Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Unit rates with fractions (complex fractions)
Ratio and proportion
CCSS 7.RP.A.1England: KS3 Ratio, proportion and rates of change
Objective and success criteria
Students will: Unit rates with fractions (complex 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: Unit rates; Divide fractions by fractions
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 (Unit rates; Divide fractions by fractions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 5 notebooks cost $75. What is the cost of one notebook? (Type the number only.) → 15Prompt: A unit rate is the amount for ONE.
- 1/4 ÷ 1/2 = ? Give your answer in simplest form. → 1/2Prompt: Dividing by a fraction is the same as multiplying by its reciprocal.
- Mateo travels 55 miles in 5 hours at a steady speed. How far does Mateo travel in one hour? → 11Prompt: Find the distance for one hour.
Hook · 5 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Unit rates with fractions (complex fractions). 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: Felix walks 3/2 mile in 1/6 hour. What is Felix's speed in miles per hour? Give a whole number, fraction or mixed number.
- Step 1: 3/2 Ă· 1/6 = 3/2 Ă— 6/1 = 18/2
- Step 2: = 9 mph
- Answer: 9
- 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 walks 5/4 mile in 1/4 hour. What is Fatima's speed in miles per hour? Give a whole number, fraction or mixed number. → 5Prompt: Speed = distance ÷ time.
- 5/6 litre of paint covers 3/4 m² of wall. How many litres are needed per square metre? → 10/9 (1 1/9)Prompt: “Per square metre” means divide by the area.
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.
- Grace walks 1/2 mile in 3/4 hour. What is Grace's speed in miles per hour? Give a whole number, fraction or mixed number. → 2/3Prompt: Speed = distance ÷ time.
- A recipe uses 3/4 cup of oats for 2/3 of a batch. How many cups of oats are needed for a whole batch? → 9/8 (1 1/8)Prompt: Find the amount for 1 whole batch: divide by the fraction of the batch.
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: Unit rates.
- 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