You will learn
- Add all sides.
- Use the rectangle and square formulas.
- Find a missing side.
- Solve perimeter problems.
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
- Perimeter is the distance around a shape.
- Add all the sides.
- Rectangle: 2 × (length + width). Square: 4 × side.
- Subtract known sides from the perimeter to find a missing side.
Words to know
Distance around.
An edge.
4 right angles.
4 equal sides.
1. Discover: fencing a field
A field is 12 m long and 8 m wide. How much fence goes all the way around?
2. Understand: perimeter
- Rectangle 12 m by 8 m: 2 × (12 + 8) = 40 m.
- Square side 9: 4 × 9 = 36.
- Triangle 5, 6, 7: 5 + 6 + 7 = 18.
- Missing side: perimeter 30, sides 8 and 10 and ?: 30 − 8 − 10 = 12.
Idea 1: Rectangle
15 by 10: 15 + 10 + 15 + 10 = 50. Or 2 × (15 + 10) = 50.
Idea 2: Square and triangle
Square of side 7: 4 × 7 = 28. Triangle 8, 8, 5: 8 + 8 + 5 = 21.
Idea 3: Missing side
P = 30 with sides 8 and 10: 8 + 10 = 18, then 30 − 18 = 12.
Why add all sides? We walk all the way around.
3. Worked examples
Example 1 (I show you): Rectangle
15 by 10
- 2 × (15 + 10).
Answer: 50
Example 2 (We do it together): Square
Side 7
- 4 × 7.
Answer: 28
Example 3 (You try): Missing
P = 30, sides 8, 10, ?
Show the steps and answer
- 30 − 18.
Answer: 12
Did you know?
A fence around a field is its perimeter.
Why this matters
Perimeter tells us how much fence, trim or border we need.
4. Explore: walk the edge
You need a ruler.
- Measure a book cover.
- Add all four sides.
- Check with 2 × (l + w).
- Find the perimeter of a square of side 9.
Think about it: what did you notice?
36.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I add ___ + ___ + ___ = ___.
- The perimeter is ___ (unit).
- The missing side is ___ − ___ = ___.
- I check by adding all sides.
Guided practice
Question 1. Perimeter 12 m by 8 m?
40 m.
Question 2. Square side 9?
36.
Question 3. Triangle 5, 6, 7?
18.
Independent practice
Level 1: Start
- Rectangle 15 by 10
- Square side 7
- Triangle 8, 8, 5
- Missing side: P=30, sides 8, 10, ?
- Rectangle 25 by 5
Level 2: Grow
- Rectangle 9 by 4
- Square of side 15
- Triangle 6, 7, 9
Level 3: Stretch
- Rectangle 18 by 7
- A triangle has perimeter 40. Two sides are 12 and 15. Find the third.
- Ben says a square of side 8 has perimeter 64. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A field is 12 m by 8 m. How long is the fence?
Show a sample answer
40 m.
Another one. A garden is 20 m by 12 m. How much fence goes around it?
Show a sample answer
2 × (20 + 12) = 64 m
7. Common mistakes
Fix: Add all sides or use 2(l + w).
Fix: Add all four sides.
Fix: Perimeter is around; area is inside.
8. Lesson summary and revision card
- I can add all sides.
- I can use the rectangle and square formulas.
- I can find a missing side.
- I can solve perimeter problems.
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
- Add all sides.
- 2(l + w) for rectangles.
- Subtract for a missing side.
11. Next lesson
Next lesson: Area of rectangles. 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 perimeter of a rectangle 15 by 10. [2 marks]
- Find the perimeter of a square with side 7. [2 marks]
- Find the perimeter of a triangle with sides 8, 8 and 5. [2 marks]
- A shape has perimeter 30. Two sides are 8 and 10. Find the missing side. [3 marks]
- Kofi says a 25 by 5 rectangle has perimeter 125. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 2 × (15 + 10) or add all sides [1]; 50 [1]
- 4 × 7 [1]; 28 [1]
- 8 + 8 + 5 [1]; 21 [1]
- 8 + 10 = 18 [1]; 30 − 18 [1]; 12 [1]
- No [1]. 125 is the area [1]. Perimeter is 2 × (25 + 5) = 60 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Rectangle 15 by 10
- Square side 7
- Triangle 8, 8, 5
- P=30, sides 8, 10, ?
- Rectangle 25 by 5
- Perimeter of 12 m by 8 m:
- Perimeter of a square of side 9:
- Perimeter of a triangle 5, 6, 7:
- P = 30, sides 8, 10, ? The missing side is
- Perimeter of 15 by 10:
Homework
Find the perimeter of three rooms at home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Rectangle 15 by 10 | 50 | 2 |
| Square side 7 | 28 | 2 |
| Triangle 8, 8, 5 | 21 | 2 |
| P=30, sides 8, 10, ? | 12 | 2 |
| Rectangle 25 by 5 | 60 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 50; 2 28; 3 21; 4 12; 5 60.
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 40 m; 7 36; 8 18; 9 12; 10 50.
Independent practice answers. Level 1: 1 50; 2 28; 3 21; 4 12; 5 60. Level 2: 1 26; 2 60; 3 22. Level 3: 1 50; 2 13; 3 He multiplied 8 × 8. The perimeter is 4 × 8 = 32..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Add all 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 Use the rectangle and square formulas | 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 | 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 Solve perimeter problems | 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 only two sides of a rectangle. Add all sides or use 2(l + w).
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Measure the edges of objects.
- 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 perimeter of shapes. You do not need to be good at mathematics to help.
- Measure around a table with string.
- Ask: how far all the way around?
- Plan a fence or a border together.
- 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: add all sides; use the rectangle and square formulas; find a missing side; solve perimeter problems.
Prerequisite knowledge. Lesson 2 and Grade 3 perimeter.
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. 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. Did I add every side? 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. Adding only two sides of a rectangle. Add all sides or use 2(l + w).
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Measure the edges of objects. 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 4 » 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 4.MD.A.3 (perimeter); Cambridge Primary Mathematics Stage 4 (perimeter). These sources informed the lesson.