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?

Here is Today

http://hereistoday.com/

I always get a little annoyed/weirded out by these kinds of time comparisons because to me the underlying message is, "Today is not that big of a deal. Get over it." It's similar to the "There are starving kids in Africa" argument for why your problems aren't that important. Yes, I know that my problems (or a 15-year old's problems) are not that dramatic in the larger scheme of things and that many of the things I'm pre-occupied with today will be relatively insignificant by the end of the year, the decade, etc. But that doesn't mean those things aren't real and important to me in this moment. It diminishes and invalidates someone else's emotions to tell them, "So what? In geological time, you're invisible." Everyone else is invisible too, but that shouldn't make them any less important or worthy of our love and attention.

But on to the math. What's cool about this interactive graphic is the proportionality and evolution of the part versus the whole. "Today" remains the numerator, but the denominator changes and our concept of "today" changes as a result. Seems like an interesting way of thinking about and understanding fractions, proportions, percents, and relative size. I think it would be interesting for kids to create or think about their own life maps in this way. What does today look like in comparison to your entire 15-year old life? Thinking about an important time period in your life, what is its relative size compared to today? Compared to an different time period in your life? It also feels like there's something interesting in there around fractions greater than 1--your life thus far is 1, so what will your 20 year old life look like?

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.

Making Babies

I saw this cartoon on someone's Facebook page. Yeah, yeah, imaginary numbers are great for puns. That's not the math I'm interested in here. The way I interpreted this column, the 8 and 4 are the parents of the 6. True, they could be two "adult" numbers of any sort (teacher and parent, two teachers, whatever), but I interpreted them as parents I think in part because 6 is the average of 8 and 4. It makes sense: we think of children as being the genetic combination of their parents ("He has mom's eyes and dad's nose") and in many ways the average. Thinking purely about skin color, mine is about the average of my dark-skinned father and white mother.

So what other questions can we ask or think about?

• Thinking about using the arithmetic mean, wouldn't all these numerical children hit a certain limit at some point? (Kind of like how people say that in 100 years everyone will have light brown skin?)
• What are other ways we could do genetic counseling for two numbers trying to procreate? Geometric mean? 
• What traits are dominant or recessive (or something else)? Two even numbers or two odd numbers will create an even child, but an even and odd will never pass on their even-ness/odd-ness to the next generation. What about multiples or 
• How could you do some eugenics to make sure you weeded out "undesirable" offspring (uh oh, I am taking this to a dark place...). 
• How far can I take this metaphor before it starts to break down? 

Maybe the most interesting question would just to give kids two numbers and ask what number their child will be. I wonder what kids would come up with. I especially wonder what elementary schoolers would come up with versus high schoolers. My guess: elementary schoolers would be more creative. 

Percents of Percents

Percent increase and percent decrease still confuse the heck out of me, no matter how many problems I do or how many times I teach the topic. The language gets 

• Has the high school graduation rate of black males increased by 6.6% or 5.1%? 
• Has their high school dropout rate decreased by 37.9% or 5.8%? 
• Has their college enrollment rate increased by 32.7% or 1.7%?
• Has their incarceration rate decreased by 25.3% or 2.1%?

Two bigger questions:

• Would the positive changes for black males highlighted by this list of statistics still be as powerful if they had cited the change in percentage rather than the percent change (of the percent)? Either way, they still show increases where we would want there to be increases (high school graduation rate, college enrollment, college "by the numbers") and decreases where we would want there to be decreases (dropout rate, "incarcerated"). 
• In what other ways could this information be presented (pure numbers, different types of graphs, etc.) that would make them more or less powerful? How do you think the author chose this table? 

An underlying question: 

What is the difference between "net increase" and "percent increase"? Is there a difference? How does this very, very subtle difference change how we present and interpret statistics about changes that are measured in and by percents? The Wikipedia article on percents has some interesting things to say, including how the use of the term "percentage points" can help clear up confusion. 

As teachers, especially teachers of English Language Learners, how do we support students in navigating this very tricky language. It seems particularly important/frustrating given that percent increase/decrease problems are a not insignificant part of the California High School Exit Exam. (Really, no concept is insignificant when one or two questions could make the difference in whether you earn a high school diploma.)

Honey, I mis-calculated my math?

In this Honey, I Shrunk the Kids trailer (an amazing movie...) at 0:41 the littlest kid does some calculations. "We're a quarter of an inch tall and 64 feet from the house. That's the equivalent of 3.2 miles."



If his calculations are correct, how tall were the kids originally? Whose height was he using to make his calculations?

Other questions that might be relevant:
-How did he know "we're a quarter of an inch tall"?
-If all the kids are a quarter of an inch tall, did the shrink ray really work? Alternately, if all kids are not a quarter of an inch tall, did the shrink ray really work?
-What evidence is there in the video that the kid's calculations are off?