Teaching Exponents

In grade 7, having mastered cube roots, factors, and divisibility, students move on to learning about exponents. This includes defining and identifying the parts of an exponential notation, writing expressions in exponential form, and expanding and evaluating exponential notations.

Whether you’re a math teacher or a homeschooling parent, there are tons of ways in which you can help students master exponents in no time! Today, we bring you a few such awesome tips. Read on and learn more.

Strategies to Teach Exponents

What Are Exponents?

You can start your lesson by explaining what exponents are. Exponents are small numbers, like superscripts, written at the upper right of a number or a variable (a letter). In a lot of countries, exponents are called indices. But the concept is the same, no matter what term is used.

Provide a few examples:

3²
5³
a⁷
x⁸

It’s also good to highlight the exponent in a different color. Point out to students that the exponent is the small number written above, that is, 2, 3, 7, and 8 in the examples respectively, whereas the number/letter under the exponent is called a base, i.e. 3, 5, a, and x.

The base may be a positive whole number, a positive fraction, a positive decimal, or a variable. The exponent, also called power or index, can be positive, negative, or zero. However, while you’re explaining this, make sure to point out that for now, we’ll only deal with whole-number exponents.

Add that in each of the four examples above, the whole expression, consisting of a base and an exponent, is called an exponential expression or exponential notation.

Exponents as Repeated Multiplication

Remind students that when they learned about multiplication in lower grades, it was explained as repeated addition (i.e. 3 × 2 = 2 + 2 + 2). Now you can ask them to think of exponents as repeated multiplication. What does this mean? Provide a few examples:

2³ = 2 × 2 × 2

4² = 4 × 4

9⁸= 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9

So basically, by using exponential notation, we’re making things easier for us. Instead of writing 9 eight times, we can present the multiplication sentence above using exponential notation and simply write 9⁸.

Thus, the simplest way to define an exponent is this: an exponent is used to write multiplication with repeated factors in a simpler and shorter way. It says how many times a number (the base) is used as a factor.

How to Read Exponential Notations?

Now you can proceed with explaining how to read exponents. The best way to do this is by providing plenty of examples. For instance, in an exponential notation, if the base is 3 and the exponent is 2, 3, 4, 5, 6, or 7, we’ll read the expression as follows:

3² can be read as “3 to the second power” or “3 squared”
3³ can be read as “3 to the third power” or “3 cubed”
3⁴ can be read as “3 to the fourth power”
3⁵ can be read as “3 to the fifth power”
3⁶ can be read as “3 to the sixth power”
3⁷ can be read as “3 to the seventh power”

Evaluating Exponents

At this point, students understand what exponents are, and they also know how to expand exponential expressions. That is, they understand how to transform the exponential form of 2³ into the expanded form of 2 × 2 × 2.

You can now move on to teaching students how to evaluate exponential notations. This simply means learning how to perform the necessary multiplication. You can write the following steps that students can follow in order to do this successfully:

Step 1: Expand the exponential expression
Step 2: Multiply the factors one at a time

Example 1:

Write an exponent on the whiteboard. Start with a simpler example, such as 3⁴. To know how to expand this exponential expression, remind students that we need to identify the base, or 3, and the exponent, or 4.

This means that we need to make 3 a factor four times. In other words, by expanding the exponential notation 3⁴, we’ll obtain the following:

3⁴= 3 × 3 × 3 × 3

The next step is multiplying one factor at a time, that is, 3 × 3 = 9, then 9 × 3 = 27, then 27× 3 = 81. In other words:

3⁴= 81

Additional Resources:

If you want to enrich your lesson on exponents with multimedia materials, such as videos, you can use this video by Math Antics to provide an introduction to what exponents are and what are the parts of an exponential notation.

In addition, you can use this video to introduce a song about exponents called “All About the Base”, which children are guaranteed to enjoy, as it represents a twist of another popular song (“All About That Bass”). Sing along and learn exponents while having fun!

Activities to Practice Exponents

Otter Rush Game

This is a fun online game that you can use to help students practice evaluating exponents. To use this game in your classroom, the only thing you need is a number of suitable technical devices (one per child).

Pair students up and provide instructions for the game. Explain that they need to choose the multiplayer option. Students are presented with different questions on evaluating exponents, as their otter races against other otters.

In the end, students in each pair compare their accuracy rate, measured in percentages, as well as their speed. The student with the highest accuracy wins the game. To avoid confusion, you can hand out a timer to each pair so that they have the same time to answer the questions.

Exponents Matching Game

This game will help students practice their skills of writing expressions in exponential form and expanding exponential notations. To implement this game in your classroom, you’ll need to prepare two sets of cards (ex: blue and orange).

On the blue cards, write the expanded form of diverse exponential expressions, whereas on the orange cards, write the exponential form. There should be one expression on each card. Make sure that for every blue card you create, there is a matching orange card.

For instance, if you create a blue card with 9⁸,make sure you also have an orange card with the expanded form of this notation, i.e. 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9. Divide students into groups of 3 or 4 and hand out a pile of cards to each group.

The cards should be face down until you provide the signal to start the game. Students have to match the blue cards with the corresponding orange cards correctly. Provide a few minutes for this. The group that manages to match all cards correctly before the time is up is the winner.

If there are several groups that got all cards right, prepare additional sets of cards for a second round. Homeschooling parents can also use this activity as an individual game where their child matches up all the cards on their own.

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This article is based on:

Unit 4 – Factors, Fractions, and Exponents