3-1 Adds, subtracts, multiplies, and divides whole numbers, fractions, decimals, integers, and rational numbers

3-2 Understands exponentiation of rational numbers and root-extraction (e.g., squares and square roots, cubes and cube roots)

3-3 Selects and uses appropriate computational methods (e.g., mental, paper and pencil, calculator, computer) for a given situation

3-4 Understands the correct order of operations for performing arithmetic computations

3-5 Uses proportional reasoning to solve mathematical and real-world problems (e.g., involving equivalent fractions, equal ratios, constant rate of change, proportions, percents)

3-6 Understands the properties of operations with rational numbers (e.g., distributive property, commutative and associative properties of addition and multiplication, inverse properties, identity properties)

3-7 Knows when an estimate is more appropriate than an exact answer for a variety of problem situations

3-8 Understands how different algorithms work for arithmetic computations and operations

Standard: 4 Understands and applies basic and advanced properties of the concepts of measurement

4-1 Understands the basic concept of rate as a measure (e.g., miles per gallon)

4-2 Solves problems involving perimeter (circumference) and area of various shapes (e.g., parallelograms, triangles, circles)

4-3 Understands the relationships among linear dimensions, area, and volume and the corresponding uses of units, square units, and cubic units of measure

4-4 Solves problems involving units of measurement and converts answers to a larger or smaller unit within the same system (i.e., standard or metric)

4-5 Understands the concepts of precision and significant digits as they relate to measurement (e.g., how units indicate precision)

4-6 Selects and uses appropriate units and tools, depending on degree of accuracy required, to find measurements for real-world problems

4-7 Understands formulas for finding measures (e.g., area, volume, surface area)

4-8 Selects and uses appropriate estimation techniques (e.g., overestimate, underestimate, range of estimates) to solve real-world problems

4-9 Understands procedures for basic indirect measurements (e.g., using grids to estimate area of irregular figures)

Standard: 5 Understands and applies basic and advanced properties of the concepts of geometry

5-1 Uses geometric methods (i.e., an unmarked straightedge and a compass using an algorithm) to complete basic geometric constructions (e.g., perpendicular bisector of a line segment, angle bisector)

5-2 Understands the defining properties of three-dimensional figures (e.g., a cube has edges with equal lengths, faces with equal areas and congruent shapes, right angle corners)

5-3 Understands the defining properties of triangles (e.g., the sum of the measures of two sides of a triangle must be greater than the measure of the third side)

5-4 Understands geometric transformations of figures (e.g., rotations, translations, dilations)

5-5 Understands the relationships between two- and three-dimensional representations of a figure (e.g., scale drawings, blueprints, planar cross sections)

5-6 Understands the mathematical concepts of similarity (e.g., scale, proportion, growth rates) and congruency

5-7 Understands the concept of tessellation (i.e., a repetitive pattern of polygons that fit together with no gaps or holes)

5-8 Understands the basic concept of the Pythagorean Theorem

Standard: 6 Understands and applies basic and advanced concepts of statistics and data analysis

6-1 Understands basic characteristics of measures of central tendency (i.e., mean, mode, median)

6-2 Understands basic characteristics of frequency and distribution (e.g., range, varying rates of change, gaps, clusters)

6-3 Understands the basic concepts of center and dispersion of data

6-4 Reads and interprets data in charts, tables, plots (e.g., stem-and-leaf, box-and-whiskers, scatter), and graphs (e.g., bar, circle, line)

6-5 Uses data and statistical measures for a variety of purposes (e.g., formulating hypotheses, making predictions, testing conjectures)

6-6 Organizes and displays data using tables, graphs (e.g., line, circle, bar), frequency distributions, and plots (e.g., stem-and-leaf, box-and-whiskers, scatter)

6-7 Understands faulty arguments, common errors, and misleading presentations of data

6-8 Understands that the same set of data can be represented using a variety of tables, graphs, and symbols and that different modes of representation often convey different messages (e.g., variation in scale can alter a visual message)

6-9 Understands the basic concept of outliers

6-10 Understands basic concepts about how samples are chosen (e.g., random samples, bias in sampling procedures, limited samples, sampling error)

Standard: 7 Understands and applies basic and advanced concepts of probability

7-1 Determines probability using mathematical/theoretical models (e.g., table or tree diagram, area model, list, counting procedures, sample space)

7-2 Determines probability using simulations or experiments

7-3 Understands how predictions are based on data and probabilities (e.g., the difference between predictions based on theoretical probability and experimental probability)

7-4 Understands that the measure of certainty in a given situation depends on a number of factors (e.g., amount of data collected, what is known about the situation, how current data are)

7-5 Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers

Standard: 8 Understands and applies basic and advanced properties of functions and algebra

8-1 Knows that an expression is a mathematical statement using numbers and symbols to represent relationships and real-world situations (e.g., equations and inequalities with or without variables)

8-2 Understands that a variable can be used in many ways (e.g., as a placeholder for a specific unknown, such as x + 8 = 13; as a representative of a range of values, such as 4t + 7)

8-3 Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them

8-4 Understands the basic concept of a function (i.e., functions describe how changes in one quantity or variable result in changes in another)

8-5 Solves linear equations using concrete, informal, and formal methods (e.g., using properties, graphing ordered pairs, using slope-intercept form)

8-6 Solves simple inequalities and non-linear equations with rational number solutions, using concrete and informal methods

8-7 Understands special values (e.g., minimum and maximum values, x- and y-intercepts, slope, constant ratio or difference) of patterns, relationships, and functions

8-8 Understands basic operations (e.g., combining like terms, expanding, substituting for unknowns) on algebraic expressions

8-9 Uses the rectangular coordinate system to model and to solve problems

8-10 Solves simple systems of equations graphically

8-11 Understands the properties of arithmetic and geometric sequences (i.e., linear and exponential patterns)

Standard: 9 Understands the general nature and uses of mathematics

9-1 Understands that mathematics has been helpful in practical ways for many centuries

9-2 Understands that mathematicians often represent real things using abstract ideas like numbers or lines; they then work with these abstractions to learn about the things they represent