One of my goals this year with my Honors Geometry class was to bring in some challenging tasks. I can't say that I've been extremely successful, but there are definitely some days that I feel like I did an okay job.
One of those days was during our Coordinate Geometry unit and the students had this task to solve:
I honestly didn't know how they would tackle it. Some groups tried to algebraically solve it with the distance formula but quickly got bogged down in the algebra. A few groups figured out a Pythagorean method by drawing a line at x = 7 and thinking about a right triangle:
but then I looked over at another group and saw this...
This group drew a line 20 units long on patty paper, placed one endpoint at (-5, 14) and used the line segment like the radius of a circle to find out where the other endpoint would have an x value of 7. I had only introduced patty paper a few days before and definitely not in this manner, so to see them make that connection and know how to use their resources to think through a problem really made me happy!
If you have any favorite geometry tasks to share, please let me know!
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