You will learn
- Choose the right operation for an area problem.
- Find the area of a floor or garden.
- Add the areas of two rectangles.
- Tell area and perimeter problems apart.
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
- Tiling and painting need area.
- Fencing and borders need perimeter.
- Add areas of two rectangles.
- Choose the right operation.
Words to know
The bottom surface of a room.
A piece of land for growing plants.
All added together.
The distance around.
1. Discover: tiling a floor
A builder must tile a floor. He needs to know how much surface to cover. Does he need the area or the perimeter?
2. Understand: area in real life
Read the problem and decide: does it ask about the surface (area) or the distance around (perimeter)?
- Covering a floor, painting a wall, planting a bed: area.
- Fencing a garden, framing a picture: perimeter.
A garden is 8 m by 5 m. Area = 8 × 5 = 40 m². Fence perimeter = 8 + 5 + 8 + 5 = 26 m.
Two rooms of 4 m by 3 m (12 m²) and 5 m by 2 m (10 m²) together have 12 + 10 = 22 m².
Idea 1: Area or perimeter
Tiling a floor needs area. Fencing a garden needs perimeter. A garden 8 m by 5 m has area 40 m².
Idea 2: Fence
A field 10 m by 4 m needs a fence of 10 + 4 + 10 + 4 = 28 m.
Idea 3: Add areas
Two rooms of 15 m² and 9 m² have a total area of 24 m². A classroom 9 m by 6 m needs 54 tiles of 1 m².
Why area for tiles? Tiles cover the surface.
3. Worked examples
Example 1 (I show you): Area
A garden 8 m by 5 m. Area?
- 8 × 5.
Answer: 40 m²
Example 2 (We do it together): Fence
A field 10 m by 4 m. Fence?
- Perimeter: 10 + 4 + 10 + 4.
Answer: 28 m
Example 3 (You try): Tiles
A classroom 9 m by 6 m. Tiles of 1 m²?
Show the steps and answer
- 9 × 6.
Answer: 54
Did you know?
Builders use area for floors and perimeter for fences and skirting boards.
Why this matters
Real jobs need area and perimeter every day.
4. Explore: plan a garden
You need paper and a pencil.
- Draw a garden 8 m by 5 m.
- Find its area.
- Find the fence length.
- Say which answer is in m² and which is in m.
Think about it: what did you notice?
Area 40 m²; fence 26 m.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- This needs area / perimeter because ___.
- Area = ___ × ___.
- The total is ___.
- The unit is ___.
Guided practice
Question 1. Garden 8 m by 5 m: area?
40 m².
Question 2. Fence for the same garden?
26 m.
Question 3. Two rooms of 12 m² and 10 m²: total?
22 m².
Independent practice
Level 1: Start
- Area of a floor 6 m by 5 m
- Fence for a field 10 m by 4 m
- Total area of 15 m² and 9 m²
- Tiles of 1 m² to cover 7 m by 3 m
- Area of a rug 3 m by 2 m
Level 2: Grow
- Area of a floor 7 m by 4 m
- Fence for a plot 6 m by 6 m
- Tiles of 1 m² for a floor 5 m by 3 m
Level 3: Stretch
- Total area of 14 m² and 11 m²
- Fence for a garden 20 m by 10 m
- Ali uses perimeter to count tiles for a floor 5 m by 4 m and gets 18. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A classroom is 9 m by 6 m. How many 1 m² tiles cover the floor?
Show a sample answer
54 tiles.
Another one. A school hall is 15 m by 10 m. Find its area and the length of the border around it.
Show a sample answer
150 m²; 50 m
7. Common mistakes
Fix: Check if it is about surface or distance around.
Fix: Covering the surface needs area.
Fix: Going around needs perimeter.
8. Lesson summary and revision card
- I can choose the right operation.
- I can find the area of a floor or garden.
- I can add the areas of two rectangles.
- I can tell area and perimeter apart.
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
- Surface means area.
- Distance around means perimeter.
- Add the areas of parts.
11. Next lesson
Next lesson: Collecting data. 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 floor 6 m by 5 m. [2 marks]
- Find the fence for a field 10 m by 4 m. [2 marks]
- Find the total area of rooms of 15 m² and 9 m². [1 mark]
- How many 1 m² tiles cover a floor 7 m by 3 m? [2 marks]
- Ana says fencing needs area. Is she right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 6 × 5 [1] = 30 m² [1]
- 10 + 4 + 10 + 4 [1] = 28 m [1]
- 24 m² [1]
- 7 × 3 [1] = 21 [1]
- No [1]. Fencing goes around [1]. It needs perimeter [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 a floor 6 m by 5 m
- Fence for a field 10 m by 4 m
- Total of 15 m² and 9 m²
- Tiles of 1 m² for 7 m by 3 m
- Area of a rug 3 m by 2 m
- Tiling a floor needs ___.
- Fencing a garden needs ___.
- A garden 8 m by 5 m has area ___.
- Fence for a field 10 m by 4 m: ___
- A classroom 9 m by 6 m needs ___ tiles of 1 m².
Homework
Measure a room at home. Find its area and how many 1 m² tiles would cover it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Area of a floor 6 m by 5 m | 30 m² | 2 |
| Fence for a field 10 m by 4 m | 28 m | 2 |
| Total of 15 m² and 9 m² | 24 m² | 2 |
| Tiles of 1 m² for 7 m by 3 m | 21 | 2 |
| Area of a rug 3 m by 2 m | 6 m² | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 30 m²; 2 28 m; 3 24 m²; 4 21; 5 6 m².
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 area; 7 perimeter; 8 40 m²; 9 28 m; 10 54.
Independent practice answers. Level 1: 1 30 m²; 2 28 m; 3 24 m²; 4 21 tiles; 5 6 m². Level 2: 1 28 m²; 2 24 m; 3 15. Level 3: 1 25 m²; 2 60 m; 3 Tiles cover the surface, so he needs the area: 5 × 4 = 20..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Choose the right operation for an area problem | 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 floor or garden | 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 Add the areas of two rectangles | 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 Tell area and perimeter problems apart | 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 perimeter when the problem asks for area. Check if it is about surface or distance around.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw simple plans on squared paper and count the squares.
- 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 solves real problems about area and perimeter. You do not need to be good at mathematics to help.
- Measure a room and find the area.
- Ask: do we need area or perimeter?
- Plan tiles for a small space.
- 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: choose the right operation for an area problem; find the area of a floor or garden; add the areas of two rectangles; tell area and perimeter problems apart.
Prerequisite knowledge. Lessons 1 to 5.
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 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. Cover or go around? What is the formula? What is the 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 perimeter when the problem asks for area. Check if it is about surface or distance around.
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. Draw simple plans on squared paper and count the squares. 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 and 3.MD.D.8; Cambridge Primary Mathematics Stage 3 (area and perimeter problems). These sources informed the lesson.