Convert Between Standard Form and Scientific Notation Lesson Plan

Warm up and introduction

Start off the class by showing slide `1` in the slideshow. Your students will already be familiar with the concept of positive and negative exponents. The key here is that we’re bringing in a base of `10` to have students easily transition into scientific notation.

Allow students a few minutes to come up with answers independently, then share with the class. Here are some answers you might expect.

Similarities:

• They both have a base of `10`.
• Their exponents have the same absolute value.

Differences:

• One has a positive exponent, one has a negative exponent.
• `10^3` simplified to `1000`, but `10^{-3}` simplifies to `1/1000` or `0.001`.

Discussion

You’ll want to focus in on what these exponential expressions simplify to. Students should understand that the positive exponent will give us a number greater than `1` and the negative exponent will give us a number less than `1`. 

Converting to standard form

Take this first example step by step by using the transitions on the slide. Since you just simplified `10^3` in the warm up, ask students again what it simplified to. Then students just need to multiply `5` by `1,000` to see that `5 \cdot 10^3` is `5,000`.

Take this opportunity to show students that since we’re multiplying by powers of `10`, we can use place value to get to the answer more quickly. Start by asking students, “since the power of `10` we’re multiplying by has a positive exponent, which direction should we move the decimal?” The key is for students to recognize that a positive exponent will make the coefficient larger, so we need to move the decimal point to the right. 

Example with a negative exponent

This next example has a negative exponent. You’ll want to carry over the thinking from the previous problem with moving the decimal point. Ask students, “since the power of `10` has a negative exponent, which direction do you think we’ll move the decimal point in `8.2`?” The key is for students to recognize that this would make `8.2` smaller, so we need to move the decimal to the left.

Key concepts of scientific notation

Typically, it’s easier for students to convert from scientific notation to standard form, since they’re really just multiplying! So up until this point, we haven’t pointed out what the key ideas are behind scientific notation. Show the next slide and point out the key points while they write this in their notebooks. 

You’ll want to highlight the following ideas:

• The coefficient is always between `1` and `10`. This includes `1` but does not include `10`.
  The base is always `10`, since in scientific notation, we’re always multiplying by a power of `10`.
• The exponent is always an integer. This tells us whether the value of the number is big or small, which helps us determine which direction to move the decimal. It also tells us how many places to move the decimal.

Determining if a number is in scientific notation

For the next slide, let students work together to determine whether each value is written in scientific notation or not. Once students are done, go over each one as a class. Ask for volunteers to come up to the board to explain whether the value is written in scientific notation or not and if not, why not!

Try an example converting to scientific notation

Now we’ll want to convert a number in standard form into scientific notation. I like to start by asking students where the decimal point would be and drawing that in. Then, tell students we’re going to move the decimal point until it’s in a place where the number would be between `1` and `10`. So in this case, we’ll move the decimal point `4` places to the left, making the coefficient `4.5`.

Next is determining the exponent. I try not to focus on “rules” like “moving left means the exponent is positive” because this confuses students when converting back and forth. Rather, I ask students to think about if the value of the number is greater than the coefficient. Since `45,000` is a large number it is definitely greater than `4.5`, so we should write a positive exponent. Since we moved the decimal point `4` times, the exponent will be positive `4`. 

Example less than 1

Follow a similar process with this example. Start moving the decimal point until the number is between `1` and `10`. Then, determine if the exponent will be positive or negative. Since `0.0000821` is smaller than `8.21`, we’ll write a positive exponent. Since we move the decimal `5` times, the exponent will be positive `5`.