# Loan Repeating Representations

Document Sample

```					                                   Math-Related Credit Crosswalk
for
Career Technical Education Classes
in Macomb County

Program Information
District:   L’Anse Creuse
F. V. Pankow Center
Program Name: Programming
CIP Code Number:       11.0201
Career Pathway: Information Technology
Instructor Name:     Nick Paterni
Date: May 2009
Strand               STANDARDS                                              CTE APPLICATION and PRACTICE
L1
REASONING ABOUT NUMBERS, SYSTEMS AND QUANTITATIVE LITERACY

L1.1                                              Number Systems and Number Sense

L1.1.1              Know the different properties that hold in      Integers, rational numbers and real numbers and all
different number systems and recognize          applicable properties are used throughout the course
that the applicable properties change in the    in a variety of programs.
transition from the positive integers to all
integers, to the rational numbers, and to the
real numbers.
L1.1.2              Explain why the multiplicative inverse of a     Students understand that multiplying by ½ is the
number has the same sign as the number,         same as dividing by 2 therefore the sign stays the
while the additive inverse has the opposite     same.
sign.                                           Students understand that subtracting 3 is the same

L1.1.3              Explain how the properties of associativity,    All properties of real numbers including the order of
commutativity, and distributivity, as well as   operation must be followed for accuracy.
identity and inverse elements, are used in      Programming language is very specific and therefore
arithmetic and algebraic calculations.          all properties of arithmetic and algebraic operations
must used.

L1.1.4              Describe the reasons for the different          When writing a compound interest program, students
effects of multiplication by, or                understand the effects of fractional exponents,
exponentiation of, a positive number by a       multiplying by a fraction and multiplying by a number
number less than 0, a number between 0          larger than 1.
and 1, and a number greater than 1.

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L1.2                                               Representations and Relationships

L1.2.1              Use mathematical symbols (e.g., interval        Mathematical symbols of =, -, *, /, ^, <. >, |, { } ,( ), \
notation, set notation, summation notation)     are used throughout the course in programming.
to represent quantitative relationships and     Ex. A statement in programming a game
situations.                                       // Ball lost?
If (ballPosition.Y > 0.985f)
{
// Play sound
L1.2.2              Interpret representations that reflect          Students use and understand the absolute value
absolute value relationships (e.g.,│x-a│< b,    function and can use the function in appropriate
or a± b) in such contexts as error tolerance.   programs.
Ex. System.math.ABS((-50.2))
L1.2.3              Use vectors to represent quantities that        Positions and movement of images on the screen are
have magnitude and direction, interpret         designated by vectors.
direction and magnitude of a vector             Ex. lineVertices[ lineNum * 2 + 0 ]
numerically, and calculate the sum and                = new VertexPositionColor(newVector3(10,20,5)
difference of two vectors.
L1.2.4              Organize and summarize a data set in a          Students can create database information charts.
table, plot, chart, or spreadsheet; find        Ex. Employee Database Information Program
patterns in a display of data; understand           Morgan Industries needs an employee
and critique data displays in the media.            database to include name, address, date of hire
and pay rate.
L1.3                                             Counting and Probabilistic Reasoning

L1.3.2              Define and interpret commonly used              When discussing the creation of a Yahtzee program,
expressions of probability (e.g., chances of    students understand that the odds of getting a
an event, likelihood, odds).                    number is 1:6 and that since these numbers are
randomly generated, the likelihood of getting a 5 is
1:6
L1.3.3              Recognize and explain common probability        When programming a Rock, Scissor, Paper game,
misconceptions such as “hot streaks” and        the outcomes are randomly generated and therefore
“being due.”                                    the winner might believe he is “due” or is on a “hot
streak” but knows the outcomes are random.
Add and Subtract Integers and Rational Numbers

N.ME.06.08          Understand integer subtraction as the           Students write a program to create a mini calculator
inverse of integer addition. Understand         which includes all functions of integers.
integer division as the inverse of integer      Ex. lngAddFirst = txtInput.Text
multiplication.                                     strOutput = “0”
Operation = 1
End Sub

N.FL.06.10          Add, subtract, multiply and divide positive     Students write a program to create a mini calculator
rational numbers fluently.                      which includes all functions of rational numbers.
