The shape of the lesson
By the end of the lesson, learners can
- Turn the arrow, keep the number: A vector is drawn as an arrow: its length shows the magnitude and the way it points shows the direction.
- Which is which: Notice the pairs that are easy to confuse: distance (scalar) versus displacement (vector), and speed (scalar) versus velocity (vector).
- Scalar: magnitude only (distance, speed, mass, time, energy).
- Vector: magnitude and direction (displacement, velocity, acceleration, force, weight, momentum).
- Sign: for a vector, opposite directions take opposite signs.
One picture every idea returns to
A scalar has magnitude (size) only. A vector has both magnitude and direction. Speed, distance, mass, time and energy are scalars; velocity, displacement, acceleration, force, weight and momentum are vectors.
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, Some quantities point somewhere.. A mass of 2 kg is just a number with a unit. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Turn the arrow, keep the number | A vector is drawn as an arrow: its length shows the magnitude and the way it points shows the direction. Project tab 2 of the lab (Scalars and vectors) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Which is which | Notice the pairs that are easy to confuse: distance (scalar) versus displacement (vector), and speed (scalar) versus velocity (vector). | Anticipation / Reaction Guide |
| 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, 14 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 Which is which, 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.
Anticipation / Reaction Guide
Before the lesson, students mark five statements true or false. After the teaching they mark them again and justify any change of mind in one sentence each. The statements come from the examiner traps below.
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 |
|---|---|
| Because a vector has direction, the sign matters. | A velocity of +5 m/s and one of −5 m/s have the same speed but opposite directions, and treating them as the same value is exactly the error that loses marks in momentum and force questions. Always decide which direction is positive before you start. |
Scalars and vectors: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
Define a scalar quantity and a vector quantity.
Give one example of a scalar quantity and one example of a vector quantity (other than speed or velocity).
State whether each of the following is a scalar or a vector: temperature, acceleration, time, force, distance, momentum.
A runner completes exactly one lap of a 400 m circular track, finishing at the same point where they started.
(a)State the distance travelled. (b)State the magnitude of the displacement, and explain your answer.Explain why weight is treated as a vector but mass is treated as a scalar.
A ball moves to the right at 6 m/s, hits a wall, and rebounds to the left at 6 m/s. Explain why its velocity has changed even though its speed has not.
Answer key and marking notes
- A scalar has magnitude (size) only. ✓
- A vector has both magnitude and direction. ✓
- Scalar: mass (or distance, time, energy, temperature). ✓
- Vector: force (or displacement, acceleration, weight, momentum). ✓
- Scalars: temperature, time, distance. ✓
- Vectors: acceleration, force, momentum. ✓
- (a) Distance = 400 m (the total path length). ✓
- (b) Displacement = 0 m. ✓
- The finish point is the same as the start, so there is no overall change in position. ✓
- Weight is a force and acts in a definite direction (downward, toward the Earth), so it has direction as well as size, making it a vector. ✓
- Mass is just a quantity of matter with no direction, so it is a scalar. ✓
- Speed is a scalar (size only), and the size is 6 m/s both before and after, so the speed is unchanged. ✓
- Velocity is a vector; the direction has reversed (for example from +6 m/s to −6 m/s), so the velocity has changed. ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
As the object moves around the circle at constant speed, its velocity...
- AIs constantly changing
- BStays constant
- CIs always zero
- DIs the same as its speed
A scalar quantity has...
- AMagnitude only
- BDirection only
- CBoth magnitude and direction
- DNeither magnitude nor direction
Which of these is a vector quantity?
- AForce
- BMass
- CTemperature
- DEnergy
The orbit keeps a fixed speed but a changing velocity because...
- ASpeed is a scalar (size only) while velocity is a vector (size and direction)
- BSpeed and velocity mean the same thing
- CSpeed is a vector and velocity is a scalar
- DVelocity has no direction
Which list contains only vector quantities?
- Adisplacement, velocity, force
- Bdistance, speed, time
- Cmass, energy, temperature
- Dspeed, distance, weight
A car moves at +8 m/s, then travels at the same speed the opposite way, written as −8 m/s. These two values describe...
- AThe same speed but opposite directions
- BThe same velocity
- CTwo different speeds
- DTwo different masses
Distance is a scalar. Its vector counterpart, which also carries a direction, is...
- Adisplacement
- Bspeed
- Cacceleration
- Dtime
Quiz key
Velocity is a vector, so it depends on direction. The direction turns every instant, so the velocity keeps changing even though the speed is fixed.
A scalar is fully described by a size and a unit alone. A vector needs a direction as well.
Force has a direction as well as a size, so it is a vector. Mass, temperature and energy are scalars.
Speed ignores direction, so it stays fixed. Velocity includes direction, which turns continuously, so the velocity changes.
Displacement, velocity and force each have a direction. The other lists each contain at least one scalar (speed, distance, mass, energy, temperature).
Speed is the size only, so both are 8 m/s. The sign shows direction, so the velocities are opposite. That sign is what matters in vector work.
Displacement is the straight-line distance in a stated direction, so it is the vector partner of distance.
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.