Algebra wrapped up solving systems by graphing today and moved on to substitution. I found an awesome intro activity over at Fawn’s 180 blog.
The first time through, I didn’t give students enough time to chew on the problem. But, for the rest of the day I gave them 20-25 minutes to work on it in small groups. A lot of students were stumped but no one was unable to at least have a start on the problem. I heard a lot of satisfying sighs of relief today after students solved the problem.
With time students came up with a lot of different solutions, I challenged all them and it was a great activity in developing reasoning.
Here are two example of student work
Several students started by assigning values certain animals and set up a system of equations ISH approach. It was fun hearing their reasoning of how they reached a solution.
The second example lends itself into a smooth transition for a conversation about substitution.
Great day today!
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!
My Geometry students lost it today over this problem.
I gave it to them and asked that they work quietly on it for 10 minutes. The automatically went for rulers and protractors. A lot of them came up with some pretty cool solutions for the drawing provided.
Then I told them it wasn’t drawn to scale.
They still have a rough time going from actual numbers to variables to represent all different cases. The most popular solution was to cut the land in half because it looked like all the little pieces would add up. When I asked them to prove to me that the areas were they same they ran into some big problems.
I ended the day by throwing them a lifeline which I have mixed feelings about.
For most of them, this is the first time they have ever come out of a math class with little to no progress on a problem. This is good. Struggle is good.
Tomorrow we are going to start class with this
I am excited to see how this goes!
Day two can be found here.