Ex. lngDivideTotal = txtInput.Text
txtInput.Text = (lngDivideFirst / lngDivideTotal)
Operation = 0

Solve Decimal, Percentage and Rational Number Problems

N.FL.06.12          Calculate part of a number given the            Students can write a program to calculate the annual
percentage and the number.                      payment on a loan.
Ex. Calculate the annual payment for a loan of \$9000
for 3 years are 5% interest rate.
Finanicial.Pmt(.05,3,9000)

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N.MR.06.13          Solve contextual problems involving                Sales Tax Program
percentages such as sales taxes and tips.          Ex. Create a program so that the user can input the
amount and then calculate a 6% sales tax.
Double.TryParse(salesTextbox.Text,sales)
tax6 = sales * 0.06
taxLabel.Text = convert.ToString(tax6)

N.FL.06.14          For applied situations, estimate the answers       To Debug a program, students must estimate
to calculations involving operations with          answers to calculations for accuracy purposes.
rational numbers
N.FL.06.15          Solve applied problems that use the four           Mini Calculator program
operations with appropriate decimal                Students write a program to simulate a calculator
numbers.                                           involving the four basic operations with decimal
numbers.

Use Exponents

N.ME.06.16          Understand and use integer exponents,              Data type
excluding powers of negative bases,                Ex. Single: a number with a decimal range
-45                   38
express numbers in scientific notation.                + /- 1.401298 x 10 to +/- 3.402823 x 10

Understand Rational Numbers and Their Location on the Number Line

N.ME.06.18          Understand that rational numbers are               Students understand that all fractions are a quotient
quotients of integers (non zero                    of two integers and are converted to decimals.
denominators).

N.ME.06.19          Understand that 0 is an integer that is            0 is used in programming to indicate a false
neither negative nor positive.                     statement and has no value.

N.ME.06.20          Know that the absolute value of a number is        Students understand that the absolute value function
the value of the number ignoring the sign; or      in Visual Basic returns the number without the sign.
is the distance of the number from 0.              Ex. System.Math.Abs((-67))
Returns 67

Understand Derived Quantities

N.MR.07.02          Solve problems involving derived quantities        Students can create a program that allows the user
such as density, velocity and weighted             to enter the points a student earns on four projects
averages.                                          and two tests.
Ex. Part of the program
Select case totalPointsAccumulator
Case is <= 360
Case is >= 320

Understand and Solve Problems Involving Rates, Ratios, and Proportions

N.FL.07.03          Calculate rates of change including speed.         Rate of Pay program
Ex. Students create a program to allow users to input
the hours worked and rate of pay per hour and
then compute wages.

N.MR.07.04          Convert ratio quantities between different         Students create a program to convert Fahrenheit to
systems of units, such as feet per second to       Celsius temperature.
miles per hour.
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Compute with Rational Numbers

N.FL.07.07          Solve problems involving operations with           Every computer programmer uses operations with
integers.                                          integers.
Ex. Age Program
age = age + 1 adds the integer 1 to the contents
of the Integer age variable, then assigns the
result to the age variable.

N.FL.07.08          Add, subtract, multiply and divide positive        Every computer program uses positive and negative
and negative rational numbers fluently.            rational numbers.
Ex. Mini Calculator program
Students write a program to simulate a calculator
involving the four operations of rational numbers.
N.FL.07.09          Estimate results of computations with              Every programmer estimates the results of
rational numbers.                                  computations with rational number for programming
accuracy.

Understand Real Number Concepts
N.ME.08.02          Understand meanings for zero and negative          Data Type
integer exponents.                                 Students understand the meaning of negative
exponents in data type variables.
Ex. Single: a number with a decimal place
-45              38
Range = -1.401298 x 10 to = -3.402823x10

When converting from decimal to binary system,
0
students understand that 2 = 1

N.ME.08.03          Understand that in decimal form, rational          In programming, all rational numbers are converted
numbers either terminate or eventually             to decimal forms and truncated to specified decimal
repeat, and that calculators truncate or           places as needed.
round repeating decimals; locate rational
numbers on the number line; know fraction
forms of common repeating decimals.
