Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Solve real-world proportion problems
Ratio and proportion
CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Solve real-world proportion problems.
- 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: Solve proportions
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 (Solve proportions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x / 60 = 4 / 10 → x = 24Prompt: What is 10 multiplied by to get 60?
- Solve: 4 / 9 = 76 / y → y = 171Prompt: Cross-multiply: a × y = b × (the other numerator).
- Solve: 6 / 2 = 54 / n → n = 18Prompt: Compare the numerators: how many times bigger?
Hook · 5 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Solve real-world proportion problems. 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 pancake recipe for 4 people uses 360 g of flour. How much flour is needed for 9 people, in grams?
- Step 1: 360 ÷ 4 = 90 g
- Step 2: 90 × 9 = 810 g
- Answer: 810
- 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 pancake recipe for 6 people uses 150 g of flour. How much flour is needed for 5 people, in grams? → 125Prompt: Find the flour for 1 person first.
- On a school trip, 1 euro buys 0.8 Swiss francs. How many francs do you get for 120 euros? → 96Prompt: Francs = euros × rate.
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 pancake recipe for 4 people uses 200 g of flour. How much flour is needed for 3 people, in grams? → 150Prompt: Find the flour for 1 person first.
- A swimmer completes 8 lengths in 32 minutes. At the same pace, how many minutes for 40 lengths? → 160Prompt: Set up a proportion: lengths/minutes.
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: Solve proportions.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder