Lesson 13 — Perimeter of Rectangles
Learners find the perimeter of a rectangle as the distance around its four sides, then discover the shortcut — add the length and width and double, or 2 × length + 2 × width — and apply it to real problems like fencing a garden. Perimeter becomes "how far around."
Objectives
- D05.S3.04.02 Apply formulas for the area and perimeter of rectangles to solve real-world and mathematical problems.
Essential question
How do I find the perimeter of a rectangle and use it to solve real problems?
Materials
Standard materials
- String or rope and a ruler · 1 per pair To walk and measure the distance around rectangles
- Paper or slate and a drawing tool · per learner To record side lengths and perimeters
Low-tech / no-cost
- A rectangle marked on the ground with stones at the corners Step around the outside and count your steps to find the perimeter
- Voice and body Walk the four sides aloud, counting each side's length
Enriched / lab & device
- A measuring tape · 1 per pair To measure real borders precisely
- A calculator · 1 per pair To compute perimeters of larger rectangles
Works in different contexts
- large-group Walk the perimeter of a large room or field together, counting the sides in one voice
- self-directed A learner measures a rectangle's sides, adds them, and checks 2 × length + 2 × width
- multi-age Older learners find a missing side from the perimeter; younger learners walk and count the outside
- level-grouped Learners who are ready solve for a missing side; others add the four sides with support
- outdoor-only Measure the fence line around a garden or field by pacing, then compute its perimeter
Lesson 13 — Perimeter of Rectangles
Summary
Learners find the perimeter of a rectangle as the distance around its four sides, then discover the shortcut — add the length and width and double, or 2 × length + 2 × width — and apply it to real problems like fencing a garden or framing a picture. Perimeter becomes “how far around.”
Objectives
- Apply formulas for the area and perimeter of rectangles to solve real-world and mathematical problems. (D05.S3.04.02)
Connection
How much fence to go around a field? How much trim to border a rug? How far is one lap around a yard? Each asks the same thing: how far around a shape. That is perimeter. Walk the four sides once and you have it; notice the two lengths and two widths, and you get a shortcut. People everywhere measure perimeter to fence fields, border cloth, and build walls — the distance around is the first thing a builder needs to know.
Materials
- String or rope and a ruler (per pair)
- Paper or slate and a drawing tool
Preparation
- Give each pair string and a ruler.
- Prepare (or plan to draw) the worked example: an 8-by-5 rectangle.
- Clear space to walk and measure.
Facilitator note
This lesson is written to the learner (“you”). Perimeter is the distance around: teach it by walking and measuring, then generalize to 2 × length + 2 × width (or 2 × (length + width)) as a shortcut (Van de Walle, Karp & Bay-Williams, 2019). Model once as a worked example (philosophy §13), then guide practice. Contrast perimeter (around) with area (cover) from Lesson 12 — naming the difference is a key retrieval-and-comparison moment. A learner’s pace at distinguishing area and perimeter is not a measure of their worth; a perimeter is a fact about a shape, never about a person. Measuring the boundary of land is a human and cross-cultural practice, from ancient field markers to modern fences. Count in the home language. For learners who are Deaf or hard of hearing, sign the walk-around; for learners who are blind or have low vision, feel the four sides of a tactile rectangle and count along the edge. Learners with limited movement direct a partner to walk the border. Mastery arrives at its own pace.
Procedure
- Gather — how far around (5 min). If you walked all the way around your desk or the room, how far would that be? That distance is the perimeter.
- Worked example — an 8-by-5 rectangle (10 min). Walk the four sides of a rectangle that is 8 long and 5 wide: 8 + 5 + 8 + 5 = 26. Notice the two lengths and two widths. Shortcut: 2 × 8 + 2 × 5 = 16 + 10 = 26. Same answer, fewer steps. Say the formula: perimeter = 2 × length + 2 × width.
- Guided practice — walk, then compute (15 min). Measure several rectangles with string, add the four sides, then check with the formula. Do the two ways always agree?
- Real problems (10 min). Solve: a garden is 12 meters by 7 meters — how much fence goes around it? A picture is 30 cm by 20 cm — how much border to frame it? For each, say the formula and the answer.
- Check with a partner (3 min). Trade a problem. Do you agree on the perimeter? Walk it together, kindly.
- Close (2 min). Remember: perimeter is the distance around — add the sides, or double the length plus the width.
Differentiation
- Support: Add the four sides only today; add the formula another day.
- Support (blind/low-vision): Feel the edges of a tactile rectangle and count the distance around.
- Extension: Given a perimeter (like 30) and one side (like 9), find the other side and explain how you know.
Assessment
- Formative (observation): Can the learner find the perimeter of a rectangle by adding its sides and by the formula, and state the answer with units?
- Self: Can the learner explain the difference between perimeter (around) and area (cover)?
Home connection
At home, measure the distance around a table, a rug, or a room with your steps or a string, and tell a grown-up the perimeter.
Resources
- Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and Middle School Mathematics: Teaching Developmentally (10th ed.). Pearson. (Perimeter as the distance around, with the formula as a shortcut.)