Rational Exponents and Solving Exponential Equations
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This learning activity provided by:
Author:
Kristy Lacks
System: Marshall County School: Douglas High School
General Activity Information
Activity ID:
2916
Title: Rational Exponents and Solving Exponential Equations
Digital Tool/Resource: Rational Exponents and Solving Exponential Equations Video
Web Address – URL:
Overview: This learning activity will be used during the lesson on rational exponents and solving exponential equations. It is a video that consists of a lesson on rational exponents and exponential equations.
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: During/Explore/Explain
Activity: This activity will be used during a lesson on radicals and rational exponents. This would be a day two activity to solidify the concepts that were previously taught. The students would need to make sure that they were taking good notes during the video. The teacher would take the notes for a grade and then return them to the students so that they would have them to study. As the video is playing the teacher would need to stop the video during the problems so that the teacher can get feedback from the students to make sure that they are understanding the material.
At approximately 2:58 the teacher should stop the video and go over the table making sure that the students understand how the speaker is getting her answers. Resume video once all questions are answered.
At approximately 5:09 the teacher should stop the video and go over any questions that the students may have on the previous problems. Resume video once all questions are answered.
At approximately 6:12 the teacher should stop the video and go over any questions that the students may have on the previous problems. Resume video once all questions are answered.
At approximately 9:16 the teacher should stop the video and go over any questions that the students may have on the previous problems. Resume video once all questions are answered.
At approximately 13:14 the teacher should stop the video and go over any questions that the students may have on the previous problems. At this point there will be some video left, however, for this lesson, I would stop the video here and move on to the after activity.
Once the video is over the class would then play the game, "Did you know?". Each student would go around the room saying, "did you know..." and then following it with an observation from the video. The goal of the game is to get to the last person without repeating something already said.
After the game, the teacher would hand out the exit ticket, Rational Exponents
Assessment Strategies: The student's notes would be examined to make sure the students had good material to study.
The teacher would assess the students during the video when she chose to stop the video and go over the problems. The teacher would also need to encourage proper listening and interaction by walking around the room and monitoring student behavior.
The teacher would also assess students' knowledge of the game and the exit ticket.
Advanced Preparation: The teacher would need to watch the video before class to determine where to stop the video and decide what questions to use and what problems to model.
Variation Tips (optional): The video could be used as a stand-alone lesson when the teacher has a substitute or wants to try a flipped classroom lesson.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
exponential equations, Exponents, fractional exponents, radical numbers, rational numbers
