2026 Montana Mathematics Content Standards

Flexibly count to 100 by ones and by tens.

Understand the relationship between numbers and quantities and connect counting to cardinality by recognizing that each ...

Count to answer "how many?" in a variety of arrangements and, given a number, produce a set within 20.

Describe the relative positions of objects in their environment. This standard should incorporate cultural context relat...

Analyze and compare two- and three-dimensional shapes using informal language and other attributes.

Model shapes in the environment. This standard should incorporate cultural context relating to Montana Indigenous People...

Describe several attributes of a single object.

Directly compare two objects with a measurable attribute in common using comparative language.

Classify, count, and sort objects into categories. This standard should incorporate cultural context relating to Montana...

Describe attributes and identify the names of coins.

Explain time in days, months, years, and seasons.

Compose and decompose numbers from 11-19 into ten ones and further ones in multiple ways and record each composition or ...

Represent addition and subtraction in multiple ways.

Solve addition and subtraction problems in context within 10. This standard should incorporate cultural context relating...

Decompose numbers less than or equal to 10 into pairs in multiple ways.

For any number from 1 to 9, find the number that makes 10 when added to the given number.

Flexibly and accurately add and subtract within 5.

Recognize the characteristics of the commutative property in addition.

Compose new shapes using two- and three-dimensional shapes.

Partition circles and rectangles into two and four equal shares. Describe the shares using the words: halves, fourths, a...

Order three objects by length and compare the lengths of two objects indirectly by using a third object. This standard s...

Express the length of an object as a whole number of length units. Understand that the measurement of an object is the n...

Identify the value of coins.

Organize, represent, and interpret data with up to three categories by: Asking and answering questions about the total n...

Flexibly count, read, write, and represent numbers to 120.

Understand that ten is a unit composed of ten ones and that a two-digit number represents tens and ones.

Compare two two-digit numbers using comparison symbols >, =, and <.

Build a foundation for addition within 100 by: Adding two-digit to one-digit numbers, and Adding multiples of 10 to two-...

Using place value, given a two-digit number, find 10 more or 10 less than the number.

Subtract multiples of 10 from a two-digit number.

Use addition and subtraction within 20 to solve problems of all types. This standard should incorporate cultural context...

Solve problems in context that call for addition of three whole numbers with a sum less than or equal to 20 in context o...

Flexibly compose and decompose numbers to add and subtract.

Flexibly, accurately, and efficiently add and subtract within 10.

Use multiple strategies to add and subtract within 20.

Understand the meaning of the equal sign and determine if equations are true or false.

Determine the unknown number in an addition or subtraction equation relating to three numbers.

Recognize and draw shapes having specified attributes.

Partition a rectangle into rows and columns of same-size squares and find the total number.

Partition circles and rectangles into equal shares, recognize that equal shares need not have the same shape, and expres...

Organize, represent, and interpret data with up to four categories. This standard should incorporate cultural context re...

Solve addition and subtraction problems of all types using data presented.

Understand the relationship between unit sizes and number of units by measuring a single object using two different unit...

Estimate lengths using units of common measurement.

Use addition and subtraction within 100 to solve problems in context involving lengths that are given in the same units....

Represent whole numbers as lengths from 0 and represent sums and differences within 100 on a number line.

Generate measurement data and present the data in multiple ways. This standard should incorporate cultural context relat...

Understand one hundred is a unit composed of ten tens and that three-digit numbers represent amounts of hundreds, tens, ...

Skip-count by 5s, 10s, and 100s.

Flexibly count, read, write, and represent numbers to 1000.

Compare two three-digit numbers using >, =, and < symbols.

Flexibly, accurately, and efficiently add and subtract within 100 using multiple strategies.

Add up to four two-digit numbers using multiple strategies.

Add and subtract within 1000 using multiple strategies.

Using place value, add or subtract 10 or 100 from a given number.

Understand and make connections between different strategies for addition and subtraction.

Use addition and subtraction within 100 to solve one- and two-step problems in context involving all problem types. This...

Flexibly, accurately, and efficiently add and subtract within 20 using mental strategies.

Determine whether a group of objects, up to 20, has an odd or even number of members.

