Multiplication Facts: 11 and 12 - Third Grade Mathematics

Stepping beyond the 10s table into the 11s and 12s gives you advanced multiplication power. These numbers show up frequently in real life—from counting eggs in dozens and months in a year to measuring inches on a foot-ruler. In this chapter, you will master the double-digit repeat trick for 11s and the "10 + 2" distributive strategy for 12s.

The Elevens Family: The Repeating Digit Rule

For single-digit numbers (1 through 9), multiplying by 11 is remarkably simple: the digit simply repeats itself in both the tens and ones places!

11 x 1 = 11
11 x 2 = 22
11 x 3 = 33
11 x 4 = 44
11 x 5 = 55
11 x 6 = 66
11 x 7 = 77
11 x 8 = 88
11 x 9 = 99

Why does this happen? Because 11 is 10 + 1:
- 11 x 4 = (10 x 4) + (1 x 4) = 40 + 4 = 44!


Elevens Beyond 9

When you multiply 11 by two-digit numbers like 10, 11, and 12, use the distributive property:
- 11 x 10 = 110

- 11 x 11 = (10 x 11) + (1 x 11) = 110 + 11 = 121

- 11 x 12 = (10 x 12) + (1 x 12) = 120 + 12 = 132


The Twelves Family: The "10 + 2" Strategy

The secret to mastering the 12s table with complete ease is breaking 12 apart into 10 and 2.

Formula: 12 x n = (10 x n) + (2 x n)

Everyone loves multiplying by 10, and everyone knows how to double a number (multiplying by 2). Combining them makes the 12s family a breeze!

Example 1: 12 x 5
- 10 x 5 = 50
- 2 x 5 = 10
- Combine: 50 + 10 = 60!

Example 2: 12 x 7
- 10 x 7 = 70
- 2 x 7 = 14
- Combine: 70 + 14 = 84!

Example 3: 12 x 8
- 10 x 8 = 80
- 2 x 8 = 16
- Combine: 80 + 16 = 96!

The Complete 12s Table:
12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72
12 x 7 = 84
12 x 8 = 96
12 x 9 = 108
12 x 10 = 120
12 x 11 = 132
12 x 12 = 144

Real-World Twelves: Dozens and Feet

The number 12 is one of the most common grouping numbers in our culture:
- 1 dozen eggs = 12 eggs. 3 dozen eggs = 3 x 12 = 36 eggs.

- 1 foot = 12 inches. A 5-foot board = 5 x 12 = 60 inches long.

- 1 year = 12 months. 4 years = 4 x 12 = 48 months.


Chapter Practice Exercises

  1. Calculate the products: a. 11 x 6 b. 11 x 8 c. 12 x 3 d. 12 x 6 e. 12 x 9
  2. Solve 12 x 4 using the (10 + 2) strategy. Show both parts and the sum.
  3. A bakery sells cupcakes in boxes of 12. If Mrs. Rivera buys 5 boxes of cupcakes, how many cupcakes does she buy in total?
  4. A carpenter has a wooden beam that is 8 feet long. If there are 12 inches in each foot, how many inches long is the wooden beam?
  5. Solve 11 x 11 and 12 x 12.

Solutions and Step-by-Step Answers

  1. Products: a. 11 x 6 = 66. b. 11 x 8 = 88. c. 12 x 3 = 36. d. 12 x 6 = 72 (60 + 12). e. 12 x 9 = 108 (90 + 18).
  2. For 12 x 4:
  3. 10 x 4 = 40
  4. 2 x 4 = 8
  5. 40 + 8 = 48.
  6. 5 boxes of 12 cupcakes: 5 x 12 = 60 cupcakes.
  7. 8 feet x 12 inches per foot: 8 x 12 = 96 inches long.
  8. 11 x 11 = 121; 12 x 12 = 144.