High School

Other Montana Math sets

• Kindergarten
• Standards for Mathematical Practice
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8

*Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by* understanding that different representations highlight different aspects of functions, and choosing the representation that is appropriate for the context.MT.HS.CORE.ALG.FUN.3.a

*Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by* comparing properties of two functions, including when each is represented in a different way.MT.HS.CORE.ALG.FUN.3.b

*Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* identifying the rate of change and initial value in each representation.MT.HS.CORE.ALG.LIN.3.a

*Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* converting between representations.MT.HS.CORE.ALG.LIN.3.b

*Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* writing equations for a line perpendicular or parallel to a given line that passes through a given point.MT.HS.CORE.ALG.LIN.3.c

*Understand that linear equations can be represented in multiple forms and the specific features of each form by* choosing the form strategically when writing an equation based on given information and intended use.MT.HS.CORE.ALG.LIN.4.a

*Understand that linear equations can be represented in multiple forms and the specific features of each form by* converting between slope-intercept, point-slope, and standard form symbolically.MT.HS.CORE.ALG.LIN.4.b

*Understand that linear equations can be represented in multiple forms and the specific features of each form by* understanding the relationship between slope-intercept form, the rate of change, and the initial value.MT.HS.CORE.ALG.LIN.4.c

*Understand that linear equations can be represented in multiple forms and the specific features of each form by* understanding the relationship between point-slope form, the rate of change, and a given point.MT.HS.CORE.ALG.LIN.4.d

*Understand that linear equations can be represented in multiple forms and the specific features of each form by* understanding the relationship between standard form and the x- and y-intercepts.MT.HS.CORE.ALG.LIN.4.e

*Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by* choosing the form strategically when writing an expression based on given information and intended use.MT.HS.CORE.ALG.QUAD.3.a

*Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by* converting between factored, standard, and vertex form symbolically and using representations.MT.HS.CORE.ALG.QUAD.3.b

*Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by* understanding the relationship between factored form and the zeros of the function.MT.HS.CORE.ALG.QUAD.3.c

*Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by* understanding the relationship between vertex form and the vertex of the function.MT.HS.CORE.ALG.QUAD.3.d

*Model situations in context, with linear, quadratic, and exponential functions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* determining if a set of data is best modeled by a linear function, quadratic function, exponential function, or none, and explaining why.MT.HS.CORE.ALG.MOD.1.a

*Model situations in context, with linear, quadratic, and exponential functions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* understanding that there are contexts where solutions may not lie on the curve.MT.HS.CORE.ALG.MOD.1.b

*Analyze the relationship between two quantitative data distributions in context that have a linear association. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* using technology strategically, represent two quantitative data distributions on scatter plots.MT.HS.CORE.DATA.INT.6.a

*Analyze the relationship between two quantitative data distributions in context that have a linear association. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* describing verbally how the variables are related.MT.HS.CORE.DATA.INT.6.b

*Analyze the relationship between two quantitative data distributions in context that have a linear association. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* using technology to find the least-squares regression line (line of best) fit for two quantitative variables.MT.HS.CORE.DATA.INT.6.c

*Analyze the relationship between two quantitative data distributions in context that have a linear association. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* understanding that the line of best fit minimizes the square of the residuals.MT.HS.CORE.DATA.INT.6.d

*Analyze the relationship between two quantitative data distributions in context that have a linear association. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* understanding correlation as a measure of linear association and using technology, compute the correlation coefficient of a linear relationship.MT.HS.CORE.DATA.INT.6.e

*Analyze the relationship between two categorical variables in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* summarizing categorical data for two categories in two-way frequency tables and visual representations.MT.HS.CORE.DATA.INT.7.a

*Analyze the relationship between two categorical variables in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* interpreting relative frequencies for categorical data in context.MT.HS.CORE.DATA.INT.7.b

*Analyze the relationship between two categorical variables in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* identifying possible associations and trends in categorical data.MT.HS.CORE.DATA.INT.7.c

*Understand the concepts of conditional probability and independence in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* determining whether two events, A and B, are independent by using two-way tables, tree diagrams, and/or Venn diagrams, and interpreting the answer in context.MT.HS.CORE.DATA.PROB.2.a

*Understand the concepts of conditional probability and independence in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* computing the conditional probability of event A given event B by using two-way tables, tree diagrams, and/or Venn diagrams, and interpreting the answer in context.MT.HS.CORE.DATA.PROB.2.b

*Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other by* using the definition of congruence in terms of rigid motions to show that two triangles are congruent if, and only if, corresponding pairs of sides and corresponding pairs of angles are congruent.MT.HS.CORE.GEOM.TRANS.2.a

*Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other by* verifying that two triangles are congruent if, but not only if, the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS).MT.HS.CORE.GEOM.TRANS.2.b

*Define the similarity of two figures in terms of similarity transformations by* verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and corresponding pairs of angles are congruent.MT.HS.CORE.GEOM.TRANS.3.a

*Define the similarity of two figures in terms of similarity transformations by* using the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.MT.HS.CORE.GEOM.TRANS.3.b

Prove theorems about lines and angles. Theorems include: vertical angles are congruent, when a transversal crosses parallel lines alternate interior angles are congruent and corresponding angles are congruent, and the points on the perpendicular bisector of a line segment are those equidistant from the segment's endpoints.MT.HS.CORE.GEOM.ARG.1.a

