The Power of Exponents
A Learning Activity is a strategy a teacher chooses to actively
engage students in learning a concept or skill using a digital tool/resource.
You may save this Learning Activity to your hard drive as an .html file by
selecting “File”,then “Save As” from your browser’s
pull down menu. The file name extension must be .html.
This learning activity provided by:
Author:
Morgan Boyd
Organization: Retirement
General Activity Information
Activity ID:
2566
Title: The Power of Exponents
Digital Tool/Resource: Apply Properties of Integer Exponents to Generate Equivalent Expressions PART 1
Web Address – URL:
Overview: In this activity, students will begin thinking about the power of exponents. They are given a choice of receiving 500 coins right now or receiving one coin the first day and doubling the amount each day for a month. Students will watch a free video tutorial to guide them through why exponents are used, how to simplify the same-base number with exponents, and how to show equivalent expressions to bases containing negative exponents. The video tutorial explains exponents in a way that all students can understand. Then, the students will revisit their choices by watching another video and work problems posed to see if their choice was wise considering the power of exponents. This activity can be used as an introduction to a lesson on exponents.
This activity results from the ALEX Resource Department Summit.
Associated Standards and Objectives
Content Standard(s):
Mathematics 14. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]
Unpacked Content
Evidence Of Student Attainment:
Students:
Use their understanding of exponents as repeated multiplication to create equivalent expressions and justify integer exponent properties. Teacher Vocabulary:
Knowledge:
Students know:
That whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced. Skills:
Students are able to:
Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents. Understanding:
Students understand that:
Just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
The exponent can be translated (visually. i.e. listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense. Diverse Learning Needs:
Mathematics 3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.
Unpacked Content
Evidence Of Student Attainment:
Students:
Use their understanding of exponents as repeated multiplication to create equivalent expressions and justify integer exponent properties. Teacher Vocabulary:
Knowledge:
Students know:
that whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced. Skills:
Students are able to:
Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents. Understanding:
Students understand that:
just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
The exponent can be translated
(visually, listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.8.3.1: Define exponent, power, coefficient, integers, equivalent, and numerical expression.
M.8.3.2: Restate negative exponents as positive exponents in the form 1/x2 .
M.8.3.3: Restate zero exponents as 1 (x0 = 1).
M.8.3.4: Recognize to add exponents when multiplying terms with like bases (Property of product of powers).
M.8.3.5: Recognize to subtract exponents when dividing terms with like bases (Property of quotient of powers).
M.8.3.6: Compute a numerical expression with positive exponents.
M.8.3.7: Restate exponential numbers as repeated multiplication.
M.8.3.8: Compute problems with adding and subtracting integers.
Prior Knowledge Skills:
Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
Compute a numerical expression with exponents, with or without a calculator.
Restate exponential numbers as repeated multiplication.
Choose the correct value to replace each variable in the expression (Substitution).
Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.
Define integers, positive and negative numbers.
Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
Discuss the measure of centering of 0 in relationship to positive and negative numbers.
Discover that the opposite of the opposite of a number is the number itself.
Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
Learning Objectives: Students:
Strategies, Preparations and Variations
Phase: Before/Engage
Activity: Distribute the worksheet titled The Power of Two Worksheet (one per student). Read aloud the choices to the students and have them highlight their choice. (Students will highlight their choice so they can not change their choice later).
Show students the video, Apply Properties of Integer Exponents to Generate Equivalent Expressions Part 1.
Bring students' attention back to The Power of Two Worksheet.
Show the students the Power of Exponents video. Then, ask the students if their choice might have changed.
Have the students complete the table starting with one coin on the first day and then double that amount each day until the end of the month. How many coins did they receive on the last day? Did they choose wisely?
Assessment Strategies: The students will be assessed on the completion of The Power of Two Worksheet. Did they choose wisely?
What is the amount of coins received on the last day of the month?
Advanced Preparation: The teacher will need an internet device to show the videos.
The teacher will need to make copies of The Power of Exponents worksheet.
Variation Tips (optional): The worksheet can be completed with partners, groups, or individually. If the teacher sees students who are struggling, they might wish to place those students in groups with a strong partner. The teacher can use closed caption on the videos if needed.
Notes or Recommendations (optional): ALCOS 2019
3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.
Keywords and Search Tags
Keywords and Search Tags:
algebraic, equivalent, Exponents, expressions, Integers, numerical
