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

                                         Program Information
                                 District:   L’Anse Creuse
                                             F. V. Pankow Center
                         Program Name: Independent Living
                                             LCHS and LCHSN
                      CIP Code Number:
                         Career Pathway:
                        Instructor Name:     Virginia Fox and Diane McDonald
                                    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 and rational numbers are used throughout
                    different number systems and recognize          the course.
                    that the applicable properties change in the    Ex. Derrick has a nest egg of $1800 in a savings
                    transition from the positive integers to all        account where it is earning 1.2% interest.
                    integers, to the rational numbers, and to the       How much interest will he earn?
                    real numbers.
L1.2                                              Representations and Relationships

L1.2.1              Use mathematical symbols (e.g., interval        The symbols of +, -, x, /, and % are use throughout
                    notation, set notation, summation notation)     the course.
                    to represent quantitative relationships and     Ex. Managing bill payments
                    situations.                                         There is a 5% late fee on Casey’s rent paid after
                                                                             rd
                                                                        the 3 of the month. If Casey’s rent is $480 a
                                                                        month, how much would he owe if he paid his
                                                                                     th
                                                                        rent on the 5 of the month?

L1.2.4              Organize and summarize a data set in a          Students organize and summarize weekly, monthly
                    table, plot, chart, or spreadsheet; find        and yearly income and expenses in a bar graph and
                    patterns in a display of data; understand       on spreadsheets.
                    and critique data displays in the media.
L1.3                                            Counting and Probabilistic Reasoning
L1.3.2              Define and interpret commonly used              Students talk about the need for insurance in terms
                    expressions of probability (e.g., chances of    of the likelihood of an accident happening and the
                    an event, likelihood, odds).                    need for insurance.

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                                     Represent Rational Numbers as Fractions or Decimals

N.ME.06.05          Order rational numbers and place them on       Shopping comparison
                    the number line.                               Ex. Students find the unit price of products and
                                                                       decide which price is the “better buy”
                    Add and Subtract Integers and Rational Numbers

N.ME.06.08          Understand integer subtraction as the          Managing a checkbook
                    inverse of integer addition. Understand        Ex. Mike has $123.78 in his checking account. He
                    integer division as the inverse of integer         wrote a check to the phone company for $130.
                    multiplication.                                    What is Mike’s balance? 123.78 - 130 = - 6.22
                                                                   Ex. Sherry’s annual salary is $32,688. What is
                                                                       Sherry’s monthly salary? 32688 = $2724
                                                                                                 12
N.FL.06.10          Add, subtract, multiply and divide positive    Weekly Payroll
                    rational numbers fluently.                     Ex. Jim’s income for the week is $615.50. If the
                                                                       Social Security deduction is 7.2% of his gross
                                                                       income, how much money is deducted from his
                                                                       check for Social Security?
                                 Solve Decimal, Percentage and Rational Number Problems

N.FL.06.12          Calculate part of a number given the           Ex. Find the amount of interest to be paid on a
                    percentage and the number.                         $1000 loan at 3% interest for 4 years.
N.MR.06.13          Solve contextual problems involving            Ex. A car costs $17,456 plus a 6% sales tax. Find the
                    percentages such as sales taxes and tips.          amount of tax.
N.FL.06.14          For applied situations, estimate the answers   Sale prices
                    to calculations involving operations with      Ex. An I-pod is on sale for 33% off the original price.
                    rational numbers                                   If the I-pod costs $125.00, what is the estimated
                                                                       sale price?
N.FL.06.15          Solve applied problems that use the four       Weekly pay with overtime.
                    operations with appropriate decimal            Ex. Harry’s hourly rate is $12.00 plus time and half
                    numbers.                                           for overtime (any hours over 8 hours). Harry
                                                                       worked 15 hours on Monday, 8 hours on
                                                                       Tuesday, 12 hours on Wednesday, 9 hours on
                                                                       Thursday and 8 hours on Friday. What was
                                                                       Harry’s weekly salary?
                         Understand Rational Numbers and Their Location on the Number Line

N.ME.06.19          Understand that 0 is an integer that is        Ex. A zero balance in your checkbook means that
                    neither negative nor positive.                     you have neither a positive balance or a negative
                                                                       balance.
                                                     Understand Derived Quantities

N.MR.07.02          Solve problems involving derived quantities    Determining averages and weighted grades
                                                                       st
                    such as density, velocity and weighted           1 quarter = 40%
                                                                       nd
                    averages.                                        2 quarter = 40%
                                                                      Exam      = 20%
                                                    Compute with Rational Numbers

N.FL.07.07          Solve problems involving operations with       Balancing a checkbook
                    integers.                                      Ex. Brett’s balance in his checking account is
                                                                       $526.43. He writes a check to Costco for
                                                                       $112.35, a check to Verizon for $78.60 and a
                                                                       check to Briarwood Apartment Company for
                                                                       $430.00. He makes one deposit for $367.25.
                                                                       What is Brett’s ending balance?

