Idaho State Standards for Mathematics: Grade 10
Currently Perma-Bound only has suggested titles for grades K-8 in the Science and Social Studies areas. We are working on expanding this.
ID.1. Number and Operation
1.1. Understand and use numbers.
10.M.1.1.1. Apply properties of rational numbers. (347.01.b)
10.M.1.1.2. Use positive and negative numbers, absolute value, fractions, decimals, percentages, and scientific notation, including application in real world situations. (347.01.a)
10.M.1.1.3. Apply properties of exponents. (347.01.c)
10.M.1.1.4. Identify exact and approximate roots without simplification.
10.M.1.1.5. Solve problems using number theory concepts (factors, multiples, primes). (347.01.d)
10.M.1.1.6. Use appropriate vocabulary.
1.2. Perform computations accurately.
10.M.1.2.1. Use the order of operations and perform operations with rational numbers. (347.02.a)
1.3. Estimate and judge reasonableness of results.
10.M.1.3.1. Apply number sense to everyday situations and judge reasonableness of results. (347.03.a)
10.M.1.3.2. Identify that error accumulates in a computation when there is rounding. (349.05.b)
ID.2. Concepts and Principles of Measurement
2.1. Understand and use U.S. customary and metric measurements.
10.M.2.1.1. Given the formulas, find the circumference, perimeter, or area of triangles, circles, and quadrilaterals, the volume of spheres, non-oblique prisms, cylinders, and cones, and the surface area of spheres, non-oblique prisms, cylinders, and right square-based pyramids. (349.01.a)
10.M.2.1.2. Solve problems involving circumference, perimeter, or area of triangles, circles, and rectangles.
2.2. Apply the concepts of rates, ratios, and proportions.
10.M.2.2.1. Use rates, ratios, proportions, map scales, and scale factors (one- and two-dimensional) in problem-solving situations. (349.03.a)
10.M.2.2.2. Apply concepts of rates and direct and indirect measurements.
10.M.2.2.3. Construct equivalent units, comparable units, and conversions. (349.02.a)
2.3. Apply dimensional analysis.
10.M.2.3.1. Use customary and metric units and their relationship to one another and to real world applications involving length, area, capacity, weight, time, and temperature. (349.04.a)
2.4. Apply appropriate techniques and tools to determine measurements.
10.M.2.4.1. Determine and use appropriate units. (349.01.a)
10.M.2.4.2. Approximate error in measurement situations.
ID.3. Concepts and Language of Algebra and Functions
3.1. Use algebraic symbolism as a tool to represent mathematical relationships.
10.M.3.1.1. Represent mathematical relationships using variables, expressions, linear equations and inequalities. (350.01.a)
3.2. Evaluate algebraic expressions.
10.M.3.2.1. Use appropriate procedures for manipulating and simplifying algebraic expressions involving variables, integers, and rational numbers. (350.02.a)
3.3. Solve algebraic equations and inequalities.
10.M.3.3.1. Use appropriate procedures to solve multi-step, first-degree equations and inequalities; such as 3(2x - 5) = 5x + 7 or 3(2x - 5) > 5x + 7. (350.03.a)
10.M.3.3.2. Differentiate between linear and non-linear equations and graphs.
3.4. Solve simple linear systems of equations.
10.M.3.4.1. Use appropriate procedures to solve linear systems of equations involving two variables; such as x + y = 7 and 2x + 3y = 21. (350.04.a)
3.5. Understand the concept of functions.
10.M.3.5.1. Given graphs, charts, ordered pairs, mappings, or equations, determine whether a relation is a function.
10.M.3.5.2. Evaluate functions written in functional notation.
10.M.3.5.3. Given a function, identify domain and range.
3.6. Apply functions to a variety of problems.
10.M.3.6.1. Model and solve real-world phenomena using multi-step, first degree, single variable equations and inequalities, linear equations, and two-variable linear systems of equations. (353.01.a)
10.M.3.6.2. Use graphs and sequences to represent and solve problems. (347.02.b)
ID.4. Concepts and Principles of Geometry
4.1. Apply concepts of size, shape, and spatial relationships.
10.M.4.1.1. Recognize and apply congruency and similarity of two-dimensional figures. (351.01.a)
10.M.4.1.2. Recognize and use similarity as it relates to size variations in two- and three- dimensional objects. (351.01.b)
4.2. Apply the geometry of right triangles.
10.M.4.2.1. Given the Pythagorean Theorem, calculate missing side lengths of right triangles without simplifying radicals. (351.02.c)
4.3. Apply graphing in two dimensions.
10.M.4.3.1. Identify attributes of the Cartesian Coordinate System, such as quadrants, origin, and axes. (351.03.a)
10.M.4.3.2. Graph scatter plots and identify informal trend lines (e.g., eyeball fit lines).
