**Middle School Number Sense Lesson 60: Estimating with Multiplication of 3 Close Whole Numbers**

Back in the summer (80 lessons ago), we first combined the concepts of multiplication and estimation (in

**EstMultWhole**). I can't remember seeing a number sense test that did NOT contain this concept. Today we will look at a specific subset of these problems--where we are asked to multiply 3 numbers that are close (or somewhat close) together. This concept appeared

**8 times**last year, mostly at either question # 30 or

**question # 60**.

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In many cases when these questions appear, the 3 numbers will be consecutive integers (or consecutive even or odd integers). It may be sufficient to simply cube the middle number. Or it may be easier to multiply 2 of the numbers together, and then round and multiply the result by the third number.

*****: The greater the spacing between the numbers, the less likely the answer will be within range if you simply cube the middle number. Let's take a look at some examples:

__NOTE__

Example 1: * 11 x 12 x 13 = ___

Example 1: * 11 x 12 x 13 = ___

- Cube the middle number. (You should have this one memorized). Your answer is
**1728**. - The exact answer is
**1716**, and the acceptable (+/- 5%) range is**from 1631 to 1801**.

**Example 2: * 13 x 14 x 15 = ___**

- Cube the middle number. If you don't have this one memorized, try this: Square 14 to get
**196**. Round this to 200, and then multiply by 14 again to get**2800**. - The exact answer is
**2730**, and the acceptable (+/- 5%) range is**from 2594 to 2866**.

**Example 3: * 11 x 14 x 17 = ___**

- The spacing here is dangerous. Let's try multiplying 11 x 14 to get
**154**. Round this down to 150, and then multiply by 17 to get**2550**. - The exact answer is
**2618**, and the acceptable (+/+ 5%) range is**from 2488 to 2748**. *** Notice**that our answer from Example 2 would've been out of range here.

**Example 4: * 20 x 25 x 30 = ___**

- Personally, I wouldn't estimate this because the multiplication is easy enough. Multiply 20 by 25 to get
**500**. Then multiply this by 30 to get**15000**. - The acceptable range is
**from 14250 to 15750**. If we had cubed 25, we would've gotten**15625**, which would be within range, but barely.

**Example 5: * 9 x 12 x 15 = ___**

- I wouldn't estimate this one either, but we can. Let's multiply 9 x 12 to get
**108**. Round this to 110. - Write down our
**0**, and then multiply 11 x 15 to get**165**; write this in front. Our answer is**1650**. - The exact answer is
**1620**, and the acceptable (+/- 5%) range is**from 1539 to 1701**.

**Here's a free worksheet to help you practice EstMult3Close:**

estmult3close.pdf |

**Up Next for Middle School: Sphere**