__determine if the coordinates of a given figure are vertices of a parallelogram or rectangle__. Today in class I gave students three options and told them to choose the one that is the most challenging to them. (Some students did more than one)

__Here were the three questions__:

I used this web app to check the points and get them displayed quickly as students shared them. As we moved through student work on each one it naturally sequenced our discussion to the higher level task #3 that some students chose to do. One kid even did the 'mind blown' motion with his hands when we substituted concrete values in for a and b in the student example below to show that it works. It was a pretty simple activity but at the same time a good motivator for some higher level discussions in math class that didn't take a whole lot of time to prepare.

- Write 4 coordinates that will make a parallelogram that is NOT a rectangle
- Write 4 coordinates that make a rectangle that has NO horizontal lines.
- Including the point (0,0), use variables a, b and c to symbolically write coordinates that will always make a parallelogram for any given values. For example maybe your coordinates would look like (0,0) (a,2b) (a,c), etc.

Here is the follow up discussion we had on #3, including the example a student came up with:

Here is a link to the document of the activity.Student example: (0,0) (2a,b) (2a,0) (0,b)How did you come up with these?Choose values for the variables a,b, and c to show it works.What if we made a bigger or smaller? What would it do to the parallelogram?Would it still work if a or b were negative? How would it change it?

Great structure for generalizing. I like that as a framework for tiering. It also might work in reverse, showing students how to try specifics when general is out of reach.

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