You will learn
- Name common 2D figures.
- Tell polygons from non-polygons.
- Classify by sides and angles.
- Describe figures with correct vocabulary.
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.
- Polygons are named by their number of sides.
- Sides and vertices are equal in number.
- Shapes with curves or gaps are not polygons.
Words to know
Closed figure with straight sides.
An edge.
A corner.
Where two sides meet.
1. Discover: shape sort
Sort these into groups: triangle, circle, pentagon, rectangle, a shape with a gap. What rule did you use?
2. Understand: 2D figures
- A polygon is closed with straight sides: triangle, quadrilateral, pentagon (5), hexagon (6), octagon (8).
- A circle and a shape with a gap are not polygons.
- Polygons are named by the number of sides; sides and vertices are equal in number.
Idea 1: Names
3 sides: triangle. 5 sides: pentagon. 6 sides: hexagon. 8 sides: octagon.
Idea 2: Vertices
A pentagon has 5 sides and 5 vertices.
Idea 3: Not polygons
A shape with a gap is not a polygon (not closed). A circle is not a polygon (curved).
Why equal numbers? Each vertex joins two sides.
3. Worked examples
Example 1 (I show you): Name
6-sided polygon
- Hexa means six.
Answer: hexagon
Example 2 (We do it together): Count
Vertices of a pentagon
- 5 sides.
Answer: 5
Example 3 (You try): Decide
Shape with a gap
Show the steps and answer
- Not closed.
Answer: not a polygon
Did you know?
The Pentagon building in the USA has five sides.
Why this matters
Polygon names help us describe shapes exactly.
4. Explore: sort
You need cut-out shapes.
- Sort polygons and non-polygons.
- Name each polygon.
- Count sides and vertices.
- Explain your rule.
Think about it: what did you notice?
Rule: closed with straight sides.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- It has ___ sides.
- So it is a ___.
- It has ___ vertices.
- It is / is not a polygon because ___.
Guided practice
Question 1. Sides of a pentagon?
5.
Question 2. Is a circle a polygon?
No.
Question 3. Vertices of an octagon?
8.
Independent practice
Level 1: Start
- Name a 6-sided polygon
- Name a 3-sided polygon
- Vertices of a pentagon
- Is a shape with a gap a polygon?
- Sides of an octagon
Level 2: Grow
- Name a 4-sided polygon
- Sides of a heptagon
- Vertices of a triangle
Level 3: Stretch
- Name a 10-sided polygon
- Sides of a polygon with 12 vertices
- Ben says a semicircle is a polygon. 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 is it?
Show a sample answer
An octagon.
Another one. A stop sign has 8 straight sides. Name its shape.
Show a sample answer
octagon
7. Common mistakes
Fix: Polygons have straight sides only.
Fix: Polygons have straight sides only.
Fix: Number of vertices equals number of sides.
8. Lesson summary and revision card
- I can name common 2D figures.
- I can tell polygons from non-polygons.
- I can classify by sides and angles.
- I can describe figures with vocabulary.
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: closed, straight.
- Name by sides.
- Sides = vertices.
11. Next lesson
Next lesson: Properties of polygons. 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.
- Name a polygon with 6 sides. [1 mark]
- How many vertices does a pentagon have? [2 marks]
- Is a shape with a gap a polygon? Explain. [2 marks]
- How many sides does an octagon have? [1 mark]
- Ali says a circle is a polygon because it is closed. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- hexagon [1]
- 5 sides [1]; 5 vertices [1]
- It is not closed [1]; no [1]
- 8 [1]
- No [1]. A polygon has straight sides [1]. A circle is curved [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
- 3-sided polygon
- Vertices of a pentagon
- Shape with a gap a polygon? (yes/no)
- Sides of an octagon
- A polygon is…
- A 5-sided polygon is a…
- A 6-sided polygon is a…
- Which is not a polygon?
- An octagon has how many vertices?
Homework
Find ten polygons around you and name them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 6-sided polygon | hexagon | 2 |
| 3-sided polygon | triangle | 2 |
| Vertices of a pentagon | 5 | 2 |
| Shape with a gap a polygon? (yes/no) | no | 2 |
| Sides of an octagon | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 hexagon; 2 triangle; 3 5; 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 closed with straight sides; 7 pentagon; 8 hexagon; 9 circle; 10 8.
Independent practice answers. Level 1: 1 hexagon; 2 triangle; 3 5; 4 no; 5 8. Level 2: 1 quadrilateral; 2 7; 3 3. Level 3: 1 decagon; 2 12; 3 It has a curved edge, so it is not a polygon..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name common 2D figures | 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 polygons from non-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 |
| O3 Classify by sides and angles | 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 Describe figures with correct vocabulary | 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 a circle a polygon. Polygons have straight sides only.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Review shapes.
- 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 and describes 2D shapes. You do not need to be good at mathematics to help.
- Spot shapes on road signs.
- Ask: how many sides? Is it closed?
- Build polygons with sticks.
- 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 common 2D figures; tell polygons from non-polygons; classify by sides and angles; describe figures with correct vocabulary.
Prerequisite knowledge. Grade 4 geometry.
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 cut-out shapes. 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? Is it closed with straight 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 a circle a polygon. Polygons have straight sides only.
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. Review shapes. 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 5 » 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; Cambridge Primary Mathematics Stage 5 (2D shapes). These sources informed the lesson.