You will learn
- Name quadrilaterals.
- List properties.
- Use the 360° angle sum.
- Find unknown angles.
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 four sides.
- Its angles add to 360°.
- Rectangles, squares, rhombuses, parallelograms and trapeziums are quadrilaterals.
- Use properties to name them.
Words to know
Four-sided shape.
Opposite sides parallel.
Four equal sides.
One pair of parallel sides.
1. Discover: four sides
A square, a rectangle and a rhombus all have four sides. How are they different?
2. Understand: quadrilaterals
- Angles of a quadrilateral add to 360°.
- Rectangle: four right angles; opposite sides equal.
- Rhombus: four equal sides; opposite angles equal.
- Three angles 90°, 80°, 100° leave 360 − 270 = 90°.
Idea 1: Angle sum
Angles add to 360°. Missing angle for 90, 90, 100: 360 − 280 = 80°.
Idea 2: Names
Four right angles: rectangle. Four equal sides and 90°: square. One pair of parallel sides: trapezium.
Idea 3: More
90, 80, 100 and ?: 360 − 270 = 90°.
Why 360°? A diagonal splits it into two triangles, 2 × 180°.
3. Worked examples
Example 1 (I show you): Angle sum
A quadrilateral
- Two triangles.
Answer: 360°
Example 2 (We do it together): Missing
90, 90, 100, ?
- 360 − 280.
Answer: 80°
Example 3 (You try): Name
One pair of parallel sides
Show the steps and answer
- Only one pair.
Answer: trapezium
Did you know?
A square is a special rectangle and also a special rhombus.
Why this matters
Quadrilaterals appear in windows, floors and tiles.
4. Explore: find
You need paper.
- Add known angles.
- Subtract from 360.
- Name the shape.
- Check.
Think about it: what did you notice?
90°.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The angles add to ___.
- The missing angle is ___.
- It has ___ equal sides, so it is a ___.
- It has ___ pair(s) of parallel sides.
Guided practice
Question 1. Sum of angles?
360°.
Question 2. Four equal sides?
rhombus.
Question 3. Missing angle 90, 80, 100?
90°.
Independent practice
Level 1: Start
- Angle sum of a quadrilateral
- Missing angle: 90, 90, 100
- Four right angles
- Four equal sides and 90° angles
- One pair of parallel sides
Level 2: Grow
- Right angles in a square
- Shape with opposite sides parallel
- Missing angle: 85°, 95°, 110°, ?
Level 3: Stretch
- Adjacent angle to 70° in a parallelogram
- Missing angle: 100°, 100°, 60°, ?
- Ben says a trapezium has two pairs of parallel sides. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Three angles are 90°, 80° and 100°. The fourth?
Show a sample answer
90°.
Another one. A tile has three angles of 90°, 80° and 100°. Find the fourth.
Show a sample answer
90°
7. Common mistakes
Fix: Use 360°.
Fix: Quadrilaterals add to 360°.
Fix: Rhombus: equal sides; rectangle: right angles.
8. Lesson summary and revision card
- I can name quadrilaterals.
- I can list properties.
- I can use the 360° angle sum.
- I can find unknown angles.
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
- Angles total 360°.
- Learn the properties.
- Squares are special rectangles.
11. Next lesson
Next lesson: 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.
- State the angle sum of a quadrilateral. [1 mark]
- Three angles of a quadrilateral are 90°, 90° and 100°. Find the fourth. [2 marks]
- Name the quadrilateral with four right angles. [1 mark]
- Name the quadrilateral with four equal sides and four right angles. [2 marks]
- Ali says a trapezium has two pairs of parallel sides. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 360° [1]
- 90 + 90 + 100 = 280 [1]; 360 − 280 = 80° [1]
- Rectangle [1]
- All sides equal and right angles [1]; square [1]
- No [1]. A trapezium has one pair [1]. Two pairs make a parallelogram [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
- Angle sum of a quadrilateral
- Missing: 90, 90, 100
- Four right angles
- Four equal sides and 90°
- One pair parallel
- Angle sum
- Missing angle 90, 90, 100
- Four right angles
- Four equal sides and 90°
- One pair of parallel sides
Homework
Sketch each quadrilateral and list its properties.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Angle sum of a quadrilateral | 360 | 2 |
| Missing: 90, 90, 100 | 80 | 2 |
| Four right angles | rectangle | 2 |
| Four equal sides and 90° | square | 2 |
| One pair parallel | trapezium | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 360; 2 80; 3 rectangle; 4 square; 5 trapezium.
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): 6 360°; 7 80°; 8 rectangle; 9 square; 10 trapezium.
Independent practice answers. Level 1: 1 360°; 2 80°; 3 rectangle; 4 square; 5 trapezium. Level 2: 1 4; 2 parallelogram; 3 70°. Level 3: 1 110°; 2 100°; 3 A trapezium has one pair. Two pairs make a parallelogram..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name 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 |
| O2 List properties | 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 Use the 360° 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 |
| O4 Find unknown 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 |
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 180°. Use 360°.
- 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 quadrilaterals and finds their angles. You do not need to be good at mathematics to help.
- Find rectangles and squares at home.
- Ask: how many sides and angles?
- Fold a paper square into shapes.
- 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 quadrilaterals; list properties; use the 360° angle sum; find unknown angles.
Prerequisite knowledge. Lessons 1–3.
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 equal sides? How many parallel pairs?
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 180°. Use 360°.
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. 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 5.G.B.4; Cambridge Primary Mathematics Stage 6 (quadrilaterals). These sources informed the lesson.