WarmupWarmup

Group the following numbers by similar characteristics.

6, ½, 3.2, 7, -5, , 3.1714…, 4, ¼, ¾, 0.75, 9, -1, 4, 0.5, 0.3, 2, 0.6,

-9, 7.1, 1/3, 0.25

Number SenseNumber Sense

AIMS MathAIMS Math

Spring, 2009Spring, 2009

Number SetsNumber Sets

Real Numbers Real NumbersRational Numbers Irrational NumbersRational Numbers Irrational Numbers

Anything that can be written as a ratio Non-RepeatingAnything that can be written as a ratio Non-Repeating

IntegersIntegers Non-EndingNon-Ending

positives and negatives Decimalspositives and negatives Decimals

Whole NumbersWhole Numbers Roots that are not Roots that are not

0 0 Perfect Perfect

Numbers that Numbers that

Natural or CountingNatural or Counting cannot be cannot be

NumbersNumbers written written

as ratiosas ratios

1, 2, 3, 4, …1, 2, 3, 4, …

DefinitionsDefinitions

Real Numbers: Any number that can name a position on a number line is a real number. Every position on a number line can be named by a real number in some form.

Irrational Numbers: Is a number that cannot be written as the quotient of two integers.

Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions.

DefinitionsDefinitions

Integers: The counting numbers (1, 2, 3, ...), their opposites (-1, -2, -3, ...), and zero are integers

 Whole Numbers: Zero and the positive integers are the whole numbers.

 Natural or Counting Numbers: This set includes all of the whole numbers except zero (1, 2, 3, ....)

DefinitionsDefinitions

Finite - having limits, a beginning and an end.

Infinite: having no limits, no beginning and no end.

Set: A collection of distinct elements as in the set of real numbers.

Subset: A set contained within another set, as in as in the set of integers contained within the set of rational numbers

Distance: Difference between locations. Usually found by subtracting. Cannot be negative.

Video LessonVideo Lesson

Khan Academy – Number Sets #1

To what number set does this To what number set does this belong?belong?

Number of people in Casa GrandeNumber of people in Casa Grande

Amount of carpet needed for this roomAmount of carpet needed for this room

Amount of oil in a carAmount of oil in a car

Sand on a BeachSand on a Beach

{-2, -5, 3, 1}{-2, -5, 3, 1}

{1/2, ¾, 7/8, 0, 16}{1/2, ¾, 7/8, 0, 16}

{1, 2, 3, …}{1, 2, 3, …}

{0, 1, 2, 3, …}{0, 1, 2, 3, …}

Square Roots Square Roots Is each rational or irrational?Is each rational or irrational?Give its value Give its value (if rational) (if rational) or approximation or approximation (if irrational).(if irrational).

√√8181√ √ 3636√ √ 8585√ √ 225225√ √ 1010√ √ 99√ √ 400400√ √ 100100√ √ 11√ √ 1,0001,000

√ 2121√ 140140√ 172172√ 356356√ 400400√ 00√ 625625√ 2525√ 2828√ 3535

Perfect SquaresPerfect Squares

0022==

1122==

2222==

3322==

4422==

5522==

6622==

7722==

8822==

9922==

101022==

111122==

121222==

131322==

141422==

151522==

161622==

171722==

181822==

191922==

202022==

252522==

What is a Square Root?What is a Square Root?

Visual of Square Roots & Estimations