To prepare for college and career, your child will study mathematics across a broad spectrum, from pure mathematics to real-world applications. Numerical skill and quantitative reasoning remain crucial even as students move forward with algebra. Algebra, functions, and geometry are important not only as mathematical subjects in themselves but also because they are the language of technical subjects and the sciences. And in a data-rich world, statistics and probability offer powerful ways of drawing conclusions from data and dealing with uncertainty. The high school standards also emphasize using mathematics creatively to analyze real-world situations — an activity sometimes called “mathematical modeling.”

Math Prioritized Standards

The high school standards are organized into six major content areas: Number and Quantity; Algebra; Functions; Modeling; Geometry; and Statistics and Probability. The following Math Standards have been identified by the Bismarck Public School District as prioritized for the school year.

(N-Q) Quantities

• MAT-HS.N-Q.01 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
• MAT-HS.N-Q.02 Define appropriate quantities for the purpose of descriptive modeling.
• MAT-HS.N-Q.03 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

(A-SSE) Seeing Structure in Expressions

• MAT-HS.A-SSE.01 Interpret expressions that represent a quantity in terms of its context.
  • a. Interpret parts of an expression, such as terms, factors, and coefficients.
  • b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
• MAT-HS.A-SSE.02 Use the structure of an expression to identify ways to rewrite it.
• MAT-HS.A-SSE.03 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.\
  • a. Factor a quadratic expression to reveal the zeros of the function it defines.
  • b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • c. Use the properties of exponents to transform expressions for exponential functions.

(A-CED) Creating Equations

• MAT-HS.A-CED.01 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• MAT-HS.A-CED.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• MAT-HS.A-CED.03 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
• MAT-HS.A-CED.04 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

(A-REI) Reasoning With Equations & Inequalities

• MAT-HS.A-REI.01 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
• MAT-HS.A-REI.03 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
• MAT-HS.A-REI.04 Solve quadratic equations in one variable.
  • a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.
  • b. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
• MAT-HS.A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
• MAT-HS.A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
• MAT-HS.A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

(N-RN) The Real Number System

• MAT-HS.N-RN.01 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
• MAT-HS.N-RN.02 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
• MAT-HS.N-RN.03 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

(F-IF) Interpreting Functions

• MAT-HS.F-IF.01 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
• MAT-HS.F-IF.02 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
• MAT-HS.F-IF.03 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
• MAT-HS.F-IF.04 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
• MAT-HS.F-IF.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
• MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  • b. Use the properties of exponents to interpret expressions for exponential functions.
• MAT-HS.F-IF.09 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

(F-BF) Building Functions

• MAT-HS.F-BF.01 Write a function that describes a relationship between two quantities.
  • a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
  • b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
  • c. Compose functions.
• MAT-HS.F-BF.02 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

(F-LE) Linear, Quadratic, & Exponential Models

• None Identified

(S-ID) Interpreting Categorical & Quantitative Data

• MAT-HS.S-ID.01 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-HS.S-ID.02 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
• MAT-HS.S-ID.03 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

(A-APR) Arithmetic with Polynomials & Rational Expressions

• MAT-HS.A-APR.01 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.