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N.FL.07.08          Add, subtract, multiply and divide positive        Shopping
                    and negative rational numbers fluently.            Ex. A dress is on sale for 25% off the original price.
                                                                           Find the sale price of the dress.
N.FL.07.09          Estimate results of computations with              Estimating cost per serving
                    rational numbers.                                  Ex. Estimate the price per serving of meat if one
                                                                           pound of meat serves 3-4 people and the price
                                                                           per pound of the meat is $3.49.
                                                  Understand Real Number Concepts
N.ME.08.03          Understand that in decimal form, rational          Students understand that a calculator truncates
                    numbers either terminate or eventually             numbers after 10 decimal places. When finding unit
                    repeat, and that calculators truncate or           pricing, students must calculate and round off.
                    round repeating decimals; locate rational
                    numbers on the number line; know fraction
                    forms of common repeating decimals.
                                                                   Solve Problems

N.MR.08.07          Understand percent increase and percent            Percent increase in pay
                    decrease in both sum and product form.             Ex. Joyce worked for the Aztec Cookie company for
                                                                           2 years, earned $35,600 a year and was due for
                                                                           a raise. Her boss gave her a 1.5% increase in her
                                                                           pay. What was Joyce’s new annual salary?
                                                                           Sum:      35600 + ( .015 x 35600) = 36134
                                                                           Product: 1.015 x 35600           = 36134

N.MR.08.08          Solve problems involving percent increases         Ex. Anne’s phone bill, which is usually $55.00
                    and decreases.                                         increased $13.00 over the last month. What was
                                                                           the percent of increase in her phone bill ?

N.FL.08.09          Solve problems involving compounded                Ex. Angelo wants to buy a shirt that cost $38.99 and
                    interest or multiple discounts.                        is on sale for 20% off the original price. He also
                                                                           has an extra coupon for 15% off one item. Find
                                                                           the final price of the shirt with a 6% sales tax.

N.MR.08.10          Calculate weighted averages such as                Determining weighted grades and students averages
                                                                           st
                    course grades, consumer price indices and            1 quarter = 30%
                                                                           nd
                    sports ratings.                                      2 quarter = 30%
                                                                         Project     = 30%
                                                                         Exam        = 10%

N.FL.08.11          Solve problems involving ratio units, such         Price per ounce.
                    as miles per hour, dollars per pound or            Ex. A 45-ounce jar of pasta sauce cost $3.39. Find
                    persons per square mile.                               the price per ounce.
                                                                           Unit price = total price
                                                                                        number of units
                                                                              .075 = 3.39
                                                                                          45
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           Determining averages and weighted grades
                                                                           st
                    averages (e.g., GNP, consumer price index,           1 quarter = 35%
                                                                           nd
                    grade point average).                                2 quarter = 35%
                                                                         Exam       = 30%

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L2.1.6              Recognize when exact answers aren’t             Unit Pricing
                    always possible or practical. Use               Ex. A 12- ounce box of cereal cost $2.49. Find the
                    appropriate algorithms to approximate               cost per ounce.
                    solutions to equations (e.g., to approximate        Unit price = total price
                    square roots).                                                  number of units
                                                                        .2075      = 2.49
                                                                                      12
                                                                        Unit price = $0.21 per ounce
L2.2                                                      Sequences and Iteration

L2.2.3              Use iterative processes in such examples        Compound Interest
                    as computing compound interest or               Students find compound interest by using the
                    applying approximation procedures.              repetitive multiplying and addition process.
                                                                    Ex. Find the interest paid upon maturity of a three
                                                                        year 4% CD of $1000 compounded annually.

