Cover lesson · Science · Year 8 · Intermediate
DCF: Data and computational thinking → Problem-solving and modelling
Name: Class: Date:
Print: this sheet, one per pupil, and the stimulus sheet “The Cwm Gwyn sponsored bike ride”, one between two. Pupils need a calculator. No computers are needed: pupils design the spreadsheet on paper and work out what it would show by hand. If computers are available, pupils who finish Step 3 may type their model into Excel or Google Sheets to check their values, but they should finish every paper step.
Run: 4 min read the stimulus sheet together · 8 min Step 1 · 8 min Step 2 · 10 min Step 3 · 8 min Step 4 · 8 min Step 5 · 9 min Step 6 · 5 min Step 7. Total 60 minutes.
Collect: this sheet. Steps 1 and 3 show the numeracy work: the speed formula written in symbols, rearranged for distance and time, translated into spreadsheet formulae, and used with values and units substituted and hours converted to minutes. The answer key is the worked example. The key numbers to check are a total riding time of 154 minutes and an arrival time of 12:04; if a pupil has different numbers, their Step 3 is wrong and later steps will be too.
Year 8 at Ysgol Cwm Gwyn are planning a 30 km sponsored bike ride. Their teacher needs to know how long it will take, what time they will arrive and whether they will catch the minibus home. You are going to answer that by building a model: a simplified version of the ride that you can run, test and change. You will design it as a spreadsheet on paper, test it against a real practice ride, fix someone else's broken version and ask “what if?”.
(a) Write the speed formula in words, then in symbols using s for speed, d for distance and t for time.
(b) Rearrange your formula to make d the subject, then to make t the subject.
(c) Complete the table. The spreadsheet has distance (km) in B2, speed (km/h) in C2 and time (h) in D2. Totals are in row 7.
| In words | In symbols | As a spreadsheet formula |
|---|---|---|
| Time in hours = distance ÷ speed | ||
| =D2*60 | ||
| d = s × t | ||
| Average speed = total distance ÷ total time |
(d) Convert these times.
| 0.75 h = ___ min | 0.4 h = ___ min | 1.5 h = ___ min | 25 min = ___ h (2 decimal places) | 2 h 34 min = ___ min |
|---|---|---|---|---|
(e) The fastest planned speed is 18 km/h. Convert it to metres per second (m/s). Show each step: change km to m, change hours to seconds, then divide.
(a) Ms Pritchard could use one speed for the whole 30 km. Why is it better to break the ride into 5 sections?
(b) Design the spreadsheet. Sections 1 to 5 go in rows 2 to 6 and the totals go in row 7. Remember: every formula starts with =, / means divide, * means multiply, and =SUM(D2:D6) adds every cell from D2 to D6.
| Cell | What it shows | Heading (with unit) or formula |
|---|---|---|
| A1 to E1 | The 5 column headings | |
| D2 | Time for section 1 in hours | |
| E2 | Time for section 1 in minutes | |
| B7 | Total distance | |
| E7 | Total time in minutes | |
| B9 | Average speed for the whole ride (km/h) |
(c) D2 is copied down to D6. What formula ends up in D4?
Copy the distances and planned speeds from the stimulus sheet, then work out what the spreadsheet would show.
| Row | A: Section | B: Distance (km) | C: Speed (km/h) | D: Time (h) | E: Time (min) |
|---|---|---|---|---|---|
| 2 | 1 | ||||
| 3 | 2 | ||||
| 4 | 3 | ||||
| 5 | 4 | ||||
| 6 | 5 | ||||
| 7 | Total |
(a) Show the full working for section 3: write the formula in symbols, substitute the numbers with their units, then give the time in hours and in minutes.
(b) The ride starts at 09:30. With no stops, what time does the model say the group arrives at Llyn Gwern?
(c) Work out the average speed for the whole ride (cell B9), showing the substitution. A pupil says “it is just the mean of the five speeds, 12 km/h”. Why are they wrong?
A model is only useful if it matches reality. Use the practice ride graph on the stimulus sheet.
(a) Which part of the graph is steepest, and what does that tell you? What were the riders doing between P and Q, and how can you tell?
(b) Work out the real speed for O to P (section 1) and for Q to R (section 2) in km/h. Show your working.
(c) Compare these with the planned speeds. Which section does the model get right, and which does it get wrong? Which input cell should Ms Pritchard change, to what, and what does the total time become?
Look at Elis's spreadsheet and formulas on the stimulus sheet.
(a) One formula in column D is wrong. Which cell? What did it actually calculate, and why does that make no sense as a time? Write the correct formula.
(b) The formula in E7 is also wrong. What does it leave out? Write the correct formula.
(c) D7 and E7 should show the same time. Convert D7 to minutes. How could Elis have used a check like this to find the errors without looking at any formulas?
Use the correct model from Step 3 each time (not your Step 4 change). For each one, say which cell changes or what you add to the model, then work out the new total time and arrival time.
| What if… | Cell changed or added | New total time | New arrival time |
|---|---|---|---|
| 1. The headwind halves the speed on section 3 | |||
| 2. A 20 minute rest stop at Rhyd y Felin | |||
| 3. Changes 1 and 2 together |
The model has no column for stops. Write the heading for a new column F and the new formula for the total time in E7.
With changes 1 and 2, will the group catch the 13:00 minibus? Suggest one change to the plan that makes it work, and prove it with the model.
The model assumes each section is ridden at one constant speed. Give two ways the real ride will differ from that, and say how each would change the prediction.