September 2007

Justyne over on Schoolless just had a neat activity on survival of the fittest using Legos. It looks like fun and I may have to remember it.

But reading over what they did reminded me of something similar that I did a few years ago for the biology labs that I taught. But instead of Legos, we used M&Ms.

Justyne asked me to send her the info and since I needed to type it up, I figured I’d post it here for anyone to use.

Now for anyone who isn’t familiar with the terms: macroevolution is the idea that we ‘came from apes,’ or at least share common ancestors with them; microevolution is the idea that creatures’ characteristics can change from one generation to another because of some kind of pressure on the population. Believe it of not, there are groups that will accept the idea of micro-, but still argue against macro-.

Anyway.

This activity uses the concept of Punnett squares to model the typical offspring produced for two individuals. For our hypothetical population:

• Red M&Ms have 2 dominate genes
• Pink M&Ms have a dominate gene and a recessive gene
• White M&Ms have 2 recessive genes

This activity also assumes that every pair of individuals produces 4 offspring that perfectly model their Punnet square probabilities. So, it helps to start this activity by developing the Punnett square for each pairing (Red-Red, Red-Pink, Red-White, Pink-White, Pink-Pink, and White-White) to have as a resource.

1. You start with putting 16 Red, 32 Pink, and 16 White M&Ms (you can use any set of colors, and any particular item for this. But the M&Ms work well, and as you’ll see, the kids love to model with them) in an opaque container.
2. Now individuals with 2 recessive genes have a potentially lethal phenotype that may kill them before they have a chance to reproduce. – Take out 8 of the White M&Ms and eat them.
3. Mix up the remaining M&Ms and then, without looking, remove them in pairs. As you remove them, log each pair in the correct column of the chart until all of the M&Ms have been pulled. These pairs are the parents of the next generation.
4. Now record the number of parent pairs for each combination in the second column of the data table Using the Punnett square predictions calculate the expected number of each type of offspring – columns 3, 4, and 5. Add up each of those columns for the composition of the next generation. (You can ignore the 4 spaces on the bottom, they were to be able to answer questions from the lab book.)
5. Begin generation 2. Take each of your totals and put that number of Red, Pink, and White M&Ms into your container.
6. Assume that half of the White M&Ms die without reproducing – take them out and eat them.
7. And so on…..

When we did it, you could see the population start to clearly shift by the 3rd generation, but we ran out of M&Ms to be able to model the next generation. (We would have needed – 176 Red, 160 Pink, and 44 White.)

And, of course, when we were done the kids got to eat all of the M&Ms.

Hubby helped me decide on the theme for the third Map Club. He thought the kids would enjoy learning about non-Euclidean geometry and studying Taxicab geometry. It looked really fun, but at first I wasn’t sure how I was going to develop sessions at all three levels. It took a little playing with, but I finally came up with a structure for the classes.

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The pages’ abilities are all over the place. I decided before I could even introduce them to coordinate systems, I needed to work in one dimension. In fact, I ended up deciding their class goal would only be to introduce the girls to a coordinate system.

So we started off with a number line (I printed them each out a numbered strip) from 1 to 20. Our guessing game focused on the terms ‘greater than’ and ‘less than’. The person who was ‘it’ would chose a number and then we’d go around trying to guess what it was. After each guess, she’d tell us whether her number was greater or less than the guess. The girls enjoyed it and it gave them some idea of order and location.

From there I explained who Rene Descartes was and that he is credited with developing the Cartesian coordinate system. Earlier in the morning a couple of the older boys had drawn a large grid on the driveway and using it as a visual, I explained that each line represented the same distance.

We then used the grid to play an oversized version of Animal Crossing from Stenmark, Thompson, and Cossey’s book Family Math.

We first played it without any walls, so they could understand the what they were trying to do and then I drew in the walls and they played again until we ran out of time.

The idea of the game is that you roll a die that just has the numbers 1, 2, or 3 and then move in a straight line that number of spaces. When you run into a wall, you need to stop moving and then on your next turn change direction to continue on your way. The goal is to reach the opposite side.

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For the knights, I started with Descartes’s quote “I think, therefore I am.” and asked them what they thought it meant. After a short discussion, I explained he was a French philosopher and a mathematician (and even a lawyer) and that unlike today when we tend to think of these as separate areas, during the Renaissance period people would be interested in a board range of ideas.

We then went over the grid (which I had now added labels to the axis) and we discussed it’s 3 characteristics: origin, perpendicular axis, and a scale for measuring distance. We also went over how to name a point (x,y).

To use the grid, we first played another game from Family Math called Hurkle. For this game, whoever is ‘it’ chooses a point and then when another player guesses, they have to tell them what direction their point is from the guess (north, west, northeast…). The kids quickly figured out that by having everyone stand on the point they chose helped narrow down where the next choice should go.

After playing that for long enough for each kid to be ‘it’ once, I discussed that on typical grids the distance from two points is a straight line. But that wouldn’t work for a taxi in a city unless it could fly like a bird, so I explained how taxicab distances are measured. We then went around again, but this time instead of indicating direction, the person who was ‘it’ would give the taxicab distance to their chosen spot.

To finish coordinate systems we ended with a discussion of 3 dimensional systems that are used in ‘real’ life. They came up with examples from GPS systems to aircraft systems.

Since we had a few minutes left, I gave them another puzzle dealing with movement. The Konigsberg Bridges problem was solved by Euler (or actually not), but it kept them busy for their last 5 mins.

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By the time of the squires’ class it was getting hot.  I think it actually hit close to 90 and we were in the sun.  It definitely had me dragging a little.

But we jumped in with Descartes’s quote and why a Renaissance philosopher was also a mathematician.  I started by introducing them to the grid by playing Animal Crossing and then we discussed the Cartesian coordinate system and how to name points.   From there we played Hurkle, had a similar discussion about measuring distance, and then played taxicab.

And with that, their  class was over.