North Carolina Essential Standards Occupational Course of Study —

1. North Carolina Essential Standards Occupational Course of Study— Introduction to Mathematics (Math 9)

2. Number and Operations Understand rational numbers. OIM.N.1.1 Compare integers, decimals and fractions. OIM.N.1.2 Identify equivalent fractions, decimals, and percents. OIM.N.1.3 Identify absolute values and opposites. OIM.N.1.4 Use order of operations to simplify numerical expressions. OIM.N.1.5 Identify the greatest common factor and least common multiple. OIM.N.1.6 Use calculators to solve non-negative integer exponential expressions. Apply mathematical operations with rational numbers to solve problems. OIM.N.2.1 Use calculators to solve real world fraction and mixed number problems. OIM.N.2.2 Use calculators to solve real world decimal problems. OIM.N.2.3 Use calculators to solve real world integer problems. OIM.N.2.4 Use addition, subtraction, multiplication and division with calculators to evaluate algebraic expressions. Apply ratios, proportions and percents to solve problems. OIM.N.3.1 Use standard ratio notation for expressing ratios in part-to-part or a part-to-whole relationship. OIM.N.3.2 Use proportional reasoning to solve real world problems including recipes and unit rates. OIM.N.3.3 Use appropriate strategies to solve percent problems. OIM.N.3.4 Use scale factors and models to solve real world problems.

3. Measurement Apply time and measurement skills to solve problems. OIM.M.1.1 Use analog and digital clocks to tell time. OIM.M.1.2 Identify regularly scheduled activities based on time. OIM.M.1.3 Use time to solve problems. OIM.M.1.4 Use a calendar to solve problems. OIM.M.1.5 Use standard measurement tools to measure length, capacity, weight and temperature.

4. Algebra Apply algebraic properties to solve problems. OIM.A.1.1 Use appropriate strategies to solve one and two-step equations resulting in positive solutions in real world contexts. OIM.A.1.2 Represent inequalities in real world situations. OIM.A.1.3 Use appropriate strategies to solve one and two-step inequalities using whole numbers in real world contexts. OIM.A.1.4 Illustrate the distributive property using area models. OIM.A.1.5 Understand the use of the distributive property and combining like terms to write equivalent algebraic expressions. Understand patterns and relationships. OIM.A.2.1 Understand the use of the Cartesian Coordinate Plane to graph and identify ordered pairs. OIM.A.2.2 Represent patterns in real world situations using a table, graph, or equation. OIM.A.2.3 Identify the slope given a table, graph, or equation. OIM.A.2.4 Represent the equation of a line in slope-intercept form, given the slope and y-intercept. OIM.A.2.5 Represent a linear equation graphically given the slope and y-intercept. OIM.A.2.6 Represent ordered pairs and linear equations.

5. Statistics and Probability Understand data in terms of graphical displays, measures of center and range. OIM.S.1.1 Interpret data from circle graphs, bar graphs, pictographs, maps, and scatter plots, in context. OIM.S.1.2 Calculate the mean, median, mode and range of a data set. OIM.S.1.3 Classify type (positive, negative, no relation) of association of data in scatterplots. OIM.S.1.4 Represent trends on scatterplots when appropriate, with a linear model.

6. North Carolina Essential Standards Occupational Course of Study— High School Mathematics A (Math 10)

7. Number and Operations Use ratios and rates to solve problems. OMA.N.1.1 Use proportions to solve problems. OMA.N.1.2 Select appropriate units and explain the result based on the problem being solved. Use properties of exponents to simplify expressions. OMA.N.2.1 Represent numerical expressions with exponents in their simplest forms. OMA.N.2.2 Represent algebraic expressions with exponents in their simplest forms. OMA.N.2.3 Use strategies to compute square roots and cube roots of numbers that are not perfect squares or perfect cubes.

8. Algebra Use appropriate properties and strategies to combine and factor algebraic expressions. OMA.A.1.1 Execute all operations with algebraic expressions (division by monomials only). OMA.A.1.2 Use associative, commutative and distributive properties to combine algebraic expressions. OMA.A.1.3 Analyze quadratic expressions to determine their factors. Use direct and indirect variation to solve problems. OMA.A.2.1 Use substitution strategies to solve equations involving direct and inverse variation. OMA.A.2.2 Use literal equations to represent direct and indirect variation. OMA.A.2.3 Explain the effect that an increase or decrease in one variable will have on the other variables. Analyze patterns of change in functional relationships. OMA.A.3.1 Differentiate between linear, quadratic and exponential patterns of change. OMA.A.3.2 Identify intervals of increase or decrease. OMA.A.3.3 Explain the rate of increase or decrease on an interval.