L3                  STANDARDS                                             CTE APPLICATION and PRACTICE

                                                   MEASUREMENT AND PRECISION
L3.2                                                   Understanding Error

L3.2.2              Describe and explain round-off error,           Students understand how to round off and that when
                    rounding, and truncating.                       using a calculator a large number is truncated after
                                                                    10 places.
                                                                    Ex. Unit Pricing
                                                                        A 20 ounce box of cereal costs $4. 89. Find the
                                                                        cost per unit.
                                                                        Unit price = $4.89
                                                                                       20
                                                                        Unit price = .2445 rounded off to $0.25
                                                                        Rounding up usually occurs when money is
                                                                        involved.
L4.1                                                      Mathematical Reasoning

L4.1.1              Distinguish between inductive and deductive     Inductive :
                    reasoning, identifying and providing               If I pay my bills on time, I will have a good credit
                    examples of each                                   score.
                                                                       If I have a good credit score, then I will be able
                                                                       to get a lower interest rate on a loan.
                                                                       If I pay my bills on time, I will be able to get a
                                                                       lower interest rate on a loan.
                                                                    Deductive:
                                                                       I pay my bills on time, therefore I am able to
                                                                       negotiate a low interest rate on a loan
L4.2                                                   Language and Laws of Logic

L4.2.4              Write the converse, inverse, and                Statement: If I come to class everyday, I will get
                    contrapositive of an “If…, then…”                          credit for attendance.
                    statement. Use the fact, in mathematical
                    and everyday settings, that the                 Converse: If I get credit for attendance, then I came
                    contrapositive is logically equivalent to the             to class everyday.
                    original while the inverse and converse are
                    not.                                            Inverse: If I don’t come to class everyday, I won’t get
                                                                            credit for attendance.

                                                                    Contrapositive: If I don’t get credit for attendance,
                                                                                    then I didn’t come to class everyday.
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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 interpret the formula I = PRT
                    that is presented in symbolic form, write an   Ex. Find the interest and the total amount of money
                    algebraic expression from a verbal                 Jane will have after 3 years of investing $500 in a
                    description, and evaluate expressions given        bank account that pays a 2% interest rate.
                    values of the variables.
A1.2                    Solutions of Equations and Inequalities (linear, exponential, logarithmic,
                                      quadratic, power, polynomial, and rational)
A1.2.1              Write and solve equations and inequalities     Interest Formula: I = PRT
                    with one or two variables to represent         Ex. Mary’s $300 account earned $18 in interest over
                    mathematical or applied situations.                a two year period. What was the interest rate on
                                                                       the account?
                                                                          18 = 300 x 2 x R
                                                                          18     = R
                                                                       300 x 2

A1.2.9              Know common formulas (e.g., slope,             Formula for Interest: I = PRT
                    distance between two points, quadratic         Formula for Area:     A=lxw
                    formula, compound interest, distance = rate
                    · time), and apply appropriately in
                    contextual situations.
                                                         Calculate Rates – Algebra

A.PA.06.01          Solve applied problems involving rates,        Unit pricing
                    including speed.                               Ex. A 30-ounce jar of salsa costs $2.69. Find the cost
                                                                       of one ounce.

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

A.FO.06.05          Use standard conventions for writing           All algebraic expressions are solved using standard
                    algebraic expressions.                         operating procedures and order of operation.

A.FO.06.06          Represent information given in words using     Ex. Carol wants to invest $500 in a savings account
                    algebraic expressions and equations.               that pays 2% interest. How much money will
                                                                       Carol have at the end of 4 years if she does not
                                                                       deposit or withdraw any money?
                                                                       I    = P + P xRxT
                                                                       540 = 500 + ( 500 x .02 x4)

                    Represent Linear Functions Using Tables, Equations, and Graphs
A.RP.06.08          Understand that relationships between          Students understand how to read and interpret
                    quantities can be suggested by graphs and      graphs to make informed decisions.
                    tables.                                        Ex. Comparing Auto Insurance coverage

A.RP.06.10          Represent simple relationships between         Students can read and interpret graphs to make
                    quantities using verbal descriptions,          informed decisions
                    formulas or equations, tables and graphs.      Ex. Graph of Job Trends: Percent change in
                                                                       employment 2004- 2014


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                                                                   Solve Equations

A.FO.06.13          Understand that multiplying or dividing both        Calculating Interest
                    sides of an equation by the same non-zero           Ex. Carlos earned $72 in interest over a three year
                    number creates a new equation that has the              period at 2%. How much was Carlos’s initial
                    same solutions.                                         investment?
                                                                              I = Px R xT
                                                                            72 = P x .02 x 3
                                                                            72 = 1200
                                                                           .06
                        Understand and Apply Directly Proportional Relationships and Relate to
                                          Linear Relationships - Algebra

A.AP.07.01          Recognize when information given in a               Information in a graph depicting the amount of
                    table, graph or formula suggests a directly         money invested monthly and interest earned is a
                    proportional or linear relationship.                direct proportion.


