High School (Montana Content Standards)

Core Numeric Reasoning (NUM)

• MT.CORE.NUM.REAL.1 Reason out the properties of integer exponents, including scientific notation.
• MT.CORE.NUM.REAL.2 Represent and compute with very large and very small numbers in scientific notation.
• MT.CORE.NUM.REAL.3 Define, work with and compare rational and irrational numbers in different forms, including in Montana Indigenous and local contexts.

Core Algebraic and Functional Reasoning (ALG)

• MT.CORE.ALG.FUN.1 Interpret the terms, factors and coefficients of an expression.
• MT.CORE.ALG.FUN.2 Understand what a function is and tell functions apart from other relations.
• MT.CORE.ALG.FUN.3 Represent functions with tables, labeled graphs, equations and words using technology, choosing the best view and comparing functions.
• MT.CORE.ALG.FUN.4 Use function notation, evaluate functions and interpret notation in context, including Montana Indigenous and local contexts.
• MT.CORE.ALG.FUN.5 Find domain and range, including limits set by context, with Montana Indigenous and local contexts.
• MT.CORE.ALG.FUN.6 Understand a two-variable equation's graph as the set of all its solutions.
• MT.CORE.ALG.FUN.7 Understand that rewriting an expression in an equivalent form can reveal different features.
• MT.CORE.ALG.FUN.8 Solve literal equations for a quantity of interest.
• MT.CORE.ALG.LIN.1 Understand that linear functions change at a constant rate.
• MT.CORE.ALG.LIN.2 Read slope as rate of change and the y-intercept as starting value.
• MT.CORE.ALG.LIN.3 Represent linear functions with tables, graphs, equations and words using technology, including Montana Indigenous and local contexts.
• MT.CORE.ALG.LIN.4 Use slope-intercept, point-slope and standard forms, choosing and converting between them and linking each to slope, points or intercepts.
• MT.CORE.ALG.LIN.5 Understand a solution to a system as a point that satisfies both equations.
• MT.CORE.ALG.LIN.6 Solve linear systems by graphing, substitution and elimination, including zero, one or infinitely many solutions.
• MT.CORE.ALG.QUAD.1 See that quadratics lack a constant rate of change but have constant second differences, and find them in tables.
• MT.CORE.ALG.QUAD.2 Represent quadratics with tables, graphs, equations and words using technology, including Montana Indigenous and local contexts.
• MT.CORE.ALG.QUAD.3 Use factored, standard and vertex forms of quadratics, choosing and converting between them and linking them to zeros and the vertex.
• MT.CORE.ALG.QUAD.4 Solve quadratics by factoring, graphing, completing the square, inverse operations and the quadratic formula.
• MT.CORE.ALG.EXP.1 See that exponential functions have a constant ratio over equal intervals and find it in tables and equations.
• MT.CORE.ALG.EXP.2 Read a as the starting value and b as the growth or decay factor in y = a·b^x.
• MT.CORE.ALG.EXP.3 Understand how a growth or decay factor relates to a growth or decay rate.
• MT.CORE.ALG.EXP.4 Represent exponential functions with tables, graphs, equations and words using technology, including Montana Indigenous and local contexts.
• MT.CORE.ALG.EXP.5 Solve exponential equations by graphing with technology.
• MT.CORE.ALG.MOD.1 Model situations with linear, quadratic or exponential functions, choosing the best fit or none and noting solutions may lie off the curve.
• MT.CORE.ALG.MOD.2 Interpret the coefficients of linear, quadratic and exponential models in context, including Montana Indigenous and local contexts.
• MT.CORE.ALG.MOD.3 Pick and interpret units in formulas, graphs and displays to guide modeling, including Montana Indigenous and local contexts.
• MT.CORE.ALG.MOD.4 Report modeled quantities with accuracy suited to measurement limits, including Montana Indigenous and local contexts.

Core Data Reasoning and Probability (DATA)

• MT.CORE.DATA.LIT.1 Tell quantitative from categorical data and use displays and analysis suited to each.
• MT.CORE.DATA.LIT.2 Pose a statistical question about whether two variables are linked, run an investigation and argue from the results.
• MT.CORE.DATA.LIT.3 Tell association apart from causation.
• MT.CORE.DATA.INT.1 Use technology to arrange data, even very large sets, into a usable structure.
• MT.CORE.DATA.INT.2 Display one-variable data on a number line in the best format and two-variable data on a scatter plot.
• MT.CORE.DATA.INT.3 Understand standard deviation as a measure of spread and compute it with technology.
• MT.CORE.DATA.INT.4 Interpret differences in shape, center and spread of distributions in context, allowing for outliers.
• MT.CORE.DATA.INT.5 Compare two or more distributions by shape, center and spread in context, including Montana Indigenous and local contexts.
• MT.CORE.DATA.INT.6 Analyze linear relationships in paired data: scatter plots, least-squares lines, residuals and correlation, with Montana Indigenous and local contexts.
• MT.CORE.DATA.INT.7 Analyze two categorical variables with two-way tables and displays, relative frequencies and trends, with Montana Indigenous and local contexts.
• MT.CORE.DATA.PROB.1 Understand sample spaces and describe events as subsets of them.
• MT.CORE.DATA.PROB.2 Judge independence and find conditional probability with two-way tables, tree or Venn diagrams, with Montana Indigenous and local contexts.

