Let’s be Rational!

Number Classifications Chart

Number Classifications Chart

Today’s topic is another foundational math concept – number classification!  (I can hear you snoring cheering already!)

So what’s the big deal, right? A number’s a number, isn’t it?  Well, yes and no, just like a square is a shape with certain attributes, numbers themselves can be categorized.  Take the chart I have so cleverly created.  (BTW, if you need it to study or use in a classroom, take it! If you need a better size, or the original .png file, let me know!)

The first great divide of numbers is if they are Real or Imaginary.  Imaginary numbers result from trying to take the square root of a negative number.  They most often occur in the school realm when you are trying to find where a parabola intersects with the x-axis.  If it doesn’t intersect, your answer will be an imaginary number.   They have lots of other uses and they will definitely be the subject of a future post.  Real numbers, on the other hand, are the ones we use everyday.

  • Decimals – how much your paycheck is worth,
  • fractions – a quarter of a cup of sugar,
  • and integers – You owe Joe $5 and you only have $3, you still owe Joe money (hopefully he’s not the gangster type…),

are all examples of Real numbers.

When you break Real numbers down, there are irrational and rational numbers – not so different from people :P.

Irrational numbers, much like some people I know, go on and on forever, without end, (much like this post if I’m not careful 🙄 ).  Examples of irrational numbers are Euler’s e, \sqrt{5} and \pi.  These numbers have approximate values, but, in fact, are infinitely long decimals.  In contrast, rational numbers do end, and can always be expressed as a fraction.  Examples of rational numbers include 27, -43, \frac{2}{7} and $403.99.

A subset (smaller group) of rational numbers is integers.  These numbers are the ones that have 1 as the bottom of the fraction (denominator), such as 34, -17, and 0.  If the integer is 0 or a positive number, we call even call it a whole number.  With the exception of 0, all whole numbers are also called natural, or counting, numbers (because we count with them – there are 5 fingers on my hand, I can’t be -7 feet tall…although sometimes I feel that way :|).

Well this has been the longest post so far, but hopefully it has presented the number family tree in an easy understandable fashion 🙂

Now go read something fattening, you just gave your brain a workout.

Does it make sense?!

As the first real math topic of this blog, it is only appropriate I start with the concept of math sense.  Ever look at your bill at a restaurant and know that your total is right, even though you didn’t memorize the exact cost of each item?  How about that time you were in math class and the answer you got after using the formula just didn’t look right?  That would be your number sense kicking in… and be glad you have it!

So many students just plug away and whatever answer they get must be right…  When I taught, I tried to instill in my students the need to check the answer.   A forgotten sign or incorrect step will result in a wrong answer, but there is no consequence to this, other than getting the answer wrong… it’s not like they are building a bridge or going to Mars … but we should teach them like they are!

If you are a teacher, I find anecdotes like the two here to be helpful in driving home my point to check you answers… and I would suggest as a teacher, to have your students check their answers as part of their work.  Maybe require it for the first quarter, by then it will become habit 😉

If you are a student, ALWAYS go back and check… it may mean the difference between an A and an A- today, but it could be a million dollar rocket explosion, or at least a bad tip at a restaurant, tomorrow!