^ Appendix Career Technical Education and Academic Standards Crosswalk NOTE: Available formatted in PDF version at http://www.cde.ca.gov/ci/ct/sf/documents/ctestandards.pdf ^ Mathematics Standards Number Sense (Grade Seven)

1.1 Read, write, and Appendix Career Technical Education and Academic Standards Crosswalk compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

1.2 Add Appendix Career Technical Education and Academic Standards Crosswalk, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

1.3 Convert fractions to decimals Appendix Career Technical Education and Academic Standards Crosswalk and percents and use these representations in estimations, computations, and applications. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

1.4 Differentiate between rational and irrational numbers. BLD, ED, ENERGY Appendix Career Technical Education and Academic Standards Crosswalk, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions Appendix Career Technical Education and Academic Standards Crosswalk. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

1.6 Calculate the percentage of increases and decreases of a quantity. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

Solve problems that Appendix Career Technical Education and Academic Standards Crosswalk involve discounts, markups, commissions, and profit and compute simple and compound interest. ARTS, BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.1 Understand negative whole-number exponents Appendix Career Technical Education and Academic Standards Crosswalk. Multiply and divide expressions involving exponents with a common base. HOSP

2.2 Add and subtract fractions by using factoring to find common denominators. ARTS, HOSP

Multiply, divide, and simplify rational numbers by using exponent rules. ARTS Appendix Career Technical Education and Academic Standards Crosswalk, HOSP

2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two Appendix Career Technical Education and Academic Standards Crosswalk integers between which its square root lies and explain why. HOSP

2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number Appendix Career Technical Education and Academic Standards Crosswalk line; and determine the absolute value of real numbers. HOSP

^ Algebra and Functions (Grade Seven)

1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of Appendix Career Technical Education and Academic Standards Crosswalk equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). ENERGY, TRANSP

3.4 Plot the values of quantities whose ratios are always the same Appendix Career Technical Education and Academic Standards Crosswalk (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of Appendix Career Technical Education and Academic Standards Crosswalk the line equals the quantities. ENERGY, TRANSP

^ Measurement and Geometry (Grade Seven)

1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second Appendix Career Technical Education and Academic Standards Crosswalk, cubic inches to cubic centimeters). ARTS, ENERGY, HLTH, TRANSP

1.2 Construct and read drawings and models мейд to scale. ARTS, HLTH

1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e Appendix Career Technical Education and Academic Standards Crosswalk.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. HLTH

2.4 Relate the changes in measurement with a change Appendix Career Technical Education and Academic Standards Crosswalk of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in Appendix Career Technical Education and Academic Standards Crosswalk3] = [16.38 cm3]). ENERGY, MANUF, TRANSP

^ Statistics, Data Analysis, and Probability (Grade Seven)

1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use Appendix Career Technical Education and Academic Standards Crosswalk the forms to display a single set of data or to compare two sets of data. F&B, IT, MSS

Represent two numerical variables on a scatterplot and informally describe how the data points are distributed Appendix Career Technical Education and Academic Standards Crosswalk and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level). F&B, IT, MSS

1.3 Understand the meaning of, and be able to compute Appendix Career Technical Education and Academic Standards Crosswalk, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set. F&B, IT, MSS, MANUF

^ Mathematical Reasoning (Grade Seven)

1.1 Analyze problems by identifying relationships, distinguishing relevant Appendix Career Technical Education and Academic Standards Crosswalk from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. ED, FASH, F&B, HLTH, HOSP, IT, MSS

1.2 Formulate and justify mathematical conjectures based on a general description Appendix Career Technical Education and Academic Standards Crosswalk of the mathematical question or problem posed. HLTH

1.3 Determine when and how to break a problem into simpler parts. ARTS, HLTH

2.1 Use estimation to verify the reasonableness of calculated results. BLD, ED, ENERGY Appendix Career Technical Education and Academic Standards Crosswalk, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.2 Apply strategies and results from simpler problems to more complex problems. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.3 Estimate unknown quantities Appendix Career Technical Education and Academic Standards Crosswalk graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.4 Make and test conjectures by using both inductive Appendix Career Technical Education and Academic Standards Crosswalk and deductive reasoning. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical Appendix Career Technical Education and Academic Standards Crosswalk reasoning. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions Appendix Career Technical Education and Academic Standards Crosswalk with evidence in both verbal and symbolic work. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.7 Indicate the relative advantages of exact and approximate solutions to problems Appendix Career Technical Education and Academic Standards Crosswalk and give answers to a specified degree of accuracy. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.8 Make precise calculations and check the validity of the results from the Appendix Career Technical Education and Academic Standards Crosswalk context of the problem. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

