College Readiness Standards - Math  

M.I.            BASIC OPERATIONS & APPLICATIONS

M.I.a.        Score Range 13–15

M.I.a.1.    Perform one-operation computation with whole numbers and decimals

M.I.a.2.    Solve problems in one or two steps using whole numbers

M.I.a.3.    Perform common conversions (e.g., inches to feet or hours to minutes)

M.I.b.        Score Range 16–19

M.I.b.1.    Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent

M.I.b.2.    Solve some routine two-step arithmetic problems

M.I.c.        Score Range 20–23

M.I.c.1.    Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average

M.I.d.        Score Range 24–27

M.I.d.1.    Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)

M.I.e.        Score Range 28–32

M.I.e.1.    Solve word problems containing several rates, proportions, or percentages

M.I.f.         Score Range 33–36

M.I.f.1.    Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts from pre-algebra and/or pre-geometry (e.g., comparing percentages or averages, using several ratios, and finding ratios in geometry settings)

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M.II.      PROBABILITY, STATISTICS & DATA ANALYSIS

M.II.a.         Score Range 13–15

M.II.a.1.     Calculate the average of a list of positive whole numbers

M.II.a.2.     Perform a single computation using information from a table or chart

M.II.b.         Score Range 16–19

M.II.b.1.     Calculate the average of a list of numbers

M.II.b.2.     Calculate the average, given the number of data values and the sum of the data values

M.II.b.3.     Read tables and graphs

M.II.b.4.     Perform computations on data from tables and graphs

M.II.b.5.     Use the relationship between the probability of an event and the probability of its complement

M.II.c.         Score Range 20–23

M.II.c.1.      Calculate the missing data value, given the average and all data values but one

M.II.c.2.      Translate from one representation of data to another (e.g., a bar graph to a circle graph)

M.II.c.3.      Determine the probability of a simple event

M.II.c.4.      Exhibit knowledge of simple counting techniques

M.II.d.         Score Range 24–27

M.II.d.1.     Calculate the average, given the frequency counts of all the data values

M.II.d.2.     Manipulate data from tables and graphs

M.II.d.3.     Compute straightforward probabilities for common situations

M.II.d.4.     Use Venn diagrams in counting

M.II.e.         Score Range 28–32

M.II.e.1.     Calculate or use a weighted average

M.II.e.2.     Interpret and use information from figures, tables, and graphs

M.II.e.3.     Apply counting techniques

M.II.e.4.     Compute a probability when the event and/or sample space are not given or obvious

M.II.f.          Score Range 33–36

M.II.f.1.      Distinguish between mean, median, and mode for a list of numbers

M.II.f.2.      Analyze and draw conclusions based on information from figures, tables, and graphs

M.II.f.3.      Exhibit knowledge of conditional and joint probability
 

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M.III.   NUMBERS: CONCEPTS & PROPERTIES

M.III.a.               Score Range 13–15

M.III.a.1.            Recognize equivalent fractions and fractions in lowest terms

M.III.b.               Score Range 16–19

M.III.b.1.            Recognize one-digit factors of a number

M.III.b.2.            Identify a digit's place value

M.III.c.               Score Range 20–23

M.III.c.1.            Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor

M.III.d.               Score Range 24–27

M.III.d.1.            Find and use the least common multiple

M.III.d.2.            Order fractions

M.III.d.3.            Work with numerical factors

M.III.d.4.            Work with scientific notation

M.III.d.5.            Work with squares and square roots of numbers

M.III.d.6.            Work problems involving positive integer exponents

M.III.d.7.            Work with cubes and cube roots of numbers

M.III.d.8.            Determine when an expression is undefined

M.III.d.9.            Exhibit some knowledge of the complex numbers

M.III.e.               Score Range 28–32

M.III.e.1.            Apply number properties involving prime factorization

M.III.e.2.            Apply number properties involving even/odd numbers and factors/multiples

M.III.e.3.            Apply number properties involving positive/negative numbers

M.III.e.4.            Apply rules of exponents

M.III.e.5.            Multiply two complex numbers

M.III.f.                Score Range 33–36

M.III.f.1.            Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers

M.III.f.2.            Exhibit knowledge of logarithms and geometric sequences

M.III.f.3.            Apply properties of complex numbers

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M.IV.     EXPRESSIONS, EQUATIONS & INEQUALITIES

