**Math 1 **

Today the students did Youcubed.org’s Week of Inspirational Math (Day 2). The materials are available for free access if you register.

The idea (for me) of the day was that there are many ways to organize a number, and finding the magic number symbol (for example: 3) is not always necessary. It is a shortcut. It is an agreed-upon symbol for the quantity three. There are other symbols for quantity…an example is »»». That also represents the quantity three. The students were given the sheet (paper…ugh!) from the Youcubed website. The pattern starts with 1 circle, then 2, then 3, and so on up to 35. The students are asked to put the number they are used to using for representing quantity on the picture and look for patterns.

Immediately, they said they didn’t understand. So I tried again with “Count the number of circles in each picture, then write what you get down.” That was understood. But Dr. Boaler and her team put those exact directions as question 1. I need to be better at talking them through directions and making them figure it out.

The next question was to describe any patterns. Again…”Wha?”. On this one, I went with “Did you count every single circle on this paper?” They said no. “But you have an answer for each number. How did you know what to write?” They said that it was easy because it went up by one. “No way! I think that’s a pattern!” Oh…yeah. So that’s the answer to question 2? “It’s one possible answer. There are probably more.” They really hated that answer.

The final question was to use color to mark a pattern they saw within each numerical pattern. Wow…that one was like pulling teeth. The prime numbers have no patterns, but composite numbers are all factors of the number. For example, 16 was four smaller clusters of 4. I told them to color the smallest group that would get them the answer without counting (in the case of 16, I had them color the block of 4).Most of them late in the day figured out what to do, so it was better at the end of the day, but early in the day was pretty rough. A big shoutout to @robertkaplinsky’s #TMathC15 presentation for giving more strategies for asking better questions.

Tomorrow I am doing Day 3, which has Dot Card Number talks. I made a Slides presentation here for a few of them. Afterwards, the students will get to attempt to give fractional representations out of square Post-It notes.

**Both Statistics Classes**

Today, they got their iPads. That was a longer procedure than it should have been, but Google Classroom and Google Drive both have updates that I’m not that familiar with. There were no new assignments today.

Tomorrow, the students will explore randomness with The Federalist Papers, another project from Daren Starnes’ book *The Practice of Statistics*. That link is https://drive.google.com/file/d/0BzjLjHjd7CS9RlN6aDFlWGZETG8/view?usp=sharing…I don’t know why WordPress puts the full link in but puts a shorter link in above…squirrel!…but the students will send me a reflection of this project via a Google Form so I can see if the Classroom is better behaved.

*Uncategorized*

Andy

August 6, 2015

Thanks for continuing to post on the youcubed lessons — your observations are very helpful!

For the Federalist Papers task, I wonder if you could also add in a computational component. Here is a quick example I wrote in Python 2.7 (you can download the interpreter for Python free online to run it and tinker yourself https://www.python.org/ftp/python/2.7.10/python-2.7.10.msi). Note that in the code, everything after the # symbol is a comment (used by humans to understand the code but not read by the computer).

text = “To what expedient, then, shall we finally resort, for maintaining in practice the…” # but you can include the whole thing here

import re # needed to run the code

word_length_map = {} # creates a dictionary to store the number of words of each length

for word in re.findall(r”[\w’]+”, text): # loops through every word in the text (without spaces/punctuation)

if len(word) in word_length_map: # checks if this word length (“the” would be length “3”) exists yet

word_length_map[len(word)] += 1 # if it exists, it adds one more tally to words of that length

else:

word_length_map[len(word)] = 1 # if it doesn’t exist, it creates a new entry with “1” word of that length

print word_length_map # prints out the results

The results look something like this: {2: 7, 3: 6, 4: 6, 5: 1, 6: 6, 7: 2, 8: 1, 9: 1, 10: 1}. This means 7 words of length 2, 6 of length 3, etc.

The idea of your lesson is to introduce random sampling and inference, but it might be important to follow-up with the fact that with modern tools we don’t NEED to sample as often as we used to because computers can handle very large populations with ease when we have access to the data.

mrsakahoshi

August 7, 2015

Thank you so much for the code!

I agree, and I made a point of “statistics is considered a newer branch of mathematics because so much can be done with computers and it would suck if everything had to be done by hand”. While that is true, I didn’t follow up on it. I did calculate the actual average word length, but I did it the long way in Excel. The average word length in that passage is 4.9 letters, FWIW. Not, of course, that you don’t already know that. 🙂