Number SenseNumber Sense

AIMS MathAIMS Math

Spring, 2009Spring, 2009

Answers to On-Line Practice Answers to On-Line Practice TestTest1.1. BB2.2. CC3.3. DD4.4. AA5.5. AA6.6. CC7.7. DD8.8. AA9.9. DD10.10. DD

11.11. AA12.12. CC13.13. DD14.14. AA15.15. BB16.16. AA17.17. CC18.18. AA19.19. BB20.20. AA21.21. BB

22.22. CC23.23. DD24.24. BB25.25. DD26.26. CC27.27. AA28.28. CC29.29. BB30.30. CC31.31. DD32.32. AA

33.33. CC34.34. BB35.35. DD36.36. BB37.37. CC38.38. BB39.39. AA40.40. DD41.41. CC42.42. BB43.43. CC

Number SetsNumber Sets

Anything that can be written as a ratioAnything that can be written as a ratio

positives and negativespositives and negatives

0 0

1, 2, 3, 4, …1, 2, 3, 4, …

``

`

`

Square Roots Square Roots Approximate & Rational or Irrational?Approximate & Rational or Irrational?

818136368585225225101099400400100100111,0001,000

212114014017217235635640040000625625252528283535

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, …}

Absolute ValueAbsolute Value

Distance from _____.Distance from _____.What is the absolute value of…What is the absolute value of…|3||3||-3||-3||5||5||2.57||2.57||1/2||1/2||-8||-8|

|346||346||-33||-33||52||52||0||0||1||1||-1||-1|

|851||851||0.13||0.13||51||51||0.58||0.58||-1/4||-1/4||455||455|

Finite versus InfiniteFinite versus Infinite

Number of people in Casa GrandeNumber of people in Casa Grande

Amount of carpet needed for this Amount of carpet needed for this roomroom

Hairs on your headHairs on your head

Sand on a BeachSand on a Beach

Finite versus InfiniteFinite versus Infinite

Natural Numbers between 1 & 5Natural Numbers between 1 & 5Rational Numbers between 0 & 5Rational Numbers between 0 & 5Even Whole Numbers between 1 & 5Even Whole Numbers between 1 & 5Whole numbers between 4 and 7Whole numbers between 4 and 7Rational numbers between 7 and 10Rational numbers between 7 and 10Negative rational numbersNegative rational numbers{5, 3, 1, 7 8}{5, 3, 1, 7 8}{…-5, -3, -1, 1}{…-5, -3, -1, 1}{…-3, -2, -1, 0, 1, 2, …}{…-3, -2, -1, 0, 1, 2, …}

Decimal places in 3½Decimal places in 3½Decimal places in 2/3Decimal places in 2/3

PropertiesProperties

CommutativeCommutative

DistributiveDistributive

AssociativeAssociative

ExponentExponent

An exponent is a little number high An exponent is a little number high and to the right of a regular or base and to the right of a regular or base number. number.

3 4Base

Exponent

What an Exponent What an Exponent RepresentsRepresents

An exponent tells how many times An exponent tells how many times a number is multiplied by itself.a number is multiplied by itself.

34= 3 x 3 x 3 x 3

Exponent ExamplesExponent Examples

3322

3344

2244

5522

7700

1144

2255

4422

111515

6644

7722

101022

Scientific NotationScientific NotationUses a number between 1 and 10 Uses a number between 1 and 10 multiplied by a power of 10.multiplied by a power of 10.

Is this proper scientific notation?Is this proper scientific notation?

3.25 x 103.25 x 1044

21.57 x 1021.57 x 1044

5 x 105 x 1022

0.5 x 100.5 x 10-2-2

0.43 x 100.43 x 101515

6.001 x 106.001 x 10-4-4

3.2 x 103.2 x 1022

5.32 x 105.32 x 1000

Scientific NotationScientific Notation

Write in expanded form.Write in expanded form.

A positive exponent moves the decimal to the ___.A positive exponent moves the decimal to the ___.A negative exponent moves the decimal to the __.A negative exponent moves the decimal to the __.

