SWBAT use scientific facts to make comparisons using scientific notation.

Sometimes we need to make quick estimates with large numbers. Rough estimation can be made easy using Scientific Notation.

5 minutes

As students are entering the classroom, I hand each an ENTRANCE TICKET. There are three questions on the ticket asking students to use scientific notation to find equivalent expressions. These should be done independently and without a calculator.

15 minutes

After students complete the Entrance Ticket, I write the following problem on the board:

**The estimated world population today is 7, 130, 700, 730 people. The estimated US population today is 317, 240, 905. How much larger is the world population than the US Population? **

I encourages students to use Scientific Notation so that they can make the comparison more easily. I ask students to:

- Write down the numbers in standard notation
- Write each number in scientific notation but using only whole numbers before the decimal

I remind students that we are making estimations.

Students should write:

**7, 130, 700, 730** or **7 x 10 ^{9}**

**317, 240, 905 **or **3 x 10 ^{8}**

Now I ask students:

- About how many times larger is 7 than 3, more or less...?
- About how many times larger is 10
^{9 }than 10^{8?}

Then, I write 2 x 10 or 20 times on the board and I ask the students to interpret what this means.

25 minutes

As we start this section of class, I hand each student a copy of the Application Sun Facts 2 sheet. I pair students up and ask them to answer the questions at the bottom of the worksheet. I want them to make rough estimates using scientific notation.

Two things should be considered before allowing students to begin:

- A common mistake when comparing large numbers is that students will simply look at the first number and decide which number is larger. Tell students that it is the power of 10 that determines the larger number.

**Example**: 3 x 10^{6} for example is larger than 5 x 10^{5}. Students may say the second value is larger because 5 is larger than 3

- When given numbers in standard notation for example, 3,135,678,300 and 568,419 students will need to estimate the first number as 31 x 10
^{8}. Although not in scientific notation, we will use it for our comparison. The second number is 5 x 10^{5}.

**Example**: 31 is 6 times larger than 5 and 10^{8} is 1000 times larger than 10^{5}. Therefore the first value is approximately 6000 times larger.

10 minutes

To bring the class to a close, I call on five volunteer students to write their work on the board. Once they are done, I allow students to ask questions about the answers on the board. When possible, I allow students to answer each other's questions. I intervene only to make a necessary clarification.