3.1 Evaluate the reasonableness of the solution in the context of the original situation. ARTS, BLD, ED, ENERGY, ENGR, FASH, F Appendix Career Technical Education and Academic Standards Crosswalk&B, HOSP, IT, MANUF, MSS, TRANSP

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. BLD, ED, ENERGY, ENGR, FASH, F&B Appendix Career Technical Education and Academic Standards Crosswalk, HOSP, IT, MANUF, MSS, TRANSP

3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations. BLD, ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

^ Algebra Appendix Career Technical Education and Academic Standards Crosswalk I (Grades Eight Through Twelve)

1.1 Students use properties of numbers to demonstrate whether assertions are true or false. ED, ENERGY, ENGR, FASH, F&B, HOSP, IT, MANUF, MSS, TRANSP

2.0 Students understand and Appendix Career Technical Education and Academic Standards Crosswalk use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. ENGR

3.0 Students solve equations Appendix Career Technical Education and Academic Standards Crosswalk and inequalities involving absolute values. ENGR

4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12. BLD

5.0 Students solve multi-step problems, including word problems, involving linear equations Appendix Career Technical Education and Academic Standards Crosswalk and linear inequalities in one variable and provide justification for each step. BLD, ENERGY, ENGR, F&B, IT, MANUF, MSS, PUB, TRANSP

6.0 Students graph a linear equation and compute the x- and y- intercepts Appendix Career Technical Education and Academic Standards Crosswalk (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). MANUF

8.0 Students understand the concepts of parallel lines Appendix Career Technical Education and Academic Standards Crosswalk and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given Appendix Career Technical Education and Academic Standards Crosswalk point. ENERGY, MANUF, TRANSP

10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. AG, MANUF

12.0 Students simplify fractions with polynomials in the numerator and denominator Appendix Career Technical Education and Academic Standards Crosswalk by factoring both and reducing them to the lowest terms. AG, ENERGY, ENGR, MANUF, TRANSP

13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by Appendix Career Technical Education and Academic Standards Crosswalk using these techniques. AG, ED, FASH, F&B, HOSP, IT, MSS

15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. AG, ARTS, BLD, ENERGY, ENGR, F&B Appendix Career Technical Education and Academic Standards Crosswalk, IT, MANUF, MSS, PUB

24.1 Students explain the difference between inductive and deductive reasoning and identify and provide examples of each. ARTS, ED, ENERGY, FASH, F&B, HOSP, IT, MSS, PUB,TRANSP Appendix Career Technical Education and Academic Standards Crosswalk

24.2 Students identify the hypothesis and conclusion in logical deduction. ARTS, ED, FASH, F&B, HOSP, IT, MSS, PUB, TRANSP

24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample Appendix Career Technical Education and Academic Standards Crosswalk is sufficient to refute an assertion. ARTS, ED, FASH, F&B, HOSP, IT, MSS, PUB, TRANSP.

25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples Appendix Career Technical Education and Academic Standards Crosswalk to, claimed assertions. ARTS, F&B, IT, MSS, PUB

25.2 Students judge the validity of an argument according to whether the properties of the real number system and the order of operations Appendix Career Technical Education and Academic Standards Crosswalk have been applied correctly at each step. ARTS, F&B, IT, MSS, PUB

25.3 Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement Appendix Career Technical Education and Academic Standards Crosswalk is true sometimes, always, or never. ARTS, F&B, IT, MSS, PUB

^ Geometry (Grades Eight Through Twelve)

3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a Appendix Career Technical Education and Academic Standards Crosswalk statement. ARTS

8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. AG, BLD, ED, FASH, HOSP, MANUF

10.0 Students compute areas Appendix Career Technical Education and Academic Standards Crosswalk of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. AG

11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. AG, BLD Appendix Career Technical Education and Academic Standards Crosswalk, ENERGY, TRANSP

12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. AG, BLD

15.0 Students use the Pythagorean theorem to determine distance Appendix Career Technical Education and Academic Standards Crosswalk and find missing lengths of sides of right triangles. BLD, ENGR

16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through Appendix Career Technical Education and Academic Standards Crosswalk a point off the line. BLD, MANUF

19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length Appendix Career Technical Education and Academic Standards Crosswalk of a side. BLD, ENGR, MANUF

^ Algebra II (Grades Eight Through Twelve)

3.0 Students are adept at operations on polynomials, including long division. ENGR

6.0 Students add, subtract, multiply, and divide complex numbers. ENERGY, ENGR, TRANSP

^ Probability and Statistics (Grades Appendix Career Technical Education and Academic Standards Crosswalk Eight Through Twelve)

3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the Appendix Career Technical Education and Academic Standards Crosswalk occurrence of five heads in 14 coin tosses. ARTS

8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf Appendix Career Technical Education and Academic Standards Crosswalk displays, scatterplots, and box-and-whisker plots. AG, ARTS