10.M.4.3.3. Identify positive and negative correlations.
4.4. Represent and graph linear relationships.
10.M.4.4.1. Create graphs and equations for linear relationships.
10.M.4.4.2. Represent linear relationships using tables, graphs, and mathematical symbols.
10.M.4.4.3. Interpret attributes of linear relationships such as slope, rate of change, and intercepts.
4.5. Use reasoning skills.
10.M.4.5.1. Use logic to make and evaluate mathematical arguments. (348.02.b)
ID.5. Data Analysis, Probability, and Statistics
5.1. Represent data with a variety of formats.
10.M.5.1.1. Analyze and interpret tables, charts, and graphs, including scatter plots, multiple broken line graphs, and box-and-whisker plots. (352.01.a)
5.2. Collect, organize, and display data.
10.M.5.2.1. Collect, organize, and display data in tables, charts, and graphs. (352.02.a)
5.3. Apply simple statistical measurements.
10.M.5.3.1. Interpret and use basic statistical concepts, including mean, median, mode, range, and distribution of data, including outliers. (352.03.a)
10.M.5.3.2. Make predictions and draw conclusions based on statistical measures. (352.05.a)
5.4. Understand basic concepts of probability.
10.M.5.4.1. Find probabilities based on dependent, independent, and compound events.
10.M.5.4.2. Contrast experimental and theoretical probability. (352.04.a)
5.5. Make predictions or decisions based on data.
10.M.5.5.1. Make predictions based on randomness, chance, equally likely events, and probability. (352.04.c)
10.M.5.5.2. Use appropriate tools/technology to conduct simulations and employ graphical models to make predictions or decisions based on data. (352.05.a)
10.M.5.5.3. Design, conduct, and interpret results of statistical experiments. (352.05.b)
ID.AI. Algebra I
AI.1. Number and Operation
AI.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. By the end of Algebra I, the student will be able to:
AI.1.1.1. Demonstrate meanings for real numbers, absolute value, integer exponents, and square roots.
AI.1.1.2. Demonstrate how the properties of real numbers apply to rational numbers.
AI.1.2: Understand meanings of operations and how they relate to one another. By the end of Algebra I, the student will be able to:
AI.1.2.1. Judge the effects of multiplication, division, addition, subtraction, exponents, and square roots on the magnitudes of quantities.
AI.1.3: Compute fluently and make reasonable estimates. By the end of Algebra I, the student will be able to:
AI.1.3.1. Perform computations with exponents, radicals, and scientific notation.
AI.1.3.2. Apply number sense to contextual situations and judge reasonableness of solutions.
AI.2. Concepts and Principles of Measurement
AI.2.1: Understand measurable attributes of objects and the units, systems, and processes of measurement. By the end of Algebra I, the student will be able to:
AI.2.1.1. Make decisions about units and scales that are appropriate for a given problem.
AI.2.2: Apply appropriate techniques, tools, and formulas to determine measurements. By the end of Algebra I, the student will be able to:
AI.2.2.1. Convert rates using dimensional analysis.
AI.3. Concepts and Language of Algebra and Functions
AI.3.1: Understand patterns, relations, and functions. By the end of Algebra I, the student will be able to:
AI.3.1.1. Represent linear patterns and functional relationships in a table and as a graph.
AI.3.1.2. Describe the graphs of linear and quadratic functions and discuss their appearances in terms of the basic concepts of intercepts and rate of change.
AI.3.2: Represent and analyze mathematical situations and structures using algebraic symbols. By the end of Algebra I, the student will be able to:
AI.3.2.1. Represent linear patterns and relationships with an equation.
AI.3.2.2. Recognize and generate equivalent forms of algebraic expressions and solve equations, inequalities, and systems of equations.
AI.3.3: Use mathematical models to represent and understand quantitative relationships. By the end of Algebra I, the student will be able to:
AI.3.3.1. Develop proportional relationships to solve problems.
AI.3.4: Analyze change in various contexts. By the end of Algebra I, the student will be able to:
AI.3.4.1. Interpret changes to the parent function y = x.
AI.4. Concepts and Principles of Geometry
AI.4.1: No objectives at this course level.
AI.5. Data Analysis, Probability, and Statistics
AI.5.1: Collect, organize, and display data using a variety of formats.
AI.5.1.1. No objectives at this course level.
AI.5.2: Select and use appropriate statistical methods to analyze data. By the end of Algebra I, the student will be able to:
AI.5.2.1. Make predictions and draw conclusions based on measures of central tendency.
AI.5.2.2. Make predictions using linear relations, scatter plots, trend lines, charts, and tables.
AI.5.3: Develop and evaluate inferences and predictions that are based on data.
AI.5.3.1. No objectives at this course level.
AI.5.4: Understand basic concepts of probability.
AI.5.4.1. No objectives at this course level.
