You cut arrays apart in Chapter 3. A rectangle can be cut the same way.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
An example
A rectangle 4 by 12 is hard. Cut it into 4 by 10 and 4 by 2.
Add the pieces
40 and 8 makes 48. So the area is 48 square units.
Why it works
The two pieces cover the whole rectangle with nothing left over and nothing counted twice.
Splitting a rectangle to make it easier
A rectangle 4 by 13 is awkward. Cut it into a 4 by 10 piece and a 4 by 3 piece: 40 + 12 = 52 square units. This is the distributive property again, and here you can literally draw the line where the split happens.
Where to cut
Split at a number that makes both pieces easy — usually a ten. 13 splits naturally into 10 and 3. You could split it into 6 and 7 instead and still get 24 + 28 = 52, but you made more work for yourself. A good split is one where both pieces use facts you know.
Where this leads
This is exactly the method behind multiplying larger numbers in Grade 4, where 4 × 13 is done as 4 × 10 plus 4 × 3 with no picture at all. Seeing it as a shape first means the written method will make sense rather than being a ritual.
Step 2: Try It Yourself
Tap and try it out.
4 × 9 = 36
4 × 9 = (4 × 5) + (4 × 4) = 20 + 16 = 36
The array is cut into 4 × 5 and 4 × 4. Two easier facts that add to the same total.
Step 3: Watch an Example
One step at a time.
Watch Leo Split a Rectangle
Leo needs the area of a rectangle 4 by 9.
- Step 1
He cuts it into 4 by 5 and 4 by 4.
Step 4: Your Turn
Practice makes it stick.
The Long Room
Problem 1 of 2
A room 3 by 12. Split it into 3 by 10 and 3 by 2. What is the total area?
square units
The Wall
Problem 2 of 2
A wall 5 by 11. Split it into 5 by 10 and 5 by 1. What is the area?
square units
Split, Then Add
1 of 3
Area of 4 by 9, split as 4 by 5 and 4 by 4?
2 of 3
Area of 6 by 8, split as 6 by 4 and 6 by 4?
3 of 3
Area of 7 by 9, split as 7 by 5 and 7 by 4?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Area of 5 by 9, split as 5 by 5 and 5 by 4?
Question 2 of 2
Does splitting a rectangle change its area?
What You Learned
- A big rectangle can be split into two smaller ones.
- Find each area, then add them.
- It is the distributive property, drawn as shapes.