Prove theorems about triangles. Theorems include: the sum of the measures of the interior angles of a triangle is 180?, the Pythagorean Theorem, the base angles of isosceles triangles are congruent, and a line parallel to one side of a triangle divides the other two sides proportionally.MT.HS.CORE.GEOM.ARG.1.b

Prove theorems about parallelograms and other quadrilaterals. Theorems include: necessary and sufficient conditions for rectangles, parallelograms, rhombi, and kites.MT.HS.CORE.GEOM.ARG.1.c

Prove theorems about circles. Theorems include: the relationship between central, inscribed, and circumscribed angles, inscribed angles on a diameter are right angles, and the radius of a circle is perpendicular to the tangent where the radius intersects the circle.MT.HS.CORE.GEOM.ARG.1.d

*Use similarity to explore and define the sine ratio, cosine ratio, and tangent ratio in terms of right triangles by* deriving and applying the trigonometric ratios in special right triangles.MT.HS.CORE.GEOM.MEAS.3.a

*Use similarity to explore and define the sine ratio, cosine ratio, and tangent ratio in terms of right triangles by* using trigonometric ratios and the Pythagorean Theorem to solve right triangles.MT.HS.CORE.GEOM.MEAS.3.b

*Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* modeling and solving problems with 2D shapes by using the perimeter and area of polygons, circles, and composite shapes with portions removed.MT.HS.CORE.GEOM.MEAS.4.a

*Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* modeling and solving problems with 3D solids by using surface area and volume of solids, including composite solids and solids with portions removed.MT.HS.CORE.GEOM.MEAS.4.b

*Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* deriving and applying the relationships between the lengths, perimeters, areas, and volumes of similar figures in relation to their scale factor.MT.HS.CORE.GEOM.MEAS.4.c

*Understand there is a complex number $i$ such that $i^² = -1$, and every complex number has the form $a + bi$ with $a$ and $b$ as real numbers by* adding, subtracting, multiplying, and dividing complex numbers.MT.HS.PLUS.NUM.REAS.2.a

*Understand there is a complex number $i$ such that $i^² = -1$, and every complex number has the form $a + bi$ with $a$ and $b$ as real numbers by* finding the conjugate of a complex number.MT.HS.PLUS.NUM.REAS.2.b

*Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by* choosing the form strategically based on given information and intended use when writing an expression.MT.HS.PLUS.ALG.POLY.2.a

*Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by* converting between factored and standard form symbolically and using representations (e.g., area model).MT.HS.PLUS.ALG.POLY.2.b

*Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by* interpreting the relationship between the factored form of the expression and the zeros of the function.MT.HS.PLUS.ALG.POLY.2.c

*Understand that exponential and logarithmic functions can be represented using multiple forms by* expressing exponential functions in the form $f(x)=ab^x$ and $f(x)=Pe^{(rt)}$.MT.HS.PLUS.ALG.EXP.3.a

*Understand that exponential and logarithmic functions can be represented using multiple forms by* expressing logarithmic functions in base 10 and base $e$.MT.HS.PLUS.ALG.EXP.3.b

*Understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers by* defining the sine and cosine functions in terms of the unit circle.MT.HS.PLUS.ALG.TRIG.1.a

*Understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers by* defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine.MT.HS.PLUS.ALG.TRIG.1.b

*Graph trigonometric functions with and without the use of technology by* graphing sine and cosine functions, identifying period, midline, and amplitude.MT.HS.PLUS.ALG.TRIG.3.a

*Graph trigonometric functions with and without the use of technology by* graphing tangent functions, identifying period and asymptotes.MT.HS.PLUS.ALG.TRIG.3.b

*Model situations in context with polynomial, exponential, logarithmic, and trigonometric functions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* determining if a set of data is best modeled by a polynomial, exponential, logarithmic, or trigonometric function or none, and explaining why.MT.HS.PLUS.ALG.MOD.1.a

*Model situations in context with polynomial, exponential, logarithmic, and trigonometric functions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by* understanding that there are contexts where solutions may not lie on the curve.MT.HS.PLUS.ALG.MOD.1.b

*Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect by* explaining the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments.MT.HS.PLUS.DATA.DES.2.a

*Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect by* evaluating where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of interest.MT.HS.PLUS.DATA.DES.2.b

*Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by* simulating a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability.MT.HS.PLUS.DATA.DES.3.a

*Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by* demonstrating that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root of the sample size.MT.HS.PLUS.DATA.DES.3.b

*Estimate a population parameter from a representative sample by* understanding why the sample statistic is the best estimate for the associated population parameter.MT.HS.PLUS.DATA.INF.2.a

*Estimate a population parameter from a representative sample by* understanding that sampling variability introduces uncertainty in the estimate, and account for the uncertainty with a confidence interval by:MT.HS.PLUS.DATA.INF.2.b

*Use data from a randomized experiment to test the hypothesis that two groups are equal by* interpreting the difference or ratio between the group means as the observed effect between the groups.MT.HS.PLUS.DATA.INF.3.a

*Use data from a randomized experiment to test the hypothesis that two groups are equal by* understanding that an observed effect may be due to randomization and using a randomization test (repeatedly reshuffling the observed data into new groups) to determine the probability that an observed effect is due to randomization alone.MT.HS.PLUS.DATA.INF.3.b