Thursday, October 19, 2017

Intro to Graphing Linear Equations

I basically started by having students create a table with x inputs from -8 to +8. I then gave the class a rule and asked them to find the outputs for each of those inputs, and have one group member write it on the table on the white board and pot the 2 sticky dots with the coordinate (x,y) written on it. I asked students to show their work and to confirm with their group, and once it came time to practice, I circulated targeting students I suspected would not know how to get an output for their input.

Instead of creating axes and doing the same rule from the book each period, I decided to make 2 classes have negative growth, and 2 of the classes have negative y intercepts and 2 with positive ones. I also carefully selected linear equations in y=mx+b form that would have clearly visible x and y intercepts.

I used y=5x-10, y=4x+12, y=-5x+10, and y=-4x-12.

So, once students had finished plotting their values, I asked if they agreed with the outputs written in the table, then copy them onto your table in your notebook. One student forgot a negative sign, and one had a calculation error, but it created a talking point for the class discussion.

I asked students if they noticed any patterns on the table. They would notice that it was increasing or decreasing by 4. I then asked them if they notice anything in the equation related to that. They said it was before the x. I tried to stress that since you are repeatedly adding the 4, repeated addition is multiplication, which is why it multiplies x.

I then directed students attention to the graph. I asked if there were any points that were easy to spot from their seat. Volunteers would identify either the x or y intercept because "the point is on the 'line' or axis." I then added the academic language of y-intercept. They then knew the latter's name since it must be the x-intercept.

Now I have butcher paper that I can reference for all my classes of various features.

Students then practiced on their own filling out a table for inputs -4 to +4 for the rule y=2x +1. Then they have to figure out how to scale their y axis based on the smallest and largest values. Some kids mistakenly scaled their x axis by 2. It's their first time, so there were plenty of issues with evenly spaced intervals, but I took photos of student work using the Google Drive app to display for our closure discussion. We also showed a rule with y=x^2. I asked them if they remember that from the Algebra walk at the beginning of the year and some remembered it's called a parabola. I asked them if it was increasing or decreasing, they said both. It decreases then increases.

All in all, a fun day in graphing linear equations for the first of many times. Here is the sample student work I shared with the classes. (having trouble uploading them, Blogger isn't updated for the new iOS version of the app I have)

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