Summary: Identify the inverse of a square or square root. Write expressions in
exponential form. Evaluate exponential expressions
Main Curriculum Tie: Mathematics Grade 8 Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^{2} × 3^{–5} = 3^{–3} = 1/3^{3} = 1/27. Materials:
Attachments
Background For Teachers: Enduring Understanding
(Big Ideas):
Exponential expressions
model real world situations
Essential Questions:
 How is n² different from 2n, n³ different from 3n?
 How is n² related to √n²
 How can I simplify exponential expressions
Skill Focus:
writing and
evaluating exponential
expressions
Vocabulary Focus:
base, power, exponent, square number, square root, cube,
exponential form, exponential expression
Instructional Procedures:
Starter: Find the answers
Circle the expression(s) or model with the greatest value in each problem below.

2 · 19 19 + 19 19²
 7 + 7 7² 7 · 7
 5 + 5 5 · 5 5²
 3 x 3 3 + 3
Lesson Segment 1: How is n² related to √n²? How is n² different from 2n?
How is n³ different from 3n?
Use “Building A Square Patio” (attached), an investigation with Color Tiles to help
students visualize the inverse relationship between squaring a number and taking the
square root of that perfect square. Student pairs or teams can build each patio using
the Color Tiles. Discuss each step as a class focusing on the relationship between the
side length and the root, between the square and total tiles, and between the root and
the square.
Briefly review with students how to write a base number and an exponent. Students
have used this notation since 5th grade. Show students how to use the 6 or 7 keys
on a Ti73 to write exponential expressions. Have them use the calculator and the
attached Foldable Perfect Squares and Square Roots to build a table of values. Copy
the foldable to make two sided page that will be folded in thirds on the dotted line.
Have students work with partners to complete the investigation, “Operations and
Exponents”. Discuss possible answers to question # 4 and 5 on the investigation.
Handout the journal page for exponents (attached).
Lesson Segment 2: What are some realworld applications for exponential
notation? How is n² related to √n² ?
Follow the instructions on the attached activity “Building Exponential Expressions With
Color Tiles and Linker Cubes” to help students broaden their understanding and see
realworld application. Complete the Journal Page.
Lesson Segment 3: Practice and application
Journal: Do MixFreezePair where students mix around the room until you say freeze.
They find the person closest to them to be their partner. If no partner is immediately
available, they raise their hand high and look for someone else with hand raise high.
During this activity, you will model an example or two for each of the vocabulary words
on the journal page and for items 14. Use the graphing calculator to show examples.
Then you will have the students use their TI73’s to give an example to their partner,
or you will give them an example and they will supply the vocabulary word for it.
Students should mix and find a new partner for each of the words.
The links on the District Math Page have some great examples of where exponents are
used in the real world. Area, Volume, Scientific Notation, Biology, Astronomy,
earthquake (Richtor Scale). You may want to assign students to find a real world
example to bring to class.
Game: Playing With Powers
Two players take turns rolling two dice and deciding which to use as a base and which
to use as an exponent. After five turns, the players find the sum of the five
exponential expressions they created. Player with the greatest sum, wins.
Assign students the attached Exponential Expressions practice attached, or appropriate
text items.
Attachments
Assessment Plan: performance task, writing
Bibliography: This lesson plan was created by Linda Bolin. Author: Utah LessonPlans
Created Date : May 12 2009 16:17 PM
