## Friday, June 26, 2015

### Examine Numbers 0-12: Focus on Zero

Early in the math year we'll watch a good film about the history of math. We'll also explore the numbers 0-13. For homework students will complete a related journal page and enrichment if they choose.

I may update the zero page in the days to come, but this sets the stage for our study to come.

History of Zero

Properties of Zero
• Addition Property: A number does not change when adding or subtracting 0 from that number. Example: 6 + 0 = 6, 125 - 0 = 125
• Additive Inverse Property: When you add two numbers and the sum is zero, those numbers are additive inverse or opposites of each other. Example: -2 + 2 =0
• Multiplication Property: Zero times any number is equal to zero. Example: 7 X 0 = 0
• A number to the 0 power is equal to one.
Number Names for Zero
• Digit: Zero is one of the ten digits that make up all numbers in the base ten system.
• Whole Number: Whole numbers are "quantity numbers." They tell how many you have. Whole numbers are positive integers.
• Integer: Integers are whole numbers, and their additive inverse (negative numbers). Integers are not fractions.
• Number: an arithmetical value, expressed by a word, symbol, or figure representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification.
• Real Number: Numbers that can be found on a number line, 0 can be found on a number line.
• Rational Number: Any number that can be written as a fraction is a rational number, since 0 can be written as 0/n, then it is a rational number. .75 is also a rational number since it can be written as 3/4, but .3333(repeating) cannot be written as a fraction so it is not a rational number, but an irrational number.
• Even: 0 is an even number because it is a multiple of 2: 0 X 2 = 0. (0 is considered a multiple of all numbers except 0 itself)
Number Names That Do Not Name 0
• Counting Numbers/Natural Numbers: When we count objects, we don't count 0 (or nothing), instead we start with 1.
• Fraction: 0 is not a fraction, but a fraction can be equal to 0 when 0 is in the numerator or when both numerator and denominator are equal to 0 A fraction is in the form a/b, where a and b are real numbers, usually integers.
• Positive Integers: Positive whole numbers greater than 0.
• Negative Integers: The opposite of positive integers, all the additive inverse or negative numbers less than 0.
• Irrational Number: 0 is not an irrational number because it is a rational number.
• Odd Number: 0 is even so it is not odd.
The "Behavior" of Zero
• By itself, it may mean NOTHING, zero quantity.*
• In a place value setting, it means that there is no amount in that specific place.*
• Behind whole numbers, it increases the whole number quantity by one place value for each zero.*
• In the number line and in graphs, it means the POINT OF ORIGIN. All numbers measure the distance from the point of origin, the bigger the number, the farther the distance from zero.*
• "Zeroing In" means to get to the source, to target, to get to the point. What point? The point of origin from where all numbers depart.*
• In a binary system, where zero and one are the only two elements, zero is "false" where one is "true." Binary systems make up our computer language.*
• In a fraction, when 0 is in the numeartor, then the fraction is equal to 0. Example: 0/7 = 0 divided by 7 = 0.
• 0/0=0, but mathematicians do not assign a value to this and consider it NaN (not a number)