# Lesson: Exponents: Lesson 1

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### Lesson Objective

The purpose of this lesson is to introduce students to the meaning and function of base-10 exponents.

### Lesson Plan

BROOKE ELEMENTARY SCHOOL – MATHEMATICS LESSON PLAN

GRADE 5                                    Unit 1                                           Day   1

Page 1 of 3

I.             Curriculum Standards

*Evaluate base 10 exponents. [M.15a.5]

II.               The Point

How do mathematicians use base 10 exponents?

III.        Materials Needed

Copies of 5.1.1 Problem Solving Task

Math Journals/glue sticks

Slates and Markers

Fact Power Copies

IV.        Lesson Outline

Time:  60 Minutes

5 min. – Understanding The Point and the Problem-Solving task

5 min. – Independent Problem-Solving

30 min. – Discussion/Practice/ Summary

5 min. – Fact power

15 min. – Slate Math

V.     Learning Activities

1. Understanding The Point and the Problem-Solving task (5 min.)

Distribute a Problem Solving Task slip to each student.

Students read and work to solve the problems independently.

2.  Independent Problem-Solving (5 min.)

Students work to solve the problem.

3.  Discussion/Practice/Summary (30 min.)

Common Mistakes when students complete these problems:

• Students can be careless with their exponents and not think carefully about what it should be.

• Students may forget the vocabulary word of exponents.

• Students sometimes make the error that 102 means 10 x 2 and not 10 x 10.

Discussion

The Big Ideas about exponents and base-10 exponents:

•  Exponents and exponential notation is a way of representing repeated multiplication by the same factor. For example 23 is 2 x 2X 2. The small, raised 3, called the exponent, indicates how many times the number 2, called the base is used as a factor.

• Base-10 exponents are really easy to use because they are directly connected to place value.  When the base number is 10 and the exponent represents how many zeros are need for that place value (this is a short cut way of thinking about it). For example if I wanted to represent 100,000 I know that there are five zeros, so it is 105. Meaning 10 x 10 x 10 x 10 x 10.

Possible Flow of Discussion:

1)      Have students share the different ways that they were about to write a 100,000 using only 10’s and any operation. Remind students that the goal was to do this in as few steps as possible. ( I would pick out a few people ahead of time, one who did it a very long way, one who did it the second longest way, one who did it a little shorter way, etc. and then try to find someone who made 100,000 using only multiplication  as your shortest way)

2)      Have students discuss and debate how to make 100,000 shorter and then call them up in the above described order.

3)      Once the class has all agreed that using multiplication and six 10’s is the fastest(10 x 10 x 10 x 10 x 10 x10), show them how to use exponents to write this.  Explain the definition of exponents: a way of representing repeated multiplication by the same factor. In this case the factor that we repeated multiplied by was 10. So this is our base number. Write this up on the board. Now we multiplied by 10 six times, so our exponent is 6. Show students how to write the exponent next to the 10.  Students should recognize this from when we did square numbers. Make sure students understand the difference, we called those numbers square because it was the base number times it self (So we multiplied the base number twice).  Make sure that students see that this is actually the shortest way to write 100,000 using only 10’s.

Whole Class Practice

Student could practice writing different place values using the powers of 10. Only have them use powers of 10. See if any one notices a short cut. They should not have to sit there and think too long about how many times you have to multiply by 10 to make a given place value.

Examples:

10

100

1,000

10,000

100,000

1,000,000,000

Summary

Stop and have students look back at the question that is The Point of today’s lesson:

How do mathematicians use base 10 exponents?

Students work as a class to form a statement to answer the question in their math journal as a summary of their learning from the lesson.