Math lesson plan · 6th grade (Year 7 in England) · 30 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 · 4 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 3:9. Type it like 3:2. → 1:3Prompt: Find a number that divides both parts.
- 5:3 = 15:__ → 9Prompt: Equivalent ratios are made by multiplying both parts by the same number.
- Simplify the ratio 10:2. Type it like 3:2. → 5:1Prompt: Find a number that divides both parts.
Hook · 3 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 · 7 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 · 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.
- Are the ratios 8:9 and 32:36 equivalent? (Yes / No) → YesPrompt: What was 8 multiplied by to get 32?
- Which ratio is equivalent to 2:3? (4:6 / 4:7 / 6:4 / 4:5) → 4:6Prompt: Equivalent ratios multiply both parts by the same number.
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.
- A juice recipe uses 3 cups of mango to 6 cups of water. Grace uses 6 cups of mango and 9 cups of water. Will it taste the same? (Yes, same ratio / No, different ratio) → No, different ratioPrompt: Same taste means an equivalent ratio.
- Which ratio is equivalent to 1:9? (45:5 / 5:14 / 5:45 / 6:14) → 5:45Prompt: Equivalent ratios multiply both parts by the same number.
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