Tag Archives: Area

Day 150: Ticket Roll (Student Work)

Continuation from yesterday’s post.

There were some interesting ways students went about finding the total tickets, have a look.

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I have been working on transitions within 3-Act problems.They always start really well then student engagement and quality of work slowly decline. Folding a sheet of plain old paper into 6 regions and having a purpose for each region has helped quite a bit.

For those interested

  1. Estimate: Guess, low, high
  2. Info they need
  3. Game plan of how they will use that info
  4. Provided information
  5.  and    6.    Work

One strategy that worked well today was I had students share out their confident calculations. I threw ’em on the board and then whoever had the closest talked about their solution process.

The tail end of lessons seems to be a weak spot in my daily instruction, I’m interested to hear in what sort of closing routines you all have.

Day 149: Ticket Roll

Geometry took a concept test today and started on The Ticket Roll from 101qs.

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3-Acts are a lot of fun, I have been working on having students develop all aspects of the problem: from the initial question I shift their thinking to what information they need. Then before giving it to ’em I ask how they would use their desired info. Here is the list my class came up with.

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A couple students reached a final number but a majority took the problem home, I am looking forward to hearing their solution methods tomorrow.

Day 147: Pick’s Theorem

An admin came in today for my second observation of the year, this time they observed geometry. The class went great, students stepped up and had a productive period.

The lesson was on finding areas of composite and irregular figures. I had crammed too much into the slides for the lesson and made a mid-lesson decision to only cover finding the areas of figures on a coordinate system or dot paper.

I pulled most of my resources from Dan Meyer’s post. Class flowed really smoothly, students struggled in places I had expected and were all successful in the end (they even derived Pick’s Theorem!)

Throughout the lesson I tried my best to keep this ratio as close to 0 as I could.

RatioA lot of times when I try to keep this at 0, students drift and I lose them. Today, I felt like I had perfect points of entry in helping students while at the same time having a minimal impact on their ownership of the material. They owned it today.

Day 143: Two Triangles

Geometry is starting a chapter on area, at the beginning of the period I put this up.

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It was fun to see students expressions as they figured out that both large triangles have the same base/height and are also made up of the same pieces. The group was able to come up with the solution after about 5 minutes.

For the rest of the period they worked on Dan’s Coffee Traveler Three-Act.

Here are some of the end results.

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Day 57: Fence Problem Part II

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.

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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!

Day 56: The Fence Problem

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.

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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

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I am excited to see how this goes!

Day two can be found here.