N.ME.08.04          Understand that irrational numbers are             Students understand that Pi is an irrational number
those that cannot be expressed as the              that cannot be expressed as the quotient of two
quotient of two integers, and cannot be            integers.
represented by terminating or repeating
decimals; approximate the position of
familiar irrational numbers.
Solve Problems

N.MR.08.07          Understand percent increase and percent            Students can write a program to find percent
decrease in both sum and product form.             increase and therefore must know the formula.
Ex. Payroll program
Write a program to determine an employee’s new
hourly pay given the employee’s current hourly
pay and raise.
Private Function GetNewpay(Byval current As
Double,_ Byval rate As Double)AsDouble
raise = current * rate
newPay = current + raise.
Return newPay
End Function

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N.MR.08.08          Solve problems involving percent increases      Ex. Calculate the new price of an item with a 5%
and decreases.                                      price increase.
Private Function CalcNew(ByVal price as
Double)as Double
Return price + price * .05
End Function
N.FL.08.09          Solve problems involving compounded             Students write a program to find compound interest
interest or multiple discounts.                 Ex. Private Sub btnCalculate_Click1
Amount = (principal
*(1+rate/periods))pow(periods*years))
msgbox(amount.ToString(C”2”))

N.MR.08.10          Calculate weighted averages such as             Grade book program
course grades, consumer price indices and       Ex. Students can create an application that displays
sports ratings.                                     the total credit hours and GPA for a student in
one semester using the following data:
A = 4 points, B= 3 points, C = 2 points,
D = 2 points and F = 1 point

N.FL.08.11          Solve problems involving ratio units, such      Students can create a program that calculates a
as miles per hour, dollars per pound or         customer’s water bill.
persons per square mile.                        Ex. Create an a program the calculates and displays
the number of gallons of water used and the total
charge. The charge for the water is \$1.75 per
gallon.

L2                  STANDARDS                                             CTE APPLICATION and PRACTICE

CALCULATION, ALGORITHMS, AND ESTIMATION

L2.1                                       Calculation Using Real and Complex Numbers

L2.1.1              Explain the meaning and uses of weighted        Students can write programs for course grades.
averages (e.g., GNP, consumer price index,      Ex. Grade Book program
msgLabel.Text = “Excellent”

L2.1.6              Recognize when exact answers aren’t             Students format numbers by using the ToString
always possible or practical. Use               function.
appropriate algorithms to approximate           Ex. commissionLabel.Text =
solutions to equations (e.g., to approximate                               commission.ToString(“C2”)
square roots).                                      If the commission variable contains the number
1250, the statement assigns the string
“\$1250.00” to Text property of the
commissionLabel

L2.2                                                       Sequences and Iteration

L2.2.3              Use iterative processes in such examples        Nested loops
as computing compound interest or               Ex. For each month in year
applying approximation procedures.                  For each day in month
msgbox(day)
Next day
Next month

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L3                  STANDARDS                                                CTE APPLICATION and PRACTICE

MEASUREMENT AND PRECISION
L3.1                                        Measurement Units, Calculations, and Scales

L3.1.1              Convert units of measurement within and            Students can convert from the decimal system to the
between systems; explain how arithmetic            binary system.
operations on measurements affect units,           Ex. 15 in decimal system = 11112 binary system
and carry units through calculations
correctly.
L3.2                                                         Understanding Error

L3.2.1              Determine what degree of accuracy is               Calculations involving decimal variables are not
reasonable for measurements in a given             subject to the small rounding errors that may occur
situation; express accuracy through use of         when using Double or Single variables. When the
significant digits, error tolerance, or percent    application contains money it is best to use the
of error; describe how errors in                   Decimal data type.
measurements are magnified by                      Ex. Formatting Decimals
computation; recognize accumulated error               Decimal.ToString(“C2”) = currency, 2 decimal
in applied situations.                                 Places

L3.2.2              Describe and explain round-off error,              Data type
rounding, and truncating.                          Students understand rounding off and truncating
when using ToDecimal function or INTEGER
function.
