Multiplication Facts: 3, 4, and 6 - Third Grade Mathematics

As you continue expanding your multiplication fluency, the 3s, 4s, and 6s offer delightful mathematical patterns and relationships. By building on the facts you already know, you can use doubling strategies and the distributive property to master these fact families with speed and understanding.

The Threes Family: The Double-Plus-One Strategy

To multiply any number by 3, you can think of 3 as (2 + 1). That means you can double the number and then add one more group!

Formula: 3 x n = (2 x n) + (1 x n)

Example: Solve 3 x 7
- Step 1: Double 7: 2 x 7 = 14

- Step 2: Add one more 7: 14 + 7 = 21

- Result: 3 x 7 = 21!


3 x 1 = 3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 6 = 18
3 x 7 = 21
3 x 8 = 24
3 x 9 = 27
3 x 10 = 30

Notice the pattern in the sums of the digits for the 3s family:
- 12 -> 1 + 2 = 3

- 15 -> 1 + 5 = 6

- 18 -> 1 + 8 = 9

- 21 -> 2 + 1 = 3

- 24 -> 2 + 4 = 6

- 27 -> 2 + 7 = 9
The digits always add up to 3, 6, or 9!

The Fours Family: Double and Double Again!

Because 4 is 2 x 2, multiplying by 4 is simply doubling twice!

Strategy: To multiply by 4, double the number, then double that answer.

Example: 4 x 6
- First double 6: 6 + 6 = 12
- Then double 12: 12 + 12 = 24
- Result: 4 x 6 = 24!

Example: 4 x 8
- First double 8: 8 + 8 = 16
- Then double 16: 16 + 16 = 32
- Result: 4 x 8 = 32!

4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24
4 x 7 = 28
4 x 8 = 32
4 x 9 = 36
4 x 10 = 40

Notice that every single product in the 4s family is even.

The Sixes Family: Double the Threes or Use Fives

The number 6 has two brilliant helper strategies:

Strategy 1: Double the Threes

Since 6 is double 3, any multiple of 6 is double the matching multiple of 3!
- 3 x 8 = 24

- Double 24: 24 + 24 = 48

- Therefore: 6 x 8 = 48!


Strategy 2: The Fives-Plus-One Strategy

Since 6 is 5 + 1, multiply by 5 first, then add one more group! Example: 6 x 7
- 5 x 7 = 35

- 1 x 7 = 7

- 35 + 7 = 42

- Therefore: 6 x 7 = 42!


6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
6 x 10 = 60

Notice that when you multiply 6 by an even number, the product ends in the exact same digit as that even number!
- 6 x 2 = 12 (ends in 2)

- 6 x 4 = 24 (ends in 4)

- 6 x 6 = 36 (ends in 6)

- 6 x 8 = 48 (ends in 8)


Chapter Practice Exercises

  1. Calculate the products using mental math strategies: a. 3 x 6 b. 4 x 7 c. 6 x 4 d. 4 x 9 e. 6 x 8
  2. Use the "double and double again" strategy to solve 4 x 8. Show both doubling steps.
  3. Use the "double the 3s" strategy to find 6 x 9. Show the 3s fact and the doubling step.
  4. A clover has 3 leaves. How many leaves are on 8 clovers?
  5. A juice carton package has 4 rows of juice boxes with 6 boxes in each row. How many juice boxes are in the package?

Solutions and Step-by-Step Answers

  1. Products: a. 3 x 6 = 18. b. 4 x 7 = 28 (double 7 is 14; double 14 is 28). c. 6 x 4 = 24. d. 4 x 9 = 36 (double 9 is 18; double 18 is 36). e. 6 x 8 = 48.
  2. For 4 x 8:
  3. First double: 8 + 8 = 16.
  4. Second double: 16 + 16 = 32. Answer: 4 x 8 = 32.
  5. For 6 x 9:
  6. Threes fact: 3 x 9 = 27.
  7. Double 27: 27 + 27 = 54. Answer: 6 x 9 = 54.
  8. 8 clovers with 3 leaves each: 8 x 3 = 24 leaves.
  9. 4 rows of 6 juice boxes: 4 x 6 = 24 juice boxes.