Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Proportional relationships
Ratio and proportion
CCSS 7.RP.A.2CCSS 7.RP.A.3England: KS3 RatioEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: 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: Unit rates; Ratio tables and double number lines
Leads to: Scale drawings and maps; Direct and inverse proportion; Similar shapes
Materials: Bar models, Double number lines, Ratio tables, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Unit rates; Ratio tables and double number lines). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 4 notebooks cost $20. What is the cost of one notebook? (Type the number only.) → 5Prompt: A unit rate is the amount for ONE.
- A recipe uses 2 eggs for every 8 pancakes. Complete the table: eggs 2, 4, 14; pancakes 8, 16, __ → 56Prompt: How many times 2 is 14?
- Daniel travels 64 km in 2 hours at a steady speed. How far does Daniel travel in one hour? → 32Prompt: Find the distance for one hour.
Hook · 5 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Proportional relationships. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Is this relationship proportional? x: 3, 8, 10 → y: 27, 72, 90
- Step 1: 27 ÷ 3 = 9 ; 72 ÷ 8 = 9 ; 90 ÷ 10 = 9
- Step 2: Always 9: proportional.
- Answer: Yes, proportional
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Is this relationship proportional? x: 3, 4, 7 → y: 24, 32, 56 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
- Mateo can type 48 words in 8 minutes. At the same rate, how many words in 15 minutes? → 90Prompt: Find the words per minute first.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Is this relationship proportional? x: 3, 5, 10 → y: 21, 35, 70 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
- Arjun can type 16 words in 4 minutes. At the same rate, how many words in 9 minutes? → 36Prompt: Find the words per minute first.
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: Unit rates.
- 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: Scale drawings and maps; Direct and inverse proportion; Similar shapes.
- 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