2023 Wyoming Mathematics Content and Performance Standards

Count to 100 by ones and by tens. Count backwards by ones from 20.

Count backwards by ones from 20.

Use one-to-one correspondence when counting objects.

Understand that the last number name said, tells the number of objects counted regardless of their arrangement.

Understand that each successive number name refers to a quantity that is one more, and each previous number name refers ...

Analyze and compare two- and three-dimensional shapes, using informal language to describe their similarities, differenc...

Use simple shapes to compose squares, rectangles, and hexagons.

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. ...

Solve word problems using objects and drawings to find sums up to 10 and differences within 10.

Decompose numbers less than or equal to 10 in more than one way.

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

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g...

Partition circles and rectangles into two and four equal shares and:

Describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter o...

Describe the whole as two of, or four of the shares.

Recognize that decomposing into more equal shares creates smaller shares.

Identify U.S. coins by value (pennies, nickels, dimes, quarters).

Extend the number sequences to 120. In this range:

Count forward and backward, starting at any number less than 120.

Read numerals.

Write numerals.

Represent a number of objects with a written numeral.

Add within 100, using concrete models or drawings and strategies based on place value:

Including adding a two-digit number and a one-digit number.

Adding a two-digit number and a multiple of 10.

Understand that in adding two-digit numbers, adds tens and tens, ones and ones; and sometimes it is necessary to compose...

Relate the strategy to a written method and explain the reasoning used.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting to...

Add and subtract within 20, demonstrating fluency in addition and subtraction within 10. Use strategies such as counting...

Partition circles and rectangles into two, three, or four equal shares by:

Describing the shares using the words halves, thirds, half of, a third of, etc.

Describing the whole as two halves, three thirds, four fourths.

Recognizing that equal shares of identical wholes need not have the same shape.

Tell and write time from analog and digital clocks in five minute increments using a.m. and p.m.

Solve word problems up to $10 involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (ce...

Three-digit numbers can be decomposed in multiple ways (e.g., 524 can be decomposed as 5 hundreds, 2 tens and 4 ones or ...

Compare pairs of three-digit numbers based on meanings of the hundreds, tens, and ones digits, using the words “is great...

Add and subtract within 100 using strategies based on place value, properties of addition, and/or the relationship betwe...

Add and subtract within 1,000, using concrete models or drawings and strategies based on place value, properties of addi...

Relate the strategy to a written method and explain the reasoning used.

Understand that in adding or subtracting three-digit numbers, add or subtract hundreds and hundreds, tens and tens, ones...

Understand that sometimes it is necessary to compose or decompose tens or hundreds.

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taki...

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know automatically all sums of two one-d...

Use attributes of quadrilaterals to classify rhombuses, rectangles, and squares. Understand that the shared attributes c...

Find the area of a rectangle with whole-number side lengths (dimensions) by multiplying them. Show that this area is the...

Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of addition, and...

Understand and represent fractions on a number line diagram.

Fluently multiply and divide with factors from 1 to 10 using mental strategies. By end of Grade 3, know automatically al...

Solve two-step word problems (limited to the whole number system) using the four basic operations. Students should apply...

Represent these problems using equations with a symbol standing for the unknown quantity.

Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems.

Use strategies based on place value and the properties of multiplication to:

Multiply a whole number of up to four digits by a one-digit whole number.

Multiply a pair of two-digit numbers.

Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models.

Use strategies based on place value, the properties of multiplication, and/or the relationship between multiplication an...

Compare two fractions with different numerators and different denominators by creating common denominators or numerators...

Recognize that comparisons are valid only when the two fractions refer to the same whole.

Record the results of comparisons with symbols >, =, or <.

Justify the conclusions by using a visual fraction model.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decompositio...

Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction, and/or...

Compare and order decimal numbers to hundredths and justify by using concrete and visual models. Record the results of c...

Solve multi-step word problems posed with whole numbers, including problems in which remainders must be interpreted.

