Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Areas in scale drawings
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: Areas in scale drawings.
- 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: Find drawing lengths and the scale of a drawing; Area of rectangles
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 (Find drawing lengths and the scale of a drawing; Area of rectangles). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A model uses 1 cm for every 10 m. A real bridge is 110 m long. How long is it on the model, in cm? → 11Prompt: Real → model: divide.
- A 5.5 m long room is drawn 11 cm long on a plan. The scale is 1 : n. What is n? → 50Prompt: Write both lengths in the same units (cm).
- A model uses 1 cm for every 4 m. A real bridge is 24 m long. How long is it on the model, in cm? → 6Prompt: Real → model: divide.
Hook · 3 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Areas in scale drawings. 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: A rectangle on a plan is 8 cm by 3 cm. The scale is 1 cm : 2 m. What is the real area, in m²?
- Step 1: 8 × 2 = 16 m, 3 × 2 = 6 m
- Step 2: 16 × 6 = 96 m²
- Answer: 96
- 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.
- A rectangle on a plan is 4 cm by 6 cm. The scale is 1 cm : 10 m. What is the real area, in m²? → 2400Prompt: Change each length to real metres first.
- Leo enlarges a scale drawing so every length is 4 times as long. Leo thinks the area will be 4 times as big. How many times as big is the area really? → 16Prompt: Area uses two lengths multiplied together.
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.
- Hana enlarges a scale drawing so every length is 2 times as long. Hana thinks the area will be 2 times as big. How many times as big is the area really? → 4Prompt: Area uses two lengths multiplied together.
- A rectangle on a plan is 6 cm by 7 cm. The scale is 1 cm : 3 m. What is the real area, in m²? → 378Prompt: Change each length to real metres first.
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: Find drawing lengths and the scale of a drawing.
- 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