Day 180: This is it…?

Ok, I have to come clean… we technically have two days of school left . Two snow days earlier this year, added two days to the school year. According to the calendar we are done today, however, June 11th and 12th are just-in-case “Snow day make-up”, which were put to use this year. But today was my last day of instruction, Thursday and Friday are all finals.

Algebra started off by filling out Who I am… Now. I hung onto the copies they filled out on the third day of school and passed those back today. It was fun looking at how their personalities and interests changed throughout the year.

After, students pulled out their phones/tablets and filled out another Teacher Report Card. Their responses were awesome. It is funny how students want their peers to think they are giving half assed responses, when in reality, they are meaningful and well thought out.

I made the mistake of not monitoring a student taking the final early close enough… So I had to reprint all the finals and shuffle the answers (I think there is a test of mine floating around).

While printing the tests I found these in my mailbox:

IMG_0710 (1)I love student letters…

I have a lot on my mind, most of which I want to write about. I am planning on re-reading my [Almost] 180 posts then writing on final post to bring closure to this 180 blog and by then, will hopefully have a game plan for what I want to do with this whole blog thing next year.  I keep coming back and adding paragraphs to this post, it is kind of like the first few days of summer; I don’t know what I am going to do with myself now.

One thing for sure… There will be more posts from me in the future.

If this is it for you, thanks for coming by. The amount of feedback and positivity I have received from this blog shifted and accelerated the growth my teaching practices in the best possible ways.I hope you continue to swing by next year.

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Day 177: Skittles

Last night I went and bought 8 pounds of Skittles; I had a fun conversation with the cashier.

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Algebra looked at the color distribution of the different sized bags of skittles and made some conclusions on the data.

Here’s how things went.

Skittles_1

I threw up this picture and asked ’em how many Skittles thy thought were in the package, then their estimated percent breakdown of each color.

After, I put this up and asked if it changed any if their answers.

Skittles_2

They saw the number of each color and calculated the percentage of each.

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111 Skittles isn’t a great size to make any conclusions, they asked for a larger bag and then made the same estimations.

Skittles_4

Skittles_5

Skittles_6

389 Skittles isn’t really enough to make conclusions either… the data was everywhere.

Then, I pulled out a 2 pound bag of Skittles, broke students into groups of 2 and had them find the frequency of each color.

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I put together a quick Excel document and had running totals throughout the day.

The results of each 2 pound bag were different, but when we put them together and looked at a sample size of 4338 some interesting talking points emerge.

SkittlesI am excited to hear what students have to say/conclude from this data on Monday.

Day 176: Perfect Squares

In geometry I put this up on the board as they walked in.

1, 4, 9, 16, 25…

I asked ’em what patterns they saw.

  • Perfect Squares
  • First difference is always odd
  • Constant second difference of 2
  • y = x²

I was wondering if they would come up with this:

Squares

I eventually put the pattern up and asked if any square multiplied by 4 is always a square. They said yes and talked about the shape a dot representation of the number would make when multiplied by 4.

Then a student asked “Is a perfect square multiplied by a perfect square also always a perfect square?” 

Well (a²)(b²) = (ab)²

We had a great 5 minute discussion about this, I had never thought of the product of two perfect squares, it is always fun when I learn along with them. I don’t talk enough about number theory, this was a great exercise in developing both number theory and sense.

Day 174: Guess My Rule

I put this up as the opener for algebra today:

Rule

A large chunk of students quickly jumped to “the previous number times two”.

That wasn’t my rule.

Then they shifted to +2, +4 +6…

That wasn’t my rule either.

Silence for about 2 minutes… Then a student asked “Is the next number 10?”

“That fits my rule” I replied.

This threw ’em all off… They dabbled around with different numbers for a bit, I had fun with it, especially when they pitched crazy numbers like 54, 81, and 1092, which fit my rule.

Eventually, they drifted into trying to find numbers that didn’t fit my rule… which is awesome problem solving.

This really is the heart of what I want to get at through all this factoring, solving, graphing and so on. To me math isn’t so much about memorizing or reproducing a certain skill, but more about taking what you know and tweaking it to solve some crazy problem you have never seen before.

That moment where you have abandoned all hope and try some crazy technique in a problem that you learned months or years ago, which ends up working is what I love about math. The struggle leading up to that moment; following hundreds of self-imposed rules and just sheer grit isn’t easy. It is even more difficult to learn and teaching it takes someone really special.

Everyday I try and very delicately move students towards that direction. With the hopes that maybe, at some point in their lives, in a situation that isn’t even close to math related, they will be able to use their critical thinking abilities, which took years to develop, to solve a difficult problem and experience that felling of having everything fall perfectly into place.

For me, that hope makes everyday worth it.

By the way… my rule was each number had to be larger than the previous. They went crazy over this, some nasty reverse psychology on my end: They automatically see something math related and dive into testing different equations and rules, when really the rule doesn’t require anything fancy. Credit. 

Day 172: Substitution Puzzles

For the last few weeks I have been using half the period on Fridays to review. A couple of weeks ago I came across some great puzzles at MathArugments180 (the actual credit seems to go to Mimi). These helped students ease back into solving systems by substitution today. I want to also make a note here for next year to use these as a follow up to Noah’s Ark.

Puzzle

A colleague showed me these puzzles about 4 months ago also… I missed out not using ’em earlier.

Day 171: Graphs

The last week of algebra consists of an introduction to statistics. They start the whole process by reviewing (for most) how to interpret graphs. Normally, this isn’t a very exciting process but I found some fun graphs to spice things up.

First I put up a blank slate and them ’em guess what it could be:

Startgraph

Turned out to be something like grams of fat for ingredients of a sandwich.

After we went through all the different types of graphs, here are my favorite examples of each:

Graph2

Graph1
Graph3

Graph4

Graph5

Gotta keep content interesting with the end of the year looming….