Lesson Plan for Teachers on Understanding Exponents

Lesson Title:Understanding Exponents

Lesson Objective: Students will be able to:

Understand the concept of exponents and how they are used to represent repeated multiplication

Use exponents to simplify and evaluate mathematical expressions

Understand the rules of exponents and how to apply them to solve problems

Materials:

Whiteboard and markers

Handouts with practice problems

Calculator (optional)

Introduction (5-10 minutes): Start the lesson by asking students if they have ever seen or heard the term “exponent” before. Allow volunteers to share any prior knowledge they have about exponents.

Next, write the number 2 on the board and ask students to raise their hand if they know how to write it as a multiplication problem (e.g. 2 x 2). Write 2 x 2 on the board and then ask students how they would write 2 x 2 x 2. Write 2 x 2 x 2 on the board and ask students how they would write 2 x 2 x 2 x 2.
As you continue this process, it will become clear that writing out repeated multiplication can be tedious and time-consuming. This is where exponents come in. An exponent is a shorthand way of expressing repeated multiplication.
Body (25-30 minutes): Explain to students that an exponent is a small number written above and to the right of a number. The number that the exponent is written above is called the base, and the exponent is the number of times the base is multiplied by itself. For example, in the expression 2^3, 2 is the base and 3 is the exponent. This tells us that 2 is being multiplied by itself 3 times: 2 x 2 x 2 = 8.
Demonstrate this concept by using the whiteboard to write out the product of a base and its exponent. For example, write 2^3 and then write out 2 x 2 x 2 = 8. Next, write out 3^4 and then write out 3 x 3 x 3 x 3 = 81.
Make sure to point out that an exponent of 1 means that the base is being multiplied by itself once, so the value is the same as the base. For example, 2^1 = 2.
Allow students some time to work on a few problems on their own or with a partner to practice simplifying expressions with exponents. You can give them examples such as:

5^2

8^3

2^4

3^3

Next, introduce the rules of exponents. Explain that when multiplying expressions with the same base, we can add the exponents. For example, 2^3 x 2^4 = 2^7. When dividing expressions with the same base, we can subtract the exponents. For example, 2^7 ÷ 2^4 = 2^3. When raising an expression with an exponent to another exponent, we can multiply the exponents. For example, (2^3)^4 = 2^12. Allow students some time to work on problems that involve applying the rules of exponents. You can give them examples such as:

(2^3) x (2^4)

(8^3) ÷ (2^2)

(3^3)^2

Conclusion (5-10 minutes): Review the main concepts of the lesson with students. Ask them to define what an exponent is, give examples of how to simplify expressions with exponents, and explain the rules of exponents. Allow volunteers to come to the board to work out a problem as a class and check for understanding.

Assessment:

Observation of students working