Scale Factor and Area

Most of you understand that the scale factor is the scale length over the original length.  But what happens if you're looking for the area and don't know the length?  To find out, let's first use scale factor to find area of a new shape.

This rectangle has an area of 3 * 8 or 24.  If we dilate it with a scale factor of 2, the new sides will be multiplied by two.  But is the area also multiplied by 2?  Let's find out if we get the same thing.  24 * 2 = 48.   But 3 * 2 = 6 and 8 * 2 = 16.  Multiplying 6 * 16 gives us 96!  96 does not equal 48, so something else must have happened.  Let's compare 96, the scale area to 24, the original.  If we divide 96 by 24 we get 4, not 2.  So something happened to the scale factor when we calculated area.  It got squared!  2 * 2 = 4.

This means that any time we are working with area only and we have a scale factor to find new area, we need to square it.  Also, we know that area is two-dimensional and that units that are two dimensional are square.  Therefore it makes sense to square it.  It also leads to the next thought.

What do we do with scale factor and volume?

Proportions in Nutrition

http://threeacts.mrmeyer.com/sugarpackets/

Work through the entire thing.

Here are some foods and drinks you like.  How many sugar packets are in each?  Don't forget to multiply the calories by the servings if you drink the whole can.

Here's the information for a bag of M&M's.

Using Probability to Learn Statistics

Probability tests using number cubes or spinners are a good way to create a set of data.  The numbers have variance without being overly large, a mode is present, the range is also not very large, and you can relate the mean to probability through the "Law of Averages".  You can also bring up the bell curve.  The data set created can be used to create circle graphs by showing experimental vs theoretical probability, bar graphs by breaking it down per probability device, histograms and line plots to show frequency of results, scatter plots to show trends between the spinner and the number cube, and box and whisker graphs to show range, median, and quartiles.  This will require a bit more care with the data sheet, as carelessness will lead to the initial part failing.