Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Write equations for proportional relationships
Ratio and proportion
CCSS 7.RP.A.2.CEngland: KS3 Ratio, proportion and rates of changeEngland: KS3 Algebra
Objective and success criteria
Students will: Write equations for proportional relationships.
- 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: Find the constant of proportionality from a table
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 (Find the constant of proportionality from a table). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Number of tickets (x): 1, 2, 9. Cost (y): 12, 24, 108. What is the constant of proportionality k (y = kx)? → 12Prompt: k = y ÷ x.
- x: 2, 4, 8. y: 5, 10, 20. Find k in y = kx. Give a fraction or decimal. → 5/2 (2 1/2)Prompt: Divide any y by its x.
- Minutes of video (x): 10, 20, 30. Data used in MB (y): 120, 240, 360. How many MB are used per minute? → 12Prompt: MB per minute = y ÷ x.
Hook · 6 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Write equations for proportional relationships. 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: Each streaming song earns 13 points. Write an equation for y in terms of s. Type only the right-hand side (y = …).
- Step 1: y = 13s
- Answer: 13s
- 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.
- Each bus ticket costs $8. Write an equation for y in terms of t. Type only the right-hand side (y = …). → 8tPrompt: A proportional relationship has the form y = k × (the variable).
- y is proportional to x, and y = 15 when x = 6. Write y in terms of x. Type the right-hand side only. → 5x/2Prompt: Find k = y ÷ x.
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 car uses fuel in proportion to distance: f = 0.06d (litres per km). How many litres for 90 km? → 5.4Prompt: Substitute the distance for d.
- y is proportional to x, and y = 9 when x = 6. Write y in terms of x. Type the right-hand side only. → 3x/2Prompt: Find k = y ÷ x.
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: Find the constant of proportionality from a table.
- 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