The student will describe the relationships between the subsets of the real number system.
Numbers are organization into a system of classification (similar to living things in Life Science). All of the numbers we will talk about in Math 8 are classified as real numbers.
The RNS (Real Number System) has groups within groups called subsets. Here's how subsets work:
Students in Mrs. King's class are a subset of students in 8th grade:
If you're in Mrs. King's class, you're also in 8th grade.
However, just because you're in 8th grade doesn't mean you automatically have Mrs. King.
Students in 8th grade are a subset of students at DMS:
If you're in 8th grade, you're automatically at DMS (and not DHS or an elementary school).
Just because you're at DMS doesn't automatically make you an 8th grader.
Students at DMS are a subset of students in DCPS.
Students in DCPS are also students in Virginia.
Subsets:
If you're in Virginia, you can be a student in DCPS, but it's not automatic.
If you're in DCPS, you can be a student at DMS, but it's not automatic.
If you're at DMS, you can be a student in 8th grade, but it's not automatic.
If you're in 8th grade, you can be a student in Mrs. King's class, but it's not automatic.
Now, back to real numbers:
Real numbers are split into two subsets (a group within a group): rational numbers and irrational numbers.
Rational numbers can be written as ratios (i.e., fractions). They have decimals that repeat or terminate (stop):
Repeating decimals:
1/3 = 0.3333333...
5/6 = 0.8333333...
1/7 = 0.142857142857... (notice that the "142857" repeats itself)
Terminating decimals stop after a certain place value:
1/2 = 0.5
1/4 = 0.25
55555/100,000 = 0.55555
Integers: a subset of rational numbers that do not have a decimal value. These are what you normally see on a number line.
Examples: ...-3, -2, -1, 0, 1, 2, 3...
Whole Numbers: a subset of integers that does not include any negative numbers. These are all the numbers you would use when counting down to zero.
Examples: 0, 1, 2, 3...
Natural Numbers (also called Counting Numbers): a subset of whole numbers that include how a child would naturally start counting.
Examples: 1, 2, 3, 4, 5...
Irrational numbers: a subset of real numbers where the decimal values do not repeat and do not terminate. These numbers include π (pi) and the square root of any nonperfect square.
Examples:
π = 3.14159265359...
√ 10 = 3.16227766...
√ 99 = 9.949874371...
√ 1,001 = 31.63858404...
Each of these subsets of numbers can be represented by a non-simplified number:
24/8 = 3 so 24/8 would classify as a real number, integer, whole number, and natural number.
Use a graphic organizer or number line to show how subsets are related.
Classify a number into all possible subsets it belongs and explain why.
Describe each subset. Give examples and nonexamples.
Desmos allows you to use a fraction function. Entering a fraction will allow you to see the value of the fraction:
Entering "6/2" displays a value of 3 (natural, whole, integer, rational, real).
7.A.11
7.H.4
8.A.9
8.D.5
A.A.8-10