Cogito
Grade 3 Math · Chapter 4 · Lesson 8
Area of Joined Shapes
Split an odd shape into rectangles.
10 problems · about 13 minutes · 3.MD.C.7
What this lesson teaches
The child finds the area of a shape made of two rectangles by adding their areas.
- An odd shape can be split into rectangles.
- Find each area, then add them.
- Any split gives the same total.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Same Area, Different Shape: A 2 by 9 rectangle. What is its area?
Answer 18
Why The area is 18 square units.
Review — 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.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA 6 by 3 part and a 4 by 2 part. Total area?
Answer 26
Why 18 + 8 = 26 square units.
What do you do with an odd-shaped floor?
Answer Split it into rectangles.
Why Splitting turns an unfamiliar shape into ones you can handle.
A 4 by 4 part and a 2 by 3 part. Total area?
Answer 22
Why 16 + 6.
Build It Up
The same ideas with more to keep track of.
1 problemA 5 by 5 part and a 2 by 2 part. Total area?
Answer 29
Why 25 + 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsA 7 by 2 part and a 3 by 4 part. Total area?
Answer 26
Why 14 + 12.
The L-Shaped Room: A room splits into a 5 by 3 part and a 2 by 4 part. What is the total area?
Answer 23 square units
Why 15 + 8 = 23 square units.
The Patio: A patio splits into a 6 by 4 part and a 3 by 3 part. What is the total area?
Answer 33 square units
Why 24 + 9 = 33 square units.