algebra

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Open-ended project: Mathematical modelling with student-collected data

For this project, students collect data on a phenomena in which they are interested, with teacher guidance, and then look for patterns in this data. They can use a variety of different means to collect their data, attempt to find a model which matches the data, and then present what they have found. Ideally students would go through multiple revisions in their data collection model to collect as clean data as possible, particularly when they end up with major problems with their results.

Some specific things which students might model:

  • The growth of plants over time;
  • Population growth of bacteria in a petri dish;
  • Temperature during the day;
  • See more ideas here.

If you want more information on what mathematical modelling looks like, see this document or this document.

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Calculator investigation

This post was shared to me by Jennifer Silverman. What do you think of this student’s inventive use of a pair of calculators?

In a ninth grade Algebra 1 class, we were studying systems of equations. The problem for the day was about drag races, so we started with: http://youtu.be/LGEWCsP1bR4 & http://youtu.be/ggxsrVWEf9E.

carproblem

One of my students, Ben, was tackling this problem with a partner, and they weren’t making a lot of progress. Suddenly, Ben jumps up and says, urgently, “Mrs. Silverman, do you have another calculator?” The “loaners” were gone so I gave him mine. Pretty soon, he looks up with a big grin and says, “The Mustang wins!” He had built two sequences, one in each calculator, and was carefully monitoring each of them as he simultaneously hit ENTER on each calculator. He knew that the Mustang won because that calculator got to 500 first. When I asked him how long the race took, he asked me to hang on a second. He repeated the process, this time counting the number of times he hit ENTER. “A little more than 11 seconds,” he said, “because at the eleventh hit, the first calculator was at 495.”

carproblemtable

Eventually Ben was able to model and solve these problems algebraically, but on the day of the final exam, he had two calculators with him, in case he needed to go back to his own intuitive approach.

Pretty cool, huh?