Math lesson plan · 8th grade (Year 9 in England) · 60 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 · 6 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.
- 4 notebooks cost $36. What is the cost of one notebook? (Type the number only.) → 9Prompt: A unit rate is the amount for ONE.
- 63.9 ÷ 9 = ? → 7.1Prompt: Divide as with whole numbers.
- Daniel travels 175 km in 5 hours at a steady speed. How far does Daniel travel in one hour? → 35Prompt: Find the distance for one hour.
Hook · 6 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 · 12 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 · 12 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 metal has density 5 g/cm³. What is the mass of 12 cm³ of it, in grams? → 60Prompt: Density = mass ÷ volume, so mass = density × volume.
- How many minutes does it take to drive 97 km at an average speed of 80 km/h? Round to the nearest minute. → 73Prompt: Time = distance ÷ speed (this gives hours).
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A train travels at 49 km/h for 2.5 hours. How far does it travel, in km? → 122.5Prompt: Distance = speed × time.
- How many minutes does it take to drive 38 km at an average speed of 120 km/h? Round to the nearest minute. → 19Prompt: 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