Continued work with recognizing circle equations

Today we continued work with recognizing circle equations. I checked with how the three assigned homework problems went. About half the class actually worked on the problems. For these students, most had success, with a few still struggling with the algebraic manipulations that are needed.

I walked through the first example problem and shared thinking of how to separate and break down the problem into parts. After this, I let students work through the next set of problems.

For these problems, students had to add a constant in order to complete the square. While there was some struggle at first, most students started to see how they would need to split the values in the area model we've been using. Most initial confusion came from dealing with negative signs.

As students worked through these problems, some still didn't recognize that the two factors had to be exactly the same, since we are squaring the expression that is created. Working with these students helped them to understand that squaring the value meant that both factors had to be the same value.

The next issue arose with the added constant to complete the square. Students found the value they needed to add but didn't see that they were adding value to one side of the equation. I had these students multiply out their squared terms and compare them to the original equation. They could now see that there was added value. Again, algebra skills were a bit lacking as some students now wanted to subtract off the added value.

I referenced the original equation and broke out their expression to match the original expression plus the added value. This helped students to see they needed to add value to the other side of the equation.

At this point, most students were rolling along on the practice problems. As I walked around, I addressed individual questions, but most were looking for reassurance they were proceeding correctly, which they were.

I left the remainder of the problems for homework. We'll try to wrap up these problems with a discussion and then use the final set of exercises as an assessment of how well they are understanding the material.

The plan is to begin looking at areas of overlapping circles, which will pull in central angles, areas of sectors, trigonometry, and coordinate planes, after this.