Use addition to find the total number of objects arranged in rectangular arrays.

Tell and write time on an analog and digital clock to the nearest minute and measure time intervals in minutes and solve...

Measure and estimate liquid volumes and masses of objects using customary and metric units by adding, subtracting, multi...

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-s...

Recognize area as an attribute of plane figures and understand concepts of area measurement by: Understanding that a squ...

Measure areas by counting unit squares.

Relate area to the operations of multiplication and addition by: Finding the area of a rectangle with whole-number side ...

Solve problems in context involving perimeters of polygons, including finding the perimeter given the side lengths, find...

Understand a fraction as a number on the number line by: Representing a unit fraction on a number line, Representing a f...

Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by: Underst...

Use multiplication and division within 100 to solve problems in context in situations involving equal groups, arrays, an...

Apply the commutative property of multiplication, associative property of multiplication, and distributive property of m...

Use division as an unknown factor problem.

Flexibly, accurately, and efficiently multiply and divide within 100, using strategies such as the relationship between ...

Solve two-step problems in context using the four operations, represent these problems using equations with a letter sta...

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded...

Know relative sizes of units within one system of measurement and within the system, express measurements of a larger un...

Use the four operations to solve problems in context using distances, intervals of time, liquid volumes, masses of objec...

Make a line plot to display a data set of measurements in fractions of a unit and solve problems involving addition and ...

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint and understand concepts o...

Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, flexibly using...

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, flexibly using strate...

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models and use this prin...

Understand a fraction a/b with a > 1 as a sum of fractions 1/b by: Understanding addition and subtraction of fractions a...

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number by: Understanding a ...

Solve multistep problems in context with whole numbers and having whole-number answers using the four operations, includ...

Find all factor pairs for a whole number in the range 1-100, recognize that a whole number is a multiple of each of its ...

Analyze a number or shape pattern that follows a given rule, identify and explain informally features of the pattern tha...

Represent problems including problems in context by graphing points in the first quadrant of the coordinate plane and in...

Convert among different-sized standard measurement units within a given measurement system and use these conversions in ...

Make a line plot to display a data set of measurements in fractions of a unit and use operations on fractions to solve p...

Recognize volume as an attribute of solid figures and understand concepts of volume measurement by: Understanding that a...

Relate volume to the operations of multiplication and addition and volume problems including problems in context by: Fin...

Flexibly, accurately, and efficiently find whole-number quotients of whole numbers with up to four-digit dividends and t...

Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings. This standard should incor...

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivale...

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction by: Expr...

Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the bas...

Solve problems in context that involve multiplication of fractions and mixed numbers. This standard should incorporate c...

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit...

Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols using the orde...

Generate two numerical patterns using given rules and complete an input-output table for the data, identify apparent rel...

Write and evaluate numerical expressions involving whole-number bases and exponents.

Write, read, and evaluate expressions with variables by: Writing expressions that record operations with numbers and wit...

Apply the properties of operations including the distributive property, to generate equivalent expressions and determine...

Understand how to solve an equation or inequality as a process by using substitution to determine whether a given number...

Write expressions when solving problems in context and understand that a variable can represent an unknown number, or an...

Write an inequality of the form x > c or x < c to represent a constraint or condition in problems including problems in ...

Use variables to represent two quantities that change in relationship to one another, analyze the relationship between t...

Find the area of triangles, quadrilaterals, and other polygons by composing them into rectangles or decomposing them int...

Find the volume of a right rectangular prism with fractional edge lengths by filling it with unit cubes of the appropria...

Draw polygons in the coordinate plane given coordinates for the vertices, find the length of a horizontal or vertical si...

Represent three-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface ...

Represent, interpret, and compute quotients of fractions and solve problems in context involving division of fractions b...

Understand a rational number as a point on the number line and extend number line diagrams and coordinate axes by: Recog...

Understand ordering and absolute value of rational numbers by: Interpreting statements of inequality as statements about...

Graph points in all four quadrants of the coordinate plane and include the use of coordinates and absolute value to find...

Use ratio and rate reasoning to solve proportional problems in context about unit rates, percentages (as a rate per 100)...

Understand that a set of data collected to answer a statistical question has a distribution that can be described by its...

