Speed Dating Rationally

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Objective

SWBAT solve a rational equation for a specified variable.

Big Idea

Efficiency and accuracy improves as students solve rational equations with their ‘date’ in this interactive and self-checking speed dating activity.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

rational expressions

Precalculus and Calculus

Standards

HSA-SSE.A.1

Interpret expressions that represent a quantity in terms of its context.*

HSA-SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

HSA-APR.D.6

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

HSA-REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

MP6

Attend to precision.

Warm-up: Become an Expert

10 minutes

As students come into class today, I am going to have the Speed Dating Cards spread out on a table with the problem facing up. I am going to ask students to pick up a card as they enter class. Students will become an expert on the problem that they choose, so I want students to be able to pick a problem that they feel is accessible.

Once all of the students arrive I present Flipchart Rational Equations Day 2 (p.1-2) and explain the plan for class. Them, students have 10 minutes to solve their problem and become an expert on how to explain the solution process to someone else. During this period, they can ask anyone for help. After ten minutes they will need to be the expert on the problem. The answers are copied on the back of the card so that students can check their work.

Lesson Preparation:

Before today’s lesson, I will photocopy the rational function cards (Speed Dating Cards - Rational Functions) so that the problem and answer are copied back to back. Each student will need their own card. I plan to make a double set of copies of these 16 problems.
When we come to the middle part of today’s lesson (The Speed Dating Activity) we are going to need to have the desks grouped so that two rows are facing each other: Speed Dating Classroom set-up
I will also have whiteboards and markers available for student work. At this point, I want students to have practice solving rational equations and seeing how others solve the equations.

Application: Speed Dating with Rational Equations

30 minutes

Time consuming to prep this lesson, but worth it!

Speed Dating in Action.MP4

Speed Dating, video reflection.MP4

Closure: Clicker Question

10 minutes

To close out today’s lesson and assess students current ability to solve rational equations, I will present Page 3 of the Flipchart and ask students to determine the area of the given rectangle. I may review with students for a moment to make sure they recall how to find the area and perimeter of a rectangle. I know I should expect students to know this by now. I want to make sure that there is no confusion. I want an accurate representation of which students can and cannot solve a rational equation when it is applied in context.

Technology Note: If students will be texting in their answers, they are not expected to text in units as it will not mark the answer correct.

Homework

1 minutes

I will assign Homework 2 - Rational Functions for homework. The assignment helps students to continue to build their skills in solving rational equations and has students review past concepts of compositions, identify zeros of a polynomial, and finding the inverse of a function.

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