Math lesson plan · 6th grade (Year 7 in England) · 60 minutes
Decide whether ratios are equivalent
Ratio and proportion
CCSS 6.RP.A.3.AEngland: KS3 Ratio, proportion and rates of change
Objective and success criteria
Students will: Decide whether ratios are equivalent.
- 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: Understand ratios
Leads to: Use a ratio to find a missing quantity
Materials: Bar models, Double number lines, Ratio tables, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Understand ratios). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify the ratio 18:27. Type it like 3:2. → 2:3Prompt: Find a number that divides both parts.
- 4:5 = 24:__ → 30Prompt: Equivalent ratios are made by multiplying both parts by the same number.
- Simplify the ratio 16:40. Type it like 3:2. → 2:5Prompt: Find a number that divides both parts.
Hook · 6 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Decide whether ratios are equivalent. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Are the ratios 1:3 and 5:14 equivalent?
- Step 1: 1 × 5 = 5
- Step 2: 3 × 5 = 15
- Step 3: 15 ≠14, so they are not equivalent.
- Answer: No
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Are the ratios 7:2 and 42:14 equivalent? (Yes / No) → NoPrompt: What was 7 multiplied by to get 42?
- Which ratio is equivalent to 4:7? (16:29 / 16:11 / 28:16 / 16:28) → 16:28Prompt: Equivalent ratios multiply both parts by the same number.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A juice recipe uses 2 cups of mango to 4 cups of water. Leo uses 8 cups of mango and 16 cups of water. Will it taste the same? (Yes, same ratio / No, different ratio) → Yes, same ratioPrompt: Same taste means an equivalent ratio.
- Are the ratios 2:5 and 12:32 equivalent? (Yes / No) → NoPrompt: What was 2 multiplied by to get 12?
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: Understand ratios.
- 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: Use a ratio to find a missing quantity.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder