Today in geometry we started incenter/circumcenter, here is a problem one of my colleagues shared with me; I really liked it. So did my students.
I passed out a paper with the same text/image on it. Here it is. Almost all my students were about to locate an point to place the tower, however most of them did this by guess and check. When I asked them to explain why that point made sense they took their compass and drew a circle, indicating they were equidistant.
I lost ’em after this. This seems to happen quite a bit, I need to think through followup and extension questions. Students pushed back when I asked them to explain how they could use math to help make sense why the point they chose made sense.
Tomorrow we are going to follow up by creating the circumcenter by finding the intersection of perpendicular bisectors and look a little deeper into the congruent distances from the three cities and what sort of triangles are created.
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!
It has been a while since I wrote a post on where I am at in Geometry. This is my first time through the curriculum so the whole deal is pretty crazy. We just wrapped up talking about proving lines parallel by pairs of angles and the transversal business. Now, we are moving into a massive chapter on triangles, which i am looking forward to.
I started off with transformations. Thegeometryteacher has a massive amount of helpful resources that I pull form on a weekly basis. The latest of which is this exploration on transformations. I added a 4th page to the sheet covering dilations, but for the most part the exploration was all student guided.
Before passing out the worksheet we went over a couple of the activators he provided.
I am really excited to challenge students by asking them how to reflect across a line that isn’t the x or y axis, say y = -2x for example. More to come in the future!