Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Decide if a graph 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 graph 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: Find the constant of proportionality from a graph
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 · 4 min
- Quick retrieval from earlier learning (Find the constant of proportionality from a graph). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
Hook · 3 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Decide if a graph 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: Which situation gives a proportional relationship between cost and amount?
- Step 1: Only the apples have no fixed fee, so cost = rate × amount.
- Answer: Apples: $6 per kg, nothing else
- 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.
- Which situation gives a proportional relationship between cost and amount? (Taxi: $3 to get in, then $6 per km / Apples: $6 per kg, nothing else / Gym: $20 joining fee plus $6 per visit / Phone: $10 a month plus $0.60 per text) → Apples: $6 per kg, nothing elsePrompt: Proportional means: 0 of the thing costs 0.
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.
- Which situation gives a proportional relationship between cost and amount? (Phone: $10 a month plus $0.40 per text / Apples: $4 per kg, nothing else / Gym: $20 joining fee plus $4 per visit / Taxi: $3 to get in, then $4 per km) → Apples: $4 per kg, nothing elsePrompt: Proportional means: 0 of the thing costs 0.
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 graph.
- 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