You will learn
- Say what a polygon is.
- Name polygons by number of sides.
- Tell polygons from shapes that are not polygons.
- Count sides and vertices.
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 closed with straight sides.
- Name polygons by their sides.
- Sides and vertices are equal in number.
- A circle is not a polygon.
Words to know
A closed flat shape with straight sides.
A straight edge.
A corner.
No gaps.
1. Discover: floor patterns
A floor has many flat shapes. Which of these shapes have only straight sides and no gaps? A circle? A shape with a curved side?
2. Understand: polygons
A polygon is a flat, closed shape made only of straight sides.
- 3 sides: triangle
- 4 sides: quadrilateral
- 5: pentagon; 6: hexagon; 7: heptagon; 8: octagon
A polygon has the same number of sides and vertices. A circle is not a polygon because it has a curved edge. A shape with a gap is not closed, so it is not a polygon.
Idea 1: What is a polygon?
A polygon is a closed flat shape with straight sides and no gaps.
Idea 2: Names
3 sides: triangle. 4: quadrilateral. 5: pentagon. 6: hexagon. 7: heptagon. 8: octagon. 10: decagon.
Idea 3: Sides and vertices
An octagon has 8 sides and 8 vertices. A circle is not a polygon because it has a curve.
Why equal numbers? Each corner joins two sides.
3. Worked examples
Example 1 (I show you): Name
What is a 6-sided polygon?
- Count 6 sides.
Answer: hexagon
Example 2 (We do it together): Count
Vertices of a heptagon?
- Same as sides: 7.
Answer: 7
Example 3 (You try): Not
Is a shape with a gap a polygon?
Show the steps and answer
- It must be closed.
Answer: No
Did you know?
Poly means many and gon means angle.
Why this matters
Polygons are in buildings, tiles and signs.
4. Explore: polygon sort
You need paper and a pencil.
- Draw a triangle, a pentagon and a hexagon.
- Count the sides and vertices of each.
- Draw a circle and an open shape.
- Say why they are not polygons.
Think about it: what did you notice?
Circle: curved. Open shape: not closed.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- This shape has ___ sides.
- It is called a ___.
- It has ___ vertices.
- It is / is not a polygon because ___.
Guided practice
Question 1. Name a polygon with 5 sides.
Pentagon.
Question 2. Is a circle a polygon?
No, it has a curved edge.
Question 3. How many vertices has an octagon?
8.
Independent practice
Level 1: Start
- Name a 6-sided polygon
- Name a 4-sided polygon
- Vertices of a heptagon
- Is a shape with a gap a polygon?
- Sides of an octagon
Level 2: Grow
- Name a 5-sided polygon
- Sides of a hexagon
- Vertices of a quadrilateral
Level 3: Stretch
- Name a 10-sided polygon
- Is a shape with an open gap a polygon?
- Ana says a circle is a polygon with one side. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A stop sign has 8 straight sides. What polygon is it?
Show a sample answer
An octagon.
Another one. Draw one polygon, name it and count its sides and vertices.
Show a sample answer
for example a pentagon has 5 sides and 5 vertices
7. Common mistakes
Fix: A polygon is closed with only straight sides.
Fix: Polygons have only straight sides.
Fix: They are equal in a polygon.
8. Lesson summary and revision card
- I can say what a polygon is.
- I can name polygons by sides.
- I can tell polygons from other shapes.
- I can count sides and vertices.
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
- Polygons are closed with straight sides.
- Name them by the number of sides.
- Sides = vertices.
11. Next lesson
Next lesson: Triangles. 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.
- What is a polygon? [2 marks]
- What is a 6-sided polygon called? [1 mark]
- How many vertices has an octagon? [1 mark]
- Is a circle a polygon? Explain. [2 marks]
- Ali says a shape with a gap is a polygon. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- A closed flat shape [1]; with straight sides [1]
- Hexagon [1]
- 8 [1]
- No [1]; it has a curve, not straight sides [1]
- No [1]. A polygon must be closed [1]. A gap leaves it open [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 6-sided polygon
- 4-sided polygon
- Vertices of a heptagon
- Is a shape with a gap a polygon? (yes/no)
- Sides of an octagon
- A polygon is a closed shape with ___ sides.
- A 5-sided polygon is a ___.
- A 6-sided polygon is a ___.
- A circle is ___ a polygon.
- An octagon has ___ vertices.
Homework
Find five polygons at home (tiles, windows, signs). Name each.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 6-sided polygon | hexagon | 2 |
| 4-sided polygon | quadrilateral | 2 |
| Vertices of a heptagon | 7 | 2 |
| Is a shape with a gap a polygon? (yes/no) | no | 2 |
| Sides of an octagon | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 hexagon; 2 quadrilateral; 3 7; 4 no; 5 8.
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 straight; 7 pentagon; 8 hexagon; 9 not; 10 8.
Independent practice answers. Level 1: 1 hexagon; 2 quadrilateral; 3 7; 4 no; 5 8. Level 2: 1 pentagon; 2 6; 3 4. Level 3: 1 decagon; 2 No; 3 A polygon has straight sides. A circle has a curve..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what a polygon is | 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 Name polygons by number of sides | 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 Tell polygons from shapes that are not 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 |
| O4 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 |
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: Calling any shape a polygon. A polygon is closed with only straight sides.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Trace shapes and count sides.
- 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 learns what polygons are and how to name them. You do not need to be good at mathematics to help.
- Look for polygons in signs and buildings.
- Ask: how many sides? what is it called?
- Draw polygons on paper.
- 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: say what a polygon is; name polygons by number of sides; tell polygons from shapes that are not polygons; count sides and vertices.
Prerequisite knowledge. Grade 2 shapes.
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 and a pencil. 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. Is it closed? Are the sides straight? How many sides?
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. Calling any shape a polygon. A polygon is closed with only straight sides.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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. Trace shapes and count sides. 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 3 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.G.A.1 (shapes and attributes); Cambridge Primary Mathematics Stage 3 (2D shapes). These sources informed the lesson.