You will learn
- Add side lengths.
- Use the rectangle formula.
- 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).
- Regular shapes: sides × side length.
Words to know
Distance around.
Edge of a shape.
All sides equal.
Measure of length.
1. Discover: fencing
A farmer fences a field 8 m long and 5 m wide. How much fence?
2. Understand: perimeter
- Rectangle: 2 × (8 + 5) = 2 × 13 = 26 m.
- Square of side 6: 4 × 6 = 24.
- A rectangle has perimeter 30 and length 9: half-perimeter 15, so width 15 − 9 = 6.
- Regular hexagon of side 5: 6 × 5 = 30; triangle 7, 8, 9: 24.
Idea 1: Rectangle
8 by 5: 2 × (8 + 5) = 2 × 13 = 26. A fence round 8 m by 5 m is 26 m.
Idea 2: Regular
Square side 6: 4 × 6 = 24. Regular hexagon side 5: 6 × 5 = 30.
Idea 3: Missing side
Triangle 7, 8, 9: 24. P = 30, L = 9: 30 − 18 = 12, so W = 6.
Why 18? There are two lengths to subtract.
3. Worked examples
Example 1 (I show you): Rectangle
8 by 5
- 8 + 5 = 13.
- × 2.
Answer: 26
Example 2 (We do it together): Regular
Square side 6
- 4 × 6.
Answer: 24
Example 3 (You try): Missing
P = 30, L = 9
Show the steps and answer
- 30 − 18 = 12.
- 12 ÷ 2.
Answer: W = 6
Did you know?
Perimeter is measured in units of length, such as cm or m.
Why this matters
Perimeter is used for fencing, framing and trimming.
4. Explore: perimeter
You need paper.
- Label the sides.
- Add them.
- Write the unit.
- Check.
Think about it: what did you notice?
26 m.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The sides are ___.
- Perimeter = ___ + ___ + ___.
- The missing side is ___.
- The perimeter is ___ units.
Guided practice
Question 1. Perimeter of 8 by 5?
26 m.
Question 2. Square of side 6?
24.
Question 3. Width if P = 30, L = 9?
6.
Independent practice
Level 1: Start
- Perimeter of 8 by 5
- Square of side 6
- Hexagon of side 5
- Triangle 7, 8, 9
- Width if P = 30, L = 9
Level 2: Grow
- Perimeter of a 10 by 4 rectangle
- Square of side 9
- Triangle 5, 6, 7
Level 3: Stretch
- Regular pentagon, side 6
- Width if P = 36, L = 12
- Ben says width is 30 − 9 = 21. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A field is 8 m by 5 m. How much fence is needed?
Show a sample answer
26 m.
Another one. A garden is 12 m by 7 m. How much fence goes round it?
Show a sample answer
38 m
7. Common mistakes
Fix: Add all sides.
Fix: Add all four.
Fix: Perimeter adds lengths; area multiplies.
8. Lesson summary and revision card
- I can add side lengths.
- I can use the rectangle formula.
- 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.
- Rectangle: 2(l + w).
- Include units.
11. Next lesson
Next lesson: Area of triangles. 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 8 by 5. [3 marks]
- Find the perimeter of a square of side 6. [2 marks]
- Find the perimeter of a regular hexagon of side 5. [2 marks]
- Find the perimeter of a triangle with sides 7, 8 and 9. [2 marks]
- Ali says the width is 21 when P = 30 and L = 9 because 30 − 9 = 21. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- Add all sides or 2 × (8 + 5) [1]; 2 × 13 [1]; 26 [1]
- 4 × 6 [1]; 24 [1]
- 6 × 5 [1]; 30 [1]
- 7 + 8 + 9 [1]; 24 [1]
- No [1]. Two lengths use 18, leaving 12 [1]. Width = 12 ÷ 2 = 6 [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
- Perimeter of 8 by 5
- Square of side 6
- Hexagon of side 5
- Triangle 7, 8, 9
- Width if P = 30, L = 9
- Rectangle 8 by 5
- Square of side 6
- Regular hexagon, side 5
- Triangle 7, 8, 9
- Width if P = 30, L = 9
Homework
Measure the perimeter of your table.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Perimeter of 8 by 5 | 26 | 2 |
| Square of side 6 | 24 | 2 |
| Hexagon of side 5 | 30 | 2 |
| Triangle 7, 8, 9 | 24 | 2 |
| Width if P = 30, L = 9 | 6 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 26; 2 24; 3 30; 4 24; 5 6.
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 26; 7 24; 8 30; 9 24; 10 6.
Independent practice answers. Level 1: 1 26; 2 24; 3 30; 4 24; 5 6. Level 2: 1 28; 2 36; 3 18. Level 3: 1 30; 2 6; 3 Two lengths and two widths: 30 − 18 = 12, so W = 6..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Add side lengths | 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 formula | 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. Add all sides.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Perimeter of rectangles.
- 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 perimeters. You do not need to be good at mathematics to help.
- Measure round a room.
- Ask: did I add every side?
- Link to fencing a garden.
- 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 side lengths; use the rectangle formula; find a missing side; solve perimeter problems.
Prerequisite knowledge. Lesson 1.
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. Have I added every side? What is missing?
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. Add all sides.
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. Perimeter of rectangles. 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 » Ratios & Proportional Relationships; 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 3.MD.D.8 and 4.MD.A.3; Cambridge Primary Mathematics Stage 6 (perimeter). These sources informed the lesson.