**Middle School Number Sense Lesson 1: Multiplying by 11**

Probably the first number sense concept I learned was

**. Since I'm a little lazy (I prefer to call it efficiency), I will refer to this concept as**

*multiplying a number by 11***Mult11**. The secret to this concept is "adding neighbors," starting from the right.

**Number Dojo Level: 11 (of course)**

**Why Mult11?**

On 2016 TMSCA middle school tests, this concept showed up

**12 times**, always within the first 10 problems. To be specific (in order of appearance), it showed up as questions 6, 5, 2, 1, 4, 5, 4, 5, 1, 4, 6, and 3.

**How to multiply by 11:**

- Write down the units digit.
- Add pairs of neighboring digits, starting with the units and tens digits. Write the sum down if it is <10; if it has 2 digits, write the units digit and regroup the 1.
- Add the tens and hundreds digit (plus the regrouped 1, if any).
- Continue this pattern until you run out of pairs, writing the sum and regrouping each time.
- Finish by writing the first digit of the number (plus any regrouped 1).

**Example 1: 11 x 52**

- Write the
**2**. - Then add the 2 and 5 to get
**7**; write this down to the left. - Finally, write the
**5**on the left. The answer is**572**.

**Example 2: 58 x 11**

- Write the
**8**. - Then add neighbors. 8 + 5 = 13, so write the
**3**and regroup the 1. - Remember that you have to add the regrouped 1. 5 + 1 =
**6**; write this down. The answer is**638**.

**Example 3: 11 x 793**

- Write the
**3**. - Then add neighbors: 3 + 9 = 12. Write the
**2**and regroup the 1. - 9 + 7 = 16, plus the regrouped 1 = 17. Write the
**7**and regroup the 1. - Now, add 7 and the regrouped 1 and write
**8**. The answer is**8723**.

**Example 4: 314159 x 11**

- Write the
**9**. - Then add neighbors: 9 + 5 = 14. Write the
**4**and regroup the 1. - 5 + 1 (+ 1) =
**7**. - 1 + 4 =
**5**. - 4 + 1 =
**5**. - 1 + 3 =
**4**. - Finally, write the
**3**on the left. The answer is**3455749**.

**Here's a free worksheet to help you practice Mult11:**

mult11.pdf |

**And a video.**

Up Next: AddSequence

Up Next: AddSequence