Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Solve constant-rate problems: speed, work and data
Ratio and proportion
CCSS 6.RP.A.3.BEngland: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Solve constant-rate problems: speed, work and data.
- 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
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 7 notebooks cost $105. What is the cost of one notebook? (Type the number only.) → 15Prompt: A unit rate is the amount for ONE.
- Hana travels 134 miles in 2 hours at a steady speed. How far does Hana travel in one hour? → 67Prompt: Find the distance for one hour.
- Pack A: 6 juice boxes for $12. Pack B: 8 juice boxes for $56. Which is better value? (Pack A / Pack B / They are the same value) → Pack APrompt: Find the price of ONE juice box in each pack.
Hook · 5 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Solve constant-rate problems: speed, work and data. 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: Isla cycles 46 km in 2 hours at a steady speed. How far will Isla cycle in 7 hours at the same speed, in km?
- Step 1: 46 ÷ 2 = 23 km/h
- Step 2: 23 × 7 = 161 km
- Answer: 161
- 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.
- Sofia cycles 40 km in 4 hours at a steady speed. How far will Sofia cycle in 6 hours at the same speed, in km? → 60Prompt: Find the distance in 1 hour (the speed).
- A student types 132 words in 4 minutes. At this rate, how many minutes will it take to type 198 words? → 6Prompt: Find the words per minute first.
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.
- A student types 152 words in 4 minutes. At this rate, how many minutes will it take to type 342 words? → 9Prompt: Find the words per minute first.
- Sam cycles 72 km in 3 hours at a steady speed. How far will Sam cycle in 7 hours at the same speed, in km? → 168Prompt: Find the distance in 1 hour (the speed).
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-6.
Free lesson plan from eurekami.com/lesson-plan-builder