L3.2.3              Know the meaning of and interpret                  Students understand that an error in writing
statistical significance, margin of error, and     programs can lead to errors in outcomes.
confidence level.                                  Garbage in Garbage out

L4.1                                                      Mathematical Reasoning

L4.1.1              Distinguish between inductive and                  Deductive Reasoning:
deductive reasoning, identifying and                  Used throughout the programming course when
providing examples of each.                            writing and developing programs and doing flow
charts.
Inductive Reasoning : Pseudocode
Uses short phrases to describe the steps a
procedure needs to accomplish its goal.

L4.1.2              Differentiate between statistical arguments        Logical Operator Unit
(statements verified empirically using             Students understand and use rules of logic and
examples or data) and logical arguments            logical arguments when writing programs.
based on the rules of logic.                       Logical operators: & (and),! (not), | (or)

L4.2                                                   Language and Laws of Logic

L4.2.1              Know and use the terms of basic logic (e.g.,       Logical Operators Unit
proposition, negation, truth and falsity,          Students understand all truth tables for all logical
implication, if and only if, contrapositive, and   statements used in programming.
converse).                                         Ex. If NOT isinsured Then
This condition evaluates to True when the
Boolean isInsured variable contains the Boolean
value False, otherwise, it evaluates to False.

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L4.2.2              Use the connectives “not,” “and,” “or,” and       Logical Operators Unit
“if…, then,” in mathematical and everyday         Students understand all truth tables for all logical
settings. Know the truth table of each            statements used in programming.
connective and how to logically negate            Ex. Math conditional formatting
statements involving these connectives.               A salesperson would get a raise if he gets an A
rating and sells more than \$10000. This would be
true only if both conditions are true.
rating = “A’ AndAlso sales > 10000

L4.2.3              Use the quantifiers “there exists” and “all” in   Logical Operators Unit
mathematical and everyday settings and            Students understand all truth tables for all logical
know how to logically negate statements           statements used in programming.
involving them.                                   Ex. IF THEN ELSE
If the sales are greater than1500
commission = sales * .02 (true)
else commission = sales *.01 (false)
End if

L4.2.4              Write the converse, inverse, and                  Discuss cause and effect of studying and doing well.
contrapositive of an “If…, then…”                 Ex.             If I score well on all projects, then I
statement. Use the fact, in mathematical                          will understand the concepts of
and everyday settings, that the                                   programming.
contrapositive is logically equivalent to the     Converse:        If I understand all concepts of
original while the inverse and converse are                       programming, then I will score well
not.                                                              on all projects.
Inverse:        If I do not score well on the projects,
then I do not understand the
concepts of programming.
Contrapositive; If I do not understand the concepts
of programming, then I will not score
well on the projects.

L4.3                                                                  Proof
L4.3.1              Know the basic structure for the proof of an      Logical Operators Unit
“If…, then…” statement (assuming the              Ex. IF THEN ELSE
hypothesis and ending with the conclusion)            Calculate and display an employee’s gross pay.
and that proving the contrapositive is                If hoursWorked >=0. AndAlso hoursWorked <=
equivalent.                                           40.0, then gross pay = hoursWorked * 10.65

L4.3.2              Construct proofs by contradiction. Use            Logical Operators Unit
counter examples, when appropriate, to            Ex. IF THEN ELSE
disprove a statement.                                 Find the Mouse game
If randomNumber = 1 Then
PictureBox1.image = mousePictureBox.Image
Else
Picturebox1.Image = notHerePictureBox.Image
End if

Find Volume and Surface Area

M.TE.06.03          Compute the volume and surface area of            Students can create programs to find surface area
cubes and rectangular prisms given the            and volume of rectangular prisms.
lengths of their sides, using formulas.           Ex. Create a program that allows the user to enter
the length, width and height of a swimming pool
and then calculates the number of cubic feet of
water the pool will contain.

