Love, and Love Lost

Visualizations of Love:
http://love.seebytouch.com/#LetMeShowYou

Clearly some are more mathy than others, but I like the variation in the types of visualizations.

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And quantifications of love no more:
http://quantifiedbreakup.tumblr.com/

Sometimes when kids tell me that they're in a bad mood or not feeling well, I respond that doing math problems always makes you feel better. Looks like I wasn't making it up. Doing math as therapy is real!

Dictionary of Numbers

A Chrome extension that gives context to numbers.

From playing around with it, it's not as easy as I'd like, but there are some cool things. Did you know that the International Space Station weights 1 million pounds? I like the idea of giving context to numbers so that kids/people can have a reference point, especially for big numbers.

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?

Food Equivalencies

What does 2000 calories look like?

There are nice visuals around how many ____ are equal to how many ____ in terms of food. The bacon to cinnabon equivalency is my favorite, I think, because we think of bacon being so unhealthy. (Not that we think of cinnabons as being so unhealthy, but I, as a teenager, was definitely more likely to get a "snack" at the mall of a cinnabon, but would never have gotten a stack of bacon as a snack).

Questions to think about:
-Are all calories the same?
-What sets of 2000 calories can you imagine eating (I can definitely imagine eating 2.5 cinnabons, but not a whole pizza)? How does the mental association of these foods impact your eating?
-These equivalencies represent calories. Which would be the same if we looked at fats/protein/carbs/etc.
-Why is 2000 calories the recommended daily allowance?

Maybe it's not super mathematically interesting, but I do think it gets into units and the meaning of the equals sign in an interesting way.

The World as You've Never Seen It Before

http://www.worldmapper.org

Worldmapper is a collection of world maps, where territories are re-sized on each map according to the subject of interest.

How Big is that Country?

This site lets you pick a country and compare a number of its quality-of-life stats to the US. But I think the most interesting part is the map that overlays the country on top of your geographic area. Given that I feel like I understand the state of California as a good scale, it's really interesting to see how the area of other countries compares.

http://www.ifitweremyhome.com/

Given how bad kids seem to be at geography, this might not be as interesting or surprising to them, but it raises questions about map scaling that at least I think are worth asking.

Lunchtime Clock

This clock speeds up and slows down such that you get an extra 12 minutes of lunch.

First, I have to say that it took me a long time to figure out just what was going on. It was confusing to me when the clock speeds up, when it slows down, when the extra 12 minutes is actually happening, and so on. It took me awhile to even figure out what time the lunch hour is supposed to be! Some googling of "Lunchtime Clock" helped me make some sense of the actual context of this. Definitely if I were to use this video there would need to be some built in sense-making time (no pun intended). See my scaffolding questions (below the interesting ones).

I'm not sure what mathematical category this fits in because I haven't done any math around it yet, but it's definitely some interesting math. Here are some questions off the top of my head.

Interesting questions
-Why is the "slow" interval longer than the "fast" interval? What is the relationship between these two intervals? What is the relationship between the intervals and the percent increase/decrease in clock speed?
-How do you know that speeding up and slowing down by 20% will add exactly 12 minutes to your lunch?
-How would you re-program if you had a 40 minute lunch instead of an hour lunch? A 90 minute lunch? (Consider differences between adding 12 minutes to a 40 minute or 90 minute lunch versus adding 20% to your lunch hour, regardless of the original lunch hour's length).
-If you wanted to start off just getting an extra 5 min of lunch (so your boss didn't notice), how would you have to re-program the clock? What percentage of the normal speed would you have to reduce/increase the clock to, and over what period of time? What if you wanted 15 extra minutes? n extra minutes?
-If you tried adding more time to your lunch hour, at what point do you think your coworkers/boss would notice the difference?
-You have an 11:30 meeting--what time will it say on the lunchtime clock? A 12:30 lunch meeting? Can you come up with a rule to tell what time it actually is by looking at the lunchtime clock?
-During that lunch hour, does the lunch time clock ever display the correct time?

Scaffolding questions
-What time does this clock assume that your lunch hour happens?
-Over what time interval is the clock moving slower than usual? Over what time interval is it moving slower than usual?
-What does it mean to "speed up by 20%" and "slow down by 20%"? 20% of what?

What other people on the internet seem to care about
Look, the internet made us a clock to play with! So many extension questions to play with!
http://www.lunchclock.com/ 

Also, check out the YouTube comments -- lots of math and interesting strategies! Might be a good hook for "evaluate the reasoning of others" to just go through and try to make sense of the comments. Of course, given that it's YouTube, probably best to screen the comments first.

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Update: I tried this task with a group of about 100 secondary teachers (6th-12th grade) and it was a HUGE hit. I gave pretty straightforward prompts:

• You planned an 11:30 phone call with someone who, strangely, hasn’t set up their own Lunchtime Clock yet. What time should you look for on the Lunchtime Clock to know when to make your phone call 
• Oops, you read the Lunchtime Clock wrong and missed the phone call! When your phone date calls back, the Lunchtime Clock reads 12:30. What time is it really?

Teachers worked for at least an hour straight and I'm not sure anyone came to an agreed upon answer. I didn't share the internet lunch clock because I just wanted people to use the video for data points. I was surprised at how few people actually found data points and tried to fit a function (piecewise or otherwise). 

I was thrilled by the different representations people worked from: lots of variations on tables, attempts at equations, some interesting graphs, and a whole array of non-standard representations and model that came out organically as people tried to explain their thinking. 

I was hoping that doing the task with teachers would give me a better idea of how to use this with students and where it might sit in a particular course or vertical progression. But the teachers left me even more unsure, actually. I really want to spend sometime working on this task myself... 

XL Wine Glass

http://www.amazon.com/DCI-10040-XL-Wine-Glass/dp/B000VKOK6O

"Holds a full bottle of wine!"

Hmm... why does this look so much smaller than a real wine glass? Is there really that little wine in a bottle? Is this glass really that big? How could we find out?

Grocery Shrink Ray

Dan Meyer's ideas on groceries...
http://blog.mrmeyer.com/?p=8713

... all came from The Consumerist website
http://consumerist.com/

So many ideas here:
-Obviously, proportional reasoning re: money
-There should be lots with different levels of math. Calc kids can look at oddly shaped bottles.

Weird Converter

http://www.weirdconverter.com

Conversions to weird units of measurement for volume, length, and weight.