Wavy walls

 https://hasanjasim.online/15-illustrations-of-british-crinkle-crankle-walls-which-require-less-bricks-to-construct-than-straight-walls/

In England you might see a lot of "wavy walls" made of brick. According to the link above, the walls actually use fewer bricks than a straight wall because straight walls need at least two layers of bricks to be sturdy, but the wavy walls are sturdy enough with one layer because of the arch support provided by the waves. 

Lots of investigate in here. 

• Why is it sturdier? 
• How "straight" could a wall get before it starts to get unstable? 
• Is there a "too wavy" wall? 
• What connections are there (if any??) to sine and cosine functions? 
• Construct a wavy wall! Could be interesting to test strength somehow. 

Not sure how much engineering and physics is necessary to understand to be able to really make sense of this. But the walls do look cool :-) 

Making Cents

One of my favorite activities with students is asking them to calculate how many pennies it takes to cover the floor. Take ~20 pennies, a ruler, some string, and go crazy.

Well, this person really figured it out:

I would want to show kids this picture and have them generate questions that come up. Some questions that come up for me:

• How big is the floor? 
• How many pennies? 
• Are there more dark-side-down or light-side-down pennies? An equal number? 

Beatmaker

I got this idea from some amazing student teachers!

Using the Beatmaker from splice.com, they had us come up with beats using different instruments that hit at different times. What I thought was really cool was that we had to draw the pattern ourselves before we played it on the Beatmaker. There was a lot of thinking about how to mix and match patterns for different instruments, and what kind of visual patterns would result in what kinds of sounds.

I feel like there's a lot more to do with it, but I haven't investigated yet!

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?!)