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.
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.
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.