Sample Lesson Plan: Exponents

The lesson plan below implements elements of universal design described throughout this website.

Lesson Overview

Unit Exponents
Subject Developmental Algebra
Lesson Description for Day Write numbers with exponents and evaluate numerical expressions that contain exponents.
Standards: NCTM Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Goals

Unit Goals Students will perform operations using real numbers and variables:

  • Add, subtract, multiply, and divide signed numbers
  • Write numbers in exponent form

Evaluate numerical expressions that contain exponents

Lesson Goals Students will understand:

  • An exponent is a way to abbreviate repeated multiplication
  • Exponent notation has two parts: the base and the exponent
  • A variable is a letter that represents an unknown number
  • Numerical expressions with exponents can be evaluated and written in expanded form

Methods

Anticipatory Set Show the student a Rubik’s Cube. Ask if anyone has ever tried to solve a Rubik’s Cube. Tell the students that according to the manufacturer, there are 43 quintillion different possible moves on the Rubik’s Cube. Show the number for 43 quintillion: 43,000,000,000,000,000,000

Discuss the problem of writing such large numbers and explain that there is a much simpler way to do it, and that is to use exponents, or scientific notation. The way to express 43 quintillion in scientific notation is 4.3 x 10 (with an exponent of 19). That means 10 multiplied by itself 19 times.

Introduce and Model New Knowledge
  • Explain that an exponent is a shorthand way to show repeated multiplication. Therefore, 9³ is really 9 X 9 X 9, which equals 729.
  • In the language of algebra, we might write x³, or (x)(x)(x). The letter x is called a variable. A variable is a letter that represents an unknown number.
  • Explain and model: There are two parts to an exponent expression – the base and the exponent. The base tells you what number is being multiplied and the exponent tells you how many times it is being multiplied.
  • Example: 3 x 3 x 3 = 3³ or (x)(x)(x) = x³
  • If a base is a positive integer, the exponent is to the right and slightly above the base, such as  6²
  • If the base is a negative number, then you have to put parentheses around the base and the exponent is to the right of the parentheses and slightly above, such as (-8)³ or (-8)(-8)(-8).
  • Teach the sign rule for exponents: If a number is written in exponent form and the base is negative, the result is positive if the exponent is an even number and negative if the exponent is an odd number. Remind students that when you multiply two or more signed numbers, the result is positive if there are an even number of signed numbers. The result is negative if there are an odd number of negative signs.
Provide Guided Practice Provide students with practice problems where they must write expanded multiplication problems in exponent form and problems where they must evaluate, or solve numbers written in exponent form. Students may benefit from working in pairs to solve these problems.
Provide Independent Practice Assign homework from text. Direct students to use the http://usablealgebra.landmark.edu website as a reference and a place where they can have more guided practice.

Assessment

Formative/Ongoing Assessment
  • Quizzes to assess learning of exponent form
  • Assign students to write a script for a video explaining exponents. A sample of such a video is available in the Exponents Learning Resource on the Usable Algebra website.
Summative/End of Lesson Assessment
  • Unit test

Materials

Rubik’s cube

Course text

Optional: computer and digital projector to demonstrate UD Algebra website