Display numerical data in plots on a number line, including dot plots, histograms, and box plots, and describe any overa...

Characterize numerical data sets from a sample in relation to their context, such as by: Reporting the number of observa...

Use properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients and gene...

Understand that rewriting an expression in different forms in a problem in context can show how the quantities in it are...

Write and solve one- and two-step equations including problems in context with rational numbers, convert between forms a...

Use variables to represent quantities and construct simple equations and inequalities to solve problems in context. This...

Know and use the formulas for the area and circumference of a circle and give an informal derivation of the relationship...

Solve geometrical problems including problems in context that involve area, volume, and surface area of two- and three-d...

Add and subtract rational numbers, represent addition and subtraction on a horizontal or vertical number line diagram, a...

Multiply and divide rational numbers and use operations of rational numbers to solve problems in context. This standard ...

Write any rational number as a fraction, decimal, and percent using long division, and know that the decimal form of a r...

Recognize and represent proportional relationships between quantities, using tables, graphs, and equations by: Deciding ...

Use proportional relationships to solve multi-step ratio and percent problems, including problems in context that involv...

Understand statistics can be used to gain information about a population by examining a representative sample of the pop...

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest and gener...

Visually analyze two data distributions to compare measures of central tendency and variability.

Use measures of central tendency and measures of variability for numerical data from random samples to draw comparative ...

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event...

Find the experimental probability of a chance event by collecting data on the chance process that produces it and observ...

Develop a theoretical probability model and use it to find probabilities of events, compare theoretical and experimental...

Represent sample spaces for compound events, identify the desired outcomes in the sample spaces, and find probabilities ...

Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a po...

Represent very large or very small quantities using scientific notation, limited to a single digit times an integer powe...

Perform operations with numbers expressed in scientific notation.

Graph proportional relationships, interpret the unit rate as the slope of the graph, and compare two different proportio...

Solve linear equations in one variable by: Giving examples of linear equations in one variable with one solution, infini...

Analyze and solve pairs of simultaneous linear equations by: Understanding that solutions to a system of two linear equa...

Compare properties of two functions using tables, graphs, and equations.

Interpret the equation y = mx + b as defining a linear function whose graph is a straight line with slope m passing thro...

Given linear data relating two quantities, construct a linear function that models the data and interpret the rate of ch...

Verify experimentally the properties of rotations, reflections, and translations and understand that these are rigid tra...

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates....

Apply the Pythagorean Theorem to determine unknown side lengths in right triangle problems, including problems in contex...

Know real numbers are made up of rational and irrational numbers, understand informally that every number has a decimal ...

Construct and interpret frequencies and relative frequencies for bivariate categorical data in a two-way table to invest...

Understand that exponential functions have a constant common ratio over equal intervals, and identify the common ratio i...

Understand a as the initial value and b as the growth/decay factor for an exponential function written in standard form,...

Understand the relationship between growth/decay factor and growth/decay rate.

Represent exponential functions using tables, graphs, equations, and verbal situations; using technology strategically. ...

Solve exponential equations graphically, while using technology strategically.

Understand the definition of a function and distinguish between functions and relations.

Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while usi...

Understanding that different representations highlight different aspects of functions, choosing the representation that ...

Comparing properties of two functions, including when each is represented in a different way.

Use function notation, evaluate functions, and interpret statements that use function notation in context. This standard...

Identify the domain and range of a function, including considering the constraints imposed by context. This standard sho...

Understand that a graph of an equation in two variables is the set of all of its solutions plotted in a coordinate plane...

Understand that expressions can be rewritten in equivalent forms to make different characteristics or features visible.

Rearrange literal equations to highlight quantities of interest.

Understand that linear functions have a constant rate of change.

Understand slope as a rate of change and y-intercept as the initial value.

Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically....

Identifying the rate of change and initial value in each representation.

Converting between representations, and

Writing equations for a line perpendicular or parallel to a given line that passes through a given point.

Understand that linear equations can be represented in multiple forms and the specific features of each form by: Choosin...