                     Understand and Solve Problems about Inversely Proportional Relationships

A.PA.07.09          Recognize inversely proportional                    Supply and Demand
                    relationships in contextual situations; know        Ex. As the price in a product increases, the demand
                    that quantities are inversely proportional if           for the product will decrease.
                    their product is constant.
                        Understand the Concept of Non-linear Functions Using Basic Examples

A.PA.08.02          For basic functions, describe how changes           Investments
                    in one variable affect the others.                  Ex. When investing money, if the interest rate
                                                                            increases/decrease, then the amount of money
                                                                            earned increase/decreases.

A.PA.08.03          Recognize basic functions in problem                Budgeting
                    context and represent them using tables,            Ex. Students calculate their monthly budget and
                    graphs and formulas.                                    represent that data in a bar graph.

G3                  STANDARDS                                              CTE APPLICATION and PRACTICES

                                        TRANSFORMATIONS OF FIGURES IN THE PLANE

                                       Draw and Construct Geometric Objects - Geometry

G.SR.07.01          Use a ruler and other tools to draw squares,        Students design a floor plan of an apartment or
                    rectangles, triangles and parallelograms            house using a ruler.
                    with specified dimensions.
                       Understand the Concept of Similar Polygons and Solve Related Problems

G.TR.07.04          Solve problems about similar figures and            Students draw a floor plan of an apartment or house
                    scale drawings.                                     and all furniture to scale.

S1                     STANDARDS                                              CTE APPLICATION and PRACTICE

                                        UNIVARIATE DATA - EXAMINING DISTRIBUTIONS



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S1.2                                                Measures of Center and Variation

S1.2.1              Calculate and interpret measures of center     Students discuss mean, mode and median when
                    including: mean, median, and mode; explain     comparing salaries of different companies.
                    uses, advantages and disadvantages of          Ex. In a certain company the salaries of the
                    each measure given a particular set of data        employees are as follows:
                    and its context.                                   Employee #1 - $ 2600.00
                                                                       Employee #2 - $ 1900.00
                                                                       Employee # 3 - $ 1760.00
                                                                       4 employees @ $ 900.00

                                                                       Mean = $1408.57
                                                                       Median = $900.00
                                                                       Mode = $ 900.00
                                                                   The students understand that in general the mean is
                                                                   most useful when data is evenly distributed, the
                                                                   median is often more useful when data is unevenly
                                                                   distributed and the mode is used to identify the most
                                                                   typical case.


S3                     STANDARDS                                           CTE APPLICATION and PRACTICE

                                             SAMPLES, SURVEYS, AND EXPERIMENTS

S3.1                                                  Data Collection and Analysis

S3.1.2              Identify possible sources of bias in data      Consumer buying
                    collection and sampling methods and            Advertising is a biased source of information
                    simple experiments; describe how such bias     because its purpose is to sell the product.
                    can be reduced and controlled by random        Consumer information includes a mixture of fact and
                    sampling; explain the impact of such bias      opinion. It’s up to the consumer to recognize the
                    on conclusions made from analysis of the       difference.
                    data; and know the effect of replication on
                    the precision of estimates.
S4                     STANDARDS                                          CTE APPLICATION and PRACTICE

                                 PROBABILITY MODELS AND PROBABILITY CALCULATION

                                 Understand the Concept of Probability and Solve Problems

D.PR.06.01          Express probabilities as fractions, decimals   Attendance
                    or percentages between 0 and 1; know that         0% attendance could mean a failing the class
                    0 probability means an event will not occur    100% attendance could mean credit for attendance
                    and that probability 1 means an event will
                    occur.
                                                       Represent and Interpret Data

D.RE.07.01          Represent and interpret data using circle      Students can read and interpret circle graphs and
                    graphs, stem and leaf plots, histograms,       histograms
                    and box-and-whisker plots and select           Ex. 70-20-10 rule circle graph
                    appropriate representation to address              70% of income on living expenses
                    specific questions.                                20% of income on investments
                                                                       10 % of income to pay off debt


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                                     Draw, Explain and Justify Conclusions Based on Data

D.AN.08.01          Determine which measure of central             The students understand that in general the mean is
                    tendency (mean, median, mode) best             most useful when data is evenly distributed, the
                    represents a data set.                         median is often more useful when data is unevenly
                                                                   distributed and the mode is used to identify the most
                                                                   typical case.




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