Apply the Perimeter Formula for Rectangles

Students use the formula P = 2l + 2w (or P = 2(l + w)) to find the perimeter of rectangles in real-world and mathematical contexts. Students also find a missing side length when given the perimeter and one dimension.

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Grade 4 · Area and Perimeter of Rectangles · question 1 of 3

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20 rungs. A star at the top.

Uma plans to wrap ribbon around the edge of each shape. Which of these shapes has the smallest perimeter?

How it is taught

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Perimeter is the distance around a rectangle.

Add length and width, then double.

Opposite sides of a rectangle match.

Read it: Count inside, then around

A 4 by 5 frame of tiles sits on the page. Twenty cells fill the inside. The walk around the edge is a different number.

Count the cells inside: 4 rows of 5 make 20.
Walk the edge: 5 + 4 + 5 + 4.
Name both: 20 inside, 18 around.

Counting every cell one by one still works, but rows of 5 get you 20 with less losing track.

The walk around uses each side once; doubling 5 and 4 is the same walk.

Inside and around are two jobs on one frame: filling tiles is not the same as fencing them.

Count the cells inside, then add the four sides to walk around.

Adding 4 and 5 once and calling 9 the walk around, or using 20 for both jobs.

Walk all four sides: 5, 4, 5, 4. That is 18, not 20 and not 9.

A rectangle is 8 by 3. What is its perimeter? — 22. Walk around: 8 + 3 + 8 + 3 = 22, so 2 × 8 + 2 × 3 = 22.

Perimeter of an 8 ft × 5 ft garden

Here's Mira's rectangular garden. She needs fence all the way around it. How much fence does she need?

Grade 4 · Using P = 2l + 2w to fence a garden

The two long sides of the garden are each eight feet.

The two short sides are each five feet.

We use the perimeter formula: P equals two times the length, plus two times the width.

Length is eight, width is five. We plug them in.

Two times eight is sixteen — that's both long sides together.

Two times five is ten — that's both short sides together.

Now add the two parts: sixteen plus ten equals twenty-six.

Mira needs twenty-six feet of fence. You applied the perimeter formula!

Now you try. Find the distance around this rectangle. How far around is it?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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