ID.G. Geometry
G.1. Number and Operation
G.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number system. By the end of Geometry, the student will be able to:
G.1.1.1. Understand the meanings of real numbers.
G.1.2: Understand meanings of operations and how they relate to one another.
G.1.2.1. No objectives at this course level.
G.1.3: Compute fluently and make reasonable estimates. By the end of Geometry, the student will be able to:
G.1.3.1. Judge the reasonableness of numerical computations and their results.
G.2. Concepts and Principles of Measurement
G.2.1: Understand measurable attributes of objects and the units, systems, and processes of measurement. By the end of Geometry, the student will be able to:
G.2.1.1. Select appropriate units for problems involving measurement.
G.2.2: Apply appropriate techniques, tools, and formulas to determine measurements. By the end of Geometry, the student will be able to:
G.2.2.1. Understand and use formulas to calculate the perimeter, circumference, area, surface area, and volume of geometric figures.
G.2.2.2. Understand and apply definitions, theorems, corollaries, and postulates to determine measurement.
G.3. Concepts and Language of Algebra and Functions
G.3.1: Understand patterns, relations, and functions. By the end of Geometry, the student will be able to:
G.3.1.1. Describe the graphs of linear functions and discuss their appearances in terms of the basic concepts of intercepts and rate of change.
G.3.2: Represent and analyze mathematical situations and structures using algebraic symbols. By the end of Geometry, the student will be able to:
G.3.2.1. Represent linear patterns and relationships with an equation.
G.3.3: Use mathematical models to represent and understand quantitative relationships.
G.3.3.1. No objectives at this course level.
G.3.4: Analyze change in various contexts.
G.3.4.1. No objectives at this course level.
G.4. Concepts and Principles of Geometry
G.4.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. By the end of Geometry, the student will be able to:
G.4.1.1. Analyze properties and determine attributes of two- and three-dimensional objects.
G.4.1.2. Explore congruence and similarity among classes of two dimensional objects and solve problems involving them.
G.4.1.3. Establish the validity of geometric conjectures.
G.4.1.4. Apply trigonometric relationships to determine lengths and angle measures.
G.4.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems. By the end of Geometry, the student will be able to:
G.4.2.1. Use Cartesian coordinates to analyze geometric situations.
G.4.3: Apply transformations and use symmetry to analyze mathematical situations. By the end of Geometry, the student will be able to:
G.4.3.1. Understand and represent translations, reflections, dilations, and rotations of objects in the plane.
G.4.4: Use visualization, spatial reasoning, and geometric models to solve problems. By the end of Geometry, the student will be able to:
G.4.4.1. Draw and construct representations of two dimensional geometric objects using a variety of tools.
G.5. Data Analysis, Probability, and Statistics
G.5.1: No objectives at this course level.
ID.AII. Algebra II
AII.1. Number and Operation
AII.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number system. By the end of Algebra II, the student will be able to:
AII.1.1.1. Compare and contrast the properties of numbers and number systems within the complex number system to include rational, irrational, and imaginary numbers and factorials.
AII.1.1.2. Demonstrate meaning of complex numbers as solutions to polynomial equations that do not have real solutions.
AII.1.1.3. Recognize matrices as a method of arranging data.
AII.1.1.4. Develop an understanding of the properties of logarithmic expressions and expressions with rational exponents.
AII.1.2: Understand meanings of operations and how they relate to one another. By the end of Algebra II, the student will be able to:
AII.1.2.1. Develop an understanding of the properties of, and representations for, the addition, subtraction, and multiplication of matrices.
AII.1.3: Compute fluently and make reasonable estimates. By the end of Algebra II, the student will be able to:
AII.1.3.1. Simplify expressions within the complex number system.
AII.1.3.2. Perform computations on expressions with matrices within the complex number system.
AII.2. Concepts and Principles of Measurement
AII.2.1: Understand measurable attributes of objects and the units, systems, and processes of measurement. By the end of Algebra II, the student will be able to:
AII.2.1.1. Recognize the relationship between radian and degree measures.
AII.2.2: Apply appropriate techniques, tools, and formulas to determine measurements.
AII.3. Concepts and Language of Algebra and Functions
AII.3.1: Understand patterns, relations, and functions. By the end of Algebra II, the student will be able to:
AII.3.1.1. Represent patterns and functional relationships in a table and as a graph.
AII.3.1.2. Describe the graphs of polynomial and absolute value functions and discuss their attributes in terms of the basic concepts of maximum, minimum, intercepts, and roots.
AII.3.2: Represent and analyze mathematical situations and structures using algebraic symbols. By the end of Algebra II, the student will be able to:
AII.3.2.1. Write equations and inequalities in multiple forms.
AII.3.2.2. Recognize and generate equivalent forms of algebraic expressions and solve equations, inequalities, and systems of equations and inequalities.
