Day 2: Broken Squares

We had full periods today so I used the first half to introduce students to visual patterns. Algebra went though a linear pattern, which students seemed to enjoy. Geometry went over a fairly complicated and challenging pattern. I told students I wanted them to struggle and that it is a good thing. Here is the pattern I gave Geometry:

I wanted them to try it first by themselves; this didn’t go as planned but I didn’t stop them because the discussions were awesome.

Students then came up to the document camera and we were able to cover 4 – 5 different solutions all of which were built around the general equation of x(x+1).These discussions lasted about half the period, then we go into broken squares.

I came across this activity in a college class and really like the ideas it communicates. Here are the goods Broken Squares

A quick run down:

  • Students are broken into groups of four and asked to each create a square.
  • They are finished when they have each created the exact same sized square.
  • The catch: They are not allowed to talk. At all.
  • They cannot communicate in anyway and may not take a piece from another group member; but may receive one.

Groups took anywhere from 2 to 20 minutes the complete the task, once finished they packed up their pieces and observed another group. In the end the entire class is surrounding the final group, once they the finish their squares, everyone gives them one clap.

photo 3 (1)

photo 1 (1)

photo 2 (2)

It is interesting to see student’s personalities. Some would complete their own square and sit back expecting everyone else to do the same, however that is not possible. Students were hesitant to backtrack and deconstruct a completed square.

After we talked about how it is important to let everyone have the satisfaction of solving a problem on their own and how difficult it is the have onlookers who expect you/your group to instantly see the solution. I hope this problem sets the stage for more productive and meaningful group work this year!


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