Career Technical Education
Rationale for High School Math-related Credit
In order to ensure that all students meet the requirements of the Michigan merit standard as defined in Public Acts 123 and 124 of 2006, Career Technical Education classes must be able to demonstrate that they can enable students to fulfill core requirements in English Language Arts, math and science as part of their CTE program. These classes operate under the following assumptions:
1. Academic content is seamlessly woven into the Career Technical Education course.
2. Students apply and are assessed on the academic skills they have learned in their classrooms.
3. Student activities and assessments will integrate core academic concepts and meet the rigor of the content expectations as defined by the Michigan Department of Education.
4. Students have multiple learning styles and will benefit from multiple modes of delivery.
Public Act 124, section 1278a. (1) states that, in order to receive a high school diploma, a pupil must complete the following:
“(i) At least 4 credits in mathematics that are aligned with subject area content expectations developed by the department and approved by the state board under section 1278b, including completion of algebra I, geometry and algebra II…and an additional mathematics credit, such as trigonometry, statistics, precalculus, applied math, accounting, business math or a retake of algebra II. Each pupil must successfully complete at least 1 mathematics course during his or her final year of high school enrollment”.
Further, section 1278a (4) states that “ A pupil is considered to have completed a credit if the pupil successfully completes the subject area content expectations or guidelines developed by the department that apply to the credit”.
Jeremy Hughes, Deputy Superintendent and Chief Academic Officer of the Michigan Department of Education, addressed a gathering of educators in Grand Blanc, January of 2007, stating:
“The 4th math credit can be math or math-related, as determined by the school district, since the law does not specify the amount of credit required. For guidance, the district should identify the proportion of math GLCE’s or HSCE’s”.
Another pertinent document is the “Frequently Asked Questions” found at which specifically deals with the new high school graduation requirements. On page 27, question 4 states “ It is the discretion of the local district to determine what credits would count as math-related”. Question 5 states that “ The law requires a 4th mathematics credit aligned with the HSCE, but provides local districts with the flexibility to determine what counts for the 4th mathematics credit. The credit could be in a basic or an applied math area, such as Business Math, Accounting, Consumer Math, Applied Math, General Math, Pre-algebra, etc”.
Clearly, the law allows the granting of math-related credit in Career Technical Education programs. It is the prerogative of the local school district to determine which CTE classes are “math-related”.
For more information, please contact Monika Leasure, Regional Administrator for Career Technical Education at 586 228 3513.
Career Technical Education
High School Math-related Credit
District:Warren ConsolidatedContact: Anthony Wright
Career Technical Education Program: Marketing
Content Expectations identified for “math-related” district credit:
Teacher’s Phone:586 574 3250Building: Warren Mott
HSCECode* / Standard - ALGEBRA / My Teaching Supports this Content Expectation / Demonstration/reference
L1.1 / Number Systems and Number Sense
L1.1.1 / Know the different properties that hold in different number systems and recognize that the applicable properties change in the transition from the positive integers to all integers, to the rational numbers, and to the real numbers. / yes / Interest , mortgage, car loans, stocks
L1.1.3 / Explain how the properties of associativity, commutatively and distributivity as well as identity and inverse elements, are used in arithmetic and algebraic calculations / yes / Interest
i=p(l+rt)
L1.1.4 / Describe the reasons for the different effects of multiplication by, or exponentiation of, a positive number by a number less than 0, a number between 0 Nd 1, and a number greater than 1. / Yes / Compounding interest
r nt
=P(1+n)
L1.2.4 / Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media. / Yes / Market share, stock market game, circle graphs, bivariate data
L2.1 / Calculation Using Real & Complex Numbers
L2.1.1 / Explain the meaning and uses of weighted averages (e.g., GNP, consumer price index, grade point average). / Yes / Performance evaluations
L2.1.6 / Recognize when exact answers aren’t always possible or practical. Use appropriate algorithms to approximate solutions to equations (e.g., to approximate square roots). / Yes / Supply & demand estimates
A1.1 / Construction, Interpretation, and Manipulation of Expressions (linear, quadratic, polynomial, rational, power, exponential, and logarithmic)
A1.1.1 / Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables. / Yes / Pricing mark-ups
Employability Unit
A1.2 / Solutions of Equations and Inequalities (linear, exponential, logarithmic, quadratic, power, polynomial, and rational) / Break-even analysis
A1.2.1 / Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations. / Yes / Mark up equations
A1.2.2 / Associate a given equation with a function whose zeros are the solutions of the equation. / Yes / Production management