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A1                  STANDARDS                                              CTE APPLICATION and PRACTICE

EXPRESSIONS, EQUATIONS, AND INEQUALITIES

A1.1                      Construction, Interpretation, and Manipulation of Expressions (linear,
quadratic, polynomial, rational, power, exponential, logarithmic, and
trigonometric)
A1.1.1              Give a verbal description of an expression       Students can write and interpret programming codes.
that is presented in symbolic form, write an     Ex. If “reno” = cityTextBox.Text.ToLowere Then
algebraic expression from a verbal                   compares the lowercase letters “reno” to the
description, and evaluate expressions given          lowercase version of the string stored in the
values of the variables.                             cityTextBox.

A1.2                    Solutions of Equations and Inequalities (linear, exponential, logarithmic,
A1.2.1              Write and solve equations and inequalities       Students use equations and inequalities for specific
with one or two variables to represent           programs.
mathematical or applied situations.              Ex. A company wants an application that the
sales manager can use to display the average
amount the company sold during the prior year.
salesCounter = salesCounter +1
salesAccumulator = salesAccumulator + sales
If sale Counter > 0
then salesAverage = salesAccumulator
/Convert.ToDecimal
(salesCounter)
averageLabel.Text = saleAverage.ToString
A1.2.4              Solve absolute value equations and               Students use the absolute value function in various
inequalities (e.g., solve │x - 3│ ≤ 6) and       programs
justify.                                         Ex. System.Math.Abs((-34.8))
A1.2.9              Know common formulas (e.g., slope,               Students know a variety of formulas to write
distance between two points, quadratic           programs given specific information.
formula, compound interest, distance = rate      Ex. Write a program to calculate monthly payments
· time), and apply appropriately in                  and interest on a loan using interest rates of 5%
contextual situations.                               through 10% and terms of 2,3,4,or 5 years.
For rate As Double = 0.05 To 0.01 Step 0.01
monthly payment =
Financial.PMT(rate/12,term*12,principal)
paymentsLabel.Text = paymentslabel.Text_
&rate.ToString(“PO”) & “->”&monthylyPayment.
ToString (“C2”)_
&ControlChars.NewLine
Next rate
A2                  STANDARDS                                               CTE APPLICATION and PRACTICE

FUNCTIONS

A2.1                               Definitions, Representations, and Attributes of Functions

A2.1.2              Read, interpret, and use function notation       Students can create a program that will display the
and evaluate a function at a value in its        multiplication tables when a user inputs a number
domain.                                          and the output is the result of multiplying that number
by the numbers 1 through 9
Ex. For count as integer = 1 to 9
msgbox(“y=” & input * count)
Next count
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A2.1.5              Recognize that functions may be defined           For…Next Statements (Loops)
recursively. Compute values of and graph          Ex. Dim x As Decimal
simple recursively defined functions (e.g.,           For x = .05D To .1D Step .01D
f(0) = 5, and f(n) = f(n-1) + 2).                         ratelabel.Text = rateLabel.Text &
x.ToString(“PO”)_ & controlChars.NewLine
Next x
Displays 5%,6%,7%,8%,9%,10%

A2.4                                                    Lines and Linear Functions

A2.4.3              Relate the coefficients in a linear function to   Collision Testing in a Pong game
the slope and x- and y-intercepts of its          Ex. In a Pong game, when the ball collides with the
graph.                                                border or a paddle, the programmer must find the
vector associated with the original movement and
invert the angle by finding the perpendicular
vector coordinates.
A2.10                                                     Trigonometric Functions

A2.10.2             Use the relationship between degree and           In programming, students convert all radian
radian measures to solve problems.                measurements to degree measurements.

A3                  STANDARDS                                               CTE APPLICATION and PRACTICE

MATHEMATICAL MODELING

A3.1                Models of Real-world Situations Using Families of Functions Example: An
initial population of 300 people grows at 2% per year. What will the population be in
10 years?

A3.1.1              Identify the family of functions best suited      Mathematical modeling
for modeling a given real-world situation         Students can write a program that takes user input
[e.g., quadratic functions for motion of an       and places it in the appropriate function to meet
object under the force of gravity or              desired outcome.
exponential functions for compound
interest. In the example above, recognize
that the appropriate general function is
t
exponential (P = P0a )].
A3.1.2              Adapt the general symbolic form of a              Mathematical modeling
function to one that fits the specifications of   Students can write a program that takes user input
a given situation by using the information to     and places it in the appropriate function to meet
replace arbitrary constants with numbers.         desired outcome.
