Math lesson plan · 6th grade (Year 7 in England) · 60 minutes
Use a ratio to find a missing quantity
Ratio and proportion
CCSS 6.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Use a ratio to find a missing quantity.
- 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: Decide whether ratios are equivalent
Leads to: the next skill in this area.
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 (Decide whether ratios are equivalent). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Are the ratios 4:7 and 24:42 equivalent? (Yes / No) → YesPrompt: What was 4 multiplied by to get 24?
- Which ratio is equivalent to 6:9? (11:14 / 30:45 / 45:30 / 30:46) → 30:45Prompt: Equivalent ratios multiply both parts by the same number.
- A juice recipe uses 2 cups of mango to 6 cups of water. Sam uses 8 cups of mango and 24 cups of water. Will it taste the same? (Yes, same ratio / No, different ratio) → Yes, same ratioPrompt: Same taste means an equivalent ratio.
Hook · 6 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Use a ratio to find a missing quantity. 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: The ratio of goals to missed shots is 4:5. There are 32 goals. How many missed shots are there?
- Step 1: One part = 32 ÷ 4 = 8
- Step 2: 5 × 8 = 40
- Answer: 40
- 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.
- The ratio of pop songs to rap songs is 2:3. There are 6 pop songs. How many rap songs are there? → 9Prompt: Each “part” is the same size. 2 parts = 6.
- In a coding club, the ratio of beginners to experienced members is 1:4. There are 20 experienced members. How many members are there altogether? → 25Prompt: 4 parts = 20. How big is one part?
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.
- The ratio of electric cars to petrol cars is 3:5. There are 12 electric cars. How many petrol cars are there? → 20Prompt: Each “part” is the same size. 3 parts = 12.
- Paint is mixed blue to yellow in the ratio 4:7. There is 6 litres more yellow than blue. How much blue is there, in litres? → 8Prompt: The difference is 7 − 4 = 3 parts.
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: Decide whether ratios are equivalent.
- 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
- 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