My First Day Activities: Survival Game & Chaos Game

Standard

I do not like waiting til the last minute – I feel so scattered and that my best simply cannot be achieved.  But here goes – my plans for Algebra II – The Survivor Game (Theoretical vs. Experimental Probability) & The Locker Problem (HW) and Geometry – The Chaos Game (Intro to Sierpinski’s Triangle – patterns, similar triangles, midsegments, etc.)

Algebra II

Looking over my rosters – most students are not fans of math – so I thought it might be appropriate to “play” the SURVIVAL GAME.  The best I can tell – none of these students were in classes where I’ve used this activity.  Survival Game was shared with me by a friend who used it as part of her NBCT process and she found it in Mathematics Teacher, February 2002.

The scenario is (you can change it of course)  – students have been in a devastating bus crash – they are all rushed to the local hospital for medical treatment.  Due to low blood supply, there is a call for blood donors.  The students chance of survival is based on the probability of a match or compatible blood type being donated.   Though parts of this set-up are not realistic – its a great learning task and gets the idea of theoretical vs. experimental probability across.

I use white poker chips with color-coded circle labels in the centers – according to % of blood types in the U.S. in 2002.  I’ll admit, I am too lazy to change the chips.  You go around the room and each student draws a chip to determine their blood type.  Discussion comes up – do we replace?  Why/Why not?

Then we look at which blood types are compatible – a very brief discussion about Rh factors, etc.  Resources are linked on the files.  Students mark on their recording sheets M-match, C-compatible, N-nonmatch.  We begin the simulation of blood donors, recording the data and writing the P(S) – probability of survival as the ratio of (Matches+Compatible) / (trial #).   When all 25 trials are complete (its fun – students cheer with matches and groan with non-matches), students compute equivalent decimal values – these are then used to create a graph of their P(S).

I love this activity – only twice in all the times I’ve used it have the Theoretical / Experimental Probabilities not “leveled out” within the 25 trials.  A discussion about “the law of large numbers” takes place – on how more trials will usually result closer to the theoretical.

I do have @MathBratt’s Locker Problem lined up just in case…

Geometry

My first day in geometry – I’m playing the chaos game.

I’m going to show a clip from Jurassic Park

I am making Chaos Game template copies on transparencies for each student to have their own triangle.  I will let them use dry-erase so the triangles can be cleaned off, filed and reused.

Everyone picks a random point (seed) inside their triangle.
They roll a # cube, if its 1 or 2, they measure the distance between their point and vertex marked 1,2.
Place a new point at the half-way mark.
They roll again, measure distance between newest point and corresponding vertex.
Place new point half-way between.
Continue about 100 times per student (or as many times as time will allow).

Overlay the triangles… and you get something close to Sierpinski’s Triangle.   Hopefully.   I have gotten one each time I’ve played this with students in the past – but you never know because nothing is really predictable.  Or is it?

We’ll take a look at an online example from Cut-the-Knot

I will then give them a section of Triangle Graph Paper and let them “color” a sierpinski trianlge – probably about 3 or 4 iterations.

HW –

1. Find as many patterns / geometry terms within our Triangle.
2. What is a Fractal?
3. What is Pascal’s Triangle and how is it related to Sierspinski’s?

I’m thinking I can use this over and over – in probability – similar triangles, midsegments, etc. throughout the semester.  Hoping so anyway.

These are 2 activities I love – they are somewhat fun, but still bring some good math related discussions.  I figure if I share something I enjoy – it’ll be a good transition to a new year.