Today's soundtrack is Stryper: God Damn Evil.
I'm on chapter 18 of Basic Math & Pre-Algebra, "Solving Geometry and Measurement Word Problems."
There are two important kind of word problems: "measurement problems and geometry problems" (p. 247). In the former, we convert from one unit to another; in the latter, we use formulas and/or pictures to solve problems.
For conversion problems requiring multiple steps, we can use conversion chains. Conversion chains "[link] together a sequence of unit conversions" (p. 248). The example given in the book is if we were to need to find out how many one-ounce servings of strawberries a 7-ton shipment would give us. Since we don't have a equation that lets us convert from ounces to tons, we could do a two-step conversion - first convert from tons to pounds, then pounds to ounces, but we could do instead a single-step conversion chain. The author of the book seems to think that a conversion chain is easier. He says that to set up the conversion chain, we set up three fractions: seven tons over 1 (to equal 7 tons), 2000 lbs over 1 ton (equals 1), and 16 oz over 1 pound (equals 1). Then we multiply all of the items on the top: 7 x 2000 x 16 = 224,000 ounces. Another example given is using a conversion chain to figure out how many seconds old a person is. Say we found out that a person was 21 years old. We create another conversion chain: 21 years x 365 days x 24 hours x 60 minutes x 60 seconds, with each value over 1.
Sometimes with geometry problems it is helpful to draw pictures to visualize what is being asked.
