You will learn
- Say that a quadrilateral has 4 sides.
- Name the common quadrilaterals.
- Describe each by sides and angles.
- Find the perimeter of a quadrilateral.
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 quadrilateral has 4 sides.
- Square, rectangle, rhombus, parallelogram, trapezium.
- Describe by sides and angles.
- Add four sides for the perimeter.
Words to know
A polygon with 4 sides.
Always the same distance apart.
4 equal sides.
Opposite sides parallel.
1. Discover: four-sided shapes
A window, a kite, a field and a book cover each have 4 sides. Are they all the same shape?
2. Understand: quadrilaterals
A quadrilateral has 4 sides and 4 vertices.
- Square: 4 equal sides and 4 right angles.
- Rectangle: opposite sides equal, 4 right angles.
- Rhombus: 4 equal sides, opposite sides parallel.
- Parallelogram: opposite sides equal and parallel.
- Trapezium: one pair of parallel sides.
Parallel lines never meet.
Idea 1: Four-sided
A quadrilateral has 4 sides and 4 vertices. Square, rectangle, rhombus, parallelogram and trapezium are quadrilaterals.
Idea 2: Describe
Square: 4 equal sides and 4 right angles. Rectangle: opposite sides equal and 4 right angles. Rhombus: 4 equal sides, no right angles. Trapezium: one pair of parallel sides.
Idea 3: Perimeter
A rectangle 7 cm by 3 cm: 2 × 7 + 2 × 3 = 20 cm.
Why many names? Each describes sides and angles exactly.
3. Worked examples
Example 1 (I show you): Name
4 equal sides and right angles.
- A special rectangle.
Answer: square
Example 2 (We do it together): Name
Opposite sides equal and 4 right angles.
- Not all sides equal.
Answer: rectangle
Example 3 (You try): Perimeter
Rectangle 7 cm by 3 cm.
Show the steps and answer
- 7 + 3 + 7 + 3.
Answer: 20 cm
Did you know?
Quadri means four and lateral means side.
Why this matters
Quadrilaterals are in doors, books and floors.
4. Explore: quadrilateral sort
You need paper, a ruler and a pencil.
- Draw a square and a rectangle.
- Draw a rhombus and a parallelogram.
- Measure the sides.
- Tick which have 4 equal sides.
Think about it: what did you notice?
Square and rhombus have 4 equal sides.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The shape has ___ sides.
- The angles are ___.
- It is called a ___.
- The perimeter is ___.
Guided practice
Question 1. How many sides has a quadrilateral?
4.
Question 2. 4 equal sides and 4 right angles?
Square.
Question 3. Opposite sides equal and 4 right angles but not all sides equal?
Rectangle.
Independent practice
Level 1: Start
- Sides of a quadrilateral
- Name the shape with 4 equal sides and right angles
- Name the shape with opposite sides equal and 4 right angles
- Perimeter of a rectangle 7 cm by 3 cm
- Is a rhombus a quadrilateral?
Level 2: Grow
- Name the shape with 4 equal sides and 4 right angles
- Perimeter of a rectangle 9 cm by 4 cm
- Number of sides of a quadrilateral
Level 3: Stretch
- Perimeter of a rectangle 20 m by 15 m
- Perimeter of a parallelogram with sides 8 cm and 5 cm
- Kofi says a square is not a rectangle. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A field is a rectangle 70 m by 30 m. What is its perimeter?
Show a sample answer
200 m.
Another one. Draw a quadrilateral, name it and describe its sides and angles.
Show a sample answer
for example a rectangle: opposite sides equal and 4 right angles
7. Common mistakes
Fix: Any 4-sided polygon is a quadrilateral.
Fix: A rhombus has 4 equal sides but need not have right angles.
Fix: A square has all sides equal.
8. Lesson summary and revision card
- I know a quadrilateral has 4 sides.
- I can name the common quadrilaterals.
- I can describe them by sides and angles.
- I can find the perimeter.
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
- Quadrilaterals have 4 sides.
- Square, rectangle, rhombus, parallelogram, trapezium.
- Parallel never meet.
11. Next lesson
Next lesson: Properties of shapes. 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 has a quadrilateral? [1 mark]
- Name the shape with 4 equal sides and 4 right angles. [1 mark]
- Name the shape with opposite sides equal and 4 right angles but not all sides equal. [1 mark]
- Find the perimeter of a rectangle 7 cm by 3 cm. [2 marks]
- Ana says a rhombus always has right angles. Is she right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- 4 [1]
- Square [1]
- Rectangle [1]
- 7 + 3 + 7 + 3 [1] = 20 cm [1]
- No [1]. A rhombus has 4 equal sides [1]. Its angles need not be right angles [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- Sides of a quadrilateral
- 4 equal sides, right angles
- Opposite sides equal, 4 right angles
- Perimeter of 7 cm by 3 cm
- Is a rhombus a quadrilateral? (yes/no)
- A quadrilateral has ___ sides.
- 4 equal sides and 4 right angles: ___
- 4 equal sides but no right angles: ___
- A trapezium has ___ pair of parallel sides.
- A field 70 m by 30 m has perimeter ___.
Homework
Find four quadrilaterals at home and name them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Sides of a quadrilateral | 4 | 2 |
| 4 equal sides, right angles | square | 2 |
| Opposite sides equal, 4 right angles | rectangle | 2 |
| Perimeter of 7 cm by 3 cm | 20 cm | 2 |
| Is a rhombus a quadrilateral? (yes/no) | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4; 2 square; 3 rectangle; 4 20 cm; 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 4; 7 square; 8 rhombus; 9 one; 10 200 m.
Independent practice answers. Level 1: 1 4; 2 square; 3 rectangle; 4 20 cm; 5 yes. Level 2: 1 square; 2 26 cm; 3 4. Level 3: 1 70 m; 2 26 cm; 3 A square has 4 right angles and opposite sides equal, so it is a special rectangle..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say that a quadrilateral has 4 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 |
| O2 Name the common quadrilaterals | 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 Describe each 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 Find the perimeter of a quadrilateral | 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: Thinking only squares are quadrilaterals. Any 4-sided polygon is a quadrilateral.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Fold paper to make a square and a rectangle.
- 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 four-sided shapes. You do not need to be good at mathematics to help.
- Find quadrilaterals in the house.
- Ask: how many sides? are they equal?
- Draw them on squared 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 that a quadrilateral has 4 sides; name the common quadrilaterals; describe each by sides and angles; find the perimeter of a quadrilateral.
Prerequisite knowledge. Lessons 1 and 2.
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, a ruler 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. Are the sides equal? Are there right angles? Are any sides parallel?
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. Thinking only squares are quadrilaterals. Any 4-sided polygon is a quadrilateral.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-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. Fold paper to make a square and a rectangle. 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 and 5.G.B.3 (classify quadrilaterals); Cambridge Primary Mathematics Stage 3 (2D shapes). These sources informed the lesson.