**Middle School Number Sense Lesson 5: Multiplying Whole Numbers**

There are at least 60 different concepts involving multiplication that have shown up on Number Sense tests in the last few years. Today we will cover one that has no real time-saving benefits. These questions

*do not include*numbers (like 5, 11, 12, 15, 25, 37, 50, 75, 101, 111, 125, 143, 625, 1001, 1111, or 3367) with special properties. The real time-saver with these problems is practice--so be sure to download and use the worksheet below!

**Number Dojo Level: 10**

**Details**

In 2016, this showed up 8 times on middle school tests, most often in the first 5 questions (specifically, # 4, 2, 11, 5, 17, 4, 2, and 1). Like almost every other question type, these problems will be written horizontally instead of vertically, with the

**multiplicand**(listed first) and

**multiplier**(listed second) separated by a "x." For simplicity, we will call these

**factors**.

For MultWhole, at least one of the factors will be a single-digit number. To solve these problems, we can multiply in the traditional way (right to left) or in another way.

**The Traditional Way: 213 x 7**

- Starting at the right, multiply 7 x 3 to get 21. Write the
**1**and regroup the 2. - Multiply 7 by 1 to get 7, plus the regrouped 2 to get
**9**. Write this down. - Multiply 7 by 2 to get
**14**; write this in front. The answer is**1491**.

**Another Way: 213 x 7**

- Think of 213 as being 2 hundreds and 1 thirteen. Multiply left-to-right.
- 200 x 7 = 1400. 13 x 7 = 91.
- Add these together to get
**1491**. I prefer to use this method when possible. My purpose here is to point out that there are many ways to solve math problems, and it is best to learn more than one way so you can better understand how the math works.

**Example 1: 214 x 6**

- Starting at the right, multiply 6 by 4 to get 24. Write the
**4**and regroup the 2. - 6 x 1 = 6, plus the regrouped 2 =
**8**. Write this in front of the 4. - 6 x 2 =
**12**. Write this in front to get**1284**.

**Example 2: 2016 x 3**

- Think of this as 2 thousands and 1 sixteen. Multiply left-to-right.
- 2000 x 3 = 6000. 16 x 3 = 48.
- Add these together to get
**6048**.

**Example 3: 47 x 8**

- Starting at the right: 8 x 7 = 56. Write the
**6**and regroup the 5. - 8 x 4 = 32, plus the regrouped 5 =
**37**. Write this in front to get**376**.

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

multwhole.pdf |

**Up Next for Middle School: DivMultiples**