Don’t let eleven and twelve timetables frighten you. They are full of patterns which make mental math and memorization easier than you think.

Eleven Timetables
Pattern One

The eleven timetables are neat to learn because the products results in a double reflection of the number multiplied by eleven.
11 x 1 =11
11 x 2 = 22
11 x 3 = 33
11 x 4 = 44 . . .11 x 9 = 99

This pattern is true for 11 x 1 through 11 x 9.

Pattern Two

This multiplication pattern and strategy applies to all two digit numbers multiplied by eleven.

11 x 11 = 121
11 x 12 = 132
11 x 13 = 143
11 x 14 = 154
11 x 15 = 165

Did you notice? First, the middle number in the product is the sum of the numbers beside it. Secondly, the outer digits in the product are the second factor. So, the following strategy can apply when multiplying 11 x 11 thru 11 x 99.

Example: 11 x 21 =

Steps:
1. Write the second factor as the product but leave a space between the numbers.11 x 21 = 2 1 (notice the space between the numbers)

2. **Add the digits of the second factor and place the sum between the two numbers in step one. (The second factor is ‘21’, so 2 + 1 = 3;
Thus 11 x 21 = 231.


**When the sum is larger than 9.
Example 11 x 39 =

1. Separate digits of second factor: 11 x 39 = 3 9
2a. Add digits of second factor (3 + 9 =12)
2b. Place the ones digit of the sum in the space, meaning ‘2’ :
2c. Add the tens place digit of the sum,’1’ to the hundred place of the product, ‘3’. Thus, 11 x 39 = 429


Twelve Timetables

Wow, you’ve made it to the twelve timetables! Don’t stop practicing all the other timetables. We’ll use them to learn the 12s. Let’s start with finding patterns. Patterns are helpful when you take the initiative to write the timetables on an assignment or test before you begin to work any problems. Then, use the patterns to check for accuracy.

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

Pattern One: Look at 12 x 1 through 12 x 4. The tens digit in the product is the same as the number multiplied by twelve. Thereafter, the tens digit in the product / answer is one more than the 2nd factor or number multiplied by twelve.

Pattern Two: The digit in the ones place of the product skip counts by 2 and starts over after the count reaches 8.

Pattern Three: The first digit(s) in the product are in numerical order with the exception ‘5’ and ‘11’ are skipped.

Mental Strategy for 12 x12 thru 12 x 19

12 x 12 = 144
12 x 13 = 156
12 x 14 = 168


Example: 12 x 13 =
Steps:
1. To get the first two numbers of the answer: Add 12 and the ones digit of the other number. 12 + 3 = 15
**2. To get the last digit of the answer: Multiply “2” which is the tens digit of “12” and the ones digit of the other number. In this case, “3.” 2 x 3 = 6
3. Thus, the answer is 156.


**When the sum in step two is larger than nine. . .
Example: 12 x 15 =
Step 1) To get the first two numbers of the answer: Add 12 and the ones digit of the other number. 12 + 5 =17
Step 2) To get the last digit of the answer: Multiply “2” which is the tens digit of “12” and the ones digit of the other number. In this case, “5.” 2 x 5 = 10
(The zero is the last digit of the answer. The “1” is added to the 17....thus the answer is 180)

Try it and check your answer below.

12 x 16 = 192
12 x 17 = 204
12 x 18 = 216
12 x 19 = 228

Did you notice the previous patterns still apply?