Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Direct and inverse proportion
Ratio and proportion
CCSS 7.RP.A.2CCSS HSA.CED.A.2England: GCSE Foundation RatioEngland: GCSE Higher Ratio
Objective and success criteria
Students will: Direct and inverse proportion.
- 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: Proportional relationships
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 · 4 min
- Quick retrieval from earlier learning (Proportional relationships). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Is this relationship proportional? x: 1, 6, 10 → y: 4, 25, 40 (Yes, proportional / No, not proportional) → No, not proportionalPrompt: Find y ÷ x for each pair.
- Kofi can type 32 words in 8 minutes. At the same rate, how many words in 13 minutes? → 52Prompt: Find the words per minute first.
- Is this relationship proportional? x: 3, 4, 9 → y: 6, 8, 18 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
Hook · 3 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Direct and inverse proportion. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: 3 painters take 6 days to paint a school. How many days would 6 painters take, working at the same rate?
- Step 1: 3 × 6 = 18
- Step 2: 18 ÷ 6 = 3
- Answer: 3
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- 7 painters take 11 days to paint a school. How many days would 14 painters take, working at the same rate? → 5.5Prompt: More painters means fewer days: this is inverse proportion.
- y is inversely proportional to x. When x = 1, y = 24. Find y when x = 3. → 8Prompt: Inverse proportion: y = k ÷ x, so x × y stays the same.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- 4 painters take 7 days to paint a school. How many days would 2 painters take, working at the same rate? → 14Prompt: More painters means fewer days: this is inverse proportion.
- y is inversely proportional to x. When x = 2, y = 12. Find y when x = 6. → 4Prompt: Inverse proportion: y = k ÷ x, so x × y stays the same.
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: Proportional relationships.
- 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