3B · Chapter 13 · Lesson 5
Perimeter
Recognize perimeter as distance around the external boundary.
Today's mathematical question
A rectangular fence is 8 cm long and 5 cm wide. What length of edging goes all the way around?
Learning target
Recognize perimeter as distance around the external boundary.
Before starting: Prior lesson: Area of Composite Figures. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
A 5-by-2 rectangle has a 4-by-1 corner removed. Find the remaining area in square units.
Reveal explanation
Answer: 6 square units
Whole rectangle: 5 × 2 = 10. Missing corner: 4 × 1 = 4. Remaining: 10 − 4 = 6.
Square-unit grid; count only visible squares without gaps or overlap. - P2
A 7-by-3 rectangle has a 2-by-2 corner removed. Find the remaining area in square units.
Reveal explanation
Answer: 17 square units
Whole rectangle: 7 × 3 = 21. Missing corner: 2 × 2 = 4. Remaining: 21 − 4 = 17.
Square-unit grid; count only visible squares without gaps or overlap. - P3
A 8-by-4 rectangle has a 2-by-3 corner removed. Find the remaining area in square units.
Reveal explanation
Answer: 26 square units
Whole rectangle: 8 × 4 = 32. Missing corner: 2 × 3 = 6. Remaining: 32 − 6 = 26.
Square-unit grid; count only visible squares without gaps or overlap.
Learn and understand
Perimeter is the distance around the outer boundary of a closed figure. Imagine walking along the outside fence and adding every edge once. Counting area squares inside answers a different question. Perimeter uses linear units such as centimeters or meters. Imagine walking around the outside of a shape once. Every outside edge contributes to perimeter, but internal grid lines do not. Include the unit of length.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Trace the outer boundary with a finger or colored pencil and sum the edge lengths. For a grid shape, count exterior edge segments, not squares.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- perimeter
- total distance around outside
- boundary
- outer edge
- linear unit
- unit measuring length
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
A rectangular fence is 8 cm long and 5 cm wide. What length of edging goes all the way around?
- Identify the whole, the units, and what the question asks.
- Walk along every outer edge once: 8 + 5 + 8 + 5 = 26 cm.
- Check that the answer uses the right units and makes sense.
Answer: 26 cm
Check your understanding 1
A rectangular fence is 4 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal answer and explanation
16 cm — Walk along every outer edge once: 4 + 4 + 4 + 4 = 16 cm.
Worked example 2
Explore, calculate, verify
A rectangular fence is 3 cm long and 5 cm wide. What length of edging goes all the way around?
- Identify the whole, the units, and what the question asks.
- Walk along every outer edge once: 3 + 5 + 3 + 5 = 16 cm.
- Check that the answer uses the right units and makes sense.
Answer: 16 cm
Check your understanding 2
A rectangular fence is 8 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal answer and explanation
24 cm — Walk along every outer edge once: 8 + 4 + 8 + 4 = 24 cm.
Worked example 3
Explore, calculate, verify
A rectangular fence is 5 cm long and 4 cm wide. What length of edging goes all the way around?
- Identify the whole, the units, and what the question asks.
- Walk along every outer edge once: 5 + 4 + 5 + 4 = 18 cm.
- Check that the answer uses the right units and makes sense.
Answer: 18 cm
Check your understanding 3
A rectangular fence is 9 cm long and 3 cm wide. What length of edging goes all the way around?
Reveal answer and explanation
24 cm — Walk along every outer edge once: 9 + 3 + 9 + 3 = 24 cm.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
A rectangular fence is 9 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 26 cm
Walk along every outer edge once: 9 + 4 + 9 + 4 = 26 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G2
A rectangular fence is 9 cm long and 5 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 28 cm
Walk along every outer edge once: 9 + 5 + 9 + 5 = 28 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G3
A rectangular fence is 3 cm long and 3 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 12 cm
Walk along every outer edge once: 3 + 3 + 3 + 3 = 12 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G4
A rectangular fence is 3 cm long and 6 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 3 + 6 + 3 + 6 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G5
A rectangular fence is 8 cm long and 3 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 22 cm
Walk along every outer edge once: 8 + 3 + 8 + 3 = 22 cm.
Square-unit grid; count only visible squares without gaps or overlap.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
A rectangular fence is 5 cm long and 2 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 14 cm
Walk along every outer edge once: 5 + 2 + 5 + 2 = 14 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I2
A rectangular fence is 4 cm long and 6 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 4 + 6 + 4 + 6 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I3
A rectangular fence is 7 cm long and 2 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 7 + 2 + 7 + 2 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I4
A rectangular fence is 7 cm long and 3 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 7 + 3 + 7 + 3 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I5
A rectangular fence is 7 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 22 cm
Walk along every outer edge once: 7 + 4 + 7 + 4 = 22 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I6
A rectangular fence is 4 cm long and 2 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 12 cm
Walk along every outer edge once: 4 + 2 + 4 + 2 = 12 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I7
A rectangular fence is 9 cm long and 2 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 22 cm
Walk along every outer edge once: 9 + 2 + 9 + 2 = 22 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I8
A rectangular fence is 8 cm long and 6 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 28 cm
Walk along every outer edge once: 8 + 6 + 8 + 6 = 28 cm.
Square-unit grid; count only visible squares without gaps or overlap.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
A rectangle is 6 cm by 3 cm. Find its perimeter and explain why the answer uses cm rather than cm².
Reveal explanation
Answer: 18 cm
Add four edges: 6+3+6+3=18 cm. Boundary distance is one-dimensional.
- C2
Two 6-by-1 rectangles share a side of length 1 along their short ends. Why is that shared side not counted twice in their outer perimeter?
Reveal explanation
Answer: It is internal
When the pieces are combined the shared edge lies inside the new 12-by-1 figure. Only the exposed boundary is counted.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
A rectangular fence is 3 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 14 cm
Walk along every outer edge once: 3 + 4 + 3 + 4 = 14 cm.
Square-unit grid; count only visible squares without gaps or overlap. - E2
A rectangular fence is 7 cm long and 5 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 24 cm
Walk along every outer edge once: 7 + 5 + 7 + 5 = 24 cm.
Square-unit grid; count only visible squares without gaps or overlap. - E3
A rectangular fence is 6 cm long and 3 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 6 + 3 + 6 + 3 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap.