Have You Algebrafied Your Word Problems?

Take a simple math textbook word problem and ALGEBRAFY it.  (I love that new word!)  A presenter at the NCTM algebra readiness conference used it.  She showed us how to take a simple math word problem and provide other numbers as well as the one in the problem for students to solve the problem multiple times.  Then students are able to make a generalization about the problem.  For example:

Bill’s Airbrushed T-shirts is giving customers a 20% discount on all T-shirts.  Find the discount on a T-shirt that had an original price of $12.

In addition to the textbook version, allow students to find the pattern when finding a discount on other prices of shirts.

Find the discount of a shirt that was originally priced at $13, $14, $15, $20, $50

If students write these in an organized way or use a table to calculate these amounts, they would easily see a pattern.

$12 x .20 = $2.40

$13 x .20 = $2.60

$14 x .20 = $2.80

$15 x .20 = $3.00

$20 x .20 =$4.00

$50 x .20 = $10.00

Math is all about finding patterns.  Students can easily see several patterns above.  Some will see the obvious pattern in the first few equations in which each product gains 20 cents.  Students will also hopefully see the pattern of doubling the first factor and counting over two places to write the decimal.  Then students can begin generalizing about multiplying any number by 20 percent.  When students are able to generalize then the learning becomes their own personal discovery.  Learning becomes fun again!