High School: Number and Quantity
1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
Word problems don't typically provide helpful hints on using probability to win the lotto or anything useful in real life. No, they tend to read more like this:
Juan, Harry, Liam, Hans, and Tom are going out to lunch. Juan contributes 35 pesos, Liam contributes 9 Euros, Harry contributes 500 Indian Rupees, Hans contributes 18 Dutch Guilders, and Tom contributes $10. How much tip should they leave?
Okay, perhaps we exaggerated just a little, but you get the point—the question is silly. (For starters, why don't they all have the same currency if they're in the same country regardless of where they're from?) But it does make a good point. In order to solve problems of this sort, we need to have everyone dealing with the same units. We're talking to you, Juan, Harry, Liam, Hans, and Tom.
Students should know that the easiest way to change from one unit of measurement to another is through the use of proportions. For example, in the problem above, it would help a whole lot to know that one Dutch Guilder is worth about $0.57. We could set up a proportion:
With a little arithmetic (or the unparalleled magic of a calculator), we know that Hans contributed about $10.26. How nice of him.
Which unit of measurement do we use? It's hard to generalize, since it depends on the situation. For example, if we're measuring the distance between cities in the U.S., miles are probably the way to go. But if you're setting up a scale drawing of where you want to put your new bedroom furniture, the odds are good that feet or even inches will make more sense. (Tell your students not to mix up their units; otherwise, they might end up with new bedroom furniture that won't fit through the doorway!)
Speaking of distances, if students ever find themselves lost (and without the GPS on their smartphones, for some reason), knowing how to use old-fashioned maps might prove useful. If they need to travel "half an inch on the map," you might want to point out the legend at the bottom of the map. That's the part that converts that half inch into 50 miles, or whatever ratio they choose.