You will learn
- Use area = length × width.
- Find area of squares.
- Find a missing side from the area.
- Use square units.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Area is the surface a shape covers.
- Rectangle: length × width.
- Square: side × side.
- Area uses square units.
Words to know
Surface covered.
Longer side.
Shorter side.
Unit for area.
1. Discover: tiling a floor
A floor is 9 m by 6 m. How many square metres of tile are needed?
2. Understand: area of rectangles
- Area = length × width. 9 × 6 = 54 m².
- Square of side 7 cm: 7 × 7 = 49 cm².
- Missing side: area 72 cm², length 8 cm: 72 ÷ 8 = 9 cm.
Area uses square units; perimeter uses units of length.
Idea 1: Rectangle
12 by 5: 12 × 5 = 60. 15 m by 4 m: 15 × 4 = 60 m².
Idea 2: Square
Side 6: 6 × 6 = 36. 20 cm by 20 cm = 400 cm².
Idea 3: Missing side
Area 90, length 10: 90 ÷ 10 = 9.
Why square units? We count squares that cover the shape.
3. Worked examples
Example 1 (I show you): Area
12 by 5
- 12 × 5.
Answer: 60
Example 2 (We do it together): Square
Side 6
- 6 × 6.
Answer: 36
Example 3 (You try): Missing
Area 90, length 10
Show the steps and answer
- 90 ÷ 10.
Answer: 9
Did you know?
1 square metre is a square 1 m on each side.
Why this matters
Area tells us how much paint, tiles or carpet we need.
4. Explore: area
You need squared paper.
- Draw a 9 by 6 rectangle.
- Count the squares.
- Compare with 9 × 6.
- Draw a 7 by 7 square.
Think about it: what did you notice?
54 and 49.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- Area = ___ × ___.
- The area is ___ square ___.
- The missing side is ___ ÷ ___ = ___.
- I give the unit ___.
Guided practice
Question 1. Area 9 m by 6 m?
54 m².
Question 2. Area of a square of side 7?
49.
Question 3. Area 72, length 8: width?
9.
Independent practice
Level 1: Start
- Area 12 by 5
- Area of a square of side 6
- Area 90, length 10: width
- Area 15 m by 4 m
- Area 20 cm by 20 cm
Level 2: Grow
- Area of 8 by 7
- Area of a square of side 9
- Area 48, length 6. Find the width.
Level 3: Stretch
- Area of 35 m by 20 m
- Area 144, width 9. Find the length.
- Ben says the area of 6 by 4 is 20. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A floor is 9 m by 6 m. How much tile?
Show a sample answer
54 m².
Another one. A classroom floor is 9 m by 7 m. Find its area.
Show a sample answer
9 × 7 = 63 m²
7. Common mistakes
Fix: Area needs square units.
Fix: Area multiplies.
Fix: Write cm² or m².
8. Lesson summary and revision card
- I can use area = length × width.
- I can find the area of a square.
- I can find a missing side.
- I can use square units.
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
- Area = l × w.
- Square units.
- Divide to find a side.
11. Next lesson
Next lesson: Area of composite rectangular figures. 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.
- Find the area of a 12 by 5 rectangle. [2 marks]
- Find the area of a square of side 6. [2 marks]
- A rectangle has area 90 and length 10. Find the width. [2 marks]
- Find the area of a 15 m by 4 m rectangle. [2 marks]
- Ali says a 20 cm by 20 cm square has area 80 cm². Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- length × width [1]; 60 [1]
- 6 × 6 [1]; 36 [1]
- 90 ÷ 10 [1]; 9 [1]
- 15 × 4 [1]; 60 m² [1]
- No [1]. Area = 20 × 20 [1]. It is 400 cm² [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
- Area 12 by 5
- Area of square side 6
- Area 90, length 10: width
- Area 15 m by 4 m
- Area 20 cm by 20 cm
- Area of 9 m by 6 m:
- Area of a square of side 7 cm:
- Area 72, length 8, width:
- Area of 12 by 5:
- Area of 20 cm by 20 cm:
Homework
Find the area of five rectangular things.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Area 12 by 5 | 60 | 2 |
| Area of square side 6 | 36 | 2 |
| Area 90, length 10: width | 9 | 2 |
| Area 15 m by 4 m | 60 m² | 2 |
| Area 20 cm by 20 cm | 400 cm² | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 60; 2 36; 3 9; 4 60 m²; 5 400 cm².
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 54 m²; 7 49 cm²; 8 9; 9 60; 10 400 cm².
Independent practice answers. Level 1: 1 60; 2 36; 3 9; 4 60 m²; 5 400 cm². Level 2: 1 56; 2 81; 3 8. Level 3: 1 700 m²; 2 16; 3 20 is the perimeter. The area is 6 × 4 = 24..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use area = length × width | 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 Find area of squares | 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 Find a missing side from the area | 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 Use square units | 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Using cm instead of cm². Area needs square units.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Count squares on a grid.
- 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 finds the area of rectangles and squares. You do not need to be good at mathematics to help.
- Count tiles on a floor.
- Ask: how many squares cover it?
- Draw a grid for a rectangle.
- 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: use area = length × width; find area of squares; find a missing side from the area; use square units.
Prerequisite knowledge. Lessons 2 and 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 squared 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. What are the length and width? What unit?
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 cm instead of cm². Area needs square units.
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. Count squares on a grid. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.MD.A.3 and 3.MD.C.7; Cambridge Primary Mathematics Stage 4 (area). These sources informed the lesson; no official alignment is claimed.