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# Elementary Mathematics

 Exit Level Competencies and Learning Objectives Course A Course B Course C Course D 1 Perform operations with fractional numbers. a. Express fractions in lowest terms and as equivalent fractions. b. Convert between mixed numbers and improper fractions. c. Determine least common denominator. d. Add fractions and mixed numbers. e. Subtract fractions and mixed numbers. f. Multiply fractions and mixed numbers. g. Divide fractions and mixed numbers. h. Solve problems which involve combined operations of fractions, mixed numbers, and complex fractions. i. Apply skills to related technical problems. 2 Perform operations with decimal numbers. a. Round decimal fractions to any required number of places. b. Express common fractions to decimals and decimals to common fractions. c. Add decimal fractions and combinations of decimals, mixed decimals and whole numbers. d. Subtract decimal fractions and combinations of decimals, mixed decimals and whole numbers. e. Multiply decimal fractions and combinations of decimals, mixed decimals and whole numbers. f. Divide decimal fractions with whole numbers and mixed decimals. g. Apply skills to related technical problems. 3 Perform fraction and decimal conversions. a. Convert fractional numbers to decimal numbers. b. Convert decimal numbers to fractional numbers. c. Apply skills to related technical problems 4 Recognize and use correct order of operations. a. Raise numbers to indicated powers using scientific calculator. b. Demonstrate understanding of algebraic order of operations. c. Solve problems which involve combinations of powers with other basic operations. d. Extract whole number roots. e. Extract indicated roots of any number using scientific calculator. f. Solve problems which involve combinations of roots with other basic arithmetic operations. g. Solve problems consisting of combinations of operations by applying the order of operations. h. Apply skills to related technical problems. 5 Solve commonly occurring percentage problems. a. Express fractional and decimal numbers as percents. b. Express percents as fractional and decimal numbers. c. Choose the correct operation for solving an application problem. d. Solve an applied problem involving fractional numbers, decimal numbers, and percents. e. Use a calculator to facilitate work with fractional numbers, decimal numbers, and percents. f. Apply skills to related technical problems. 6 Demonstrate ability to use various measurement systems. a. Express English lengths as larger or smaller English linear units. b. Express metric lengths as larger or smaller metric linear units. c. Express metric length units as English length units. d. Express English length units as metric length units. e. Apply skills to related technical problems. 7 Recognize and perform basic algebraic operations. a. Express word statements as algebraic expressions. b. Express diagram dimensions as algebraic expressions. c. Evaluate algebraic expressions by substituting numbers for symbols. d. Compare signed numbers according to size and direction using the number scale. e. Determine absolute values of signed numbers. f. Perform basic operations of addition, subtraction, multiplication, division, powers, and roots using signed numbers. g. Solve expressions which involve combined operations of signed numbers. h. Perform the basic algebraic operations of addition, subtraction, multiplication, division, powers, and roots. i. Remove parentheses which are preceded by a plus or minus sign. j. Simplify algebraic operations which involve combined operations. k. Apply skills to related technical problems. 8 Apply algebraic principles to problems from program area. a. Express diagram dimensions as algebraic expressions. b. Evaluate shop formulas by substituting numbers for symbols. c. Utilize trade handbooks to find appropriate formulas and solve by substitution of numbers for symbols. d. Apply skills to related technical problems. 9 Solve first degree algebraic equations. a. Express word problems as equations. b. Express problems given in graphic form as equations. c. Solve equations using the subtraction principle of equality. d. Solve equations using the addition principle of equality. e. Solve equations using the division principle of equality. f. Solve equations using the multiplication principle of equality. g. Solve equations using transposition. h. Solve equations involving several operations. i. Solve equations using the root principle of equality. j. Solve equations using the power principle of equality. k. Apply skills to related technical problems. 10 Demonstrate ability to manipulate algebraic formulas and solve equations by substitution. a. Rearrange formulas in terms of any letter value. b. Substitute values in formulas and solve for unknowns. c. Apply skills to related technical problems.