9. Algebra Understand functions based on mathematical and real-world phenomena. OMA.A.4.1 Categorize relations as functions or “not functions”. OMA.A.4.2 Use appropriate terminology and notation (function, domain, range and intercepts) associated with functions. OMA.A.4.3 Interpret the relationship of constants and coefficients for data presented in graphs, tables and equations. OMA.A.4.4 Represent linear functions in a variety of equivalent forms (including point-slope). OMA.A.4.5 Use graphs, tables and symbols to solve linear equations. OMA.A.4.6 Use tables and graphs to solve exponential equations. OMA.A.4.7 Use graphs, tables, and properties to solve quadratic equations. Use strategies to find solutions for linear and exponential relationships. OMA.A.5.1 Represent linear and exponential relationships in the form of models. OMA.A.5.2 Use strategies to solve systems of linear equations in two variables, graphically and symbolically. OMA.A.5.3 Use tables and graphs to solve pairs of linear inequalities in two variables. OMA.A.5.4 Use tables and graphs to solve systems with linear and exponential inequalities.

10. Algebra Understand functions based on mathematical and real-world phenomena. OMA.A.4.1 Categorize relations as functions or “not functions”. OMA.A.4.2 Use appropriate terminology and notation (function, domain, range and intercepts) associated with functions. OMA.A.4.3 Interpret the relationship of constants and coefficients for data presented in graphs, tables and equations. OMA.A.4.4 Represent linear functions in a variety of equivalent forms (including point-slope). OMA.A.4.5 Use graphs, tables and symbols to solve linear equations. OMA.A.4.6 Use tables and graphs to solve exponential equations. OMA.A.4.7 Use graphs, tables, and properties to solve quadratic equations. Use strategies to find solutions for linear and exponential relationships. OMA.A.5.1 Represent linear and exponential relationships in the form of models. OMA.A.5.2 Use strategies to solve systems of linear equations in two variables, graphically and symbolically. OMA.A.5.3 Use tables and graphs to solve pairs of linear inequalities in two variables. OMA.A.5.4 Use tables and graphs to solve systems with linear and exponential inequalities.

11. Geometry Analyze properties of geometric shapes in the Cartesian coordinate system. OMA.G.1.1 Use strategies to calculate the slope, distance between points, coordinates of the midpoints and the distance from a point to a line. OMA.G.1.2 Use geometric properties to identify geometric shapes. Use formulas to solve problems involving area and volume. OMA.G.2.1 Recognize examples of chord, tangent and secant in visual displays. OMA.G.2.2 Use formulas to solve problems involving the areas of polygons. OMA.G.2.3 Understand the 3:1 relationship between volumes of right circular cylinders and cones with the same height and circular base and between the volume of a prism and pyramid with the same base area and height. OMA.G.2.4 Use formulas to solve problems involving volume of right prisms, pyramids, circular cylinders and right circular cones. OMA.G.2.5 Represent the relationship between the surface area of prisms, cylinders and pyramids to the sum of the area(s) of their base(s) and lateral surfaces using planar nets to illustrate and sum the relevant measures.

12. Statistics and Probability Analyze statistical distributions in terms of the relationships among shape, center, spread and outliers. OMA.S.1.1 Explain the effect of an outlier on the mean, median and range of various graphical displays. OMA.S.1.2 Compare shape, center, and spread of univariate data using graphical displays, quartiles, percentiles, outliers, means and standard deviations. Infer trends in bivariate data. OMA.S.2.1 Use formal strategies for placement of lines of best fit to model bivariate data. OMA.S.2.2 Infer trends in bivariate data displayed in scatter plots to determine informally if the data is best fit with a linear, exponential or quadratic model.