Core Geometric Reasoning (GEOM)

• MT.CORE.GEOM.TRANS.1 Represent plane transformations using a variety of methods.
• MT.CORE.GEOM.TRANS.2 Define congruence by rigid motions, use it to show triangle congruence, and verify the ASA, SAS and SSS tests.
• MT.CORE.GEOM.TRANS.3 Define similarity by similarity transformations, verify triangle similarity conditions and establish the AA test.
• MT.CORE.GEOM.ARG.1 Investigate, conjecture and prove theorems about lines and angles, triangles, quadrilaterals and circles, sharing proofs in varied ways.
• MT.CORE.GEOM.MEAS.1 Use the Pythagorean Theorem to find distances on the coordinate plane.
• MT.CORE.GEOM.MEAS.2 Derive the equation of a circle from its center and radius with the Pythagorean Theorem.
• MT.CORE.GEOM.MEAS.3 Use similarity to define sine, cosine and tangent, apply them in special right triangles and solve right triangles.
• MT.CORE.GEOM.MEAS.4 Model objects with shapes to solve problems on perimeter, area, surface area, volume and scale factor, with Montana Indigenous and local contexts.

Core Plus Number and Quantity (NUM)

• MT.PLUS.NUM.REAS.1 Extend exponent properties to rational exponents and convert between exponent and radical forms.
• MT.PLUS.NUM.REAS.2 Know complex numbers a + bi with i squared = −1, and add, subtract, multiply, divide and conjugate them.

Core Plus Algebraic and Functional Reasoning (ALG)

• MT.PLUS.ALG.FUN.1 Describe how adding or multiplying by k inside or outside f changes its graph, for positive and negative k.
• MT.PLUS.ALG.FUN.2 Understand how a function and its inverse relate.
• MT.PLUS.ALG.POLY.1 Understand polynomials as products of linear factors.
• MT.PLUS.ALG.POLY.2 Use factored and standard forms of polynomials, choosing and converting between them and linking factors to zeros.
• MT.PLUS.ALG.POLY.3 Graph polynomials with and without technology, showing zeros, relative extremes and end behavior.
• MT.PLUS.ALG.POLY.4 Solve quadratics with complex solutions and explain why they come in conjugate pairs.
• MT.PLUS.ALG.EXP.1 Understand logarithms as inverses of exponential functions.
• MT.PLUS.ALG.EXP.2 Understand why e is the natural base.
• MT.PLUS.ALG.EXP.3 Write exponential functions as a·b^x and P·e^(rt), and logarithms in base 10 and base e.
• MT.PLUS.ALG.EXP.4 Graph exponential and log functions with and without technology, showing intercepts, asymptotes and end behavior.
• MT.PLUS.ALG.EXP.5 Solve exponential and log equations with inverse operations, with and without technology.
• MT.PLUS.ALG.TRIG.1 Use the unit circle to extend trig functions to all real numbers, defining sine and cosine and the other four from them.
• MT.PLUS.ALG.TRIG.2 Understand and use radians and convert between degrees and radians.
• MT.PLUS.ALG.TRIG.3 Graph sine and cosine with period, midline and amplitude, and tangent with period and asymptotes.
• MT.PLUS.ALG.TRIG.4 Solve trig equations with and without technology.
• MT.PLUS.ALG.TRIG.5 Use the Laws of Sines and Cosines to find unknown parts of non-right triangles.
• MT.PLUS.ALG.MOD.1 Model situations with polynomial, exponential, log or trig functions, choosing the best fit or none, with Montana Indigenous and local contexts.
• MT.PLUS.ALG.MOD.2 Interpret coefficients of polynomial, exponential, log and trig models in context, including Montana Indigenous and local contexts.
• MT.PLUS.ALG.MOD.3 Use and interpret units correctly when modeling.
• MT.PLUS.ALG.MOD.4 Report modeled quantities with accuracy suited to measurement limits.

Core Plus Data Reasoning (DATA)

• MT.PLUS.DATA.NORM.1 Decide whether a data set is normally distributed.
• MT.PLUS.DATA.NORM.2 Find mean and standard deviation of normal data with technology and use the empirical rule to estimate percentages.
• MT.PLUS.DATA.NORM.3 Estimate areas under a normal curve in context with calculators, spreadsheets or tables.
• MT.PLUS.DATA.DES.1 Tell apart surveys, experiments and observational studies and explain the role of randomization in each.
• MT.PLUS.DATA.DES.2 Contrast random sampling with random assignment, explaining effects of non-random groups and where bias can enter surveys.
• MT.PLUS.DATA.DES.3 Simulate sampling distributions of means to see how sample size affects variability, relating spread to sigma over root n.
• MT.PLUS.DATA.INF.1 Tell a statistic from a parameter and use random samples to infer population parameters.
• MT.PLUS.DATA.INF.2 Estimate a parameter from a sample and express uncertainty with a confidence interval built by resampling.
• MT.PLUS.DATA.INF.3 Test whether two groups differ using the observed difference and a randomization test to see if chance explains it.