Hamburger & pizza
A1.2.3 / Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately. / Yes / Payroll, break-even analysis
C(x)=2.50x+250
R(x)=5.00y
A1.2.8 / Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable. Justify steps in the solution. / Yes / Payroll, interest
A2.1 / Definitions, Representations, and Attributes of Functions
A2.1.2 / Read, interpret, and use function notation and evaluate a function at a value in its domain. / Yes / Break-even, stock, graphs
A2.1.3 / Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations. / Yes / Marketing, frequency table
A2.1.4 / Recognize that functions may be defined by different expressions over different intervals of their domains. / Yes / Stocks, scarcitgo surplus
A2.1.5 / Recognize that functions may be defined recursively. Compute values of and graph simple recursively defined functions (e.g., f(0) = 5, and f(n) = f(n-1) + 2). / Yes / Payroll and interest, stock ratios and inventory plan
A2.3 / Families of Functions (linear, quadratic, polynomial, power, exponential, and logarithmic)
A2.3.1 / Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize that different families of functions have different asymptotic behavior at infinity and describe these behaviors. / Yes / Linear or direct & inverse variation
A2.3.2 / Describe the tabular pattern associated with functions having constant rate of change (linear) or variable rates of change. / Yes / Scheduling
A2.4 / Lines and Linear Functions
A2.4.2 / Graph lines (including those of the form x = h and y = k) given appropriate information. / Yes / Market share, graphs
A3.1 / Models of Real-world Situations Using Families of Functions (linear, quadratic, exponential and power)
Example: An initial population of 300 people grows at 2% per year. What will the population be in 10 years?
A3.1.2 / Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers. In the example above, substitute thegiven values P0 = 300 and a = 1.02 to obtain P = 300(1.02)t. / Yes / Interest, forecasting, stock and inventory turnover
A3.1.3 / Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled. In the example above, the exact solutionis 365.698, but for this problem, an appropriateapproximation is 365. / Yes / Throughout, sales, tax, etc…
S2.1 / Scatter plots and Correlation
S2.1.1 / Construct a scatter plot for a bivariate data set with appropriate labels and scales. / Yes / Payroll, break-even analysis, market research
S2.1.2 / Given a scatter plot, identify patterns, clusters, and outliers. Recognize no correlation, weak correlation, and strong correlation. / Yes / Market research
S2.1.3 / Estimate and interpret Pearson’s correlation coefficient for a scatter plot of a bivariate data set. Recognize that correlation measures the strength of linear association. / Yes / Look at graphs
S2.1.4 / Differentiate between correlation and causation. Know that a strong correlation does not imply a cause-and-effect relationship. Recognize the role of lurking variables in correlation. / Yes / Mark downs - Law of diminishing, marginal utility
HSCE Code / STANDARD L1
Reasoning About Numbers,
Systems, and Quantitative Situations / GEOMETRY
L2.1 / Calculation Using Real and Complex Numbers
L2.1.6 / Recognize when exact answers aren’t always possible or practical. Use appropriate algorithms to approximate solutions to equations (e.g., to approximate square roots). / Yes / Supply & demand, (range) y affecting the x (domain)
L3.1 / Measurement Units, Calculations, and Scales
L3.1.1 / Convert units of measurement within and between systems; explain how arithmetic operations on measurements affect units, and carry units through calculations correctly. / Yes / World currency
L4.1 / Mathematical Reasoning
L4.1.1 / Distinguish between inductive and deductive reasoning, identifying and providing examples of each. / Yes / Does not distinguish labor law, but uses examples (48 hr. rule)
L4.1.2 / Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic. / Yes / Survey w/marketing recommendations
G1.4 / Quadrilaterals and Their Properties
G1.4.1 / Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids. / Yes / Store display by area, no proof
HSCE Code / STANDARD L1
Reasoning About Numbers, Systems and Quantitative Literacy / ALGEBRA II
STANDARD L2
Calculation, Algorithms And Estimation
L2.1 / Calculation Using Real and Complex Numbers
L2.1.6 / Recognize when exact answers aren’t always possible or practical; use appropriate algorithms to approximate solutions to equations (e.g., to approximate square roots). / Yes / Rounding with turnover in stocks
L2.2 / Sequences and Iteration
L2.2.3 / Use iterative processes in such examples as computing compound interest or applying approximation procedures. / Yes / Interest I=P(1+rt)
STANDARD L3
Measurement and Precision
L3.2 / Understanding Error
L3.2.2 / Describe and explain round-off error, rounding, and truncating. / Yes / Rounding with turnover in stocks
A1.2 / Solutions of Equations and Inequalities (linear, exponential, logarithmic, quadratic, power, polynomial, rational, and trigonometric)
A1.2.9 / Know common formulas (e.g., slope, distance between two points, quadratic formula, compound interest, distance = rate · time), and apply appropriately in contextual situations. / Yes / Compound interest, advertising, return on investment
STANDARD A3
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?
