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.
- 5 notebooks cost $65. What is the cost of one notebook? (Type the number only.) → 13Prompt: A unit rate is the amount for ONE.
- A recipe uses 4 eggs for every 9 pancakes. Complete the table: eggs 4, 8, 20; pancakes 9, 18, __ → 45Prompt: How many times 4 is 20?
- Arjun travels 232 miles in 4 hours at a steady speed. How far does Arjun travel in one hour? → 58Prompt: 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: 4, 7, 10 → y: 24, 42, 60 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
- Ines can type 28 words in 4 minutes. At the same rate, how many words in 11 minutes? → 77Prompt: 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, 4, 5 → y: 9, 13, 15 (Yes, proportional / No, not proportional) → No, not proportionalPrompt: Find y ÷ x for each pair.
- Ana can type 35 words in 7 minutes. At the same rate, how many words in 15 minutes? → 75Prompt: 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