Talking Math With Your Kids

I don't have kids, but the title of this post comes from the title of Chris Danielson's blog by the same name.

I was at the laundromat tonight, and as I was pulling my clothes out of the washer, I noticed an elementary-aged girl working on math homework. She was telling the adult with her that she had to "count by fives from six to fifty-five." She was working on the list when she said with frustration, I hate math! The adult said you can't county by fives like that because it doesn't work out evenly. She ten started counting out loud: "five, ten, fifteen..." The woman then read the problem from the math book herself, and it turned out that it asked students to county by fives from six to fifty six. The girl started sharing her sequence of numbers: 6, 11, 17, 23, 29, ... Another woman with her said: How did you get 29 from that? The girl noticed that she was counting by six's instead of by fives. So she started over. She wrote down 5, 11, 16, 21, counting up from one number to the next. I wanted so much to ask her if she saw a pattern, but I waited patiently as she kept working. When she reached 26, she exclaimed, I got it! I asked her to share her list of numbers. She had erased them, so she started writing them again. The list came more quickly to her this time, and she pointed out that all of the numbers end with a 1 or 6. I wanted to ask her to explain the pattern more, but her parents were talking to me about other things.

Normally, I wouldn't poke my nose in other people's business. I would go about unloading my clothes from the washer, trying to listen unnoticed to the conversation, and leave when I was done. But because I have been reading Chris' work for a couple of months, I was intrigued by what I learn from this girl and her mathematical thinking. So I watched, and in the end got to see a girl go from frustrated to excited about her math homework, which made me very glad!

GeoGebra success!

At the beginning of the year, I had my Geometry students use the free software GeoGebra to model an orienteering situation. They really struggled with it for a number of reasons I won't get into now. We are currently working with circles in class, and I had gotten to a section of the book that includes four theorems about inscribed angles. I didn't like any of the types of problems provided by the textbook - I found them uninspiring and I felt that students could learn how to do the problems without understanding the theorems. So I created a short project in which students would create models of the theorems in GeoGebra. I hoped it would give them a sense of what the theorems say and how they work. I also hoped they would gain some familiarity with a new digital environment, which I think is important for students. They had to create the models so that even if I dragged some of the points around in the program, the theorem would still hold up. In addition, students had to write up the steps they took to create the model. I had many trepidations going into this project - Would the technology work? Would students be able to work in the environment of the software? Would it be too easy or too hard? Would it take more or less than the three days I was allotting for it? In the end, it worked out beautifully. It was the right amount of challenge for my students. They worked at their own pace, and few students had real difficulty figuring out how to use the tools in GeoGebra. I led them through the steps of the first theorem, and they created the other three on their own. I am including samples of their work, as well as the project description and grading rubrics.

For the students who got done early, I asked them to spend a little time on this awesome geometry construction website:  http://sciencevsmagic.net/geo/
 

Materials

Project Description and Rubrics
Steps for Theorem 10.6
Steps for Theorems 10.7, 10.8, 10.9