Friday, December 6, 2013

Best Card Trick Ever, or Algebra Without Tears

I am not, and have never been, pop culture's idea of the homeschool mom: sit the kids at the table to work through lessons, have them do chores to keep the house spotless, make three healthy meals a day to support mental and physical stamina. I mean, I try, but let's talk reality. And how far I have fallen. These days, I have farmed out both math and French lessons to the girls' favorite teacher. Want to guess who it is?

Hello, iPad. Please keep your charge until Kathy has finished that level of Duolingo.

Taryn has been learning algebra with an app called Dragon Box. Multiple friends had given it rave reviews, so despite its price -- $5.99 for an app, really? -- I installed it on all of our iPads. (Yes, each of us has one. Yes, that is excessive. My husband is an early adopter and technophile. We have held off on the 3D printer, at least.)
Screen capture from Dragon Box. The goal for this puzzle is to isolate the box on the left, using the cards available at the bottom of the screen. 
 When Taryn finished all the levels, even the bonus rounds, of the game, I thought it would be straightforward to jump from solving equations on the iPad to solving them with pencil and paper. 
Screen capture from a bonus level puzzle. Don't tell the kids, it's ALGEBRA.
She was up for it, but at the first attempt to solve an equation, the tears began to flow. Uh oh.

The rules of the game mirror the rules of algebra. The jump from the game's tactile and visual solution of a puzzle, to the process of solving for x on paper, was too big for Taryn.
Feeling angry about algebra. Let's take a break.
She needed a stepping stone to make the transition from iPad game to real math.

I puzzled over this for a while. Could I print out cards that look like the items in Dragon Box and play with those? Well, yes, I could, but I didn't really want to take the time to design, print, cut, and laminate a zillion cards. For some reason, it was playing out in my head as a Pinterest-worthy project.

Simplify, simplify. Could I skip the part where I design the cards on the computer? Maybe just draw some by hand? That's an option. What are the essentials? Cards that have pictures, and for each card its "opposite." The game calls the picture card opposites "night" cards. The numbers and symbols get the standard negative sign in front of them.

More musing. Earlier in the day, the girls and I had talked about the phrase "Being in the red." How in a ledger, you might see the negative numbers written in red. How you don't want your bank card balance [a topic for another post] to be red, but black.

Red, black. Cards. Pictures. Numbers. Wait, this sounds familiar. Oh!
A standard deck of cards becomes a tool to learn algebra
I pulled out a standard deck of cards, and sorted them by number. I gave Taryn these rules:
  • Black number cards are have positive value: spades and clubs are numbers 1-10.
  • Red number cards have negative value: hearts and diamonds are numbers -1 through -10.
  • Ace and face cards are variables, with positive or negative value depending on suit: Ace of hearts represents -a, Jack of clubs represents j, and so on.
The last item we needed was something to represent the Box in the game, which sometimes appears as the variable x. Handy solution: a chip from the Poker set the cards came from. So now we were ready. The last rule:
  • Isolate Chip on one side of the pencil, following the rules of Dragon Box. (These are the same as the algebraic rules to solve for a variable.)
Next, we set up space to work out the puzzle, aka math problem. A pencil was a boundary, with the areas on the right and left for playing the game. 

Here's an example of a problem. Remember, black cards are positive, reds are negative, the pencil stands in for the equal sign, and the chip is what we are solving for. Forgive the photo quality.

The problem set up:
6 = x + a - 2

2 + 6 = x + a - 2 + 2
Taryn starts to isolate the chip on the right side of the pencil by adding black 2s to each side.

Simplify on the right: -2 + 2 is 0.
  She removes the red and black 2s because they cancel each other out.
2 + 6 = x + a
 What's next to go? The black Ace.
- a + 2 + 6 = x + a - a
 Add a red Ace to each side.
Simplify on the right: a - a is 0
 She removes the red and black Aces because they cancel each other out.
- a + 2 + 6 = x
 The chip is alone, but there's still work to do.
Simplify on the left: 2 + 6 is 8
 Taryn replaces the black 2 and black 6 with a black 8.
Final answer: - a + 8 = x
Ta-da! The solution.

Once she got used to this, we started solving the problems simultaneously using the cards and with pencil and paper, as in the captions for each of the steps above. 

Now here's the magic part. That same bunch of problems that Taryn crumpled up, she was able to solve. Twenty minutes of playing cards made the difference between tears and pride. And it's kind of fun.

Thank you, iPad. Take a break, and go get charged up. With my coffee and my deck of cards, I've got this one covered.