# 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.

# The Candy Problem

This is a great video of some students sharing their thinking while solving a problem posed by their teacher.

See this blog post where Deirdre Bailey and Amy Park frame the problem posed for the students (as well to get a copy of the text of the problem itself).

# 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.

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.”

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?

# What is my area?

I love this activity by Bruce Ferrington with his students.

What Is My Area?

Wait – before you say anything – I know your body is 3-dimensional and area is a measurement of two dimensions – so I probably should say, “What is the area of my silhouette?”

So…

What is the area of my silhouette?

In the past week we have measured height and width, talked about Vitruvian Man, combined our heights, compared them with other classes.

Time to have a look at comparing areas.

My chief interest here is to look at how the kids are going to approach this question. I want to see if they can come up with any short-cuts that will speed up the calculations, so they don’t have to cover their entire body in 1cm grid paper and count out each square.

# Number patterns

My son and I played a game tonight. Each of us took turns giving patterns of numbers to the other who was to guess what the next number in the pattern was. Here are some of our number patterns we challenged each other with:

1, 2, 4, 8, …

1, 3, 5, …

2, 10, 18, …

1, 3, 9, …

150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1500, ….

3, 5, 4, 4, 4, 4, … (this one is sneaky, so I’ll give away the answer. One has three letters, three has five letters, five has four letters, four has four letters, and so on. My son came up with this one. An aside: does this sequence always end up with a repeating four, no matter which number you begin with?)

I finally stumped my son with the following:

1, 1, 2, 3, 5, 8, 13, …

# Open-ended investigation: The Math of Voting

Students could look at different ways of voting, and see what impact each of these ways has on a local election in their own school. They could compare the different methods, decide on ways to check for “fairness” of the election results, and even attempt to come up with their own system of voting. This project is likely to work better and have more interest from the students if they use actual data from things they are voting on for their experiments, as well as data from other sources.