AII.3.3: Use mathematical models to represent and understand quantitative relationships.
AII.3.3.1. No objectives at this course level.
AII.3.4: Analyze change in various contexts. By the end of Algebra II, the student will be able to:
AII.3.4.1. Interpret how changes to an equation affect the parent graph of the equation.
AII.4. Concepts and Principles of Geometry
AII.4.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. By the end of Algebra II, the student will be able to:
AII.4.1.1. Use trigonometric relationships to determine lengths and angle measures.
AII.4.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
AII.4.2.1. Analyze the graphs of circles and parabolas.
AII.4.3: Apply transformations and use symmetry to analyze mathematical situations.
AII.4.3.1. No objectives at this course level.
AII.4.4: Use visualization, spatial reasoning, and geometric models to solve problems.
AII.4.4.1. No objectives at this course level.
AII.5. Data Analysis, Probability, and Statistics
AII.5.1: No objectives at this course level.
ID.PC. Pre-Calculus
PC.1. Number and Operations
PC.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
PC.1.1.1. No objectives at this course level.
PC.1.2: Understand meanings of operations and how they relate to one another.
PC.1.2.1. No objectives at this course level.
PC.1.3: Compute fluently and make reasonable estimates. By the end of Pre-Calculus, the student will be able to:
PC.1.3.1. Apply the properties of exponents and logarithms.
PC.1.3.2. Perform operations with real and complex numbers.
PC.1.3.3. Perform operations on matrices.
PC.2. Concepts and Principles of Measurement
PC.2.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.
PC.2.1.1. No objectives at this course level.
PC.2.2: Apply appropriate techniques, tools, and formulas to determine measurements. By the end of Pre-Calculus, the student will be able to:
PC.2.2.1. Compute co-terminal angles and reference angles given an angle in standard position.
PC.2.2.2. Convert between degree and radian measures.
PC.3. Concepts and Language of Algebra and Functions
PC.3.1: Understand patterns, relations, and functions. By the end of Pre-Calculus, the student will be able to:
PC.3.1.1. Verify and simplify trigonometric identities.
PC.3.1.2. Select and use various representations for relations and functions.
PC.3.1.3. Perform transformations such as: arithmetic combinations, inverses, and compositions of functions.
PC.3.1.4. Apply the Fundamental Theorem of Algebra to determine roots of polynomial functions.
PC.3.2: Represent and analyze mathematical situations and structures using algebraic symbols. By the end of Pre-Calculus, the student will be able to:
PC.3.2.1. Write equations of circles, parabolas, and ellipses in standard form.
PC.3.2.2. Solve trigonometric equations.
PC.3.2.3. Solve exponential equations.
PC.3.2.4. Solve logarithmic equations
PC.3.2.5. Solve rational equations.
PC.3.2.6. Solve polynomial equations.
PC.3.2.7. Solve systems of linear equations.
PC.3.2.8. Solve systems of linear inequalities.
PC.3.2.9. Apply matrices to solve systems of equations.
PC.3.3: Use mathematical models to represent and understand quantitative relationships. By the end of Pre-Calculus, the student will be able to:
PC.3.3.1. Identify the domain and range of sine and cosine functions.
PC.3.4: Analyze change in various contexts. By the end of Pre-Calculus, the student will be able to:
PC.3.4.1. Apply and compare the properties of classes of functions, including polynomial, rational, exponential, and logarithmic functions.
PC.4. Concepts and Principles of Geometry
PC.4.1: Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships. By the end of Pre-Calculus, the student will be able to:
PC.4.1.1. Find the period and amplitude of sine and cosine functions.
PC.4.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems. By the end of Pre-Calculus, the student will be able to:
PC.4.2.1. Sketch and convert coordinates of the rectangular and polar systems.
PC.4.2.2. Draw an angle in standard position given degree or radian measure.
PC.4.2.3. Locate the quadrant in which an angle lies given its radian or degree measure.
PC.4.3: Apply transformations and use symmetry to analyze mathematical situations. By the end of Pre-Calculus, the student will be able to:
PC.4.3.1. Graph trigonometric functions of the form y = D + Asin(Bx) and y = D + Acos(Bx).
PC.4.4: Use visualization, spatial reasoning, and geometric models to solve problems. By the end of Pre-Calculus, the student will be able to:
PC.4.4.1. Apply unit circle trigonometry to determine exact values using sine, cosine, and tangent ratios.
PC.5. Data Analysis, Probability, and Statistics
PC.5.1: Collect, organize, and display data using a variety of formats. By the end of Pre-Calculus, the student will be able to:
PC.5.1.1 Choose an experimental design or survey sampling method appropriate to collect data.
PC.5.1.2. Choose an appropriate table or graph to display data.
PC.5.2: Select and use appropriate statistical methods to analyze data. By the end of Pre-Calculus, the student will be able to:
PC.5.2.1. Identify and apply arithmetic, geometric, and infinite notation.
