Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Find the constant of proportionality from a table
Ratio and proportion
CCSS 7.RP.A.2.BEngland: KS3 Ratio, proportion and rates of change
Objective and success criteria
Students will: Find the constant of proportionality from a table.
- 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: Decide if a table shows a proportional relationship
Leads to: Find the constant of proportionality from a graph; Write equations for proportional relationships
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 (Decide if a table shows a proportional relationship). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Hours worked (x): 3, 5, 6, 7. Pay (y): 27, 43, 51, 59. Is y proportional to x? (Yes / No) → NoPrompt: Work out y ÷ x for every pair.
- Which table shows a proportional relationship? (x 1, 2, 3, 4 → y 2, 8, 18, 32 / x 1, 2, 3, 4 → y 2, 4, 6, 8 / x 1, 2, 3, 4 → y 3, 4, 5, 6 / x 1, 2, 3, 4 → y 3, 5, 7, 9) → x 1, 2, 3, 4 → y 2, 4, 6, 8Prompt: Check y ÷ x in each table.
- Hours worked (x): 1, 2, 9, 12. Pay (y): 6, 12, 54, 72. Is y proportional to x? (Yes / No) → YesPrompt: Work out y ÷ x for every pair.
Hook · 6 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Find the constant of proportionality from a table. 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: Number of tickets (x): 6, 7, 10. Cost (y): 66, 77, 110. What is the constant of proportionality k (y = kx)?
- Step 1: 66 ÷ 6 = 11
- Answer: 11
- 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.
- Number of tickets (x): 1, 3, 8. Cost (y): 9, 27, 72. What is the constant of proportionality k (y = kx)? → 9Prompt: k = y ÷ x.
- x: 4, 8, 16. y: 1, 2, 4. Find k in y = kx. Give a fraction or decimal. → 1/4Prompt: Divide any y by its 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.
- x: 2, 4, 8. y: 1, 2, 4. Find k in y = kx. Give a fraction or decimal. → 1/2Prompt: Divide any y by its x.
- Number of tickets (x): 1, 5, 10. Cost (y): 10, 50, 100. What is the constant of proportionality k (y = kx)? → 10Prompt: 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: Decide if a table shows a proportional relationship.
- 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: Find the constant of proportionality from a graph; Write equations for proportional relationships.
- 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