In the example above, substitute the given        Ex. A sales manager wants an application that
values P0 = 300 and a = 1.02 to obtain P =            determines the number of salespeople selling
t
300(1.02) .                                           above a specified amount. To accomplish this:
For Each salesAmount As Integer In sales
If salesAmount > search For Then
Counter =m Counter + 1
End if
Next Sales Amount.

A3.1.3              Using the adapted general symbolic form,          Mathematical modeling
draw reasonable conclusions about the             Students can write a program that takes user input
situation being modeled. In the example           and places it in the appropriate function to meet
above, the exact solution is 365.698, but for     desired outcome.
this problem, an appropriate approximation        Ex. In the above example, the sales manager can
is 365.                                               input the specified amounts.

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A.PA.06.01          Solve applied problems involving rates,           Rate of Pay program
including speed.                                  Ex. Students write a program that allows the user to
input hours worked and rate of pay, then
computes wages earned including overtime pay.
Understand the Coordinate Plane

A.RP.06.02          Plot ordered pairs of integers and use            All positioning of images on the screen is indicated
ordered pairs of integers to identify points in   by vector ordered pairs.
all four quadrants of the coordinate plane.       Ex. A triangle with three vertices
Vector 1 (0,1,5), Vertex 2 (-0.5,0,0.7),
Vector 3 (1,1, 0.2)

Use Variables, Write Expressions and Equations, and Combine Like Terms

A.FO.06.03          Use letters with units, to represent              Choosing variables that make sense
quantities in a variety of contexts.              When writing programs and choosing variables to
represent data, students must choose a variable that
makes sense for the program.
Ex. When writing a program to calculate age,
a = age is an appropriate variable.

A.FO.06.04          Distinguish between an algebraic                  Expression: Aspect Ratio
expression and an equation.                                  aspectRatio = (float)width/(float)height
Equation : Any algebraic equation use in
programming
bonus = sales * .05

A.FO.06.05          Use standard conventions for writing              All algebraic expressions are written in standard
algebraic expressions.                            algebraic order and all expressions are solved using
the standard order of operation.

A.FO.06.06          Represent information given in words using        Visual Basic Programming
algebraic expressions and equations.              Ex. Convert the contents of an Integer variable
named testScore to String, and then assign the
result to the totalLabel’s Text property.
totalLabel.Text = Convert.ToString(testScore)

Represent Linear Functions Using Tables, Equations, and Graphs
A.RP.06.08          Understand that relationships between             Students can write programs to display data in a
quantities can be suggested by graphs and         table.
tables.                                           Ex. The president of the Harvey Company wants an
application that performs the payroll calculations
including employee’s weekly gross pay, Social
Security and Medicare tax, federal withholding
tax and net pay to be displayed in a table.

A.RP.06.10          Represent simple relationships between            Students can write programs, using appropriate
quantities using verbal descriptions,             equations, and display the information in a table
formulas or equations, tables and graphs.         spreadsheet.
Ex. Students use the TOE (Task, Object, Event)
chart to create order forms including name,
address, phone numbers of the customer, price
and total number of products ordered and total
amount of order including sales tax.

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Apply Basic Properties of Real Numbers in Algebraic Contexts

A.PA.07.11          Understand and use basic properties of real     Students understand all basic properties of real
numbers: additive and multiplicative            numbers and the order of operation for programming
inverses commutativity, associativity, and
the distributive property of multiplication
Understand the Concept of Non-linear Functions Using Basic Examples

A.PA.08.02          For basic functions, describe how changes       Any program involving user input changes the value
in one variable affect the others.              of the output.

