Rational and Radical 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:
2915
Title: Rational and Radical Exponents
Digital Tool/Resource: Properties of Exponents Worksheet from Education.com
Web Address – URL:
Overview: This learning activity is intended to be used as an introductory lesson on rational exponents and solving exponential equations. It can also be used as a bellringer for a day two lesson on rational exponents.
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: Before/Engage
Activity: This activity will be used to introduce a lesson on radicals and rational exponents. This would be a great day two bellringer to solidify the concepts that were previously taught. The properties on the worksheet act as a reminder from the previous day's lesson and can be helpful as students complete the problems.
1.) The teacher will need to display a copy of the worksheet on the board and pass out one copy for each of the students.
2.) The teacher should verbally review each property on the worksheet aloud with the students.
3.) Once the teacher has reviewed the different properties the teacher should have the students complete the sections.
4.) In the challenge section, the teacher should instruct the students to work together to complete the problems.
Assessment Strategies: The worksheet will be used as the assessment to check for student understanding.
Advanced Preparation: The teacher would need to make copies of the worksheet for each student.
Due to the length of the worksheet, the teacher could allow extra time for completion or allow students to work with a partner.
Variation Tips (optional): This worksheet could also be used as an after-activity. It could be divided up with page one being a bellringer and page two being an exit ticket.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
exponential equations, Exponents, fractional exponents, radical numbers, rational numbers