PC.5.2.2. Identify nth terms of arithmetic and geometric sequences.
PC.5.2.3. Find the nth term in arithmetic and geometric series.
PC.5.2.4. Find sums of arithmetic, geometric, and infinite series.
PC 5.2.5. Use Pascal's Triangle to calculate binomial coefficients.
PC 5.2.6. Use the Binomial Theorem to calculate binomial coefficients.
PC.5.3: Develop and evaluate inferences and predictions that are based on data.
PC.5.3.1. No objectives at this course level.
PC.5.4: Understand basic concepts of probability.
PC.5.4. No objectives at this course level.
ID.MPF. Mathematics of Personal Finance
MPF.1. Money Management
MPF.1.1: Understanding and using effective money management. By the end of Mathematics of Personal Finance, the student will be able to:
MPF.1.1.1. Analyze account statements for accuracy and reconcile a checking/debit account.
MPF.1.1.2. Construct a cash flow statement.
MPF.1.1.3. Create, balance and use a personal budget including fixed and variable expenses including analyzing past expenses and income patterns.
MPF.1.2: Making responsible consumer choices. By the end of Mathematics of Personal Finance, the student will be able to:
MPF.1.2.1. Create and analyze short term goals for disposable income (ex. calculate the necessary income to maintain or improve upon current standards of living, recreation, vacation, gifts, appliances)
MPF.1.2.2. Analyze how inflation affects financial decisions (ex investments, purchasing power).
MPF.1.2.3. Calculate and compare different types of insurance costs (life, auto, health, deductibles, co-pay, stop-loss, inclusions, exclusions, factors that affect rates).
MPF.1.2.4. Compare and contrast renting or leasing vs. purchasing of an asset (ex automobile)
MPF.1.2.5. Calculate appreciation and depreciation of assets over time
MPF.1.3. Credit and Debt
MPF.1.3.1: Compare the costs associated with various types of credit. (ex credit cards, installment credit, revolving credit, mortgages, pay day loans, automobiles, student loans, home equity)
MPF.1.3.2. Compute the total cost of various types of credit (ex credit cards, installment credit, revolving credit, mortgages, pay day loans, automobiles, student loans, home equity, repayment options).
MPF.1.3.3. Interpret credit reports and analyze the financial implications of credit scores. (ex credit reports, credit scores, and debt ratios)
MPF.2. Saving and Investment
MPF.2.1: Implement a diversified saving and investment strategy. By the end of Mathematics of Personal Finance, the student will be able to:
MPF.2.1.1. Apply and analyze financial strategies to create wealth and build assets including use of tax deductions and shelters (ex time value of money, investment options) (ex lottery, inheritance, stock market)
MPF.2.1.2. Compare investment alternatives based on risk, return, and liquidity. (ex Certificates of Deposit, bonds, stocks, money market accounts, mutual funds, real estate)
MPF.2.1.3. Evaluate the effect of compounding earned interest
MPF.2.1.4. Create a model for comparing savings and investment results using appropriate technology (ex graphing or internet calculator)
MPF.3. Education Employment and Income
MPF.3.1: Understand the relationship between education, income, career, and desired lifestyle. By the end of Mathematics of Personal Finance, the student will be able to:
MPF.3.1.1. Explain how income reflects choices made about jobs, careers, education, and skill development
MPF.3.1.2. Calculate and compare how sources of income affect lifestyle choices and spending decisions. (ex. Wage commission, welfare/transfer payments, Medicaid, alimony, bonuses, inheritance, trusts, annuities, self employment, non-profit, public sector, private sector)
MPF.3.1.3. Calculate gross versus net income and the value of benefits. (ex payroll deductions and benefits, commissions, tips, taxes, FLEX plans, profit sharing, exemptions, 401 (k), 403 (b) and other related plans)
MPF.4. Taxation
MPF.4.1: Understand the purposes, roles, and responsibilities related to taxation. By the end of Mathematics of Personal Finance, the student will be able to:
MPF.4.1.1. Compare the returns of taxable investments with those that are tax-exempt or tax-deferred, including traditional IRA vs. Roth IRA.
MPF.4.1.2. Complete sample tax forms (ex Understanding Taxes by the IRS, forms such as 1040EZ, W-2, W-4 and 1099)
MPF.4.1.3. Analyze the application and impact of various forms of taxation on individuals, families, and public agencies (estate tax, inheritance tax, luxury tax, sales taxes, property taxes, usage tax, etc.).
