Saturday, February 22, 2014

Number System


Introduction to the Number System


Videos for introduction of Number System
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    Student HandOut :                            
 Natural Numbers
Natural numbers are what you use when you are counting one to one objects. You may be counting pennies or buttons or cookies. When you start using 1,2,3,4 and so on, you are using the counting numbers or to give them a proper title, you are using the natural numbers.
N = {1,2,3 ,4,……………………}

Whole Numbers
Whole numbers are easy to remember. They're not fractions, they're not decimals, they're simply whole numbers. The only thing that makes them different than natural numbers is that we include the zero when we are referring to whole numbers. However, some mathematicians will also include the zero in natural numbers and I'm not going to argue the point. I'll accept both if a reasonable argument is presented. Whole numbers are 1, 2, 3, 4, and so on.
W = {0 ,1,2,3,4 ,………}

Integers
Integers can be whole numbers or they can be whole numbers with a negative signs in front of them. Individuals often refer to integers as the positive and negative numbers. Integers are -4, -3, -2, -1, 0, 1, 2, 3, 4 and so on.
Z = {…….-3 ,-2 ,-1 ,0 ,1 ,2 ,3 ,…………}

Rational Numbers
Rational numbers have integers AND fractions AND decimals. Now you can see that numbers can belong to more than one classification group. Rational numbers can also have repeating decimals which you will see be written like this: 0.54444444... which simply means it repeats forever, sometimes you will see a line drawn over the decimal place which means it repeats forever, instead of having a ...., the final number will have a line drawn above it. Decimal form of rational numbers could be terminating or non-terminating and repeating. The collection of rational numbers is denoted by Q. It is written in the form of p/q where p and q are integers and q ≠ 0.
In the form of p/q, when p and q have no common factors other than 1, p and q are called co-prime.

Irrational Numbers
Irrational numbers can have a decimal value that continues forever WITHOUT a pattern, unlike the example above. An example of a well known irrational number is pi which as we all know is 3.14 but if we look deeper at it, it is actually 3.14159265358979323846264338327950288419.....and this goes on for somewhere around 5 trillion digits!

Real Numbers
Here is another category where some other of the number classifications will fit. Real numbers include natural numbers, whole numbers, integers, rational numbers and irrational numbers. Real numbers also include fraction and decimal numbers.

In summary, this is a basic overview of the number classification system, as you move to advanced math, you will encounter complex numbers. I'll leave it that complex numbers are real and imaginary.

Student Activity:


Student Handout - Venn Diagram of the Number System


Student Activity : Fun With Classification of Numbers

Learning Objective:
Students will classify numbers within the real number system.
 Students will identify numbers as rational or irrational. Students will classify rational numbers as integers, whole numbers, or natural numbers.

Activity:


Select six students to sit in chairs in the front of the room facing the class. The first round should probably be with students who have a good understanding of the concept.

1)Give each student a sign to wear: (in this order) Real, Rational, Irrational, Integer, Whole, Natural.

2)The remaining students will draw numbers from a container. As each student reads his/her number, the students in the front will stand if the number meets the constraints of their classification.

3)Teacher observation and assessment will determine how many rounds are played. When the teacher feels the connections have been made, a discussion will evolve. Students will begin to see that Irrational and Rational never stand at the same time. They will also see that Real always stands. If Natural is standing, then Whole and Integer will also. Allow students to make these observations. 

Worksheet for the Students : (Group Activity/ Individual work )
Classifying numbers worksheet 1
Classifying numbers worksheet 2
Classifying numbers worksheet 3