By the end of day two of our class, you will have completed your 5 Practices lesson plan. Please post your lesson plan here.
While not required, you may want to read through the lesson plans others post and comment on them to continue the 5 Practices collaboration.
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ReplyDeleteLesson Plan for Five Practices
Task:: Radical Equations Task from Illustrative Mathematics
Solve the following two equations by isolating the radical on one side and squaring both sides:
2x+1 - 5 = - 2
2x+1 + 5 = 2
Be sure to check your solutions.
Standards
A.SSE.2 - Use the structure of an expression to identify ways to rewrite it.
A.REI.A.2 - Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Mathematical Goal: Students will understand that
In order to solve a radical they must first isolate the radical (A.SSE.2)
Solving radicals can generate solutions that really aren’t solutions (A.REI.A.2)
Anticipated Responses
Students will state that (i.) can’t be solved because square roots are restricted to be for zero and positive numbers.
Students will state that (ii.) can’t be solved because after isolating the radical the radical is equal to a negative number and square roots are restricted to zero and positive numbers.
Students will square the radical side of the equation before isolating the radical.
Students in solving will effectively square the radical, but in doing so will only square the radical and not the other side of the equation
Students will rationalize in their mind in (ii) 5 is already greater than 2 and therefore there will be no possible answer
Students may guess and check until they find an answer
Students may get to the two-step solution portion of the problem and make an error.
Students won’t check their answers to determine if the solution is erroneous
Students will correctly follow the process from start to finish, find the solution, and check their solution
Monitoring
What questions will be important
What should you do first?
What does the graph of the square root look like? What does that tell you about the domain and range of the function?
Do negative numbers have square roots?
What does’ equation’ mean? If you do something to one side of an equation and not the other, do you still have an equation?
Square a radical, get the
What are the steps for solving a two-step equation?
What can you do, that would give you confidence that your answer is correct?
What is the name for finding roots that really aren’t? What does that mean?
Selecting
To be determined based on monitoring
Sequencing
First, I would ask do both equations have a solution?.
Which one doesn’t have a solution? Explain. How did you know that?
For the one that had a solution, first step of the process
For the one that had a solution, second step of the process
Complete the solution and check
Connecting
I want the students to see the necessity and value in rewriting the equation, isolating the radical.
I want the students to see the possibility that solutions really aren’t solutions
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