Understand Solutions and Solve Equations, Simultaneous Equations and
Linear Inequalities
A.FO.08.10          Understand that to solve the equation f(x)      Pay Raise program allows user input of rate of raise
means to find all values of x for which the     and then computes the wages for all employees.
equation is true.                               Ex. newHourPay = GetNewPay(pay,raise)
newPaylabel.Text = newHourPay.ToString(“C2”)
End Sub

G1                     STANDARDS                                         CTE APPLICATION and PRACTICE

FIGURES AND THEIR PROPERTIES

G1.2                                                  Triangles and Their Properties

G1.2.2              Construct and justify arguments and solve       Collision Testing in a Pong game
multi-step problems involving angle             Ex. In a Pong game, when the ball collides with the
measure, side length, perimeter, and area           border or a paddle, the programmer must find the
of all types of triangles.                          vector associated with the original movement and
invert the angle by finding the perpendicular
vector coordinates.

G1.4.1              Solve multi-step problems and construct         Students can create programs to find the area and
proofs involving angle measure, side length,    perimeter of various polygons.
diagonal length, perimeter, and area of         Ex. Create a program that allows a user to input the
squares, rectangles, parallelograms, kites,         length and width of a rectangle and the price of a
and trapezoids.                                     square foot of tile, then calculate and display the
total area and the total price of the tile.

G1.5                                              Other Polygons and Their Properties

G1.5.2              Know, justify, and use formulas for the         Students write programs to find perimeter and area
perimeter and area of a regular n-gon and       of various polygons and therefore must know the
formulas to find interior and exterior angles   formulas.
of a regular n-gon and their sums.              Ex. Area of a Square
Public Function CalculateArea () As Integer
Return _side * _side
End Function

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G1.6                                                    Circles and Their Properties

G1.6.1              Solve multi-step problems involving             Students create a program to find the area and
circumference and area of circles.              circumference of circles.
Ex. Create a program to calculate area of a circle.
AreaLabel.Text = Convert.ToString(area)

G2                     STANDARDS                                         CTE APPLICATION and PRACTICE

RELATIONSHIPS BETWEEN FIGURES
G2.2                          Relationships Between Two-dimensional and Three-dimensional
Representations
G2.2.1              Identify or sketch a possible three-            3D programming
dimensional figure, given two-dimensional       Students can import 3D data in a 2D screen using
views (e.g., nets, multiple views). Create a    WorldMatrix. They can also rotate the image for
two-dimensional representation of a three-      multiple views.
dimensional figure.
G3                  STANDARDS                                          CTE APPLICATION and PRACTICES

TRANSFORMATIONS OF FIGURES IN THE PLANE

G3.1                                    Distance-preserving Transformations: Isometries

G3.1.1              Define reflection, rotation, translation, and   Importing 3-D data from a model file on your 2D
glide reflection and find the image of a        screen.
figure under a given isometry.                  Ex. To rotate, scale and position a rocket in3D
studio Max use WorldMatrix
Matrix.CreateRotationX(MathHelper.Pi/2*
Matrix.CreateScale(2.5f)*
Matrix.CreateTranslation(rocketPositiion);

G3.1.2              Given two figures that are images of each       Students can describe the transformation used in
other under an isometry, find the isometry      image position and placement.
and describe it completely.

G3.1.3              Find the image of a figure under the            When programming, more than one isometry is
composition of two or more isometries and       usually used when positioning and placement of an
determine whether the resulting figure is a     image on a screen.
reflection, rotation, translation, or glide
reflection image of the original figure.
G3.2                                      Shape-preserving Transformations: Isometries

G3.2.1              Know the definition of dilation and find the    Converting 3D data to a 2D screen is called
image of a figure under a given dilation.       projection (dilation). The ProjectionMatrix converts
the matrix values to a 2D screen and specifies how
deep one can look into the screen.

G3.2.2              Given two figures that are images of each       Converting 3D images to a 2D screen
other under some dilation, identify the         Ex. Use the Matrix CreateScale(2.5f)*
center and magnitude of the dilation.