ID.TM. Technical Math
TM.1. Number and Operation
TM.1.1: Understand and use numbers. By the end of Technical Math, the student will be able to:
TM.1.1.1. Apply properties of rational numbers. (e.g. necessary skill for applying numbers)
TM.1.1.2. Perform operations using positive and negative numbers, fractions, absolute value, decimals, percentages, and scientific notation. (e.g. given the cost of a project, determine what percentage of the budget went for salaries)
TM.1.1.3. Apply properties of exponents. (e.g. calculate the power dissipated by a resistor when its current and voltage drop are given in exponent form)
TM.1.1.4. Identify perfect squares and their principal roots. (e.g. 4, 9, and 16 are perfect squares and their respective roots are 2, 3, and 4)
TM.1.1.5. Solve problems using number theory concepts. (e.g. given initial expenses, money needed for reserve and start-up inventory, calculate the start up costs for a business by using a Starting Cost Calculator)
TM.1.1.6. Estimate the value of an irrational number expressed as a radical. (e.g. calculate the impedance of an inductive series circuit when given the circuit's total resistance and total inductive reactance)
TM.1.1.7. Apply properties of common and natural logarithms. (e.g. determine medication absorption rate)
TM.1.1.8. Use Fundamental Counting Principles. (e.g. calculate number of outfits from set number of separates)
TM.1.1.9. Use combinations and permutations. (e.g. calculate the number of ways to order the digits for a phone number)
TM.1.2: Understand and perform computations accurately. By the end of Technical Math, the student will be able to:
TM.1.2.1. Perform fundamental rational expression and number operations that involve a variety of applications. (e.g. determine wage and benefits)
TM.1.2.2. Read, write, and solve problems using scientific notation. (e.g. determine voltage of a circuit)
TM.1.2.3. Solve problems using direct and inverse variation. (e.g. determine the mechanical advantage of gears)
TM.1.2.4. Perform operations on complex numbers. (e.g. find amperage of current, knowing voltage and impedance if the impedance includes inductors or capacitors)
TM.1.2.5. Calculate nth powers and nth roots. (e.g. compute interest on investments)
TM.1.3: Estimate and judge reasonableness of results. By the end of Technical Math, the student will be able to:
TM.1.3.1. Estimate square roots between consecutive integers. (e.g. necessary foundation information)
TM.1.3.2. Determine relative and percent of error. (e.g. scale drawings must be within (+,- ) 1/16th of an inch)
TM.1.3.3. Apply number sense to everyday situations. (e.g. approximate grocery totals)
TM.2. Concepts and Principles of Measurement
TM.2.1: Understand and use U.S. customary and metric measurements. By the end of Technical Math, the student will be able to:
TM.2.1.1. Perform metric conversions within the system. (e.g. convert medicine dosage from adult to child)
TM.2.1.2. Solve problems by converting between English and metric systems. (e.g. trip planning from miles to kilometers and gallons to liters)
TM.2.1.3. Determine length, distance, area, surface area, volume, and weight, with appropriate unit labels. (e.g. determine number of flowers needed to fill a flower bed)
TM.2.1.4. Calculate circumference, area, radius, diameter, area of sector, arc length of a circle with appropriate unit labels. (e.g. develop a circular watering system)
TM.2.2: Apply the concepts of rates, ratios, and proportions. By the end of Technical Math, the student will be able to:
TM.2.2.1. Determine an unknown term in a ratio. (e.g. comparing cost of living between Cities
TM.2.3: Apply dimensional analysis. By the end of Technical Math, the student will be able to:
TM.2.3.1. Solve U.S. customary weights and measures problems using dimensional analysis. (e.g. feet per second to miles per hour)
TM.2.3.2. By use of estimation convey knowledge of volume versus mass. (e.g. determine dosage of medicine per weight)
TM.2.4: Apply appropriate techniques, tools, and formulas to determine measurements. By the end of Technical Math, the student will be able to:
TM.2.4.1. Determine and use appropriate units. (e.g. using an existing recipe, calculate a recipe for a larger group, simplify and label new amounts)
TM.2.4.2. Calculate area, surface area for two dimensional objects and volume for three-dimensional objects. (e.g. compute amount of cement needed for a sidewalk; calculate the cost of heating a building based on square footage)
TM.3. Concepts and Language of Algebra and Functions
TM.3.1: Use algebraic symbolism as a tool to represent mathematical relationships. By the end of Technical Math, the student will be able to:
TM.3.1.1. Represent mathematical relationships using variables, expressions, linear equations and inequalities. (e.g. using spreadsheet functions, determine sale price of items)
TM.3.1.2. Perform operations on polynomial expressions. (e.g. compute regular and overtime gross and net earnings)
TM.3.1.3. Perform operations on radical expressions. (e.g. determine flow rate of water through a fire hose)
TM.3.1.4. Perform operations on rational expressions. (e.g. determine earnings for a given time frame)
TM.3.1.5. Factor quadratics and other polynomial expressions. (e.g. determine flight time of a rocket)
TM.3.1.6. Represent application problems as linear equations. (e.g. level of education versus pay; rate of speed versus fuel consumption; caloric intake versus expenditure)
TM.3.2: Evaluate algebraic expressions. By the end of Technical Math, the student will be able to:
