Wednesday, September 10, 2014

Algebra & Mathemagic

The 7th graders recently started studying algebraic expressions.  We started with combining like terms with a heavy emphasis on algebra tiles.  This really helps the 7th graders make it visual.  So we spent a couple days playing around with the algebra tiles and combining like terms.  All this sets the stage for


So we started today's class with a little "my favorite mistake" to review expressions.
The students then we told "we are going to have a little contest."

  • Students were asked to pick a number from 0-50.  
  • I told the students they would be asked to perform 5 steps with the number.
  • At the end of the steps, whichever student was closest to the "magic number" would win.
  • The students were instructed to keep their numbers a secret.  
  • The students then performed the following steps.
    • Add 5 to your number
    • Double the result
    • Subtract 4 from the result
    • Divide the result by 2
    • Subtract the number you originally chose
  • The instructions were given slowly, deliberately, and in a way that increases the drama
  • (really the slowness is to make sure students are doing their arithmetic correctly)
  • After the final step, students are instructed to keep their final number a secret
  • The magic number is then revealed by playing this video
Watching the joy cross the faces of the students as they realize their number is the magic number, and then the subsequent confusion is priceless.  They are completely hooked by these magical results.  Every student (no matter what number they picked) ends up with an answer of 3.

I then challenge students to think of a number that will break this trick.  Students vary in their suggestions but the fun ones include super large numbers, decimals, and negative numbers.  Today I had 1,000,000,001 suggested along with -2.51515.  By allowing the students to chose the numbers they are more invested in the process and it really hits home that "any number" ends up with an answer of 3.
After the students realize they can not "break the trick" we break down the trick with algebra tiles.  We walk through each step and perform the operation with algebra tiles.

This is pretty much the end of day 1.

The next couple days are spent practicing number tricks with algebra tiles and eventually being able to seamlessly manipulate algebraic expressions without algebra tiles.

The lesson is loosely based off of a CPM lesson.


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