INSIDE THE CLASSROOM:
Alex Sczesnak, math teacher, Lower East Side Prep High School, Manhattan
New York’s new Common Core-aligned algebra I course emphasizes systems of linear equations, functions (particularly linear, quadratic and exponential), statistics, and modeling. Probability, trigonometry, and much of the linear equations unit are now covered in other courses.
In my classroom, this means we spend a lot of time learning about different types of functions and how to interpret them in real-world situations. I find it best to lead with context, rather than the mathematics underlying it. I begin most l essons with a situation from everyday life that students intuitively understand, then give them the opportunity to explore it independently. Only after the topic make s sense to them in terms of their personal experience do we formally connect it to our study of algebra.
For example, we recently completed a lesson in which students were asked to list all the ways a basketball team could score 30 points by making only two- or three-point shots — say, by mak- ing 6 three-point shots and 6 twopoint shots. They were then asked to narrow down their lists and limit them to the ways that required the team to make exactly 13 total baskets. Only one solution meets both requirements.
This problem set perfectly illustrates the concept of a system of linear equations, an essential idea that algebra 1 students must master.
In algebra I, I focus primarily on two of the standards for mathematical practice. The first requires students to move fluidly between abstract mathematics and the real-world quantities it can be used to represent. They must know, for example, that in the equation 2x + 3y = 30, x and
y represent the number of twopoint shots and three-point shots respectively, and that the solutions to this equation represent all the possible combinations of two- and three-point shots that will make exactly 30 points.
The other standard we focus on requires students to justify their arguments and critique the arguments of others. In the basketball example, students should be able to argue that a total of 8 two-point and 5 three-point shots will not make 30 points, because they can show that 2(8) + 3(5) = 31, not 30.
The algebra I standards set the stage for the rigorous modeling and proof techniques that students will focus on in geometry, algebra II, and beyond.