**Elementary School Number Sense Lesson 1: Expanded Notation**

Now that we have taken our journey through the middle school and high school number sense tests, I thought I should get back to the basics and help the "young-uns" with the beginner concepts. This blog will now alternate between elementary, middle, and high school concepts. But instead of covering 10 concepts in a row from the same difficulty level (questions 1-10, 11-20, 21-30, etc.), I'll just do one at a time. In other words, today's post will be from questions

**1-10**, and my next elementary school post will come from questions

**11-20**. Also, I will address the most common questions from

**this year's tests** that haven't already been covered previously.

Questions with expanded notation have appeared

**5 times**so far this year on elementary tests with a median placement at

**question # 6**.

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One way to represent today's concept is to think about how we "read" numbers (either in our minds or aloud). For example, the number

**1974**reads "

**one thousand nine hundred seventy-four**." Or we could think of it as:

**1 thousand + 9 hundreds + 7 tens + 4 ones**

**expanded notation**. For these questions, a number can be written with or without

**parentheses**(because of the order of operations), with or without

**exponents**, with or without

**decimals**, and with or without

**words**. Also, they can be written in descending order of place value or not, and with addition or subtraction. The secret to success is to pay careful attention to all the numbers and signs. Brilliant, right?

*Focus on EVERYTHING*. :)

**Example 1: (6 x 100) + (8 x 10) + (2 x 1) = ___**

- This is 600 + 80 + 2.
- The answer is
**682**.

**Example 2: 4 x 1000 + 5 x 100 + 3 x 1 = ___**

- This is 4000 + 500 + 3.
- The answer is
**4503**. (Notice there were no tens in there).

**Example 3: (6 x 100) + (7 x 10) - (3 x 1) = ___**

- This is 600 + 70 - 3. (Notice the subtraction).
- This becomes 670 - 3, which is
**667**.

**Example 4:**

**9 x 10**

^{4}+ 8 x 10^{2}+ 6 x 10^{0}= ___1. This is 9 x 10000 + 8 x 100 + 6 x 1, or 90000 + 800 + 6.

2. The answer is

**90806**.

**Example 5:**

**5 x 10**

^{2}+ 3 x 10^{0}+ 6 x 10^{-1}+ 8 x 10^{-2}= ___1. This is 5 x 100 + 3 x 1 + 6 x .1 + 8 x .01, or 500 + 3 + .6 + .08

2. The answer is

**503.68**.

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

expandnota.pdf |

**Up Next for Elementary School: Mult12**