Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Use a scale to find real lengths
Ratio and proportion
CCSS 7.G.A.1England: KS3 Ratio, proportion and rates of changeEngland: KS3 Geometry and measures
Objective and success criteria
Students will: Use a scale to find real lengths.
- 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: Scale drawings and maps
Leads to: Find drawing lengths and the scale of a drawing
Materials: Bar models, Double number lines, Ratio tables, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Scale drawings and maps). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- On a map, 1 cm represents 20 km. Two towns are 4 cm apart on the map. How far apart are they really, in km? → 80Prompt: Each centimetre on the map stands for the same real distance.
- A plan has scale 1:500. A wall is 15 m long in real life. How long is it on the plan, in cm? → 3Prompt: Change metres to centimetres first.
- On a map, 1 cm represents 50 km. Two towns are 3 cm apart on the map. How far apart are they really, in km? → 150Prompt: Each centimetre on the map stands for the same real distance.
Hook · 6 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Use a scale to find real lengths. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: On a map, 1 cm represents 20 km. Two towns are 15.5 cm apart on the map. How far apart are they really, in km?
- Step 1: 15.5 × 20 = 310 km
- Answer: 310
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- On a map, 1 cm represents 50 km. Two towns are 9 cm apart on the map. How far apart are they really, in km? → 450Prompt: Every 1 cm on the map is 50 km in real life.
- A floor plan uses a scale of 1 : 25. A wall is 19 cm long on the plan. How long is the real wall, in metres? → 4.75Prompt: Multiply the plan length by 25 (same units).
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- On a map, 1 cm represents 10 km. Two towns are 9 cm apart on the map. How far apart are they really, in km? → 90Prompt: Every 1 cm on the map is 10 km in real life.
- A hiking map has scale 1 : 50 000. A trail measures 13 cm on the map. How long is the trail, in km? → 6.5Prompt: 1 cm on the map is 50 000 cm in real life.
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: Scale drawings and maps.
- 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
- Move on to: Find drawing lengths and the scale of a drawing.
- 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