Math lesson plan · 6th grade (Year 7 in England) · 60 minutes
Area of parallelograms using the perpendicular height
Geometry
CCSS 6.G.A.1England: KS3 Geometry and measures
Objective and success criteria
Students will: Area of parallelograms using the perpendicular height.
- 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: Area of parallelograms and trapezoids
Leads to: Area of trapezoids (trapeziums)
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Area of parallelograms and trapezoids). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A parallelogram has base 13 m and perpendicular height 12 m. What is its area, in m²? → 156Prompt: Cut off a triangle from one end and move it to the other: it becomes a rectangle.
- A trapezoid (trapezium) has parallel sides 10 cm and 13 cm, and height 16 cm. What is its area, in cm²? → 184Prompt: Area = ½ × (a + b) × h.
- A parallelogram has base 10 m and perpendicular height 10 m. What is its area, in m²? → 100Prompt: Cut off a triangle from one end and move it to the other: it becomes a rectangle.
Hook · 6 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Area of parallelograms using the perpendicular height. 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: A parallelogram has base 4 m and perpendicular height 3 m. Find its area in m².
- Step 1: 4 × 3 = 12 m²
- Answer: 12
- 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.
- A parallelogram has base 16 cm and perpendicular height 6 cm. Find its area in cm². → 96Prompt: Cut off a triangle from one end and move it to the other: you get a rectangle.
- A parallelogram has area 32 cm² and base 8 cm. What is its perpendicular height, in cm? → 4Prompt: Area = base × height, so height = area ÷ base.
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.
- A parallelogram has area 77 cm² and base 7 cm. What is its perpendicular height, in cm? → 11Prompt: Area = base × height, so height = area ÷ base.
- A parallelogram has base 11 cm, slanted side 9 cm and perpendicular height 6 cm. Liam says the area is 99 cm². What is the correct area, in cm²? → 66Prompt: Which length did they multiply by? Is it perpendicular to the base?
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Area of parallelograms and trapezoids.
- Use concrete materials: rulers and protractors.
- 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: Area of trapezoids (trapeziums).
- 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