Number Bracelets

I went to Ruth Parker's session at CMC North 2015 and loved it. Of the many things I learned, I am perhaps most excited about Number Bracelets.

Here's how they work:

• Start with any two single digits. Say, 3 and 6. So the start of your bracelet is 6,3
• Add them together. You get 9. Now your bracelet looks like 6,3,9
• Add the last two digits in the bracelet. When you get a double-digit number, you only write down the 1's digit. So now our number bracelet looks like 3,6,9,2 (because 3+9=12, and 2 is the 1's digit)
• Keep going until it starts to repeat: 6,3,9,2,1,3,4,7,1,8,9,7,6,3,9 --> notice that it starts to repeat here. 
• The length of your number bracelet is the number of digits/terms before it starts to repeat. So in this example, the number bracelet starting 6,3 has a length of 12

I have so many questions I want to answer about these!!!

Bongard Problems

https://en.wikipedia.org/wiki/Bongard_problem
http://www.foundalis.com/res/bps/bpidx.htm

So awesome for understanding what a property is.

It would be interesting to do these with numbers in addition to diagrams.

Thanks, CMC North 2015!

Average book length

Some statistics are useful, and some are not. I don't know if this one is useful, but it's kind of fun:

The average book has 64,500 words.

I don't know exactly what I'd do with this in class, but it seems like an interesting opportunity to discuss why we use different statistical measures to describe data, and to get kids thinking about which measures feel useful in which situations. Is mean really the right measure of central tendency for this statistic? Is comparing a measure of central tendency even useful? Why do we care?

There also might be something (less exciting, more practice-y) about using all the stats for each book to work backwards to calculate the standard deviation. That also raises the question of whether mean and standard deviation are really the right descriptors. I am very curious whether word length is a normal distribution. It might depend on what genres of books you include (children's books seem like the have the potential to skew the data).

What other statistical questions might kids generate? How could they use info about the books they're reading in English class to do some further exploration?

Counting Trees

The "Counting Trees" Formative Assessment Lesson from MARS/Shell Centre is one of my favorites. I think it's open ended in an interesting way and I love that kids need to be okay with not knowing the exact right answer.
The other day I heard this story on NPR about how many trees there are in the entire world.


Of course my first thought was the FAL and how I would use this story in conjunction with that lesson. I wonder how I would structure it. Would it be a hook to the lesson or a "beyond"? What parts would I have kids listen to or read? I haven't read the Nature article yet, so I wonder what's in there.

I loved that the story went through a whole process of asking a question, making a conjecture, revising the conjecture, and so on--exactly the kind of thinking process that I want to highlight for kids.

It also raises some interesting questions about rate (how long it would take to plant 1 billion trees), density (if so much forest has been depleted, what did forests used to look like?), and large numbers (what does 3 trillion trees even mean?!)

Where in the world?

I'm not sure whether this would be a fun problem or not. I definitely think it falls into the "doing math" category when it comes to that math task categorization taxonomy.

Lots of famous cities have those signs with lots of arrows pointing in different directions with distances to famous cities. My math problem idea: show a picture and ask "Where in the world is this?" I'd want kids to figure out what to do from there, and to use the power of the internet and Google maps to go crazy.

I also found this sign that gives times instead of distances. Definitely an added level of challenge.

To me, this is a problem about loci and intersections of loci, so I can imagine asking a follow up question about how much information from the sign is actually needed to figure out where you are. In theory, this could get pretty interesting because you're working on a sphere instead of a cartesian plane.

Here's why I have questions about this activity:
-How do you find a picture of a sign that's not too easy to google?
-Just by typing in "___ kilometers from Moscow" how quickly will kids find their answer?
-Does a sign with obscure cities (like a road sign on the freeway) make the task more interesting or less interesting? More challenging or less challenging?
-Which is really all to say: how much math is in this task? What math is it?

Also: in searching for a good picture to add to this post, I found a 3D Signpost App. This feels like it has more potential. I especially like this screen:

It feels like there's lots of potential for kids to make their own versions of the screens from this app. And if there's some crossover with a geography or world history class or something, even better. 

Could you be an Olympian?

http://www.theguardian.com/sport/datablog/2012/aug/07/olympics-2012-athletes-age-weight-height

The Guardian has stats on height, weight, and age across athletes in the 2012 Olympics. Some questions I would want kids to ask/investigate:

• For your height/weight/age what sport are you most likely to play. That is, for what sport are you most "normal"? 
• I don't know if I'd include age depending on how old my kids are. If I mostly had 14 year olds, it would be tough because most athletes are older. But it would probably be fine for 17 year olds
• I might also leave out weight because that's a touchy subject, but maybe I'd give kids the choice. 
• It would be interesting to see how kids combined all three variables
• If you played ___, what percentile would you be in for height/weight/age? (I think this would require the assumption that the variables are normally distributed)
• Some kind of comparison of shape, center, spread across sports. Which sport has the longest window of time where you can reasonably play (we could discuss whether this referred to range or standard deviation)? For which sports is mean a better measure of center and vice versa? 
• For which sport are athletes the most different from the general American population

What's best is that all the data is available in a spreadsheet, so you can do whatever you want with it

How big a TV should I buy?

This article made me think about some geometry:

http://www.cnet.com/news/how-big-a-tv-should-i-buy/ 

The graphic is interesting because it involves angles and lengths. It seems like there's a lot that kids could play with.

• If a couch is positioned at exactly 9 ft from the TV, what size TV should you buy? 
• If your couch is positioned at a different distance, what size TV should you buy to keep the same ratio? 
• If you own a TV of a given size, how far away should you place your couch? Does it matter if the given size refers to the diagonal or the width? 
• When the article says "the TV should fill 40 degrees of your field of vision" what percentage of your field of vision is this (you'd need to think about your peripheral vision)? 
• THX and SMPTE recommend 40 degrees and 30 degrees respectively. How does this change the size TV you should buy? Or where you should put your couch if you have a specific size TV? 
• This could easily be connected to costs
• Does it matter where a person sits on their couch? The diagram works from a person sitting in the middle of the couch. Will other people on the couch still have the TV fill 40 degrees (or 30 degrees) of their vision? How much more or less of your vision will the TV fill at different points along the couch? 
• What do these distances and angles mean about where you should (or shouldn't) sit in a movie theater? 

The article also includes a link to a chart that accounts for pixel resolution. I haven't looked at it closely, but I'd be interested in exploring the patterns in the table: 

http://referencehometheater.com/2013/commentary/4k-calculator/