Math lesson plan · 6th grade (Year 7 in England) · 45 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 · 5 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 9:18. Type it like 3:2. → 1:2Prompt: Find a number that divides both parts.
- 3:1 = 15:__ → 5Prompt: Equivalent ratios are made by multiplying both parts by the same number.
- Simplify the ratio 10:5. Type it like 3:2. → 2:1Prompt: Find a number that divides both parts.
Hook · 5 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 · 10 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 · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A playlist has 1 pop songs, 3 rock songs and 5 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3). → 1:3:5Prompt: Keep the order given: pop, then rock, then jazz.
- There are 8 red counters and 2 blue counters. Is the ratio 8:10 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?
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- There are 3 cyclists and 9 walkers. Is the ratio 3:9 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?
- A playlist has 8 pop songs, 6 rock songs and 4 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3). → 4:3:2Prompt: 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