Tuesday, March 22, 2016

Day 126: WODB Linear Functions, Angles & Linear Inequalities

Today's WODB for all classes was the following linear functions:

For some reason, many students in multiple classes said that the bottom right graph was the only one with "negative association." I replied that a scatterplot that had points going down was negative association. They eventually came up with negative slope.
I also prompted students to add on to thoughts of the top right being the only one that passes through the origin (0,0). I liked when students mentioned bottom left was the only one with a negative y-intercept.
This class found that the top left was the only one with a negative x intercept. We also discussed what was true about what was visible which had to be added to some observations. For example. the bottom left was the only one that intersected only one axis.
In each class we came up with conjectures for corresponding, alternate interior, and same side interior angles. I stressed that interior comes from being in between the parallel lines.

More conjectures again.
Then students used the conjectures to find angles by writing and solving equations. This proved to be quite challenging for them. Some moved on to identifying if angles were corresponding, alternate interior, same side, straight, or none of these.

In accelerated we reviewed two of the homework problems first. I targeted one where you had to divide by a negative on both sides which then reversed the direction of the inequality sign. We had not covered that last year. To demonstrate this I had students write 12 and 8 with and ask which inequality symbol should I put between them. They said greater than. Then I divided both sides by -2, and they said ahh.. they saw that the inequality couldn't face the same direction anymore. I should have demonstrated with a positive number as well to show it didn't change the direction because students asked about that later.

For students who were still new to it, I wrote "when you multiply or divide by a negative on both sides of an inequality, the direction of the sign reverses."

In the classwork, students tested whether coordinates were on the line of the equation y=-2x+3 graphically as well as algebraically by using the equation. This lead right in to me passing out green sticker dots and 8 coordinate pairs for students to test if they were solutions. The results were awesome. We had 2 misplaced points that students pointed out. Grace saw that the equation of the line was the "boundary point" and that everything to the right was a possible solution. They said there were infinite solutions. The class discussion was focused and productive.

Then students moved on to a graph in the book that was shaded on the other side of the line. They were asked what inequality this represents. Students reasoned it was the same inequality, except the direction of the inequality was reversed. Then they were asked to reason about what would you do to the graph to make it y<2x+3. This was great. Jason came up with it must be a hollow or invisible line like on the number line. Then he reasoned that it must be a dashed line. He earned a 3 second clap from the class for coming up with it, knowing he had not known that prior to today. I pointed out to one group that that was what the textbook philosophy is about, build the understanding yourself on your intuition and thinking.

There wasn't time to practice the 4 practice problems, but we will jump right into that tomorrow, then start 9.3.1, applying linear inequalities to real life world problems.

Always a good result when students are empowered to get out of their seat to contribute to a graph.
What a great activity. I reused my algebra walk laminated posters from earlier in the year and drew the boundary line on there. I asked students what we should do to signify all points to the right were solutions. They said shade it, so I did with the expo marker.

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