Reflection: Rational Approaches to Solving Rational Equations - Section 2: Explanation: Solving Rational Equations


During the notes today, my students and I had an interesting conversation about factoring. This probably would have been a much better placed conversation to have at the start of the polynomials unit; however, it’s better late than never.  My students started by expressing concern when I mentioned that the trick with rational equations is to be sure to factor everything first and see if common factors divide out. There was that deep sigh that resonated throughout the classroom with that statement.  I knew their factoring skills were lacking in the last unit. They are slow to get the factored form of a polynomial and aren’t confident in their answers. They often mix up signs and really mess up factoring when the leading coefficient is not 1. But my even bigger concern is that some students are still struggling with WHEN they should even factor. Many of my students are still trying to solve equations that require factoring or the quadratic formula by direct solving.

So for about 10 minutes of today’s lesson I turned it over to the kids. I asked students that felt comfortable factoring to show the rest of class how they factored and how they know when to factor. Here are some of the methods that arose during this conversation:

Generic Squares Method: Factoring Reflection, Factoring using Generic Squares

Factoring by Grouping: Factoring Reflection, Factoring by Grouping

Helicopter Method: Factoring Reflection, Helicopter Method

I am really curious what other structures teachers are using to help students to factor.


Furthermore, this whole conversation started making me think more deeply about the necessity of factoring polynomials. What is the purpose? Is it really necessary in math curriculum? Factoring Reflection, Necessary Evil


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Rational Approaches to Solving Rational Equations

Unit 3: Rational Functions and Equations
Lesson 1 of 12

Objective: SWBAT solve a rational equation for a specified variable.

Big Idea: Factoring polynomials and simplifying fractions while solving equations are key skills to review at the start of this unit.

  Print Lesson
Math, rational equations, Precalculus and Calculus, PreCalculus, solving rational equations
  50 minutes
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