Algebra B is working on absolute value equations. We started off using Dan Meyer’s “How Old” game where students see a picture of a celebrity and have to guess the age. I made sure to throw in a picture of my daughter at the end. It is amazing how excited the students get when I bring a picture or talk about her. Plus, it was a gimme answer. Who doesn’t like to be exactly right at least once. After about 10 people, ages are revealed and the best guesser is announced. It was a small class, but we had a good split of students who calculated their guess score by using absolute values and those that kept signs and even a few that explained the idea of the calculation correctly but still had negatives in the answer. We looked at two student’s calculations on the projector to pick a winner. The lower number actually was farther off (used negatives) so we talked about ow we wanted to determine how far off each was without caring if they were low or higher. It was quick, about 5-10 minutes for the whole thing and a good introduction to the idea of absolute value.
I introduced the mathematical notation and then asked students to come up with examples of when the sign didn’t matter (use absolute values) and when the sign would matter (not absolute values.) Then I threw up a quick number line on the board and had students place sticky notes where they should belong.
We then moved on to graphing. I had all the students predict what they thought the graph would look like, graph the parent function, and then discuss why they looked how they did. As time allowed, student then started to graph transformations of the parent graph, mostly by using tables and plugging in values. A few caught on that the transformations work like all the others we’ve done so far and skipped some of the plugging in steps. (All this work is still in the student’s notebook, and I didn’t take pictures as I was walking around working with students, but I’ll get it up soon.)
Lastly, we started looking at the graphs to find solutions to absolute value equations. I like starting graphically for two reasons. It reinforces the skill of find solutions from a graph (especially the multiple solution part) and it highlights the need for careful thought when solving algebraically since there are two solutions.
Our last few minutes together, I put up a couple absolute value equations which could easily be solved by sight and had students think of both solutions. We’ll follow up tomorrow with more involved equations.
**Last semester’s Algebra B class did a more involved graphic introduction which I really liked. We graphed the parent function and then in different sets 3-4 transformations of the equations on the same graph in different colors. I liked that graphing activity better, but it was also the first major transformation example. I did radical graphs and transformation first this time, so I skipped the longer discovery this go round. I think I might bring it back next time. Having 4 graphs together gives a better comparison. and allows for finding solutions to lots of equations at once.