Incredible Math Stories

There is a great section of Homeschool Hangout Zone dedicated to math that you should definitely check out. Its blog posts feature several links that talk about math and how it relates to the real world, rather than just how the numbers add up in your homework. Stories range from calculating the theoretical fastest sprint time of an athlete on a track, to describing how your brain changes when you do math problems, to using math to create incredible visual patterns. I highly recommend you visit the site to see the many interesting stories that it has to offer!

Great site for lessons and worksheets

I'd like to also direct some attention to Homeschool Math. It is a very informative site that has plenty of lessons and worksheets available for practice that cover several different math concepts. Maria also does something rather unique on her site, in that she presents many math concepts and lessons through the use of youtube videos embedded on her page (such as here). I highly recommend her site... the questions you have might have solutions there as well!

Math Puzzles and Fun

This is just a short little post. If you have an interest in math puzzles and things like this, it might be worth the trip for you to check out http://wildaboutmath.com/. I've been linking to their site for a long time now, and I just thought I would try to introduce some of my more recent followers to that site. There are math puzzles and all sorts of interesting bits of info over there. It's really well done. Check them out!

Which Measure of Central Tendency to Use? Mode, Mean, or Median?

A concept which may need a bit more explanation is: which average is appropriate for a given question? What is the best measure of central tendency? When would you use a median instead of a mean, or perhaps use a mode instead?

For any data set, you can perform the analysis to come up with a value for each average. However, here are a few basic guidelines to help you choose the most appropriate form of central tendency to describe your data.  If this is helpful, it would be great if you could please hit the +1 button to share it!

1. For a normal, random distribution of data (evenly distributed), the mean is preferred.
2. For a skewed data set, a median is more appropriate than a mean. The skewed data set (ie. extreme data points) will cause the mean value to be much more extreme than the median, and therefore less central.
3. The mode can be used for non-numerical data. Eg. hair colour in a classroom.

Here are a few examples of where each would be appropriate:

Mean:
1) students' heights in a classroom
2) temperature over a length of time

Median:
1) income of a group of people
2) test scores for a group of students

Mode:
1) finding the most common hair colour in a room
2) finding the most common car in a parking lot

Hopefully these guidelines will help you to determine which is the most appropriate measure of central tendency to report for your data set.

Again, if this was helpful, please share and hit the +1 for me! :)

Perfect Squares

This post should have been put up when I posted about square roots (here, here, and here), because it is the exact opposite of a square root!

Where a square root of a number "x" is some number "y" that, when multiplied by itself, gives "x", a (perfect) square of a number is the result of multiplying a number by itself. That is to say, the square of "y", by multiplying "y" by "y", is "x". You can also talk about "squaring" a number, which is to find what the square is. (It can be both a noun and a verb.)

For example: the square of 4 is "4 x 4" = 16. Also, if you square 4, you get 16.

If you want to think of a visual representation of it, "what is the square of 5" is essentially the same as asking "what is the area of a square with a length of 5?" (Of course, all sides have equal lengths in a square.) As you can probably figure out already, to find the area of a square (or, in general, a rectangle) you multiply the length by the width. So here, it is obviously 5 x 5 and the area, or the square of 5, is 25.

This concept of perfect squares can also be extended to polynomials. For example, let's look at the following case:

(x+1)*(x+1) is the square of (x+1). It can also be written as (x+1)^2. You can do the visual trick i just described above if you want, using x+1 as the side length.

If you multiply (FOIL) these binomials, you get (x^2 + 2x + 1). As it is equal to our original expression, you can also say that this product is a perfect square, just as you can say that 16 or 25 is a perfect square. To find out what the square root of this is expression is, it is the same as asking what the square root of (x+1)*(x+1). Over time you will see patterns and be able to quickly notice that the square root of (x^2 + 2x + 1) is (x+1).

This shouldn't be too difficult of a concept to understand. I will do a few short examples, but post comments if you require clarification:

Find the square of 12:
12 x 12 = 144

Find the square of 25:
25 x 25 = 625

Find the square of (x-1):
(x-1)*(x-1) = (x-1)^2 = (x^2 - 2x + 1)

Find the square of (2x+3):
(2x+3)*(2x+3) = (2x+3)^2 = (4x^2 + 12x + 9)

It can also be noticed, and should be kept in mind, that squares will always be positive. Try it to see: plus x plus = plus... negative x negative = plus. A plus times a negative is NOT a square! Squares multiply the SAME number (sign and all!).

See my previous post about "completing the square" for some more stuff relevant to this post.