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Math lesson plan · 6th grade (Year 7 in England) · 30 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 · 4 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.
  1. Are the ratios 4:6 and 24:37 equivalent? (Yes / No) → NoPrompt: What was 4 multiplied by to get 24?
  2. Which ratio is equivalent to 1:3? (6:2 / 2:7 / 3:5 / 2:6) → 2:6Prompt: Equivalent ratios multiply both parts by the same number.
  3. A juice recipe uses 1 cups of mango to 2 cups of water. Hiro uses 4 cups of mango and 5 cups of water. Will it taste the same? (Yes, same ratio / No, different ratio) → No, different ratioPrompt: Same taste means an equivalent ratio.

Hook · 3 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 · 7 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 · 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.
  1. The ratio of electric cars to petrol cars is 1:2. There are 3 electric cars. How many petrol cars are there? → 6Prompt: Each “part” is the same size. 1 parts = 3.
  2. In a coding club, the ratio of beginners to experienced members is 1:6. There are 48 experienced members. How many members are there altogether? → 56Prompt: 6 parts = 48. How big is one part?

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.
  1. Paint is mixed blue to yellow in the ratio 2:9. There is 28 litres more yellow than blue. How much blue is there, in litres? → 8Prompt: The difference is 9 − 2 = 7 parts.
  2. In a coding club, the ratio of beginners to experienced members is 6:2. There are 12 experienced members. How many members are there altogether? → 48Prompt: 2 parts = 12. How big is one part?

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

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Use a ratio to find a missing quantity

Name

Date

Score/ 6

  1. Question 1

    Paint is mixed blue to yellow in the ratio 4:9. There is 25 litres more yellow than blue. How much blue is there, in litres?

    Answer

  2. Question 2

    The ratio of electric cars to petrol cars is 5:2. There are 20 electric cars. How many petrol cars are there?

    Answer

  3. Question 3

    In a coding club, the ratio of beginners to experienced members is 6:1. There are 3 experienced members. How many members are there altogether?

    Answer

  4. Question 4

    Paint is mixed blue to yellow in the ratio 3:4. There is 7 litres more yellow than blue. How much blue is there, in litres?

    Answer

  5. Question 5

    The ratio of red counters to blue counters is 2:6. There are 12 red counters. How many blue counters are there?

    Answer

  6. Question 6

    In a coding club, the ratio of beginners to experienced members is 4:3. There are 18 experienced members. How many members are there altogether?

    Answer

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Answer key: Use a ratio to find a missing quantity

  1. 1. 20

  2. 2. 8

  3. 3. 21

  4. 4. 21

  5. 5. 36

  6. 6. 42