Cogito
Grade 3 Math · Chapter 3 · Lesson 5
The Associative Property
Multiply three numbers in any order you like.
10 problems · about 13 minutes · 3.OA.B.5
What this lesson teaches
The child regroups three factors to make a multiplication easier.
- Three factors can be grouped in any order.
- Do the easy pair first.
- The product never changes.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Multiplying by 8 and 9: 7 × 9 = ?
Answer 63
Why 7 × 9 = 63, and 6 + 3 = 9.
Review — Multiplying by 7: 8 × 7 = ?
Answer 56
Why 8 × 7 = 56.
Review — Multiplying by 6: 9 × 6 = ?
Answer 54
Why 9 × 6 = 54.
Warm Up
Straightforward practice. Get the method working first.
3 problems2 × 5 × 6 = ?
Answer 60
Why Grouping the 2 and 5 first makes it 10 × 6.
Does regrouping change the product?
Answer No. Only the work changes.
Why The product stays the same however you group.
2 × 3 × 5 = ?
Answer 30
Why 6 × 5.
Build It Up
The same ideas with more to keep track of.
1 problem5 × 2 × 7 = ?
Answer 70
Why 10 × 7.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problems3 × 12 = ? Try 3 × 2 × 6.
Answer 36
Why 6 × 6.
Three Factors: 2 × 4 × 5 = ?
Answer 40
Why 2 × 20 = 40.
The Crates: 3 crates each hold 2 boxes of 6 apples. How many apples?
Answer 36 apples
Why 6 × 6 = 36 apples.