Choosing the form strategically when writing an equation based on given information and intended use,

Converting between slope-intercept, point-slope, and standard form symbolically,

Understanding the relationship between slope-intercept form, the rate of change, and the initial value,

Understanding the relationship between point-slope form, the rate of change, and a given point, and

Understanding the relationship between standard form and the x- and y-intercepts.

Understand that a solution to a system of equations is a coordinate pair that makes both equations true.

Solve systems of linear equations by graphing, substitution, and elimination, including systems with zero, one, or infin...

Model situations in context, with linear, quadratic, and exponential functions. This standard should incorporate cultura...

Determining if a set of data is best modeled by a linear function, quadratic function, exponential function, or none, an...

Understanding that there are contexts where solutions may not lie on the curve.

Interpret the coefficients in a linear, quadratic, and exponential model in context. This standard should incorporate cu...

Choose and interpret measurement units in formulas, graphs, and data displays to understand problems and to guide proble...

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities in modeling situations. T...

Understand that quadratic functions do not have a constant rate of change but have a constant second difference over equ...

Represent quadratic functions using tables, graphs, equations, and verbal situations, while using technology strategical...

Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Ch...

Choosing the form strategically when writing an expression based on given information and intended use,

Converting between factored, standard, and vertex forms symbolically and using representations,

Understanding the relationship between factored form and the zeros of the function, and

Understanding the relationship between vertex form and the vertex of the function.

Solve quadratic equations by factoring, graphing, completing the square, using inverse operations, and the quadratic for...

Use technology to organize data, including very large data sets, into a useful and manageable structure.

Represent the distribution of univariate quantitative data with plots on the real number line, choosing a format most ap...

Understand that standard deviation measures the variability of a data distribution, and calculate standard deviation usi...

Interpret differences in the shape, center, and spread of quantitative data distributions, in context, accounting for po...

Compare and contrast two or more quantitative data distributions, using shape, center, and spread in context. This stand...

Analyze the relationship between two quantitative data distributions in context that have a linear association. This sta...

Using technology strategically, represent two quantitative data distributions on scatter plots,

Describing verbally how the variables are related,

Using technology to find the least-squares regression line (line of best) fit for two quantitative variables,

Understanding that the line of best fit minimizes the square of the residuals, and

Understanding correlation as a measure of linear association and using technology, compute the correlation coefficient o...

Analyze the relationship between two categorical variables in context. This standard should incorporate cultural context...

Summarizing categorical data for two categories in two-way frequency tables and visual representations,

Interpreting relative frequencies for categorical data in context, and

Identifying possible associations and trends in categorical data.

Distinguish between quantitative and categorical data and use representations and analysis techniques that are appropria...

Ask a statistical question to determine whether there appears to be an association between two variables, design and car...

Distinguish between association and causation.

Understand the concept of a sample space and describe events as subsets of a sample space.

Understand the concepts of conditional probability and independence in context. This standard should incorporate cultura...

Determining whether two events, A and B, are independent by using two-way tables, tree diagrams, and/or Venn diagrams, a...

Computing the conditional probability of event A given event B by using two-way tables, tree diagrams, and/or Venn diagr...

Investigate, conjecture, prove theorems, and communicate the proofs in a variety of ways by: Proving theorems about line...

Proving theorems about lines and angles. Theorems include: vertical angles are congruent, when a transversal crosses par...

Proving theorems about triangles. Theorems include: the sum of the measures of the interior angles of a triangle is 180˚...

Proving theorems about parallelograms and other quadrilaterals. Theorems include: necessary and sufficient conditions fo...

Proving theorems about circles. Theorems include: the relationship between central, inscribed, and circumscribed angles,...

Use the Pythagorean Theorem to calculate distance in the coordinate plane.

Derive the equation of a circle of a given center and radius using the Pythagorean Theorem.

Use similarity to explore and define the sine ratio, cosine ratio, and tangent ratio in terms of right triangles by: Der...

Deriving and applying the trigonometric ratios in special right triangles, and

Using trigonometric ratios and the Pythagorean Theorem to solve right triangles.

Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in co...

Modeling and solving problems with 2D shapes by using the perimeter and area of polygons, circles, and composite shapes ...

Modeling and solving problems with 3D solids by using surface area and volume of solids, including composite solids and ...

