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Math lesson plan · 6th grade (Year 7 in England) · 60 minutes

Write part-to-part and part-to-whole ratios

Ratio and proportion

CCSS 6.RP.A.1England: Y6 Ratio and proportionEngland: KS3 Ratio, proportion and rates of change

Objective and success criteria

Students will: Write part-to-part and part-to-whole ratios.

  • 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: 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 (Understand ratios). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Simplify the ratio 6:8. Type it like 3:2. → 3:4Prompt: Find a number that divides both parts.
  2. 4:3 = 28:__ → 21Prompt: Equivalent ratios are made by multiplying both parts by the same number.
  3. Simplify the ratio 32:24. Type it like 3:2. → 4:3Prompt: 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: Write part-to-part and part-to-whole ratios. 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: A playlist has 9 pop songs, 12 rock songs and 3 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3).
  • Step 1: 9:12:3
  • Step 2: = 3:4:1
  • Answer: 3:4:1
  • 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.
  1. A playlist has 4 pop songs, 2 rock songs and 6 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3). → 2:1:3Prompt: Keep the order given: pop, then rock, then jazz.
  2. There are 7 cyclists and 5 walkers. Is the ratio 7:5 part-to-part or part-to-whole? (Part-to-part / Part-to-whole) → Part-to-partPrompt: Does the second number count one group, or everything?

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.
  1. There are 9 pop songs and 4 rap songs. Is the ratio 9:13 part-to-part or part-to-whole? (Part-to-part / Part-to-whole) → Part-to-wholePrompt: Does the second number count one group, or everything?
  2. A playlist has 3 pop songs, 3 rock songs and 5 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3). → 3:3:5Prompt: Keep the order given: pop, then rock, then jazz.

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

  • 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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Write part-to-part and part-to-whole ratios

Name

Date

Score/ 8

  1. Question 1

    There are 2 red counters and 4 blue counters. Is the ratio 2:4 part-to-part or part-to-whole?

    • A. Part-to-part
    • B. Part-to-whole

  2. Question 2

    A playlist has 2 pop songs, 4 rock songs and 6 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3).

    Answer

  3. Question 3

    There are 4 red counters and 10 blue counters. Write the ratio of red counters to all of them, in simplest form (like 2:5).

    02468104red counters10blue counters

    Answer

  4. Question 4

    There are 9 goals and 2 missed shots. Is the ratio 9:2 part-to-part or part-to-whole?

    • A. Part-to-part
    • B. Part-to-whole

  5. Question 5

    A playlist has 3 pop songs, 6 rock songs and 9 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3).

    Answer

  6. Question 6

    There are 7 sunny days and 9 rainy days. Write the ratio of sunny days to all of them, in simplest form (like 2:5).

    02468107sunny days9rainy days

    Answer

  7. Question 7

    There are 4 pop songs and 9 rap songs. Is the ratio 4:13 part-to-part or part-to-whole?

    • A. Part-to-part
    • B. Part-to-whole

  8. Question 8

    A playlist has 12 pop songs, 8 rock songs and 4 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3).

    Answer

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Answer key: Write part-to-part and part-to-whole ratios

  1. 1. A. Part-to-part

  2. 2. 1:2:3

  3. 3. 2:7

  4. 4. A. Part-to-part

  5. 5. 1:2:3

  6. 6. 7:16

  7. 7. B. Part-to-whole

  8. 8. 3:2:1