Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 48675
Radical Mathematical
In this lesson students will solve radical equations, showing how extraneous solutions may arise. Students will solve radical equations that model realworld relationships.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Basic Calculators
Instructional Time: 1 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: radical equations, extraneous solutions
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
The students will solve simple radical equations in one variable and give examples showing how extraneous solutions may arise. Students will solve radical equations
that model real-world relationships.
Prior Knowledge: What prior knowledge should students have for this lesson?
The students should have a basic understanding of radicals.
The students should have a basic understanding of solving equations.
The students should know how to solve quadratic equations.
Guiding Questions: What are the guiding questions for this lesson?
What is the process for solving radical equations?
How are radical equations different from linear equations?
What are extraneous solutions?
How do you determine if you have extraneous solutions?
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will present the following slide show to assess prior knowledge and to introduce the lesson.
High School Mathematics Presents.pptx
Teacher says, "We will solve this sailboat problem later, first we need to look at solving simple radical equations."
The teacher will present the following radical equations after reviewing the "Golden Rule of Algebra" as follows:
Pose the question: "How do we solve equations? (Answer: We isolate the variable on one side by using inverse operations.) We must remember the Golden Rule of
Algebra, 'Do unto one side, as you would do to the other.' For example, if you multiply the left side of an equation by a number, then you must multiply the other side
by the same number."
Let's try these problems:
page 1 of 3 Say: "Sometimes radical equations produce extraneous solutions. These solutions may appear to be correct answers, but when substituted into the equation, the
result is a false statement. Let's look at an equation with extraneous solutions."
When we square both sides we get
.
When we move everything to the right side (because that is where
is located) we get
.
We then solve the equation by factoring:
0=(x-2)(x+1)
(x-2) = 0 and (x+1) = 0
x=2 and x=-1
We must check both answers to see if we have any extraneous solutions. The solution x = 2 produces the result 2=2 when substituted into the equation. This is a true
statement. The solution x = -1 produces the result 1 = -1 when substituted into the equation. This is a false statement; therefore, x = -1 is an extraneous solution.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The students will complete the following exercises for Guided Practice. Students will be assigned to groups of 2 or 3 to complete this assignment. The teacher will
circulate around the room to check for accuracy and guide students when necessary.
Try these:
[2] Daniel and Clair are sailing on a sailboat. They find the hull speed to be 10 nautical miles per hour. What is the length of the sailboat's waterline?
Let's recall the formula:
represents the length of the sailboats waterline in feet.
represents the hull speed.
We know that the hull speed, , is 10 nautical miles per hour. If we substitute in we get
.
Now we need to solve for .
Answer: about 55.65 ft.
Answer: x = -1
(x = -7 is an extraneous solution.)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The students will complete the following handout for independent practice. The teacher will check for accuracy and review if necessary.
Radical Mathematical--Independent Practice.docx
Radical Mathematical--Independent Practice KEY.docx
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The students will be given an exit question to complete at the end of class.
Exit Question:
Radical Mathematical Exit Question.docx
page 2 of 3 Summative Assessment
The students will complete an exit question to determine if the learning targets have been reached.
Formative Assessment
The students answer questions throughout a slide show presentation to assess prior knowledge.
Feedback to Students
The students will complete assignments throughout the lesson to check for understanding. Students will use corrected assignments to guide them as they complete
assignments independently.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students may receive additional time to complete the assignments. The teacher my provide step by step instructions in written form explaining how to solve radical
equations. The teacher may provide problems with some steps completed leaving some steps for the students to complete.
Extensions:
Show graphs of square root equations.
Show how the graphs of radical equations differ from the original (parent graph)
.
Suggested Technology: Computer for Presenter, Basic Calculators
Special Materials Needed:
Independent Practice handouts need to be ready for distribution.
Graphing calculators (optional) to show extraneous solutions graphically.
Further Recommendations:
Encourage students to show work and/or provide reasons for each step during their solving process.
Additional Information/Instructions
By Author/Submitter
Standards for Mathematical Practice:
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.2.1 Reason abstractly and quantitatively.
MAFS.K12.MP.6.1 Attend to precision
SOURCE AND ACCESS INFORMATION
Contributed by: Lisa Purvee
Name of Author/Source: Lisa Purvee
District/Organization of Contributor(s): Holmes
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.A-REI.1.2:
Description
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may
arise.
page 3 of 3