Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Connect ratios and fractions
Ratio and proportion
CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Connect ratios and fractions.
- 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 · 4 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 6:12. Type it like 3:2. → 1:2Prompt: Find a number that divides both parts.
- 4:1 = __:6 → 24Prompt: Equivalent ratios are made by multiplying both parts by the same number.
- Simplify the ratio 6:9. Type it like 3:2. → 2:3Prompt: Find a number that divides both parts.
Hook · 3 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Connect ratios and fractions. 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: Juice and water are mixed in the ratio 6:8. What fraction of the drink is juice? Give a fraction in simplest form.
- Step 1: 6/14 = 3/7
- Answer: 3/7
- 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.
- Juice and water are mixed in the ratio 3:9. What fraction of the drink is juice? Give a fraction in simplest form. → 1/4Prompt: The whole drink has a + b parts.
- 5/9 of a choir are sopranos and the rest are altos. What is the ratio of sopranos to altos, in simplest form? Type it like 2:3. → 5:4Prompt: If there are 9 parts, how many are sopranos?
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.
- Red and blue tiles are in the ratio 9:10. How many times as many blue tiles as red tiles are there? Give a fraction, whole or mixed number. → 10/9 (1 1/9)Prompt: Compare blue with red: blue ÷ red.
- Juice and water are mixed in the ratio 5:8. What fraction of the drink is juice? Give a fraction in simplest form. → 5/13Prompt: The whole drink has a + b 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: 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder