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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. D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 1 11/13/2010 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? D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 2 11/13/2010 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% D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 3 11/13/2010 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. D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 4 11/13/2010 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 D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 5 11/13/2010 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 D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 6 11/13/2010 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 D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 7 11/13/2010 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. D:\Docstoc\Working\pdf\29aa9d4e-c035-470f-8118-33a4d12a32bb.doc 8 11/13/2010