13. Discrete Use vertex-edge graphs to route and optimize critical paths. OMA.D.1.1 Apply the properties of vertex-edge graphs. OMA.D.1.2 Use vertex-edge graphs and algorithmic thinking (a step-by-step plan) to model and solve problems involving efficient route, Euler Circuits, and Hamiltonian Circuits

14. North Carolina Essential Standards Occupational Course of Study— Financial Management (Math 11)

15. Number and Operations Understand personal financial planning. OFM.1.1 Identify steps in financial planning. OFM.1.2 Compare personal and family needs versus wants. OFM.1.3 Identify various sources of income. OFM.1.4 Compare fixed, variable, and periodic expenses. OFM.1.5 Identify income and expenses to prepare a budget. OFM.1.6 Understand forms of record keeping involved with budgeting and cash management. Understand appropriate methods for personal financial management and independent living. OFM.2.1 Compare the various types of financial institutions and their purposes. OFM.2.2 Demonstrate the maintenance of a checking account. OFM.2.3 Understand how checking and savings accounts work. OFM.2.4 Compare the advantages and disadvantages of the use of credit cards and debit cards. Understand state and federal income taxes. OFM.3.1 Identify records needed for tax purposes. OFM.3.2 Understand how to obtain sources of free and low cost assistance for completing tax forms. OFM.3.3 Understand the process to complete a W-4 form, 1040 EZ federal income tax form, and an equivalent state income tax form. OFM.3.4 Explain the consequences of failure to comply with federal and state tax laws. Understand wages and compensation. OFM.4.1 Identify the various sections of a paycheck stub. compensation. OFM.4.2 Calculate hourly wage including overtime wages. OFM.4.3 Calculate gross and net pay. OFM.4.4 Calculate production rates and gross pay for piecework. OFM.4.5 Identify possible job related expenses.

16. Algebra Use appropriate properties and strategies to combine and factor algebraic expressions. OMA.A.1.1 Execute all operations with algebraic expressions (division by monomials only). OMA.A.1.2 Use associative, commutative and distributive properties to combine algebraic expressions. OMA.A.1.3 Analyze quadratic expressions to determine their factors. Use direct and indirect variation to solve problems. OMA.A.2.1 Use substitution strategies to solve equations involving direct and inverse variation. OMA.A.2.2 Use literal equations to represent direct and indirect variation. OMA.A.2.3 Explain the effect that an increase or decrease in one variable will have on the other variables. Analyze patterns of change in functional relationships. OMA.A.3.1 Differentiate between linear, quadratic and exponential patterns of change. OMA.A.3.2 Identify intervals of increase or decrease. OMA.A.3.3 Explain the rate of increase or decrease on an interval.

17. Algebra Understand functions based on mathematical and real-world phenomena. OMA.A.4.1 Categorize relations as functions or “not functions”. OMA.A.4.2 Use appropriate terminology and notation (function, domain, range and intercepts) associated with functions. OMA.A.4.3 Interpret the relationship of constants and coefficients for data presented in graphs, tables and equations. OMA.A.4.4 Represent linear functions in a variety of equivalent forms (including point-slope). OMA.A.4.5 Use graphs, tables and symbols to solve linear equations. OMA.A.4.6 Use tables and graphs to solve exponential equations. OMA.A.4.7 Use graphs, tables, and properties to solve quadratic equations. Use strategies to find solutions for linear and exponential relationships. OMA.A.5.1 Represent linear and exponential relationships in the form of models. OMA.A.5.2 Use strategies to solve systems of linear equations in two variables, graphically and symbolically. OMA.A.5.3 Use tables and graphs to solve pairs of linear inequalities in two variables. OMA.A.5.4 Use tables and graphs to solve systems with linear and exponential inequalities.

18. Algebra Understand functions based on mathematical and real-world phenomena. OMA.A.4.1 Categorize relations as functions or “not functions”. OMA.A.4.2 Use appropriate terminology and notation (function, domain, range and intercepts) associated with functions. OMA.A.4.3 Interpret the relationship of constants and coefficients for data presented in graphs, tables and equations. OMA.A.4.4 Represent linear functions in a variety of equivalent forms (including point-slope). OMA.A.4.5 Use graphs, tables and symbols to solve linear equations. OMA.A.4.6 Use tables and graphs to solve exponential equations. OMA.A.4.7 Use graphs, tables, and properties to solve quadratic equations. Use strategies to find solutions for linear and exponential relationships. OMA.A.5.1 Represent linear and exponential relationships in the form of models. OMA.A.5.2 Use strategies to solve systems of linear equations in two variables, graphically and symbolically. OMA.A.5.3 Use tables and graphs to solve pairs of linear inequalities in two variables. OMA.A.5.4 Use tables and graphs to solve systems with linear and exponential inequalities.