Geometric Fruits & Vegetables

http://laughingsquid.com/geometric-fruits-veggies-photo-series/

Seems like there is a lesson on fractions here. How many watermelons are there in the first picture?

Another thought: This could totally be done as a number talk!

Another thought: I wonder how some of these pictures are analogous to the border problem? Is there something about making the pictures larger or smaller that could lead to a generalization? This one seems like it would work well for growing/shrinking/generalizing.

Another thought: This one is hecka cool for kids to think about visualizing how shapes get dissected and put back together in 3-D.


UPDATE:

My colleagues and I included some of these photos for Number Talks in our Math 6 curriculum. (For those who are unfamiliar with Number Talks, I highly recommend learning more!) We called them "Tasty Number Talks" and they have been a huge hit with teachers and students. Unfortunately I have not yet gotten to see a Tasty Number Talk in action, but I hear good reviews! I wonder what the artist Sakir Gokcebag would think about his art being used for math class...

Exploratorium Math: The Square Wheel

What happens when three math teachers go to the Exploratorium? We briefly pass through all the fancy science exhibits and then spend like 20 minutes staring at this seemingly simple display of a square wheel rolling on arched ground. 

The key is keeping the center of the wheel always at the same height above the ground. So how do you design the piece of the circle that makes up the "ground"? I still haven't figure it out, but we came up with some interesting stuff that was too difficult to continue without pen and paper. 

In summation: my kids are going to build square wheels. But I should probably try it first. 

Questions: 

• Is it better to start with the ground or the wheel? 
• If bottom of each circular ground piece is a chord, does the central angle intersecting the ends of that chord always have to be the same? 

Exploratorium Math: The real-life hyperbola

This still amazes me every time I see it:

How incredible is it that you can move a straight line and it makes a curve?! I guess that's what math is all about. But I like this exhibit because if you just showed me the tilted bar spinning around without the plexiglass, then asked me what kind of hole I should cut in the plexiglass that will allow the tilted bar to pass through... I would never guess the hyperbola. 

Questions I want to ask (myself or my students): 

• How does the angle/slope of the tilted bar relate to the shape/equation of the hyperbola?
• How does the angle/slope of the tilted bar relate to the slopes of the hyperbola's asymptotes? 
• What's up with the intersection of the hyperbola's asymptotes? Are they perpendicular (I can't tell at all from this picture)? What changes can you make to the tilted bar or the way its rotated that will either (1) keep the asymptotes perpendicular (if they already are)? (2) make them perpendicular if they're not already?
• Where are the foci of the hyperbola? How do they relate to the position of the tilted bar? 
• If you make the bar longer, but keep it at the same angle, what will need to change about the hyperbola and the way it's cut out of the plexiglass? 

I pretty much just want to make kids build this.

How many servings?

Can you figure out what's wrong with the serving size for this Trader Joe's deliciousness? Can you figure out what's right with the serving size?

I already hate it when the nutritional info tells me that the serving size is something 1/x of a package and there are x servings. Duh. But this takes it to an even more ridiculous level. I'm not sure what interesting mathematical questions you could ask, there's gotta be something.

One potentially less math-y, but still interesting thing for kids to think about is how manufacturers decide to label how much one serving is. I know I've looked at things like candy bars and the nutritional info says 2 servings, despite the fact that no one would ever eat half a candy bar and think, "I'm good. I'll save the other half for my next meal." But then I look at the calories and think, "Dang, at over 500 calories in this whole candy bar, maybe I should eat just one 'serving' and save the other half for later." But 260 calories in a serving doesn't look so bad. I wonder if there's something interesting around having kids think about how much a serving size actually is for, say, potato chips, and then rewrite the nutritional label to match their serving. Along the same lines, it would be interesting to compare "1 serving" of potato chips as measured in weight vs. number of chips. Did the manufacturer accurately represent the weight of a serving of 10 chips? How would it change all the other nutritional info? This is starting to sound like a middle school proportional reasoning exercise for sure.

What could you add for older kids to make it more challenging math? Package design and labeling has got to include a ton of math. Any packaging designers out there who want to help me out?

Culturally Situated Design Tools

http://csdt.rpi.edu/

There's a lot of stuff on here and I haven't had time to make sense of it, but I don't want to lose this link. I especially appreciate that so much of it is connected to higher-level math because authentic, interesting culturally relevant pedagogy feels nearly impossible to find for upper-level high school math. This feels like it's using the "gimmick" of the cultural connection in a useful, non-cheesy way.

The thing I'm most interested in right this second is how to adapt the concepts and ideas presented to activities that (1) do not require use of technology--or that build from the technology to push beyond guess and check, (2) are more groupworthy.

Thoughts?