You will learn
- Name polygons.
- Tell regular from irregular.
- Count sides and vertices.
- Find the interior angle sum.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- A polygon is a closed shape with straight sides.
- Regular means equal sides and equal angles.
- Angle sum = (sides − 2) × 180°.
- Divide the sum by the sides for a regular polygon.
Words to know
Closed shape with straight sides.
All sides and angles equal.
Corner.
Angle inside.
1. Discover: many sides
A stop sign has 8 sides. What is it called and what are its angles?
2. Understand: polygons
- Pentagon 5, hexagon 6, heptagon 7, octagon 8, decagon 10 sides.
- Interior angle sum = (n − 2) × 180°: hexagon (6 − 2) × 180 = 720°.
- A regular hexagon has each angle 720 ÷ 6 = 120°.
- A regular octagon has each angle (6 × 180) ÷ 8 = 135°.
Idea 1: Names
An octagon has 8 sides and a pentagon has 5. A hexagon has 6.
Idea 2: Angle sum
Pentagon: (5 − 2) × 180 = 3 × 180 = 540°.
Idea 3: Regular
Regular octagon: (8 − 2) × 180 = 1080, ÷ 8 = 135°. Regular hexagon: 720 ÷ 6 = 120°.
Why n − 2? A polygon splits into n − 2 triangles.
3. Worked examples
Example 1 (I show you): Sides
Octagon
- Oct means eight.
Answer: 8
Example 2 (We do it together): Angle sum
Pentagon
- 3 triangles.
- 3 × 180.
Answer: 540°
Example 3 (You try): Each angle
Regular octagon
Show the steps and answer
- 1080 ÷ 8.
Answer: 135°
Did you know?
The angles of any polygon always add to a multiple of 180°.
Why this matters
Polygons are used in tiles, signs and honeycombs.
4. Explore: sum
You need paper.
- Count sides.
- Subtract 2.
- Multiply by 180.
- Divide by n if regular.
Think about it: what did you notice?
720°.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The polygon has ___ sides.
- It splits into ___ triangles.
- The angle sum is ___.
- Each angle is ___ ÷ ___ = ___.
Guided practice
Question 1. Sides of a hexagon?
6.
Question 2. Angle sum of a hexagon?
720°.
Question 3. Each angle of a regular hexagon?
120°.
Independent practice
Level 1: Start
- Sides of an octagon
- Sides of a pentagon
- Angle sum of a pentagon
- Each angle of a regular octagon
- Is a regular polygon equal in sides and angles?
Level 2: Grow
- Sides of a hexagon
- Angle sum of a hexagon
- Each angle of a square
Level 3: Stretch
- Each angle of a regular pentagon
- Angle sum of a heptagon
- Ben says regular polygons only need equal sides. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A stop sign is a regular octagon. Each angle?
Show a sample answer
135°.
Another one. A stop sign is a regular octagon. What is each interior angle?
Show a sample answer
135°
7. Common mistakes
Fix: Use (n − 2) × 180.
Fix: Use (n − 2) × 180°.
Fix: Angles must be equal too.
8. Lesson summary and revision card
- I can name polygons.
- I can tell regular from irregular.
- I can count sides and vertices.
- I can find the interior angle sum.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Names come from side counts.
- Angle sum (n − 2) × 180°.
- Regular means all equal.
11. Next lesson
Next lesson: Coordinate plane. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- How many sides does an octagon have? [1 mark]
- How many sides does a pentagon have? [1 mark]
- Find the angle sum of a pentagon. [3 marks]
- Find each angle of a regular octagon. [3 marks]
- Ali says a polygon with equal sides is always regular. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 8 [1]
- 5 [1]
- (5 − 2) = 3 triangles [1]; 3 × 180 [1]; 540° [1]
- Angle sum 6 × 180 = 1080° [1]; 1080 ÷ 8 [1]; 135° [1]
- No [1]. Regular means equal sides and equal angles [1]. Some shapes with equal sides have unequal angles [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Sides of an octagon
- Sides of a pentagon
- Angle sum of a pentagon
- Each angle of a regular octagon
- Regular polygon: equal sides and angles? (yes/no)
- Sides of an octagon
- Sides of a pentagon
- Angle sum of a pentagon
- Each angle of a regular octagon
- Does a regular polygon have equal sides and angles?
Homework
Find three polygons in signs or buildings.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Sides of an octagon | 8 | 2 |
| Sides of a pentagon | 5 | 2 |
| Angle sum of a pentagon | 540 | 2 |
| Each angle of a regular octagon | 135 | 2 |
| Regular polygon: equal sides and angles? (yes/no) | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 8; 2 5; 3 540; 4 135; 5 yes.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 8; 7 5; 8 540°; 9 135°; 10 yes.
Independent practice answers. Level 1: 1 8; 2 5; 3 540°; 4 135°; 5 yes. Level 2: 1 6; 2 720°; 3 90°. Level 3: 1 108°; 2 900°; 3 Regular needs equal sides and equal angles..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name polygons | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Tell regular from irregular | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Count sides and vertices | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Find the interior angle sum | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Using n × 180. Use (n − 2) × 180.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Shape names.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child names polygons and finds their angles. You do not need to be good at mathematics to help.
- Spot hexagons in honeycombs.
- Ask: how many sides?
- Split a shape into triangles.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: name polygons; tell regular from irregular; count sides and vertices; find the interior angle sum.
Prerequisite knowledge. Lessons 3 and 4.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. How many sides? Regular or irregular?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Using n × 180. Use (n − 2) × 180.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Shape names. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 6 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.G.B.3 and 7.G.B.5; Cambridge Primary Mathematics Stage 6 (polygons). These sources informed the lesson.