April 21st Math SAT Question: What’s the area of the triangle?
This column contains at least five strategies that are fast and accurate to get points for you on the math test. These tips are all about visualizing—starting with multiplying the low numbers while looking at the triangle.
Guess what? This was a RACECAR Q&A for Rocketcat. We did this one right behind the blue eye and the green eye. 2.5 x 3 =7.5!
Notice that the official explanation is much different—and, yet, not so different! The SAT Board advocates multiplying the sides (b)(h) or (5)(3)=15 and dividing by 2 =7.5.
This is such a nice drawing—no warnings, as on some problems, that it is not to scale!
Here is a lovely triangle on a graph. You are asked: What’s the area?
No problem. The numbers were so low that Rocketcat used the RACECAR strategy that we only use in math when we can zoom forwards—and then backwards (palindrome style) and get the same answer (like the word RACECAR).
Guess what? This was a RACECAR Q&A for Rocketcat. We did this one right behind the blue eye and the green eye. 2.5 x 3 =7.5! (Rocketboy,Rocketcat’s hero, also had one sapphire eye and one emerald eye.)
We love the visual stuff—like the graph and the triangle.
Here is a strategy from a ‘non-math’ teacher who teaches math often: If you do have a page on a standardized test with formulae, keep that marked to glance over when you encounter a formulae-based problem. But just let it remind you. Learn the formulae with your own visual flashcards or PowerPoint displays—with pictures. ‘See’ these visuals in your mind when working on problems.
Do visualize area as a rug over the area. Do visualize perimeter and circumference as fences around an area. Do visualize a cylinder as a can of soup. Visualize taking off the label and seeing that it is a rectangle around the can, and the top and bottom of the can are circles. To find the area of a cylinder, you have to get the area of those can ends AND the label around the can. Visualize how the actual can can be pulled apart into two circles and a rectangle.
Know the formula for the area of a triangle by putting this on your list of a few things to know before taking a math test. In fact, this is one of the things to put on your sheet for the last day or so.
Here is something funny that ‘real’ math teachers never mention. I think it is because they are so used to this. Visualize what I am saying here for a minute.
What if you are ready to do a problem using a formula, and you forget what ‘b’ and ‘h’ are? What if you have not done circles for a while and you forget that r is radius and d is diameter in some versions of the formulae?
Take today’s question, for example. Under test conditions, you may forget that ‘b’ is base and ‘h’ is height. What you need to know is: Wow! Look at this great graph and right angle triangle. I know all about this figure! What do you want to know? Oh, well to get the number to make a rug to cover this area, we take one-half of that 5 side (2.5) and multiply it by the vertical (height) side (3) because to get the area of a triangle, you take ½ of the base and multiply that number times the height or A=1/2 bh.
Here is a neat thing about the College Board style explanation—PEMDAS—First you multiply. Then, you divide.
Just to be sure Rocketcat did not ‘get’ this one in a fluke way, he tried out some more possibilities for the base and height measurements. It works out just fine to take ½ of the base and to multiply that figure times the height. We get it!!!judiethcarol&RocketcatApril2010