TM.3.2.1. Perform fundamental operations on polynomial expressions. (e.g. calculate the total cost of various items within a meal)
TM.3.3: Solve algebraic equations and inequalities. By the end of Technical Math, the student will be able to:
TM.3.3.1. Find solutions to simple quadratic equations. (e.g. calculate water content of soil based on its weight)
TM.3.3.2. Solve exponential equations. (e.g. determine atmospheric pressure)
TM.3.3.3. Solve logarithmic equations. (e.g. determine power of a satellite needed to transmit signals)
TM.3.3.4. Solve absolute value equations. (e.g. stopping distance of a car)
TM.3.3.5. Solve systems of inequalities in two variables. (e.g. determine needed sales for a company given overhead)
TM.3.3.6. Solve basic one and two step rational equations. (e.g. determine amount of medication to administer based on packaging size)
TM.3.4: Solve simple linear systems of equations. By the end of Technical Math, the student will be able to:
TM.3.4.1. Solve a system of two linear equations in an application setting. (e.g. child care facility - sq. footage to number of children; solving electrical current in a circuit with multiple paths)
TM.3.5: Understand the concept of functions. By the end of Technical Math, the student will be able to:
TM.3.5.1. Determine whether a relation is a function given graphs, charts, ordered pairs, mappings, or equations. (e.g. graph the distance a ballistic device travels at different angles and determine if the data is a function of the angle)
TM.3.5.2. Differentiate between linear and non-linear functions and graphs. (e.g. differentiate between a thrown object and the distance a car travels)
TM.3.5.3. Identify domain and range for given graphs, charts, ordered pairs, mappings, or linear functions. (e.g. constraints of any situation such as a budget)
TM.3.5.4. Evaluate functions. (e.g. work with the function V=I*R and solve for different I and R)
TM.3.6: Apply functions to a variety of problems. By the end of Technical Math, the student will be able to:
TM.3.6.1. Model real-world phenomena with linear functions. (e.g. graph fuel consumption versus speed)
TM.3.6.2. Use graphs and tables to represent and solve problems. (e.g. stress test of cardiovascular system)
TM.3.6.3. Solve application problems by isolating a specific variable in a formula and then substituting values. (e.g. determining interest rate on a loan)
TM.4. Concepts and Principles of Geometry
TM.4.1: Apply concepts of size, shape, and spatial relationships. By the end of Technical Math, the student will be able to:
TM.4.1.1. Identify and apply congruency and similarity of two-dimensional figures. (e.g. compare trusses or wall panels)
TM.4.1.2. Identify the scale factor of similar three-dimensional figures and find the ratios of their surface areas and volumes. (e.g. compare blueprint to actual model )
TM.4.1.3. Use transformational geometry to rotate, translate, and reflect figures in a coordinate plane. (e.g. flip a house plan)
TM.4.1.4. Describe and apply magnitude and direction of vectors. (e.g. determine resultant direction due to wind)
TM.4.2: Apply the geometry of right triangles. By the end of Technical Math, the student will be able to:
TM.4.2.1. Understand and apply the Pythagorean Theorem for problem solving. (e.g. checking accuracy on gate construction)
TM.4.2.2. Identify and apply special right triangle relationships. (e.g. isometric drawing in drafting)
TM.4.2.3. Use right triangle trigonometry to solve right triangles. (e.g. determine angle of elevation using sine, cosine and tangent)
TM.4.2.4. Use trigonometric ratios to solve problems. (e.g. angle of depression)
TM.4.3: Apply graphing in two dimensions. By the end of Technical Math, the student will be able to:
TM.4.3.1. Determine the length and midpoint of a segment in the coordinate plane. (e.g. on-center carpentry from a blueprint would include the coordinate plane)
TM.4.3.2. Graph quadratic and absolute value functions. (e.g. maximize profit from revenue)
TM.4.3.3. Graph exponential functions. (e.g. rate of bacterial growth)
TM.4.3.4. Graph systems of equations and inequalities in two variables. (e.g. mixing solutions for weed control)
TM.4.4: Apply concepts of parallel lines. By the end of Technical Math, the student will be able to:
TM.4.4.1. Identify the special angle pairs formed by parallel lines and a transversal. (e.g. building a gate; designing a quilt)
TM.4.4.2. Apply the properties of special angle pairs formed by parallel lines and a transversal (e.g. building a gate; designing a quilt)
TM.4.5: Apply concepts of polygons. By the end of Technical Math, the student will be able to:
TM.4.5.1. Classify triangles and quadrilaterals based on their attributes. (e.g. label triangles and quadrilaterals in a house plan)
TM.4.5.2. Find the sum of the interior and exterior angles of a polygon. (e.g. add the interior and exterior angles of a pentagonal swimming pool)
TM.4.5.3. Find the measure of each interior and exterior angle of a regular polygon. (e.g. find the degree of angles to create a stop sign)
TM.4.5.4. Determine whether or not a polygon is regular. (e.g. design a hexagon table using a circle)
TM.4.6: Understand basic concepts of a circle. By the end of Technical Math, the student will be able to:
TM.4.6.1. Identify the parts of a circle including radius, diameter, major/minor arcs, chords, secants and tangents. (e.g. necessary foundation information)
TM.4.6.2. Determine the lengths of segments and the measures of angles formed by radii, chords, secants, and tangents. (e.g. calculate trim for an arched window)
TM.4.7: Apply Reasoning Skills.
