IMP Fireworks - Using Vertex Form, Crossing the Axis, and Is It a Homer?

In Using Vertex Form, the students have another picture to create with their graphing calculators. Then they are given equations in vertex form and asked to give the vertex. Most of the students could do this without using the graphing calculators but a few still depended on them. I advised them to use the "Trace" feature of the calculator to find the coordinates of the highest point and then compare the coordinates to the equation. This improved their confidence in finding the vertex.

I gave my students a quiz where they had 6 questions in which they matched quadratic equations to their graphs. Then they had a couple where they had the equation and had to list 3 things they know about the equation. The last 2 questions had them describe how to flip a graph so that it was concave down and then sketch a graph with 3 different parabolas and give their equations. I was so excited about the quiz results. I wish I could say that all my students aced it but that is so not true! However, the large majority of my students passed the quiz and many made As and Bs. I have never expected my students to be able to do so much with graphing quadratic equations. The way the activities led the students through the process was so thorough it made the quiz seem easy.

The Crossing the Axis lesson gets students to start thinking about how many x-intercepts the graph of each quadratic equation will have based on the phase shifts. The activity also has students to write the equation given the vertex and another point on the parabola. They have to use the information to solve for the value of a. Numbers 5 and 6 are very important to complete because they give the students the tools they will need to complete the Is It a Homer activity.

Is It a Homer is an awesome activity to me as a former softball player and coach. It was also fun to the students. Mr. Webb shared a link with me of a Youtube video of a "dramatic reading" of a poem about the "Mighty Casey." We watched it before we read the activity. They are challenged to figure out if the ball clears the fence and they must prove it mathematically. I had the students sketch the graph with height on the y-axis and distance from home plate on the x-axis (which was advised in the teacher's guide). I gave the students the hint that they will be using the same process they did on 5 and 6 of the previous activity. After giving the students some time to think I went to the board and sketched the graph and labeled the vertex. I asked the students if there was another time when we knew what the height of the ball was. My 2nd block students chose to use (0,0) and but my 4th block students pointed out that the ball was not hit off the ground so they used (0,3). They struggled some with the computation of this problem but a few students in each class got the answer correct based on the height of the ball at contact. I had one student who told me that he estimated that the ball would fly 400 feet because the maximum height was after the ball flew 200 feet. Even though we have not yet talked about the symmetry of the graphs he had recognized it and used it for his reasoning. Unfortunately he didn't tell me his thoughts until AFTER class. I will be sharing it with my classes tomorrow.

IMP Fireworks - Parabolas and Equations I, II, and III and The Vertex Form of a Parabola

I am absolutely loving the way Meaningful Math develops the Fireworks unit. These graphing activities go through each of the ways that parabolas are transformed using phase shifts. The students explore each of the phase shifts using graphing calculators. They start with different equations to enter and analyze and then they are given a picture of multiple graphs on the same coordinate plane. They areasked to create the picture by typing equations into the calculator.

The first few activities I gave each student a TI-83 and each group also had an Ipad. Once they figured out the correct combination of equations the group displayed their graphs on Desmos which I projected on the board using Airplay. This was a neat way to have the students to "show off" their work. However, as we were going through the activities I noticed that many of the students were just waiting for the person with the Ipad to type in the equations. They were not using their calculators like I had intended. I wanted them to use the calculators first and then display their findings using Desmos. Therefore, today I had the students to let me know when they got each of the pictures correct. I initialed their papers where they had written down the equations that gave the picture. We did not use the Ipads today. I liked the change - especially since we were working on the activity that pulls all the shifts together. By requiring initials for each of the problems I was able to formatively assess each individual instead of each group. Since each graph took a good bit of  time to create it was feasible for me to initial.

Today's activity introduced the students to the vertex form of a parabola. It combined all the pieces that we have been working on in the last few days. I feel that after working on getting the equations that generate the pictures the students were beginning to demonstrate a firm understanding of the phase shifts. 

On a side note...Thursday Tom Laster and Laura Murphy from It's About Time came to our school to observe our classes and discuss plans for next year. Observe is really the wrong word...they actually came into my class and sat with my students and participated in the graphing activity. My students really enjoyed this and I was honored that they came to visit!