Are We Being Totally Irrational?

In 8th grade math class we've been playing around with numbers.
Perfect squares.
Cubes.
Square roots.
Cube roots.
We've been ordering them and plotting them on number lines.
Today we sorted them into two groups,
And through close analysis discovered something else about these numbers we had been working with!

Ask your student...
1.  What is an irrational number?
2.  What is a rational number?
3.  How can you tell the difference between an irrational and rational number?
4.  Can a number be both irrational and rational?
5.  How did you learn the differences between irrational and rational numbers?
6.  What is the hardest thing to remember?

Using ScreenChomp to Communicate How to Subtract Integers

How does one subtract positive and negative numbers?
It's harder to see and do than addition, that's for sure!
After learning several methods
(ask your student which method they prefer...positive and negative notation, driving along the number line, or adding the opposite),
Students focused on explaining the process to others using an iPad App...ScreenChomp.

Real Numbers Meet the Real World

Last Monday, 2nd hour math class got to Skype with Mr. McBryant from Arkansas about his job as a Wireline Engineer and how he uses real numbers (and their subcategories) in his job everyday.

What a great way to see math in action in the world outside our classroom walls!

The Real Number System Represented in Real World Terms

How do you see the Real Number System?

It's a complex system for categorizing all the numbers that we work with.

Here is how one student sees the categories.

How do you see the Real Number System?

What is the Math Behind Multiplying & Dividing by Negative Integers?

A question was raised today in Algebra class after going over the rules of HOW to multiply and divide by negative numbers...

"WHY does that work mathematically?"

In class, we were able to figure out why a negative divided by a negative equals a positive.

Now...the next question.
WHY does a negative multiplied by a negative equals a positive?

A Math Discussion...

Today in math, a great math conversation was in the making as Mr. Archbold broke down the Real Number categories into easier to understand segments.

Mr. Archbold gave several references of the Real Number System in "un-mathy" examples.  Ask your student how the following items are related to the Real Number System.

Today the floor diagram looked like this.

Yesterday, it looked a little different.
The diagram was a little simpler.
Students moved through the diagram categorizing various numbers of the  Real Number System.

(Sorry for the blurry pictures!  Will have to check my camera!)

Sorting numbers into the correct categories can be tricky.

There are new vocabulary words to learn.

Plus, the categories overlap, so the sorting becomes even more tricky!

Some good questions to ask your student...

1)  What is an integer? (ans. Any positive or negative number)

2)  What is the most specific category for 2/3? (ans. Rational Numbers)

3)  How are natural and whole numbers the same? (ans. They both contain the numbers 1, 2, 3, 4, and so forth)

4)  How are irrational numbers different than rational numbers? (ans. Irrational numbers cannot be made into a fraction.  Irrational numbers are decimals that go on FOREVER and NEVER REPEAT any of the digits...there is no pattern.)

Good Enough to Eat!

The Real Number System...
who would have known it could be connected to a
delicious,
yummy,
juicy cheeseburger.
With ketchup on the side!

One RVMS student got creative and aligned the real number system to something we see everyday.
Way to go!

Real Number Metaphors...An Algebra Moment

Parents...
~ If you have a student in Algebra, ask them to tell you how the following pictures represent the Real Number System.

Students...
If you are in 8th Grade Math, just wait!  You will be learning the same thing in about a week or so!  :)