3 NUMBERS
Real Numbers: Real numbers are all numbers that can be represented in a number line.
Natural Numbers: Natural numbers are all counting numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, …
Whole Numbers: Whole numbers are all positive numbers and zero such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, …
Integers: Integers are all positive and negative numbers and zero such as …-12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, …
Rational Numbers: Rational numbers are all integers and fractions.
Irrational Numbers: Irrational numbers are numbers that cannot be written as fractions such as √3 or π
Prime Numbers: Prime numbers are divisible only by 1 and itself such as 2, 3, 5, 7, 11, …
Composite Numbers: Composite numbers are positive integers which are not prime, with factors other than 1 and itself such as 4, 6, 8, 9, 10, 12, …
Cardinal Numbers: Cardinal numbers are natural numbers used in counting such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …
Ordinal Numbers: Ordinal numbers describes the numerical position of an object or number such as first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, …
Even Numbers: Even numbers are numbers that can be evenly divided by 2 such as 2, 4, 6, 8, 10, 12, …
PRACTICE 3A: Below, practice writing the definition of whole numbers to the best of your ability (continue practicing until mastered).
4 NUMBER LINE
Number Line: A line which consists of
2, 2, 0, 5,1, 4,1, 3, 0, 0, 1, 4, 4, 0,1, 4, 3, 4, 2, 1
Arabic numerals arose from the transferring of ideas from Hindu scholarship into Islamic caliphates of the Golden Age, and from there, into European culture. One thing from Indian culture that transcended into Islamic culture was the concept of zero. This was something that was not considered in earlier mathematic studies. It reads in "Math Roots: Zero: A Special Case," "the Arabs recognized the value of the Hindu system, adapted the numerals and computation, and spread the ideas in their travels." The Arabic people saw the power in this numbering system because there
Measurement that shows the order or rank of items. An example of ordinal could be ranking places in a contest, or test scores.
The square root of 16 is 4 and 4 is an integer, rational number, whole number, natural numbers.
2, 2, 0, 5,1, 4,1, 3, 0, 0, 1, 4, 4, 0,1, 4, 3, 4, 2, 1
Ordinal data has the variables that include rank and satisfaction. An everyday example of ordinal data can be surveys.
Imagine the number eight. People would probably think that it’s just eight and nothing but eight. Now imagine the number eight tilted 90° to the left. People now see the infinity symbol. Now, people would probably think of it as an expanding number that never ends.
1, 3, 5, 7, 9, 11, … (The common difference is 2. (Bluman, A. G. 2500, page 221)
6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
) Determine whether each of these set is finite, countably infinite, or uncountable. Justify your answer
Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.
Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter view encompasses mathematical or symbolic logic, the science of using symbols to provide an exact theory of logical deduction and inference based on
The implications of infinity (co) are actualiy not that old. The Greeks were some of the first mathematicians recorded to have imagined the concept of infinity. However, they did not actuaily delve into the entirety of this number. The Greeks used the term “potentially infinite," for the concept of an actual limitless value was beyond their comprehension. The actual term “infinity” was defined by Georg Cantor, a renowned German mathematician, in the late nineteenth century. It was originally used in his Set Theory, which is a very important theory to the mathematical world. The value of infinity can get a bit confusing, as there are different types of infinity. Many claim that infinity is not a number. This is true, but it does have a value. So, infinity may be used in mathematical equations as the greatest possible value. i The value of infinity Infinity (00) is the greatest possibleivalue that can exist. However, there are different infinities that, by logic, are greater than other forms of itself. Here is one example: to the set of ait Naturai numbers Z43, 2, 3, 4,...}, there are an infinite amount of members. This is usualiy noted by Ko, which is the cardinality of the set of alt natural numbers,