 50-second repeat sits inside the 10 seconds to about 3 minutes range. |
| Priya | 140 ÷ 206 = 68.0% | Aerobic zone, by heart rate only | Creatine phosphate | Flat-out (highest intensity) and only about 5 seconds long, under the 10-second limit. 2 minutes’ rest lets the creatine phosphate stores recover between sprints. |
| Dafydd | 190 ÷ 207 = 91.8% | Above 90%: near maximal | Lactic acid | A race effort lasting 2 minutes 40 seconds, inside the 10 seconds to about 3 minutes range. The aerobic system is also working hard by the end. |
| Mari | 107 ÷ 178 = 60.1% | Aerobic zone (only just) | Aerobic | 30 minutes of low-intensity walk-jog: long duration, low intensity. |
(a) No. Mari’s sheet used her typed-in 180, which gave a threshold of 108. Her real model MHR is 220 − 42 = 178, so her aerobic threshold is 106.8 bpm (shown as 107). 107 ÷ 178 = 60.1%, so she was just inside the aerobic zone. With the error, 107 ÷ 180 = 59.4%, which is why the sheet told her the wrong thing.
(b) No. Each sprint lasted about 5 seconds at maximum effort, so the creatine phosphate system was predominant. Heart rate takes time to rise, so it was still only 140 bpm when each sprint ended. The heart rate tells you how hard the heart was working at that moment, not which energy system the muscles were using.
Every percentage is correct and uses the corrected MHR. Each energy system is justified by intensity and duration from the fact card, and the answer to Mari’s note separates what the model outputs from what was really happening. Evidences criterion 4.
Exactly 60% counts as aerobic, because the aerobic threshold is the point where you enter the aerobic zone. Exactly 80% counts as anaerobic for the same reason. Exactly 90% is still the top of the anaerobic zone. The order of the checks matters: if the rule checked “<= 90” first, every heart rate under 90% would come out as anaerobic.
| Heart rate | % of MHR (200) | Expected output | Rule agrees? |
|---|---|---|---|
| 119 | 59.5% | below aerobic threshold | ✓ |
| 120 | 60.0% | aerobic zone | ✓ |
| 159 | 79.5% | aerobic zone | ✓ |
| 160 | 80.0% | anaerobic zone | ✓ |
| 180 | 90.0% | anaerobic zone | ✓ |
| 181 | 90.5% | above 90% | ✓ |
A self-contained algorithm with one output for every possible input, clear decisions at each boundary with a physiological reason, and tests on and next to every boundary. Evidences criterion 3.
| Limitation and evidence | Improvement or advice | |
|---|---|---|
| 1 | Heart rate lags behind very short efforts. Priya’s 5-second sprints were creatine phosphate work, but her heart rate was only 140 bpm (68.0%), so the model calls it an aerobic session. | Add an input column for how long each effort lasted. If an effort is 10 seconds or less at maximum intensity, label it creatine phosphate whatever the heart rate says. |
| 2 | 220 − age is only an estimate. Two athletes of the same age can have quite different real maximums, so a sharp boundary like Mari’s 107 bpm against 106.8 means little. | Treat the zones as a guide, not an exact line. Also use how the session felt, such as whether the athlete could talk. |
A third limitation: resting heart rate (column C) is typed in but ignored, so two 16-year-olds with very different fitness get the same zones. Mari could lock the formula cells and colour the input cells so no one types over a formula again, which is what went wrong in D6.
Each limitation is backed by evidence from the pack or from the pupil’s own answers and comes with a practical fix. Evidences criterion 5.
Heart rate reserve for Nia: reserve = 204 − 64 = 140. At 60%: 64 + 140 × 0.6 = 148 bpm. At 80%: 64 + 140 × 0.8 = 176 bpm. The simple model gives 122 and 163, so the heart rate reserve method sets higher targets, a harder session.
One formula for I2: =IF(H2/D2<0.6,"below aerobic threshold",IF(H2/D2<0.8,"aerobic zone",IF(H2/D2<=0.9,"anaerobic zone","above 90%")))
Owain’s aerobic session: with his fixed row, 122 to 162 bpm, for example 30 minutes of steady running with his watch between about 130 and 155 bpm.