Rational Exponents
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This learning activity provided by:
Author:
Kristy Lacks
System: Marshall County School: Douglas High School
General Activity Information
Activity ID:
2917
Title: Rational Exponents
Digital Tool/Resource: Simplifying Rational Exponents from Kuta Software
Web Address – URL:
Overview: In this learning activity, students will practice using the properties of exponents to rewrite expressions involving radicals and rational exponents. linear expressions using the properties of operations. This learning activity should be used after a lesson on rational exponents and solving exponential equations. It can be used as extra practice or as an assessment.
Associated Standards and Objectives
Content Standard(s):
Mathematics 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]
Unpacked Content
Evidence Of Student Attainment:
Students:
Convert from radical representation to using rational exponents and vise versa. Teacher Vocabulary:
Radical
Rational exponent
Expression Knowledge:
Students know:
the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand. For example, 51/2=5 and 163/2=(161/2)3= (16)3=43=64.
The root index of the radical is the denominator of the rational exponent and the exponent of the radicand is the numerator of the rational exponent. For example, 4103= 103/4. Skills:
Students are able to:
Rewrite expressions from radical representations to rational exponents and vice versa. Understanding:
Students understand:
The meaning of rational exponents and how to convert between them and radical representations. Diverse Learning Needs:
Mathematics 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given expressions involving radicals and rational exponents, use reasoning and properties of exponents to demonstrate that various forms of radicals and roots actually represent the same quantity, Teacher Vocabulary:
Rational exponent
Power of a power
Product of a power
Power of a product
Zero exponent
Negative exponent
Quotient of a power Knowledge:
Students know:
Properties of exponents.
The meaning of algebraic symbols such as radicals and rational exponents. Skills:
Students are able to:
Use mathematical reasoning to justify the equality of various forms of radical expressions.
Correctly perform the manipulations of exponents which apply properties of exponents. Understanding:
Students understand that:
The properties of exponents are true regardless of the type of numbers being used. Diverse Learning Needs:
Essential Skills:
Learning Objectives: ALGI. 2.1: Rewrite expressions involving radicals using the properties of exponents.
ALGI. 2.2: Rewrite expressions involving rational exponents using the properties of exponents.
ALGI. 2.3: Recognize the properties of exponents.
Prior Knowledge Skills:
Compute problems with adding and subtracting integers.
Restate exponential numbers as repeated multiplication.
Compute a numerical expression with positive exponents.
Recognize to subtract exponents when dividing terms with like bases (Property of quotient of powers).
Recognize to add exponents when multiplying terms with like bases (Property of product of powers).
Restate zero exponents as 1 (Xo = 1).
Restate negative exponents as positive exponents in the form 1/xy .
Define exponent, power, coefficient, integers, equivalent, and numerical expression.
Identify perfect squares and square roots.
Recall how to compare numbers.
Identify properties of exponents.
Define square root, expressions, and approximations.
Identify and give examples of rational numbers.
Recognize the mathematical operations of rational numbers in any form, including converting between forms. (Ex. 0.25=1/4 =25%).
Define rational numbers.
Restate exponential numbers as repeated multiplication.
Define exponent.
Alabama Alternate Achievement Standards
AAS Standard:
Learning Objectives: The students will be able to use the properties of exponents to rewrite expressions involving radicals and rational exponents.
Strategies, Preparations and Variations
Phase: After/Explain/Elaborate
Activity:
The teacher will display the worksheet whole-group and allow students enough time to complete problems 1 through 8 on the worksheet.
After the students have had ample time to work on problems 1 through 8 on the worksheet, the teacher will review the answers.
Once the students have proven they understand how to use the properties of exponents to rewrite expressions involving radicals and rational exponents, the teacher will tell the students to complete problems 9 through 22 individually for an assessment grade. The teacher will remind students to simplify. The teacher will also remind students that their answer should contain only positive exponents with no fractional exponents in the denominator.
At the end of class, the teacher will bring the students back to a whole-group discussion to determine any problems they faced while completing the worksheet.
Assessment Strategies: The students' worksheets would be graded to assess students' understanding of using the properties of exponents to rewrite expressions involving radicals and rational exponents.
Advanced Preparation: The teacher will need to secure a way to display the worksheet whole group.
The teacher would need to make copies of the worksheet for each student.
Variation Tips (optional): The worksheet could be started in class and finished for homework.
The teacher could also work on the even-numbered problems with the students in class and have them do the odd-numbered problems for homework.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
exponential equations, Exponents, fractional exponents, radical numbers, rational numbers
