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Math Help

Learning Target: I can use math to solve technological problems.

When you go to work through the prototype worksheets to create a prediction for your dragster, you'll find that you are being asked to do a lot of different kinds of math. This is why we take the time learn some of these operations in class, take quizzes and tests. This is a real situation that you can apply your math and science knowledge to make a prediction. This page is here to help you study in case you need it.

Average (MEAN)

Knowing how to calculate averages is pretty important. When you average a set of numbers, you are finding the trend or tendency of that group of numbers.Knowing the trend of a group of numbers can be important if you want to know the next number to occur in the group in the future, say batting average or average balance of a bank account. In Applied Tech, you will need to find the average of a set of times from past races in order to predict the time your dragster.

Tendency can be calculated different ways, mean, median and mode. From this point on, when we say average, we mean MEAN. Average (MEAN) is calculated by first adding all the numbers in your set and then dividing the sum by how many numbers in the set.

2 + 3 + 4 + 5 = 14
14 divided by 4 (how many numbers we added together) = 3.5

Rounding

When you do you averaging in Applied Tech, you'll be working with times accurate to the thousandths of a second. You'll want to be able to round your numbers to the nearest thousandth of a second. (That's three numbers after the decimal point) 0.001 = one thousandth. If the number in the ten thousandth place, 0.0001 = one ten thousandth, is 5 or higher, then you add one to the thousandth place.

2.2247 ≈ 2.224 rounded to the nearest thousandth, because the number to the right was less then 5.
2.2476 ≈ 2.248 because the number to the right of the 7 is greater 4, so we add one to the thousandth place.

Volume

So before we talk about volume lets talk about area. (Some of the things we do in volume will make more sense.)
Area of a rectangle and triangle.

Notice that finding the area of a triangle requires dividing by two, you may have been taught do the divide operation before the multiplication and that's fine.
Area of a trapizoid.


See that little trick where we add the two bases together first? Yeah, remember that...
Volume of a cuboid and wedge.

Volume of a dragster blank.

The Dragster Blank is basically a 3D trapezoid on it's side. You can add the two heights together just like when dealing with a trapezoid and then continue on as though it was a wedge. There is another way of doing this, but I find the above to be the easiest.

Density

Density is the amount of material in a given volume. Usually we are dealing with density as grams per milliliter, g/ml. And that's the clue to calculating density, divide the mass of an object by it's volume.
                      MASS
Density = ------------
                    Volume

You'll also need to be able to calculate the Mass of your dragster given a volume and density. You can isolate the Mass on one side of the equation above by multiplying both side by volume...

Density X Volume = Mass

Speed

Speed is how far an object travels in a given amount of time. In our calculations, we will need to convert our times for the dragster into speed in miles per hour. The track length is 65 ft, so our distance remains constant. Lets see how fast a dragster is if the time is 1.250 seconds.

                 Distance                   65 ft.
Speed = ----------------        -------------------- = 52 ft. per second (FPS)
                   Time                      1.250 seconds

Our example dragster travels at a speed of 52 FPS, but we want to know speed in miles per hour. We need to convert feet per second to feet per minute, then feet per hour, multiplying 52 FPS time 60, number of seconds in a minute, and 60 again, number of minutes in an hour.

52 X 60 = 3,120 feet per minute   X 60 = 187,200 feet per hour (FPH).

Now we don't usually measure speed in feet per hour, rather we use miles here in the states. There are 5,280 feet in a mile. Now we need to divide our feet per hour by 5,280 to get miles per hour.

    187,200
------------------- = 35.455 miles per hour.
     5,280



Need more help?
Check out this section of Khan Academy about Geometry.
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