ALEX | Alabama Learning Exchange

Extraneous Solutions

Classroom Resource Information

Title:

Extraneous Solutions

URL:

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:eq/x2ec2f6f830c9fb89:extraneous-sol/v/extraneous-solutions

Content Source:

Other
Khan Academy

Type:

Audio/Video

Overview:

Extraneous solutions are values that you may get when solving equations that aren't really solutions to the equation. This video will explain how and why you can arrive at extraneous solutions, by understanding the logic behind the process of solving equations. There is an additional video to explain this concept, as well as two question sets.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability

8. Explain why extraneous solutions to an equation involving absolute values may arise and how to check to be sure that a candidate solution satisfies an equation.

Unpacked Content

Evidence Of Student Attainment:

Students:

Solve problems involving absolute value equations.
Identify extraneous solutions to these equations if any.
Produce examples of equations that would or would not have extraneous solutions and communicate the conditions that lead to the extraneous solutions.

Teacher Vocabulary:

Absolute Value
Equations
Extraneous solution

Knowledge:

Students know:

Algebraic rules for manipulating absolute value equations.
Conditions under which a solution is considered extraneous.

Skills:

Students are able to:

Accurately rearrange absolute value equations to produce a set of values to test against the conditions of the original situation and equation, and determine whether or not the value is a solution.
Explain with mathematical reasoning from the context (when appropriate) why a particular solution is or is not extraneous.

Understanding:

Students understand that:

Values which arise from solving absolute value equations may not satisfy the original equation.
Values which arise from solving the equations may not exist due to considerations in the context.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
ALGI. 8.1: Define integers.
ALGI. 8.2: Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
ALGI. 8.3: Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
ALGI. 8.4: Discuss the measure of centering of 0 in relationship to positive and negative numbers.
ALGI. 8.5: Substitute for the variable to find the value of a given expression.
ALGI. 8.6: Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.
ALGI. 8.7: Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

Prior Knowledge Skills:

Recall how to order positive and negative numbers. (Use number line if needed).
Evaluate a statement about order using comparisons of absolute value.
Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
Arrange integers and/or rational numbers on a horizontal or vertical number line.
Recognize the absolute value of a rational number is its' distance from 0 on a vertical and horizontal number line.

Tags:

absolute values, algebra I, equation, extraneous solutions

License Type:

Custom Permission Type
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Accessibility

Video resources: includes closed captioning or subtitles

Comments

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

Extraneous Solutions