Math lesson plan · 5th grade (Year 6 in England) · 60 minutes
Angles in a quadrilateral add to 360°
Geometry
CCSS 5.G.B.3England: Y6 Geometry
Objective and success criteria
Students will: Angles in a quadrilateral add to 360°.
- 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: Classify triangles; angles in a triangle; Missing angles on a straight line and around a point
Leads to: Interior angles of regular polygons
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 (Classify triangles; angles in a triangle; Missing angles on a straight line and around a point). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Four angles meet at a point: 114°, 66°, 102° and x. Find x. → 78Prompt: Angles around a point add up to 360°.
- A triangle has one angle of 90°. What type of triangle is it? (equilateral / scalene / right-angled / isosceles) → right-angledPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
- Four angles meet at a point: 112°, 84°, 71° and x. Find x. → 93Prompt: Angles around a point add up to 360°.
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: Angles in a quadrilateral add to 360°. 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 quadrilateral has angles of 70°, 75°, 67° and x. Find x.
- Step 1: 360 − 70 − 75 − 67 = 148
- Step 2: x = 148°
- Answer: 148
- 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 quadrilateral has angles of 123°, 107°, 63° and x. Find x. → 67Prompt: A quadrilateral can be split into two triangles.
- A parallelogram has one angle of 85°. Opposite angles are equal. What is the size of each of the other two angles? → 95Prompt: Two angles are 85°. The other two are equal to each other.
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 one angle of 78°. Opposite angles are equal. What is the size of each of the other two angles? → 102Prompt: Two angles are 78°. The other two are equal to each other.
- A quadrilateral has angles of 88°, 76°, 115° and x. Find x. → 81Prompt: A quadrilateral can be split into two triangles.
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: Classify triangles; angles in a triangle.
- 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: Interior angles of regular polygons.
- 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-5.
Free lesson plan from eurekami.com/lesson-plan-builder