A3.1.2 / Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers. In the example above, substitute the given values P0 = 300 and a = 1.02 to obtain P = 300(1.02)t. / Yes / Various formulas work
A3.1.3 / Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled. In theexample above, the exact solution is 365.698, but forthis problem an appropriate approximation is 365. / Yes / Stock, decimals, productive management rounding
STANDARD S1
Univariate Data – Examining Distributions
S1.1 / Producing and Interpreting Plots
S1.1.1 / Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics. / Yes / Scatter plots and tables
S1.1.2 / Given a distribution of a variable in a data set, describe its shape, including symmetry or skewness, and state how the shape is related to measures of center (mean and median) and measures of variation (range and standard deviation) with particular attention to the effects of outliers on these measures. / Yes / Ages, statistics, outspending, ER
S1.2 / Measures of Center and Variation
S1.2.1 / Calculate and interpret measures of center including: mean, median, and mode; explain uses, advantages and disadvantages of each measure given a particular set of data and its context. / Yes / Ages, statistics of production
S1.3 / The Normal Distribution
S1.3.1 / Explain the concept of distribution and the relationship between summary statistics for a data set and parameters of a distribution. / Yes / Surveys & analyzing data
STANDARD S3
Samples, Surveys, and Experiments
S3.1 / Data Collection and Analysis
S3.1.1 / Know the meanings of a sample from a population and a census of a population, and distinguish between sample statistics and population parameters. / Yes / Surveys & demographics
S3.1.2 / Identify possible sources of bias in data collection and sampling methods and simple experiments; describe how such bias can be reduced and controlled by random sampling; explain the impact of such bias on conclusions made from analysis of the data; and know the effect of replication on the precision of estimates. / yes / Surveys
S3.1.3 / Distinguish between an observational study and an experimental study, and identify, in context, the conclusions that can be drawn from each. / Yes / Survey, discount cards
STANDARD S4
Probability Models and Probability Calculation
S4.2 / Application and Representation
S4.2.2 / Apply probability concepts to practical situations, in such settings as finance, health, ecology, or epidemiology, to make informed decisions. / Yes / Marketing, strategies, surveys
S3.1.4* / Design simple experiments or investigations to collect data to answer questions of interest; interpret and present results. (Recommended) / Yes / Survey
S3.1.5* / Understand methods of sampling, including random sampling, stratified sampling, and convenience samples, and be able to determine, in context, the advantages and disadvantages of each. (Recommended) / Yes / Random Sampling
S3.1.6* / Explain the importance of randomization, double-blind protocols, replication, and the placebo effect in designing experiments and interpreting the results of studies. (Recommended) / Yes / Invoice checking
S3.2.2* / Read and interpret basic control charts; detect patterns and departures from patterns. (Recommended) / Yes / Market Shares
S4.1.3* / Design and carry out an appropriate simulation using random digits to estimate answers to questions about probability; estimate probabilities using results of a simulation; compare results of simulations to theoretical probabilities. (Recommended) / Yes / Toys in cereal, McDonald games
1
Conser/Leasure 2006 2007/High School Requirements/WC Marketing CTE and math