Multiplication Facts: 0, 1, 2, 5, and 10 - Third Grade Mathematics

Mastering multiplication facts begins with the foundational fact families: 0s, 1s, 2s, 5s, and 10s. These numbers have powerful, consistent patterns that make them easy to learn, easy to visualize, and effortless to recall. In this chapter, you will master these core facts and uncover the special mental math secrets behind each one.

The Zero and One Families

The 0s and 1s are the easiest facts in the entire multiplication table because they follow unbreakable universal rules.

The 0 Facts Rule: Anything x 0 = 0
0 x 4 = 0       7 x 0 = 0       12 x 0 = 0

The 1 Facts Rule: Anything x 1 = Itself
1 x 6 = 6       9 x 1 = 9       12 x 1 = 12

The Twos Family: The Double Machine

Multiplying by 2 is the exact same thing as doubling a number (adding the number to itself)!

2 x 1 = 2       (1 + 1)
2 x 2 = 4       (2 + 2)
2 x 3 = 6       (3 + 3)
2 x 4 = 8       (4 + 4)
2 x 5 = 10      (5 + 5)
2 x 6 = 12      (6 + 6)
2 x 7 = 14      (7 + 7)
2 x 8 = 16      (8 + 8)
2 x 9 = 18      (9 + 9)
2 x 10 = 20     (10 + 10)

Pattern Check: Every multiple of 2 is an even number ending in 0, 2, 4, 6, or 8.

The Fives Family: Nickel Counting and the Clock Face

Multiplying by 5 is identical to counting nickels or reading minutes on an analog clock!

Look at the clock face connection:
- When the minute hand points to 1: 1 x 5 = 5 minutes.

- When it points to 2: 2 x 5 = 10 minutes.

- When it points to 6: 6 x 5 = 30 minutes (half past the hour).

- When it points to 9: 9 x 5 = 45 minutes.

5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
5 x 6 = 30
5 x 7 = 35
5 x 8 = 40
5 x 9 = 45
5 x 10 = 50

Pattern Check:
- Every multiple of 5 ends in either 5 or 0.

- When multiplying 5 by an even number, the product ends in 0 (e.g., 5 x 4 = 20).

- When multiplying 5 by an odd number, the product ends in 5 (e.g., 5 x 7 = 35).

The Tens Family: The Place Value Shift

Multiplying by 10 is one of the most powerful mental math shortcuts in base-ten arithmetic. When you multiply a whole number by 10, every digit shifts one place to the left, and a zero fills the empty ones place.

10 x 1 = 10
10 x 2 = 20
10 x 3 = 30
10 x 4 = 40
10 x 5 = 50
10 x 6 = 60
10 x 7 = 70
10 x 8 = 80
10 x 9 = 90
10 x 10 = 100

Mental Math Tip: To multiply any number by 10, simply append a 0 to the end of the number: 8 x 10 = 80!

The Connection Between 5s and 10s

Because 10 is double 5, a product in the 10s family is always double the matching product in the 5s family:
- 5 x 6 = 30

- 10 x 6 = 60 (which is double 30!)

If you ever forget a 10s fact, take the 5s fact and double it. Or if you know a 10s fact, cut it in half to get the 5s fact!

Chapter Practice Exercises

Solve these quick-fire mental math facts: a. 2 x 7 b. 5 x 8 c. 10 x 4 d. 1 x 9 e. 0 x 8
Fill in the missing factors: a. 2 x ___ = 16 b. 5 x ___ = 35 c. 10 x ___ = 90 d. ___ x 6 = 12
Use the clock face strategy to solve: What minute mark does the minute hand reach when it points to 7? Write the multiplication fact.
Maya has 6 nickels in her coin purse. How many cents does Maya have?
Leo bought 9 packs of stickers. Each pack had 10 stickers inside. How many stickers does Leo have in all?

Solutions and Step-by-Step Answers

Quick-fire facts: a. 2 x 7 = 14 (double 7). b. 5 x 8 = 40. c. 10 x 4 = 40. d. 1 x 9 = 9. e. 0 x 8 = 0.
Missing factors: a. 2 x 8 = 16. b. 5 x 7 = 35. c. 10 x 9 = 90. d. 2 x 6 = 12.
When the minute hand points to 7, each number represents 5 minutes: 7 x 5 = 35 minutes.
Each nickel is worth 5 cents: 6 x 5 = 30 cents.
9 packs of 10 stickers: 9 x 10 = 90 stickers in all.