Look for patterns in the number sentences below.

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

• Describe a pattern that will help you multiply numbers by 11.
• Clearly explain how you could use your pattern to find the answer to 11 x 16.

The ones and tens digit in the answer increase by one each time. The next number in the pattern is 176 because 5 + 1 = 6 and 6 + 1 = 7. Therefore, 11 x 16 = 176.

The ones digit in the answer is the same as the ones digit in the number being multiplied by 11; the tens digit in the answer is equal to the sum of the ones and tens digits in the number being multiplied by 11; and the hundreds digit in the answer is equal to the tens digit in the number being multiplied by 11.

Therefore, 11 x 16 = 176 because the ones digit must be 6, the tens digit must be 6+1 or 7, and the hundreds digit must be 1.

A 1 point response may describe the pattern in the number sentences, but does not explain how the pattern can be used to find 11 x 16. Or they may explain a way to find 11 x 16 using the number sentences given but does not clearly state a pattern.

A 0 point response will show little or no algebraic sense in recognizing and extending a pattern.