Monday, June 29, 2015

Numbers 0-12: Focus on One

After studying the properties of one, students will complete this page for home study.

What do we know about one?

Names for One
  • Digit: One 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. 1 is a whole number. 
  • Integer: Integers are whole numbers, and their additive inverse (negative numbers). Integers are not fractions. Both 1 and -1 are integers.
  • 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.  1 is a number.
  • Real Number: Numbers that can be found on a number line, 0 can be found on a number line. 1 can be found on a number line.
  • Rational Number: Any number that can be written as a fraction is a rational number, since  1/1 = 1, 1 is a rational number. 
  • Odd: 1 is an odd number. It cannot be split into two same whole numbers. 
  • Counting Numbers/Natural Numbers: When we count objects, we start with 1.
  • Positive Integers: Positive whole numbers greater than 0.
Number Names that Don't Describe One
  • Fraction: 1 is not a fraction, but a fraction can equal one when the the numerator and denominator are equal (unless it is 0): a/a = 1 when a is not qual to 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. 
  • Even Number: 1 is not an even number because it cannot be split into two equal whole numbers.
Properties of One (A property is a trait, characteristic, attribute)
  • Multiplication Property: Multiplying any number by one does not change its value. Example: 5 X 1 = 5 (the multiplicative identity property)
  • Division Property: Dividing any number by one does not change its value. Example: 6 divided by 1 = 6. 
The "Behavior" of One  ("Behavior" is the way one acts in an equation or expression)
  • Powers of One: The number one raised to any power always equals one. Example: one raised to the power of 10 is still equal to one. 
  • Any number raised to the power of one remains unchanged. Example: 4 to the power of one is equal to 4. 
  • Any nonzero number divided by itself is equal to one. a/a = 1 when a is not equal to 0.
  • First nonzero number in the natural numbers and first odd number in the natural numbers.
  • One is considered a unit. One is neither composite or prime. 
  • One is the only positive integer divided by exactly one positive integer.
  • One is the probability that an event will occur. 
  • When the denominator is equal to one, the value of the fraction will be equal to the numerator (except when the numerator is 0) Example a/1=1 when a is not equal to 0

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