Deriving and applying the relationships between the lengths, perimeters, areas, and volumes of similar figures in relati...

Represent transformations in the plane using a variety of methods.

Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps on...

Verifying that two triangles are congruent if, but not only if, the following groups of corresponding parts are congruen...

Define the similarity of two figures in terms of similarity transformations by: Verifying that two triangles are similar...

Verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and correspondin...

Use reasoning to establish properties of integer exponents, including scientific notation.

Represent and perform operations within very large and very small numbers using scientific notation.

Define, manipulate, interpret, and compare real numbers presented through different representations, including both rati...

Understand logarithmic functions as the inverse of exponential functions.

Understand why e is defined as the natural base.

Understand that exponential and logarithmic functions can be represented using multiple forms by: Expressing exponential...

Expressing exponential functions in the form f(x) = a · b^x and f(x) = Pe^(r·t), and

Expressing logarithmic functions in base 10 and base e.

Graph logarithmic and exponential functions with and without the use of technology by identifying intercepts, asymptotes...

Solve exponential and logarithmic equations using inverse operations with and without the use of technology.

Identify the effect on the graph of replacing f(x)f(x) by f(x) + k, k · f(x), f(k · x), and f(x + k) for specific values...

Understand the relationship between a function and its inverse.

Model situations in context with polynomial, exponential, logarithmic, and trigonometric functions. This standard should...

Determining if a set of data is best modeled by a polynomial, exponential, logarithmic, or trigonometric function or non...

Understanding that there are contexts where solutions may not lie on the curve.

Interpret the coefficients in a polynomial, exponential, logarithmic, and trigonometric model in context. This standard ...

Use and interpret units correctly in modeling situations.

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities in modeling situations.

Understand polynomials are created by multiplying linear factors.

Understand that polynomial expressions can be represented in both factored and standard form, and the specific features ...

Choosing the form strategically based on given information and intended use when writing an expression,

Converting between factored and standard form symbolically and using representations (e.g., area model), and

Interpreting the relationship between the factored form of the expression and the zeros of the function.

Graph polynomial functions with and without the use of technology, by identifying zeros, relative maxima and minima, and...

Solve quadratic equations that have complex solutions and understand why the solutions form a conjugate pair.

Understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numb...

Defining the sine and cosine functions in terms of the unit circle, and

Defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine.

Understand and use the radian measure of an angle and convert between degree and radian measures.

Graph trigonometric functions with and without the use of technology by: Graphing sine and cosine functions, identifying...

Graphing sine and cosine functions, identifying period, midline, and amplitude, and

Graphing tangent functions, identifying period and asymptotes.

Solve trigonometric equations with and without the use of technology.

Apply the Law of Sines and the Law of Cosines to find unknown measurements in non-right triangles.

Describe the purposes of and differences among sample surveys, experiments, and observational studies and explain how ra...

Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups...

Explaining the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experi...

Evaluating where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are ...

Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by: Si...

Simulating a sampling distribution of sample means from a population with a known distribution, observing the effect of ...

Demonstrating that the standard deviation of each simulated sampling distribution is the known standard deviation of the...

Distinguish between a statistic and a parameter and use statistical processes to make inferences about population parame...

Estimate a population parameter from a representative sample by: Understanding why the sample statistic is the best esti...

Understanding why the sample statistic is the best estimate for the associated population parameter,

Understanding that sampling variability introduces uncertainty in the estimate, and account for the uncertainty with a c...

Use data from a randomized experiment to test the hypothesis that two groups are equal by: Interpreting the difference o...

Interpreting the difference or ratio between the group means as the observed effect between the groups, and

Understanding that an observed effect may be due to randomization and using a randomization test (repeatedly reshuffling...

Determine if a data set is normally distributed.

Use technology to find the mean and standard deviation of a normally distributed data set and apply the empirical rule t...

Estimate areas under a normal curve to solve problems in context, using calculators, spreadsheets, and tables as appropr...

Extend the properties of exponents to rational exponents, including converting between exponential and radical forms.

Understand there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b as r...

Adding, subtracting, multiplying, and dividing complex numbers, and

Finding the conjugate of a complex number.