Exponents
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This learning activity provided by:
Author:
Morgan Boyd
Organization: Retirement
General Activity Information
Activity ID:
2577
Title: Exponents
Digital Tool/Resource: Exponents
Web Address – URL:
Overview: In this free interactive math learning activity from Math is Fun , students learn to gain an understanding of exponents as repeated multiplication by “playing” with an interactive exponent tool.
This activity was created as a result of the ALEX Resource Development 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 will be able to use their understanding of exponents as repeated multiplication to develop equivalent expressions and justify integer exponent properties.
Strategies, Preparations and Variations
Phase: During/Explore/Explain
Activity: Provide the students with a link to the website Exponents from Math is Fun . The class will begin by reading the webpage aloud together from the website. Stop at the Try This section and give the students time to “play” with the interactive by entering numbers of their choice as the base and the exponent. The interactive will generate the solution almost immediately as both the base and exponent are entered. Have the students write an equation as repeated addition, solve, and compare.
Continue scrolling down and reading the webpage aloud with the students while working the examples given. Stop at the section, “What if the exponent is 1, or 0?” Have the students go back up to the interactive and enter any number as the base but enter a 1 as the exponent. What happened?
Now, have the students enter any number as the base, but enter a 0 as the exponent. What happened?
Continue scrolling down and reading the webpage aloud with the students while working the rest of the examples. Stop at the YOOO TOOO assessment section and have the students complete this ten-question quiz.
Assessment Strategies: The ten questions in the section titled YOOO TOOO will be used as an assessment tool to check for mastery of the standard.
Advanced Preparation: The teacher and students will need internet-connected devices.
Variation Tips (optional): Students who are struggling may need to be paired with stronger students.
This learning activity can be completed as a whole class activity or as an independent activity.
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