3.25 x 103.25 x 1044

2.157 x 102.157 x 1066

5 x 105 x 1022

8.5 x 108.5 x 1055

2.43 x 102.43 x 10-4-4

6.001 x 106.001 x 10-3-3

3.2 x 103.2 x 10-2-2

5.32 x 105.32 x 1000

Scientific NotationScientific Notation

Write in scientific notation.Write in scientific notation.

321.5321.5

31.431.4

11051105

1.731.73

0.0250.025

0.00720.0072

0.0003170.000317

432432

Integer Addition and Integer Addition and SubtractionSubtraction

Positive + Positive =Positive + Positive =

Negative + Negative =Negative + Negative =

Positive + Negative =Positive + Negative =

Real Live Uses of Integer Real Live Uses of Integer Arithmetic IArithmetic I

Jesus boards a plane in Jesus boards a plane in Phoenix where the Phoenix where the temperature is 80temperature is 80F and flies F and flies to Grand Island, Nebraska, to Grand Island, Nebraska, where the temperatures is -where the temperatures is -10 10 F . What number F . What number represents the change in represents the change in temperature in degrees temperature in degrees Fahrenheit going from Fahrenheit going from Phoenix to Grand Island?Phoenix to Grand Island?

Real Live Uses of Integer Real Live Uses of Integer Arithmetic IIArithmetic II

Rita’s business showed a loss of Rita’s business showed a loss of $5,000 in 2007 and a loss of $2,000 in $5,000 in 2007 and a loss of $2,000 in 2008. How much better did the 2008. How much better did the business do in 2008 than in 2007?business do in 2008 than in 2007?

Real Live Uses of Integer Real Live Uses of Integer Arithmetic IIIArithmetic III

A plane is flying at 2,000 feet A plane is flying at 2,000 feet above sea level, directly above sea level, directly above a submarine that is above a submarine that is 500 feet below the surface. 500 feet below the surface. How far are they apart?How far are they apart?

Real Live Uses of Integer Real Live Uses of Integer Arithmetic IVArithmetic IV

Matt has $500 in his banking Matt has $500 in his banking account. During January, he account. During January, he made 3 transactions: made 3 transactions: deposited $200, withdrew deposited $200, withdrew $50, and wrote a check for $50, and wrote a check for $80. In addition, he paid the $80. In addition, he paid the bank a fee of $25. If there bank a fee of $25. If there were no other transactions, were no other transactions, what was Matt’s balance on what was Matt’s balance on February 1?February 1?

UnitsUnits

In what units (miles, feet, inches) would In what units (miles, feet, inches) would you measure the following?you measure the following?

Your fingerYour finger

Distance to PhoenixDistance to Phoenix

Length of a bookLength of a book

Width of a football fieldWidth of a football field

Height of a treeHeight of a tree

Length of a doorwayLength of a doorway

MatricesMatrices

043

121

401

237BA

Find:

A + B

A – B

2A

3A + B

Order of OperationsOrder of Operations

In what order do you do addition, subtraction, In what order do you do addition, subtraction, multiplication, division, exponents, absolute multiplication, division, exponents, absolute values, parenthesis and other grouping values, parenthesis and other grouping symbols?symbols?

Order of OperationsOrder of Operations

5432

4|324|2

8|3|4

61523

2

2

Order of OperationsOrder of Operations

5432

4|324|2

8|3|4

31523

2

2

More on SimplifyingMore on Simplifying

5342

3|221|2

4|3|25

520)3(24

2

2

More on SimplifyingMore on Simplifying

103

33

2103

23

3210

243

92

)(

)(

)(

)(

)(

hh

t

aa

mmmm

nn

uuuu

ff

More on SimplifyingMore on Simplifying

73

4

3

9

5

4

4

8

5

2

5

)2(

12

3

4

8

aa

a

a

k

k

a

a

j

j

a

a

SubstitutionSubstitutionLet x = 2, y = -3 and z = 1Let x = 2, y = -3 and z = 1

xzyx

xxzyx

xyy

zyyx

2

2||

||