Geometry spent their second day on the The Fence Problem. I went over the opener (in yesterday’s post) and it was interesting to see that a majority of students created a right triangle.
To create an area of 15 u^2 students needed some x value of 6. After I put the right triangle on the board I paused for a bit and just let students process the situation. A couple minutes passed and a student raised their hand and said (6,-10) will also work. We drew the triangle then I started getting other responses; (6, 2.5), (6, -5), (6,-100) ect.
I asked students to take out the fence problem again and used this new knowledge to help them.
They struggled still in proving a general case. I am OK with this.
We eventually worked through the solution as a class.
Here are a few of my thoughts after this activity:
- I need to do more problems where I introduce a key idea on the second day and give students an entire period to struggle.
- I am still too helpful.
- These are students on the advanced track; they probably have never had a problem that takes them more than a day to solve.
- Generalizing is a huge idea in geometry (proofs) I need to do a better job of tying everything together.
I encourage everyone out there to try this activity; it is worth the time and struggle for students!
Quadrant Dan 
Could be x = -6 also
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