Math lesson plan · 6th grade (Year 7 in England) · 30 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 · 4 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.
- 4 notebooks cost $24. What is the cost of one notebook? (Type the number only.) → 6Prompt: A unit rate is the amount for ONE.
- Mateo travels 168 miles in 3 hours at a steady speed. How far does Mateo travel in one hour? → 56Prompt: Find the distance for one hour.
- Pack A: 4 juice boxes for $16. Pack B: 6 juice boxes for $42. 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 · 3 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 · 7 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 · 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.
- Kai cycles 92 km in 4 hours at a steady speed. How far will Kai cycle in 7 hours at the same speed, in km? → 161Prompt: Find the distance in 1 hour (the speed).
- A student types 230 words in 5 minutes. At this rate, how many minutes will it take to type 460 words? → 10Prompt: Find the words per minute first.
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.
- A student types 116 words in 4 minutes. At this rate, how many minutes will it take to type 116 words? → 4Prompt: Find the words per minute first.
- Ben cycles 16 km in 2 hours at a steady speed. How far will Ben cycle in 9 hours at the same speed, in km? → 72Prompt: 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