M.IV.a.                Score Range 13–15

M.IV.a.1.            Exhibit knowledge of basic expressions (e.g., identify an expression for a total as b + g)

M.IV.a.2.            Solve equations in the formx + a = b, where aand b are whole numbers or decimals

M.IV.b.                Score Range 16–19

M.IV.b.1.            Substitute whole numbers for unknown quantities to evaluate expressions

M.IV.b.2.            Solve one-step equations having integer or decimal answers

M.IV.b.3.            Combine like terms (e.g., 2x + 5x)

M.IV.c.                Score Range 20–23

M.IV.c.1.            Evaluate algebraic expressions by substituting integers for unknown quantities

M.IV.c.2.            Add and subtract simple algebraic expressions

M.IV.c.3.            Solve routine first-degree equations

M.IV.c.4.            Perform straightforward word-to-symbol translations

M.IV.c.5.            Multiply two binomials

M.IV.d.                Score Range 24–27

M.IV.d.1.            Solve real-world problems using first-degree equations

M.IV.d.2.            Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions)

M.IV.d.3.            Identify solutions to simple quadratic equations

M.IV.d.4.            Add, subtract, and multiply polynomials

M.IV.d.5.            Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)

M.IV.d.6.            Solve first-degree inequalities that do not require reversing the inequality sign

M.IV.e.                Score Range 28–32

M.IV.e.1.            Manipulate expressions and equations

M.IV.e.2.            Write expressions, equations, and inequalities for common algebra settings

M.IV.e.3.            Solve linear inequalities that require reversing the inequality sign

M.IV.e.4.            Solve absolute value equations

M.IV.e.5.            Solve quadratic equations

M.IV.e.6.            Find solutions to systems of linear equations

M.IV.f.                 Score Range 33–36

M.IV.f.1.             Write expressions that require planning and/or manipulating to accurately model a situation

M.IV.f.2.             Write equations and inequalities that require planning, manipulating, and/or solving

M.IV.f.3.             Solve simple absolute value inequalities

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M.V.        GRAPHICAL REPRESENTATIONS

M.V.a.       Score Range 13–15

M.V.a.1.  Identify the location of a point with a positive coordinate on the number line

M.V.b.       Score Range 16–19

M.V.b.1.  Locate points on the number line and in the first quadrant

M.V.c.       Score Range 20–23

M.V.c.1.   Locate points in the coordinate plane

M.V.c.2.   Comprehend the concept of length on the number line

M.V.c.3.   Exhibit knowledge of slope

M.V.d.       Score Range 24–27

M.V.d.1.  Identify the graph of a linear inequality on the number line*

M.V.d.2.  Determine the slope of a line from points or equations*

M.V.d.3.  Match linear graphs with their equations*

M.V.d.4.  Find the midpoint of a line segment*

M.V.e.       Score Range 28–32

M.V.e.1.  Interpret and use information from graphs in the coordinate plane

M.V.e.2.  Match number line graphs with solution sets of linear inequalities

M.V.e.3.  Use the distance formula

M.V.e.4.  Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point

M.V.e.5.  Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)†

M.V.f.        Score Range 33–36

M.V.f.1.   Match number line graphs with solution sets of simple quadratic inequalities

M.V.f.2.   Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c

M.V.f.3.   Solve problems integrating multiple algebraic and/or geometric concepts

M.V.f.4.   Analyze and draw conclusions based on information from graphs in the coordinate plane

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M.VI.     PROPERTIES OF PLANE FIGURES

M.VI.a.           Score Range 13–15

M.VI.b.           Score Range 16–19

M.VI.b.1.       Exhibit some knowledge of the angles associated with parallel lines

M.VI.c.           Score Range 20–23

M.VI.c.1.       Find the measure of an angle using properties of parallel lines

M.VI.c.2.       Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)

M.VI.d.           Score Range 24–27

M.VI.d.1.       Use several angle properties to find an unknown angle measure

M.VI.d.2.       Recognize Pythagorean triples*

M.VI.d.3.       Use properties of isosceles triangles*

M.VI.e.           Score Range 28–32

M.VI.e.1.       Apply properties of 30°-60°-90°,45°-45°-90°,similar, and congruent triangles

M.VI.e.2.       Use the Pythagorean theorem

M.VI.f.            Score Range 33–36

M.VI.f.1.       Draw conclusions based on a set of conditions

M.VI.f.2.       Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas

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