Cogito
Grade 3 Math · Chapter 1 · Lesson 2
Arrays and the Commutative Property
Turn the array and the product stays the same.
10 problems · about 12 minutes · 3.OA.A.1, 3.OA.B.5
What this lesson teaches
The child recognizes that multiplication can be done in either order, and uses it to halve the facts to learn.
- Multiplication can be done in either order.
- 3 × 4 and 4 × 3 both give 12.
- That halves how many facts you have to learn.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Equal Groups and Multiplication: 4 groups of 5. What is the product?
Answer 20
Why 4 × 5 = 20.
Review — Equal Groups and Multiplication: What does multiplication do?
Answer Adds equal groups the short way.
Why Multiplication only works when the groups are the same size.
Warm Up
Straightforward practice. Get the method working first.
4 problemsYou know 9 × 2 = 18. What is 2 × 9?
Answer 18
Why The commutative property gives it free.
Why is the commutative property useful?
Answer It halves the facts you must learn.
Why One fact learned gives you its partner for nothing.
You know 8 × 2 = 16. What is 2 × 8?
Answer 16
Why Same product.
5 × 3 = ?
Answer 15
Why 3 fives or 5 threes.
Build It Up
The same ideas with more to keep track of.
2 problems10 × 4 = ?
Answer 40
Why 4 tens.
Does 7 × 6 give the same product as 6 × 7?
Answer Yes. Order does not matter.
Why Turn the array sideways.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Garden: A garden has 5 rows of 7 plants. How many plants? What is 7 × 5?
Answer 35 plants
Why 5 × 7 and 7 × 5 are both 35.
Two Ways: You know 6 × 4 = 24. What is 4 × 6?
Answer 24
Why The order does not change the product.