Standards:

**Act 1**

**What do you notice?**

**What do you wonder?**

4

First, a little background.

The theme of our spring unit is always financial literacy. As teachers of students with varying degrees of need, strength, and interest this means different things for different groups of students. One of my groups is working on selling tickets for our school play, Alice in Wonderland.

We sell tickets at two price points. An adult ticket costs $10 and a child/student ticket costs $8. This is partly my doing, because having two different prices sometimes allows my students to investigate more interesting mathematical questions. Today was one of those days.

Show-goers are also able to purchase play tickets in one of three ways: cash, check, or online with a credit card. My students record the type of ticket and the method of purchase for each order in a table. Students then represent this information visually using graphs. We will use these tables and graphs later on to reflect on the trends and patterns in the ticket sales to make suggestions to our play directors for future ticket sales initiatives. But that’s the bigger picture and I promised you a snapshot. So here it is.

I realized I had been giving my students too much information. As they recorded the total amounts of cash, checks, and credit, I was also telling them the type of ticket. Today we began our routine of using math to figure out the type of tickets using our knowledge of the ticket prices and total amount of money. I gave them this problem as a warm-up:

One of the most popular ways to critically describe mathematics education in the United States is “a mile wide and an inch deep.” The TL;DR is that most mathematics education focuses on too broad an array of topics with a lack of emphasis on conceptual understanding and critical thinking.

My worry is that most special education math classes are an *inch wide and an inch deep*. I ran across this chart from Browder, Spooner, Ahlgrim-Delzell, Harris, Wakeman (2008).

Demonstrated here is a clear focus on an extremely small amount of topics and the only one investigated in any kind of depth is financial literacy, which admittedly is an extremely important topic for students with disabilities. For students with disabilities to be successful members of their communities they need to be financially literate. But this need should not preclude students with disabilities from exploring other mathematical topics.

Well, to be more precise we made a puzzle-y, game-y type thing.

Let me explain.

If you follow me on twitter, then you saw this little bit of nerdiness…

I am definitely unreasonably excited about this! pic.twitter.com/5ClM7YBgLa

— Andrew Gael (@bkdidact) December 29, 2014

I bought this dice bonanza bucket at Target during Christmas break. I was very motivated to put the new dice to work for my students!

As I wrote about previously, one of my classes is studying algebra. The contents of the dice bonanza varied between number dice, dot dice, color dice, and others it reminded me of Transition to Algebra like this:

So my assistant teacher and I put the dice to work in this puzzle game we called *Dice ID*. Here is the instruction booklet and here is the game board.

And here is how it went in our class last Friday…

I teach at a self-contained special education high school in SoHo in NYC. Our math department does a good job of incorporating “algebraic thinking” into every problem we pose or task we assign. Though, as they are in high school, our students are aware of what they “should be learning.” In other words, they see what their peers without disabilities are doing in math class and generally it is not what they are doing.

So the desire to learn *Algebra* comes up quite frequently. (The capital A is intentional in this case!) Algebra is like our student’s white whale. So, I try to be the boat to their Ahab.

My frustration, however, is that the typical approach to Algebra, with a capital A, is heavily language based. Vocabulary such as *variable, dependent, independent, inverse, and substitute* are very basic to capital *A-lgebra*, but they are also complex terms (and ones which have alternate meanings in everyday speech) that our students would require most of the year just committing to memory.

So I have been on a search for capital *A-lgebra* work that bypasses this vocabulary at least at the very beginning. Cut to Fawn Nguyen’s Visual Patterns and Heinemann’s Transition to Algebra.

I began with a pre-assessment task about toothpicks…

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