Each day, students complete a Warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.
For a video narrative about how I structure each lesson, and how the warm-up fits in, click Warm Up.
In this case, the warm-up addresses a problem that many students missed on the last unit assessment. Only one of them has a negative slope... and so the question I ask to open is:
"In which of these cases should there be a positive slope?" We then analyze the incorrect answer choices to finally arrive at the correct answer choice, a strategy I often use.
Because students often have only an emerging understanding that positive slopes represent a positive association (in other words, as x increases, y increases also) - this is a wonderful learning opportunity to continue to develop this understanding.
This year, I decided to focus on the idea of multiple representations of the same line - a line is NOT just a line on a graph, but a relationship between two quantities that has a constant rate of change. I had students create their own line in slope-intercept form, and then graph the line, create a table from that line, and create a verbal description of the line, pushing on their creativity. I really think it pushed on their understanding of what a line is, a key idea underlying the major work of 8th grade.
And all you need is some graph paper! :) See the resource section for some examples of student work.
The homework file is a resource that generally includes 5-7 problems that include questions related to this lesson, as well as spiraled review. I also give the kids the answers to all the problems.
Tonight's homework assignment: 4 - 1 HW40 Define and graph linear functions