Lesson 3.3.1: Writing Linear Functions (Days 55-57)

In the eighth grade classes, we proceed with Lesson 3.3.1 in APEX, on writing linear functions. This lesson is mainly on using functions in slope-intercept form to solve word problems -- including what the slope and y-intercept correspond to in the real world.

One notable thing about this chapter is that it asks students to write the equation of a line given two points on the line. This always begins with using the slope formula to find the slope of the line. At this point, most Algebra I texts do one of two things -- either they take the slope and one of the points and use the point-slope form to find the equation, or they go back to slope-intercept and have the students plug in one of the points (x, y) and the slope m in order to solve for b.

But the example in the APEX lesson does something different. After finding the slope, the lesson just asks students to graph the line to see where it intersects the y-axis. This is akin to graphing two lines to determine their point of intersection -- in this case, one line is the y-axis.

Looking ahead to the Unit 3 Test in APEX, I notice that in the questions where students are asked to find a line given two points, one of the points lies on the y-axis. In this case, students don't need to do any work to find the y-intercept.

This would make these two-point problems easier to do. But unfortunately, there is also a word problem on the test which gives the speed of its car and its location after a certain amount of time. In this case, students are expected to plug in values of x, y, and m to find b. This sort of question also appeared on the first quiz of the unit, and it definitely tripped the students up (especially since after finding b, they are directed to compare this function to another graph).

And it appears that students are still struggling with slope. I'm still looking at the worksheets of the students who are turning it in late, and they continue to show a lack of understanding. Today I give more assignments to improve this, including one on Quizizz. In this case, I finally created my own Quizizz account and assigned a quiz on linear functions. Some of the students enjoyed this, and kept on trying it again and again to improve their score. (The only problem was that the background music was for Halloween, even though it's four days past the holiday.)

There is also a Go Formative Unit 3 Practice Test, and I took advantage of tutorial being assigned to first period to give the eighth graders extra time to work on their Practice Test.

After school, the math department head entered my classroom. In addition to Math 7, she also teaches Math 6, and right now the APEX sixth grade unit is so easy that the students finish it quickly. So she wants to play a sort of bingo game with them, but isn't sure how to do so in the pandemic era. Thus she asks me to give her some ideas. This is the sort of thing I will ask on Twitter over the weekend. In addition to this, I will make my usual tweets describing my own class and the next Eugenia Cheng chapter. So therefore this is shaping to be a three-tweet weekend coming up.