Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Solve proportions
Ratio and proportion
CCSS 7.RP.A.2CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Solve proportions.
- 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: Solve real-world proportion problems
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: 3, 4, 6 → y: 18, 25, 36 (Yes, proportional / No, not proportional) → No, not proportionalPrompt: Find y ÷ x for each pair.
- Ravi can type 16 words in 4 minutes. At the same rate, how many words in 5 minutes? → 20Prompt: Find the words per minute first.
- Is this relationship proportional? x: 8, 9, 10 → y: 24, 27, 30 (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: Solve proportions. 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: Solve: x / 9 = 4 / 3
- Step 1: 3 × 3 = 9
- Step 2: x = 4 × 3 = 12
- Answer: x = 12
- 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.
- Solve: x / 30 = 5 / 5 → x = 30Prompt: What is 5 multiplied by to get 30?
- Solve: 11 / 5 = 154 / y → y = 70Prompt: Cross-multiply: a × y = b × (the other numerator).
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.
- Solve: 4 / 7 = 16 / n → n = 28Prompt: Compare the numerators: how many times bigger?
- Solve: x / 4 = 8 / 2 → x = 16Prompt: What is 2 multiplied by to get 4?
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
- Move on to: Solve real-world proportion problems.
- 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