Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Share an amount in a ratio with three parts
Ratio and proportion
CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Share an amount in a ratio with three parts.
- 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: Share in a given ratio
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 (Share in a given ratio). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Ben and Ravi share $21 in the ratio 5:2. How much does Ben get? (Type the number only.) → 15Prompt: How many parts are there altogether?
- The ratio of adults to children at a show is 5:3. There are 20 more adults than children. How many people are there in total? → 80Prompt: The difference in parts is 2.
- Jamal and Amara share $25 in the ratio 2:3. How much does Amara get? (Type the number only.) → 15Prompt: How many parts are there altogether?
Hook · 5 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Share an amount in a ratio with three parts. 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: Omar, Ana, Grace share $125 in the ratio 1:3:1. How much does Grace get? (Type the number only.)
- Step 1: 1 + 3 + 1 = 5
- Step 2: 125 ÷ 5 = 25
- Step 3: 1 × 25 = 25
- Answer: 25
- 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.
- Fatima, Zara, Sofia share $80 in the ratio 4:1:3. How much does Fatima get? (Type the number only.) → 40Prompt: Total parts = 4 + 1 + 3.
- Concrete is made from cement, sand and gravel in the ratio 3:4:1. A builder uses 40 kg of sand. How many kg of concrete mix is that altogether? → 80Prompt: 4 parts of sand = 40 kg. Find one part.
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.
- Votes for three games were in the ratio 1:2:6. The most popular game got 60 more votes than the first game. How many votes were there in total? → 108Prompt: The difference is 6 − 1 = 5 parts.
- Concrete is made from cement, sand and gravel in the ratio 2:3:5. A builder uses 36 kg of sand. How many kg of concrete mix is that altogether? → 120Prompt: 3 parts of sand = 36 kg. Find 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: Share in a given ratio.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder