Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Speed, density and other rates
Ratio and proportion
CCSS 7.RP.A.1CCSS HSN.Q.A.1England: KS3 RatioEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Speed, density and other rates.
- 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: Unit rates; Divide decimals
Leads to: the next skill in this area.
Materials: Bar models, Double number lines, Ratio tables, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Unit rates; Divide decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 9 notebooks cost $126. What is the cost of one notebook? (Type the number only.) → 14Prompt: A unit rate is the amount for ONE.
- 67.2 ÷ 8 = ? → 8.4Prompt: Divide as with whole numbers.
- Fatima travels 63 km in 3 hours at a steady speed. How far does Fatima travel in one hour? → 21Prompt: Find the distance for one hour.
Hook · 5 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Speed, density and other rates. 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: A train travels at 50 km/h for 1.5 hours. How far does it travel, in km?
- Step 1: 50 × 1.5 = 75 km
- Answer: 75
- 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.
- A train travels at 26 km/h for 2.5 hours. How far does it travel, in km? → 65Prompt: Distance = speed × time.
- How many minutes does it take to drive 120 km at an average speed of 120 km/h? Round to the nearest minute. → 60Prompt: Time = distance ÷ speed (this gives hours).
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.
- A cyclist covers 60 km in 2 hours. What is the average speed in km/h? → 30Prompt: Speed = distance ÷ time.
- How many minutes does it take to drive 208 km at an average speed of 48 km/h? Round to the nearest minute. → 260Prompt: Time = distance ÷ speed (this gives hours).
Watch out for
- Adding the same amount to both parts instead of multiplying.
- Mixing up part-to-part and part-to-whole ratios.
Support and stretch
Support
- Review first: Unit rates.
- Use concrete materials: bar models.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- 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/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder