Cogito
Grade 3 Math · Chapter 4 · Lesson 4
Breaking a Big Area Apart
The distributive property, in shapes.
10 problems · about 13 minutes · 3.MD.C.7
What this lesson teaches
The child finds the area of a large rectangle by splitting it into two smaller rectangles.
- A big rectangle can be split into two smaller ones.
- Find each area, then add them.
- It is the distributive property, drawn as shapes.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Finding a Missing Side: Area 42, one side 6. What is the other side?
Answer 7
Why The other side is 7.
Review — Area by Multiplying: A rectangle 8 by 7. What is its area?
Answer 56
Why The area is 56 square units.
Review — What Area Is: A rectangle 7 across and 3 down. What is its area?
Answer 21
Why The area is 21 square units.
Warm Up
Straightforward practice. Get the method working first.
3 problemsArea of 5 by 9, split as 5 by 5 and 5 by 4?
Answer 45
Why 25 + 20 = 45 square units.
Does splitting a rectangle change its area?
Answer No. The pieces still cover the same space.
Why The two pieces cover exactly the same space as the whole.
Area of 4 by 9, split as 4 by 5 and 4 by 4?
Answer 36
Why 20 + 16.
Build It Up
The same ideas with more to keep track of.
1 problemArea of 6 by 8, split as 6 by 4 and 6 by 4?
Answer 48
Why 24 + 24.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsArea of 7 by 9, split as 7 by 5 and 7 by 4?
Answer 63
Why 35 + 28.
The Long Room: A room 3 by 12. Split it into 3 by 10 and 3 by 2. What is the total area?
Answer 36 square units
Why 30 + 6 = 36 square units.
The Wall: A wall 5 by 11. Split it into 5 by 10 and 5 by 1. What is the area?
Answer 55 square units
Why 50 + 5 = 55 square units.