General Information
Subject(s): Mathematics
Grade Level(s): 8
Suggested Technology:
Document Camera, Basic Calculators, LCD Projector
Instructional Time:
20 Minute(s)
Keywords: exponents, powers, base, factor, exponential form, expanded form, properties of exponents
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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
 The student will be able multiply numbers in exponential form with the same base.
 The student will be able to identify when the property of exponents can be applied, and when it cannot be applied.
 The student will be able to explain and justify their responses to a variety of questions.

Prior Knowledge: What prior knowledge should students have for this lesson?
 Students understand the parts to a power (base, exponent)
 Students understand how to write a number in standard form
 Students understand how to write a number in expanded form

Guiding Questions: What are the guiding questions for this lesson?
 What are the parts of a power?
 What does the exponent indicate?
 Explain why you can or cannot use the "product property" in each of the following examples. (to be used with examples such as in figure 5)
 How can we use the product property, along with the commutative and associative properties, to simplify the following examples? (to be used with examples such as in figures 8 and 9)

Teaching Phase: How will the teacher present the concept or skill to students?
 The instructor will present an expression written as repeated multiplication. Students will be asked to rewrite the expression in exponential form and in standard form.
 The instructor should present the same expression using the associative property of multiplication. The grouped powers should also be written in standard form, and the product verified (see figure 3).
 The instructor should prompt the students to regroup the expression in different ways.
 The instructor should list the different ways that students completed this, for all students to see.
 The instructor should repeat this with additional expressions given in figure 3.
 The instructor should note that in all examples, a pattern emerges for identifying the exponent. This allows the students to discover the property for multiplying powers with the same base
(See figure3)
 Formalize the pattern by stating explicitly and having students write down the statement, "when multiplying terms with same base, wekeep the base and add the exponents." It is essential that the teacher emphasize the meaning of this statement, and how it applies to the examples that have already been completed.
This is the point in the lesson to present the rule in algebraic form, and name it the "Product Property". After presenting the algebraic form, have students write it on their own papers; then explain how this represents the examples that have been completed as well as the verbal statement of the property. This property will be used by students in all higher levels of Math. (see Figure 4) It is vital that the circumstances for using the Product Property be reiterated numerous times, and that the students become familiar with it in verbal and algebraic form.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
 Students should be given an exponential expression and asked to simplify using the property for multiplying powers with the same base.
 Repeat this process until mastery is attained.
 Examples with very large numbers can be used that will overload the calculator, so that students will have to use the rule (see figure 6). Note the second example results in the number known as "Googol". Students can look up this fun math fact and see how it is related to "Google."
 Counter examples should be used to identify the appropriate time to employ this property (See figure 5). Discussion/debate can make for exciting understanding of this concept. If students are grouped, the instructor may have students create their own expression(s) to share with classmates to prove/disprove the rule.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
 Students should repeat this process until mastery occurs. The teacher should circulate among the class to ensure the given problems are answered correctly.
 Additional expressions can be included to build number fluency and reinforce the main objective of the lesson. Have students complete a list of powers without using a calculator (see figure 7)
 Examples with more than two(2) terms can be used to reenforce the concept. (See figure 8)
 For high performing students or classes, examples with more than one variable can be introduced. (See figure 9).

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The student should be given 8 exponential expressions to simplify or identify as counterexamples. Students should also write in words the property for multiplying terms with the same base.
(See figure 10)

Summative Assessment
The students will be assessed to see if they understand how to multiply terms with the same base, and to identify when they can and cannot use the property of exponents discussed in this lesson. This can be completed as part of a quiz or done at the completion of the class period. Examples similar to those in the Closure section may be used.

Formative Assessment
At the beginning of the lesson, the teacher will instruct the students to complete four examples involving the meaning of exponents, standard form, and expanded form of a number. This will ensure that the necessary prior knowledge has been confirmed. The teacher should circulate and observe student work, conferencing with students where appropriate, and then leading a brief discussion of the correct answers. (See figure 1)

Feedback to Students
The teacher will provide feedback to students about the reason this property of exponents is true and what specific type of examples it applies to. Teacher should acknowledge student work on student paper at student desk.
Assessment
 Feedback to Students:
The teacher will provide feedback to students about the reason this property of exponents is true and what specific type of examples it applies to. Teacher should acknowledge student work on student paper at student desk.
 Summative Assessment:
The students will be assessed to see if they understand how to multiply terms with the same base, and to identify when they can and cannot use the property of exponents discussed in this lesson. This can be completed as part of a quiz or done at the completion of the class period. Examples similar to those in the Closure section may be used.
Accommodations & Recommendations
Accommodations:
 Provide students with a calculator.
 Students with special needs can be paired or grouped with peer tutors for individual assistance if needed.
 Teacher should provide additional examples and oneonone assistance for students who have difficulty understanding the general property.
Extensions:
 Provide exponential expressions that have different bases
 Introduce expressions which contain negative numbers, fractions, decimals for the common base. Use of parentheses around the negative base is necessary and should be emphasized. Further discussion may/should result on this concept leading to a deeper understanding. See figure 11.

Suggested Technology: Document Camera, Basic Calculators, LCD Projector
Special Materials Needed:
Further Recommendations:
 It is suggested to use expressions that contain 1 digit bases and include several examples using base of 2, 3, 4, and 5 so students develop familiarity with these common powers.
Additional Information/Instructions
By Author/Submitter
This resource is also likely to support student engagement with the following Standards for Mathematical Practice:
MAFS.K12.MP.1.1  Make sense of problems and persevere in solving them.
MAFS.K12.MP.2.1  Reason abstractly and quantitatively.
MAFS.K12.MP.3.1  Construct viable arguments and critique the reasoning of others.
MAFS.K12.MP.7.1  Look for and make use of structure.
MAFS.K12.MP.8.1  Look for and express regularity in repeated reasoning.
Source and Access Information
Contributed by:
Dennis Whalen
Name of Author/Source: Dennis Whalen
District/Organization of Contributor(s): Seminole
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.