Represent the elements of a set of numbers, including the empty set.

Describe a set of numbers as finite or infinite.

Justify whether a set of numbers is a subset of another.

Represent natural, integer, rational, and irrational number subsets of real numbers.

Identify the subsets to which a real number belongs.

Investigate the role of parentheses in powers.

Justify exponent laws, using repeated multiplication.

Justify the zero exponent law.

Justify the negative exponent law.

Simplify expressions that include powers, using exponent laws limited to integer values for a, b, m, n.

Investigate the relationship between powers of 10 and place value.

Express a power of 10 as a decimal number and as a fraction.

Express numbers of very large and very small magnitude, using scientific notation.

Convert between scientific notation and decimal numbers.

Discuss scientific notation in real-world situations.

Multiply monomials.

Expand and simplify two polynomials with three terms or less.

Factor polynomial expressions involving common factors.

Factor polynomials in the form x² + bx + c.

Factor polynomial expressions, using difference of squares, limited to integer numbers.

Justify the factors of a polynomial through expansion.

Determine when a polynomial is non-factorable.

Determine the number of solutions for a quadratic equation in the form x² = a for values of a less than, greater than, and equal to 0.

Solve quadratic equations in the form x² = a, including in real-world situations.

Solve quadratic equations in the form x² + c = 0, where c is an integer.

Solve single-variable linear inequalities.

Determine whether a number is a solution to an inequality.

Relate various representations of the solution set for an inequality.

Represent the solution set for an inequality on the number line.

Represent the solution set for an inequality, using set-builder notation.

Solve problems by using inequalities, including in real-world situations.

Model congruent and similar triangles, using hands-on materials or a digital geometry environment.

Verify the three properties of triangle congruence.

Justify the congruence of two triangles, using the properties of triangle congruence.

Represent congruence of two triangles, using symbolic notation.

Determine the three pairs of equal sides and three pairs of equal angles, given the congruence statement for two triangles.

Justify triangle theorems, using hands-on materials or a digital geometry environment.

Verify the properties of triangle similarity.

Justify the similarity of two triangles, using the properties of triangle similarity.

Write a similarity statement for two similar triangles.

Determine the three pairs of equal angles and the three pairs of proportional sides, given the similarity statement for two triangles.

Solve problems involving triangles.

Visualize and model the 2-D shapes that compose the surface of a composite 3-D shape, using 2-D models or a digital geometry environment.

Compare the surface area of a composite 3-D shape to the sum of the surface areas of the 3-D shapes from which it is composed.

Describe the effect of adding or removing one or more 3-D shapes on the surface area of a composite 3-D shape.

Calculate the surface area of composite 3-D shapes composed of prisms, pyramids, and cylinders.

Visualize and model a composite 3-D shape as a composition of multiple 3-D shapes, using 3-D models or a digital geometry environment.

Describe the effect of adding or removing one or more 3-D shapes on the volume of a composite 3-D shape.

Visualize the decomposition of a rectangular prism into rectangular pyramids, using 3-D models or a digital geometry environment.

Calculate the volume of composite 3-D shapes composed of prisms, pyramids, and cylinders, given the relevant formulas.

Solve problems involving surface area and volume of composite 3-D shapes.

Compare the surface areas of various rectangular prisms that have equal volumes, using cube structures or 2-D models.

Investigate the effect of decreasing the height and increasing the dimensions of the base on the volume of prisms, pyramids, and cylinders.

Solve problems involving surface area and volume in real-world situations.

Express a linear function in function notation, given two points from the graph.

Express a linear function in function notation, given the slope and one point from the graph.

Interpret the meaning of x- and y-intercepts of linear functions within the context of real-world situations.

Express the domain and range of a linear function, using set-builder notation.

Relate various representations of a linear function.

Evaluate a function in function notation, given an input value.

Determine the input value, given the output value of the function in function notation.

Generate an arithmetic sequence, given a function.

Predict input and output values of a linear function, using interpolation and extrapolation.

Solve problems involving linear functions.

Determine the range, five-number summary, and interquartile range for a distribution.

Identify outliers in a distribution.

Examine the effect of outliers on measures of central tendency and spread.

Justify the inclusion or exclusion of an outlier from a data set.

Represent distributions, using box plots.

Interpret the spread of distributions represented by box plots.

Compare the spread of distributions of two different samples of the same population, using box plots.

Calculate the probability of the intersection of two independent events.

Determine whether two events are mutually exclusive.

Model sample spaces and events with Venn diagrams.

Calculate the probability of the union of two non-mutually exclusive events.

Calculate the probability of the union of two mutually exclusive events.

Identify complementary events.

Calculate the probability of an event, given the probability of its complement, and vice versa.