Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Decide if a table shows a proportional relationship
Ratio and proportion
CCSS 7.RP.A.2.AEngland: KS3 Ratio, proportion and rates of change
Objective and success criteria
Students will: Decide if a table shows a proportional relationship.
- 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: Find the constant of proportionality from a table
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: 2, 3, 10 → y: 12, 18, 60 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
- Diego can type 21 words in 3 minutes. At the same rate, how many words in 10 minutes? → 70Prompt: Find the words per minute first.
- Is this relationship proportional? x: 4, 7, 9 → y: 8, 15, 18 (Yes, proportional / No, not proportional) → No, not 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: Decide if a table shows a proportional relationship. 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: Hours worked (x): 1, 5, 7, 9. Pay (y): 6, 30, 42, 54. Is y proportional to x?
- Step 1: 6 ÷ 1 = 6, 30 ÷ 5 = 6, 42 ÷ 7 = 6, 54 ÷ 9 = 6
- Step 2: Always the same: proportional.
- Answer: Yes
- 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.
- Hours worked (x): 1, 3, 4, 11. Pay (y): 9, 27, 36, 99. Is y proportional to x? (Yes / No) → YesPrompt: Work out y ÷ x for every pair.
- Which table shows a proportional relationship? (x 1, 2, 3, 4 → y 4, 7, 10, 13 / x 1, 2, 3, 4 → y 3, 12, 27, 48 / x 1, 2, 3, 4 → y 4, 5, 6, 7 / x 1, 2, 3, 4 → y 3, 6, 9, 12) → x 1, 2, 3, 4 → y 3, 6, 9, 12Prompt: Check y ÷ x in each table.
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.
- Hours worked (x): 1, 8, 10, 11. Pay (y): 7, 21, 25, 27. 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 9, 17, 25, 33 / x 1, 2, 3, 4 → y 8, 16, 24, 32 / x 1, 2, 3, 4 → y 9, 10, 11, 12 / x 1, 2, 3, 4 → y 8, 32, 72, 128) → x 1, 2, 3, 4 → y 8, 16, 24, 32Prompt: Check y ÷ x in each table.
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: Find the constant of proportionality from a table.
- 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