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Science lesson plan · 8th grade (Year 9 in England) · 45 minutes

Scalars and vectors: distance vs displacement, speed vs velocity

Forces and motion

CCSS NGSS.HS-PS2-1England: GCSE Combined Science: Forces (scalar and vector quantities)

Objective and success criteria

Students will: Scalars and vectors: distance vs displacement, speed vs velocity.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Speed = distance ÷ time

Leads to: Momentum (p = m v); Orbits and orbital speed (v = 2Ï€r / T)

Materials: Force meters, Toy cars and ramps, Mini whiteboards, A diagram or short video clip of the idea, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Speed = distance ÷ time). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A toy train travels 120 m in 10 s. What is the average speed, in m/s? → 12 m/sPrompt: speed = distance ÷ time
  2. A car travels at an average speed of 90 km/h for 2.5 hours. How far does it travel, in km? → 225 kmPrompt: distance = speed × time
  3. A remote-control car moves at 8 m/s. How long does it take to travel 160 m, in seconds? → 20 sPrompt: time = distance ÷ speed

Hook · 5 min

  • Drop a sheet of paper and a scrunched-up sheet together and ask why one falls faster.
  • Share the objective: Scalars and vectors: distance vs displacement, speed vs velocity. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Is distance a scalar or a vector quantity?
  • Step 1: Scalars have size (magnitude) only.
  • Step 2: So the answer is: scalar (size only)
  • Answer: scalar (size only)
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Is momentum a scalar or a vector quantity? (scalar (size only) / vector (size and direction)) → vector (size and direction)Prompt: Does it make sense to give it a direction?
  2. A dog runs 30 m east, then 70 m west. What total distance does it run, in m? → 100 mPrompt: Distance is the total path length; it ignores direction.

You do: independent practice · 10 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. A ball is thrown up at 10 m/s and later falls back past the same point at 10 m/s. Has its velocity changed? (Yes: the speed is the same but the direction is reversed / No: velocity is a scalar / Yes: the ball is heavier on the way down / No: the speed is the same) → Yes: the speed is the same but the direction is reversedPrompt: Velocity includes direction.
  2. Is time a scalar or a vector quantity? (scalar (size only) / vector (size and direction)) → scalar (size only)Prompt: Does it make sense to give it a direction?

Watch out for

  • Everyday meanings of words getting in the way of the science meaning: define key words explicitly.
  • Remembering facts without the reason: ask "why?" and "what is the evidence?"

Support and stretch

Support

  • Review first: Speed = distance ÷ time.
  • Use concrete materials: force meters.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Momentum (p = m v); Orbits and orbital speed (v = 2Ï€r / T).
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/science/grade-8.

Free lesson plan from eurekami.com/lesson-plan-builder

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Scalars and vectors: distance vs displacement, speed vs velocity

Name

Date

Score/ 8

  1. Question 1

    Is acceleration a scalar or a vector quantity?

    • A. scalar (size only)
    • B. vector (size and direction)

  2. Question 2

    A dog runs 50 m east, then 70 m west. What total distance does it run, in m?

    Answerm

  3. Question 3

    A ball is thrown up at 10 m/s and later falls back past the same point at 10 m/s. Has its velocity changed?

    • A. Yes: the speed is the same but the direction is reversed
    • B. No: velocity is a scalar
    • C. Yes: the ball is heavier on the way down
    • D. No: the speed is the same

  4. Question 4

    A dog runs 40 m east, then 20 m west. What total distance does it run, in m?

    Answerm

  5. Question 5

    A runner completes one full lap of a 400 m track. What is their displacement?

    • A. 0 m
    • B. 400 m
    • C. 200 m
    • D. 800 m

  6. Question 6

    Is mass a scalar or a vector quantity?

    • A. scalar (size only)
    • B. vector (size and direction)

  7. Question 7

    A dog runs 30 m east, then 50 m west. What is the size of its displacement from the start, in m?

    Answerm

  8. Question 8

    A car drives round a roundabout at a steady 20 km/h. Is its velocity constant?

    • A. Yes: velocity has no direction
    • B. Yes: the speed is constant
    • C. No: its speed keeps changing
    • D. No: its direction keeps changing, so its velocity changes

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Answer key: Scalars and vectors: distance vs displacement, speed vs velocity

  1. 1. B. vector (size and direction)

  2. 2. 120 m

  3. 3. A. Yes: the speed is the same but the direction is reversed

  4. 4. 60 m

  5. 5. A. 0 m

  6. 6. A. scalar (size only)

  7. 7. 20 m

  8. 8. D. No: its direction keeps changing, so its velocity changes