Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Find the constant of proportionality from a graph
Ratio and proportion
CCSS 7.RP.A.2.BCCSS 7.RP.A.2.DEngland: KS3 Ratio, proportion and rates of change
Objective and success criteria
Students will: Find the constant of proportionality from a graph.
- 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; Coordinates in the first quadrant
Leads to: Decide if a graph shows a proportional relationship
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 table; Coordinates in the first quadrant). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Number of tickets (x): 2, 5, 6. Cost (y): 12, 30, 36. What is the constant of proportionality k (y = kx)? → 6Prompt: k = y ÷ x.
- x: 4, 8, 16. y: 3, 6, 12. Find k in y = kx. Give a fraction or decimal. → 3/4Prompt: Divide any y by its x.
- Number of tickets (x): 1, 4, 6. Cost (y): 3, 12, 18. What is the constant of proportionality k (y = kx)? → 3Prompt: k = y ÷ x.
Hook · 3 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 graph. 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.
- Model one question from the student sheet, thinking aloud.
- 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.
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.
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
- Move on to: Decide if a graph shows a proportional relationship.
- 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