Solving Quadratics by Factoring-Day 2

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Objective

SWBAT solve a quadratic equation and using technology to check their answer graphically.

Big Idea

This lesson allows student to get LOTS of algebraic practice while using technology to build conceptual understanding.

Launch

10 minutes

This launch is a concept_attainment and the process is explained via video at this link.  This launch connects to the closure of the previous lesson where students simplified an expression and solved an equation.

Technology Note: Please view the launch presentation (Solve_Quadratics_Day2) in slide show mode. On Slide 2 there are many expressions lumped together at the top of the slide.  In slide show mode they appear one at a time and then populate the table below. 

Practice

25 minutes

My intention in this practice section is to give my students an opportunity for lots of practice solving quadratic equations. As they work on Solve_Quadratics Day 2_Practice Students will work with their partner on this practice assignment.  However, while they are practicing, I want them to be developing the conceptual understanding. In order to promote this I will question students about the meaning of what they are actually finding when they obtain a solution (MP2).

In order to get students to think about the solutions in multiple ways, I ask them to graph the associated function using technology as a check. As they visually inspect the roots of the function (see roots_of_quadratic.png -- the picture shown here is from desmos.com), they can see a pattern with respect to the location of their solutions.  

Technology Note: The desmos.com website provides a particularly friendly interface for students. They can evaluate a root by clicking or tapping on it.  A graphing calculator could also be used for this purpose.

Once students graph the function, I ask them to make a sketch next to their solution to the equation. I also request that they clearly label the roots.  

Ultimately, there are too many questions here for students to get through in 25 minutes. That said, I provide a lot and I choose an appropriate number for my class on a particular day. It is always better to have extra problems. For my current class, I asked students to pick two questions from each row.  At the end of class, I asked students to complete the remaining questions at home.

 

Teaching Notes:

  1. For questions like #14, it may be necessary to explain to students that in order to graph the associated function all of the terms should be on one side of the equal sign.  If a students tries to graph the equation as written using desmos, they will be graphing the points of intersection of two functions: the quadratic equation and the line.  For some students, this could be an interesting extension!
  2. Problem 17 and Problem 22 are both linear equations.  I want to make sure that students don't get so caught up in a procedure, that they incorrectly apply that procedure without inspecting the equation first.  Of course, both of these equations could be solved by setting the equation equal to zero and factoring. Depending on how many students solve the equation in this way, I may decide to address the fact that this is probably not the most efficient method of solving. I can imagine doing this by direct instruction or by having students share their solutions.

Closure

5 minutes

Today's Ticket Out (Solve_Quadratics_Day2_Close) gives the students the opportunity to express their ideas in writing.  Now that students have worked through several examples that look similar to this, they need to try to express their reasoning in a clear, coherent way (MP3).

I plan to post the vocabulary words: roots (zeros), solutions, quadratic equation, quadratic function, and solve on the board so that students can use these words in their explanation. I find that providing a list of vocabulary words can also help to spark student thinking.