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Understand the Concept of Congruence and Basic Transformations

G.TR.06.03          Understand the basic rigid motions in the       Importing 3-D data from a model file on a 2D screen.
plane (reflections, rotations, translations).   Ex. To rotate, scale and position a rocket in3D
Relate these to congruence, and apply               studio Max use WorldMatrix
them to solve problems.                             Matrix.CreateRotationX(MathHelper.Pi/2*
Matrix.CreateScale(2.5f)*
Matrix.CreateTranslation(rocketPositiion);

G.TR.06.04          Understand and use simple compositions of       Importing 3-D data from a model file on a 2D screen.
basic rigid transformations.                    Ex. To rotate, scale and position a rocket in3D
studio Max use WorldMatrix
Matrix.CreateRotationX(MathHelper.Pi/2*
Matrix.CreateScale(2.5f)*
Matrix.CreateTranslation(rocketPositiion);

Understand the Concept of Similar Polygons and Solve Related Problems

G.TR.07.03          Understand that in similar polygons,            3D programming
corresponding angles are congruent and          Students can write a code to scale images from 3D
the ratios of corresponding sides are equal;    data to a 2D screen and understand that the resulting
understand the concepts of similar figures      image is similar to the original image with sides in
and scale factor.                               proportion and equal angles.

G.SR.08.03          Understand the definition of a circle; know     Students create a program to find the area and
when to use the formulas for circumference      circumference of circles.
and area of a circle to solve problems.         Ex. Create a program to calculate area of a circle.
AreaLabel.Text = Convert.ToString(area)

G.SR.08.05          Solve applied problems involving areas of       Students create a program to find the area and
triangles, quadrilaterals and circles.          circumference of circles.
Ex. Create a program to calculate area of a circle.
AreaLabel.Text = Convert.ToString(area)

Understand and Apply Concepts of Transformation and Symmetry

G.TR.08.09          Understand the definition of a dilation from    Converting 3D data to a 2D screen is called
a point in the plane and relate it to the       projection (dilation). The ProjectionMatrix converts
definition of similar polygons.                 the matrix values to a screen and specifies how deep
one can look into the screen.

G.TR.08.10          Understand and use reflective and               Importing 3-D data from a model file on your 2D
rotational symmetries of two-dimensional        screen.
shapes and relate them to transformations       Ex. To rotate, scale and position a rocket in3D
to solve problems.                                  studio Max use WorldMatrix
Matrix.CreateRotationX(MathHelper.Pi/2*
Matrix.CreateScale(2.5f)*
Matrix.CreateTranslation(rocketPositiion);
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S2                     STANDARDS                                          CTE APPLICATION and PRACTICE

BIVARIATE DATA - EXAMINING RELATIONSHIPS

S2.1                                                    Scatterplots and Correlation

S2.1.4              Differentiate between correlation and          Students understand that there is a strong correlation
causation. Know that a strong correlation      between time spent on creating a program and the
does not imply a cause-and-effect              quality of the program. Waiting until the last minute
relationship. Recognize the role of lurking    to finish a program can put undo pressure on the
variables in correlation.                      programmer and can result in a poor quality program.
S3                     STANDARDS                                           CTE APPLICATION and PRACTICE

SAMPLES, SURVEYS, AND EXPERIMENTS

S3.1                                                   Data Collection and Analysis

S3.1.1              Know the meanings of a sample from a           Customer Satisfaction
population and a census of a population,       Ex. Students understand that the needs and
and distinguish between sample statistics          requirements of a customer must be met for
and population parameters.                         customer satisfaction, therefore, using a TOE
(Task, Object, Event) chart is useful in planning
the application.
S3.1.2              Identify possible sources of bias in data      Customer Satisfaction
collection and sampling methods and            Ex. There is a self bias involved in programming that
simple experiments; describe how such bias         must be overcome to meet the customer’s needs
can be reduced and controlled by random            and requirements when planning a program.
sampling; explain the impact of such bias          A client might have different requirements than
on conclusions made from analysis of the           what the programmer would like to do.
data; and know the effect of replication on
the precision of estimates.
S4                     STANDARDS                                          CTE APPLICATION and PRACTICE

PROBABILITY MODELS AND PROBABILITY CALCULATION

Understand Probability Concepts for Simple and Compound Events

D.PR.08.06          Understand the difference between              Lottery Program
independent and dependent events and           Students understand that the numbers generated
recognize common misconceptions                randomly are mutually exclusive events and that the
involving probability.                         output must not contain any duplicate numbers.
References: XNA Programming – Benjamin Nitschke
Microsoft: Visual basic 2008 – Diane Zak

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