Cogito
Grade 3 Math · Chapter 4 · Lesson 7
Same Area, Different Shape
Rectangles can share an area and look nothing alike.
10 problems · about 13 minutes · 3.MD.C.7, 3.MD.D.8
What this lesson teaches
The child finds several rectangles with a given area and compares their perimeters.
- Rectangles with the same area can have different shapes.
- They can have very different perimeters.
- The squarest rectangle has the smallest perimeter.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Telling Area and Perimeter Apart: A rectangle 9 by 4. What is its area?
Answer 36
Why The area is 36 square units.
Review — Perimeter: A rectangle 9 by 5. What is its perimeter?
Answer 28
Why The perimeter is 28 units.
Review — Breaking a Big Area Apart: Area of 5 by 9, split as 5 by 5 and 5 by 4?
Answer 45
Why 25 + 20 = 45 square units.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA 2 by 9 rectangle. What is its area?
Answer 18
Why The area is 18 square units.
Which rectangle with area 36 has the smallest perimeter?
Answer 6 by 6.
Why 6 by 6 has perimeter 24; 4 by 9 has 26.
A 2 by 6 rectangle. What is its perimeter?
Answer 16
Why 2 + 6 + 2 + 6.
Build It Up
The same ideas with more to keep track of.
1 problemA 3 by 4 rectangle. What is its perimeter?
Answer 14
Why 3 + 4 + 3 + 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsBoth have area 12. Do they have the same perimeter?
Answer No.
Why Compare 16 and 14.
The Pen: A pen with area 16 can be 4 by 4 or 2 by 8. Which needs less fence?
Answer The 4 by 4.
Why The squarer shape has the smaller perimeter.
The Long One: A rectangle 1 by 12. What is its perimeter?
Answer 26 units
Why The perimeter is 26 units.