You will learn
- Use area = length × width.
- Find the area of a rectangle from its sides.
- Find a missing side from the area.
- Write the answer in square units.
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
- Area of a rectangle = length × width.
- Multiply the side lengths.
- Use division to find a missing side.
- Write the answer in square units.
Words to know
The longer side.
The shorter side.
The answer to a multiplication.
A side we need to find.
1. Discover: a classroom floor
A floor is 6 m long and 4 m wide. Do you need to draw every square metre to find its area?
2. Understand: area and multiplication
For a rectangle, area = length × width.
- 6 m by 4 m: 6 × 4 = 24 m².
- 9 cm by 3 cm: 9 × 3 = 27 cm².
To find a missing side, divide the area by the known side. If the area is 24 m² and the length is 6 m, then width = 24 ÷ 6 = 4 m.
A square of side 5 cm has area 5 × 5 = 25 cm².
Idea 1: Formula
Area of a rectangle = length × width. 7 cm by 3 cm: 7 × 3 = 21 cm².
Idea 2: Square
A square of side 4 cm: 4 × 4 = 16 cm².
Idea 3: Missing side
Area 30 m² and length 6 m: width = 30 ÷ 6 = 5 m.
Why multiply? Each row has length squares and there are width rows.
3. Worked examples
Example 1 (I show you): Area
7 cm by 3 cm?
- 7 × 3.
Answer: 21 cm²
Example 2 (We do it together): Square
Square of side 4 cm?
- 4 × 4.
Answer: 16 cm²
Example 3 (You try): Missing
Area 30 m², length 6 m. Width?
Show the steps and answer
- 30 ÷ 6.
Answer: 5 m
Did you know?
The area of a square is its side times itself, which is why we say “squared”.
Why this matters
Area formulas help us tile floors and plan fields.
4. Explore: measure and multiply
You need a ruler and a book.
- Measure the length of the book cover.
- Measure the width.
- Multiply to find the area.
- Write the unit.
Think about it: what did you notice?
The answer is in cm².
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 ___ ÷ ___.
- The unit is ___.
Guided practice
Question 1. Area of 6 m by 4 m?
24 m².
Question 2. Area of 9 cm by 3 cm?
27 cm².
Question 3. Area 24 m² and length 6 m: width?
4 m.
Independent practice
Level 1: Start
- Area of 7 cm by 3 cm
- Area of 8 m by 5 m
- Area of a square of side 4 cm
- Area 30 m², length 6 m: width?
- Area 36 cm², width 4 cm: length?
Level 2: Grow
- 5 cm by 4 cm
- A square of side 3 cm
- Area 24 cm², length 6 cm. Width?
Level 3: Stretch
- 15 m by 6 m
- Area 63 m², width 7 m. Length?
- Kofi says the area of 8 cm by 5 cm is 26 cm². What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A rectangular hall is 12 m long and 5 m wide. What is its area?
Show a sample answer
60 m².
Another one. A floor is 7 m long and 4 m wide. Find its area and how many 1 m² tiles are needed.
Show a sample answer
28 m²; 28 tiles
7. Common mistakes
Fix: Multiply: 6 × 4 = 24.
Fix: Multiply length by width.
Fix: Use cm² or m².
8. Lesson summary and revision card
- I can use area = length × width.
- I can find the area from the sides.
- I can find a missing side.
- I can write the answer in 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 = length × width.
- Divide to find a missing side.
- Use square units.
11. Next lesson
Next lesson: Practical area problems. 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.
- Write the formula for the area of a rectangle. [1 mark]
- Find the area of a rectangle 7 cm by 3 cm. [2 marks]
- Find the area of a square of side 4 cm. [2 marks]
- The area is 30 m² and the length is 6 m. Find the width. [2 marks]
- Ama says a hall 12 m by 5 m has area 34 m². Is she right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- Length × width [1]
- 7 × 3 [1] = 21 cm² [1]
- 4 × 4 [1] = 16 cm² [1]
- 30 ÷ 6 [1] = 5 m [1]
- No [1]. She added and doubled [1]. 12 × 5 = 60 m² [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Area of 7 cm by 3 cm
- Area of 8 m by 5 m
- Area of a square of side 4 cm
- Area 30 m², length 6 m: width
- Area 36 cm², width 4 cm: length
- Area of a rectangle = ___ × ___
- Area of 7 cm by 3 cm =
- Area of a square of side 4 cm =
- Area 30 m², length 6 m: width =
- A hall 12 m by 5 m has area ___.
Homework
Measure two rectangles at home and calculate their areas.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Area of 7 cm by 3 cm | 21 cm² | 2 |
| Area of 8 m by 5 m | 40 m² | 2 |
| Area of a square of side 4 cm | 16 cm² | 2 |
| Area 30 m², length 6 m: width | 5 m | 2 |
| Area 36 cm², width 4 cm: length | 9 cm | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 21 cm²; 2 40 m²; 3 16 cm²; 4 5 m; 5 9 cm.
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 length; width; 7 21 cm²; 8 16 cm²; 9 5 m; 10 60 m².
Independent practice answers. Level 1: 1 21 cm²; 2 40 m²; 3 16 cm²; 4 5 m; 5 9 cm. Level 2: 1 20 cm²; 2 9 cm²; 3 4 cm. Level 3: 1 90 m²; 2 9 m; 3 26 is the perimeter. Area = 8 × 5 = 40 cm²..
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 the area of a rectangle from its 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 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 Write the answer in 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 |
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: Adding length and width, 6 + 4 = 10. Multiply: 6 × 4 = 24.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Build rectangles from squares and write the multiplication.
- 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 a rectangle by multiplying its sides. You do not need to be good at mathematics to help.
- Measure a room and find its area.
- Ask: what is length × width?
- Use squared paper to check.
- 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 the area of a rectangle from its sides; find a missing side from the area; write the answer in square units.
Prerequisite knowledge. Lesson 4 and division facts.
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 a ruler and a book. 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 is the length? What is the width? What is the product?
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. Adding length and width, 6 + 4 = 10. Multiply: 6 × 4 = 24.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Build rectangles from squares and write the multiplication. 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 » Measurement & Data. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.MD.C.7 (relate area to multiplication); Cambridge Primary Mathematics Stage 3 (area). These sources informed the lesson.