The shape of the lesson
By the end of the lesson, learners can
- The area is the distance: For a speed that changes, you cannot just multiply the final speed by the total time.
- Reading each graph.
- Distance-time: gradient = speed; a flat line means stationary.
- Speed-time: gradient = acceleration; area under the line = distance.
- Changing speed: split the area into triangles and rectangles, then add. Never use peak speed × total time.
One picture every idea returns to
On a distance-time graph, the gradient (slope) is the speed. On a speed-time graph, the gradient is the acceleration and the area under the line is the distance travelled.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, The shape of a journey.. A graph turns a journey into a picture you can read at a glance. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: The area is the distance | For a speed that changes, you cannot just multiply the final speed by the total time. Project tab 2 of the lab (Motion graphs) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Reading each graph | Reading each graph. | Round Table |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 16 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Reading each graph, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Round Table
One sheet travels round the team. Each student adds one line of working or one idea and passes it on, so the solution is built four hands at a time and every contribution is visible.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| When the speed is changing, the distance is not the final speed multiplied by the final time. | That treats the whole graph as one massive rectangle. The distance is the area under the line, found by splitting it into triangles and rectangles and adding them: area = ½ × base × height for each triangle and length × width for each rectangle. |
Distance-time and speed-time graphs: worksheet
6 questions, 16 marks. Written in the style of the papers; no past paper question is reproduced.
On a distance-time graph, state what is represented by:
(a)the gradient of the line; (b)a horizontal (flat) line.On a speed-time graph, state what is represented by:
(a)the gradient of the line; (b)the area under the line.On a speed-time graph, a car accelerates uniformly from rest to 15 m/s in 6.0 s, then travels at a steady 15 m/s for 10 s. Calculate the total distance travelled.
A cyclist accelerates from rest to 8.0 m/s in 4.0 s, holds 8.0 m/s for 6.0 s, then slows uniformly to rest in 2.0 s. Calculate the total distance travelled.
To find the distance from a speed-time graph where the speed changes, a student multiplies the final speed by the total time. Explain why this is wrong and state the correct method.
On a distance-time graph, an object's line rises steadily from 0 to 100 m over the first 8.0 s, then stays flat at 100 m for the next 5.0 s.
(a)Calculate the speed during the first 8.0 s. (b)State what the object is doing during the flat section.Answer key and marking notes
- (a) The gradient represents the speed. ✓
- (b) A flat line means the object is stationary (not moving). ✓
- (a) The gradient represents the acceleration. ✓
- (b) The area under the line represents the distance travelled. ✓
Triangle. ½ × 6.0 × 15 = 45 m
Rectangle. 15 × 10 = 150 m
total = 195 m
Speeding up. ½ × 4.0 × 8.0 = 16 m
Steady. 8.0 × 6.0 = 48 m
Slowing. ½ × 2.0 × 8.0 = 8 m
total = 72 m
- That treats the whole graph as one rectangle, but the object was not at the final speed for the whole time, so it over-counts the distance. ✓
- Correct method: find the area under the line, splitting it into triangles and rectangles and adding them. ✓
(b) It is stationary (staying at the same distance). ✓
2 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
The distance-time graph shows a cyclist's journey in three labelled sections. During which section is the cyclist stationary?
- Asection OA
- Bsection AB
- Csection BC
- Dthe cyclist is never stationary
The speed-time graph shows a car over 10 s. What total distance does it travel?
- A12 m
- B48 m
- C84 m
- D120 m
Quiz key
AB is horizontal, so the distance from the start stays the same: the cyclist is at rest. OA and BC both slope upward (moving), and BC is steeper, so the cyclist is fastest there.
triangle = ½ × 6 × 12 = 36 m; rectangle = 12 × 4 = 48 m; total = 84 m. Option D (120 m) uses 12 × 10 as one full rectangle, ignoring the triangular start.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.