TM.4.7.1. No objectives for this course.
TM.4.8: Represent and graph linear relationships. By the end of Technical Math, the student will be able to:
TM.4.8.1. Construct graphs and write equations and inequalities for linear relationships. (e.g. relationship between cost and demand)
TM.4.8.2. Given a linear relationship, interpret the rate of change (slope) and the intercepts. (e.g. rate of feed to fill a grain truck)
TM.4.8.3. Write equations of lines given various information including parallel, perpendicular, vertical, and horizontal lines. (e.g. alignment of restaurant with layout of city street)
TM.4.8.4. Graph linear equations. (e.g. constant increase in water temperature over time; monthly changes in sales)
TM.5. Data Analysis, Probability, and Statistics
TM.5.1: Represent data with a variety of formats. By the end of Technical Math, the student will be able to:
TM.5.1.1. Analyze and interpret tables, charts and graphs. (e.g. interpret a body mass index (BMI) chart)
TM.5.2: Collect, organize, and display data. By the end of Technical Math, the student will be able to:
TM.5.2.1. Graph scatter plots and informal trend lines. (e.g. growth of state economy)
TM.5.2.2. Identify positive and negative correlations. (e.g. vehicle depreciation)
TM.5.2.3. Collect, organize, and display data in tables, charts and graphs. (e.g. chart change in stock values over 4 weeks)
TM.5.3: Apply simple statistical measurements. By the end of Technical Math, the student will be able to:
TM.5.3.1. Make predictions and draw conclusions based on statistical measures. (e.g. predict the number of new jobs based on growth in population; predict the number of sunny days in a given area for a given time frame)
TM.5.4: Understand basic concepts of probability.
TM.5.4.1. No objectives at this course level
TM.5.5: Make predictions or decisions based on data. By the end of Technical Math, the student will be able to:
TM.5.5.1. Make predictions based on randomness, chance, equally likely events, and probability. (e.g. predict the likelihood of having an accident using past accident data)
TM.5.5.2. Use data to predict the chance of an event. (e.g. calculate the odds of a hit based on the batting average)
ID.APC. AP Calculus
APC.I. Functions, Graphs, and Limits
APC.I.A. Analysis of graphs
APC.I.B. Limits of functions (including one-sided limits)
APC.I.C. Asymptotic and unbounded behavior
APC.I.D. Continuity as a property of functions
APC.I.E. Parametric, polar, and vector functions
APC.II. Derivatives
APC.II.A. Concept of the derivative
APC.II.B. Derivative at a point
APC.II.C. Derivative as a function
APC.II.D. Second derivatives
APC.II.E. Applications of derivatives
APC.II.F. Computation of Derivatives
APC.III. Integrals
APC.III.A. Interpretations and properties of definite integrals
APC.III.B. Applications of integrals
APC.III.C. Fundamental Theorem of Calculus
APC.III.D. Techniques of antidifferentiation
APC.III.E. Applications of antidifferentiation
APC.III.F. Numerical approximations to definite integrals
APC.IV. Polynomial
APC.IV.A. Concept of series
APC.IV.B. Series of constants
APC.IV.C. Taylor series
ID.APS. AP Statistics
APS.I. Exploring Data: Describing patterns and departures from patterns.
APS.I.A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot)
APS.I.B. Summarizing distributions of univariate data
APS.I.C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)
APS.I.D. Exploring bivariate data
APS.I.E. Exploring categorical data
APS.II. Sampling and Experimentation: Planning and conducting a study.
APS.II.A. Overview of methods of data collection
APS.II.B. Planning and conducting surveys
APS.II.C. Planning and conducting experiments
APS.II.D. Generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys
APS.III. Anticipating Patterns: Exploring random phenomena using probability and simulation.
APS.III.A. Probability
APS.III.B. Combining independent random variables
APS.III.C. The normal distribution
APS.III.D. Sampling distributions
APS.IV. Statistical Inference: Estimating population parameters and testing hypotheses.
APS.IV.A. Estimation (point estimators and confidence intervals)
APS.IV.B. Tests of significance