Represent these problems using equations with a letter standing for the unknown quantity.

Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situati...

Relate volume to the operations of multiplication and solve real-world and mathematical problems involving volume.

Find the volume of a right rectangular prism with whole number dimensions by multiplying them. Show that this volume is ...

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving divisi...

Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equ...

Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.

Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers b...

Write simple expressions requiring parentheses that record calculations with numbers, and interpret numerical expression...

Identify parts of an expression using mathematical terms (sum, difference, term, product, factor, quotient, coefficient,...

Use Order of Operations to evaluate algebraic expressions using positive rational numbers and whole-number exponents. In...

Use variables to represent unknown numbers and write expressions when solving a real-world or mathematical problem.

Write and solve real-world and mathematical problems in the form of one-step, linear equations involving non negative ra...

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by us...

Add, subtract, multiply, and divide manageable multi-digit decimals using efficient and generalizable procedures includi...

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Find distan...

Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages.

Use ratio reasoning to convert measurement units; convert units appropriately when multiplying or dividing quantities.

Display numerical data in plots on a number line, including dot plots, stem-and-leaf plots, histograms, and box plots.

Summarize numerical data sets in relation to their real-world context.

Describe the context of the data under investigation, including how it was measured and its units of measurement.

Find quantitative measures of center (median, mode and mean) and variability (range and interquartile range). Describe a...

Justify the choice of measures of center (median, mode, or mean) based on the shape of the data distribution and the con...

Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

Write and fluently solve linear equations of the form ax +b = c and a(x + b) = c where a, b, and c are rational numbers.

Write and solve multi-step linear equations that include the use of the Distributive Property and combining like terms. ...

Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.

Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

Investigate the concept of circles.

Demonstrate an understanding of the proportional relationships between diameter, radius, and circumference of a circle.

Understand that π is defined by the constant of proportionality between the circumference and diameter.

Given the formulas for circumference and area of circles, solve real-world and mathematical problems.

Solve real-world and mathematical problems involving:

Area and surface area of objects composed of triangles and quadrilaterals;

Volume of objects composed only of right prisms having triangular or quadrilateral bases.

Solve real-world and mathematical problems involving the four arithmetic operations with rational numbers. (Computations...

Decide whether two quantities in a table or graph are in a proportional relationship.

Solve multi-step real-world and mathematical problems involving ratios and percentages.

Solve real-world and mathematical problems involving:

Understand that a sample is a subset of a population.

Differentiate between random and non-random sampling.

Understand that generalizations from a sample are valid only if the sample is representative of the population.

Understand that random sampling is used to gather a representative sample and tends to support valid inferences about th...

Given measures of center and variability (mean, median and/or mode; range, interquartile range, and/or standard deviatio...

Find and interpret the probability of a random event. Understand that the probability of a random event is a number betw...

Collect multiple samples to compare the relationship between theoretical and experimental probabilities for simple event...

Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequaliti...

Solve linear equations and inequalities with rational number coefficients that include the use of the Distributive Prope...

Recognize the three types of solutions to linear equations: one solution, infinitely many solutions, or no solutions.

Solve systems of two linear equations in two variables with integer solutions by graphing the equations.

Solve simple real-world and mathematical problems leading to two linear equations in two variables given y = mx + b form...

Apply the concepts of linear functions to real-world and mathematical situations.

Understand that the slope is the constant rate of change and the y-intercept is the point where x = 0.

Determine the slope and the y-intercept of a linear function given multiple representations, including two points, table...

Construct a function in slope-intercept form that models a linear relationship between two quantities.

Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation.

Recognize through visual comparison that a two-dimensional figure is congruent to another if the second can be obtained ...

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical proble...

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal exp...

Make comparisons between rational and irrational numbers.

Understand that all real numbers have a decimal expansion.

Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.

Convert repeating decimals to fractions.

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and rel...

Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Estimate solutions graphically and determine algebraic solutions to linear systems, focusing on pairs of linear equation...

Write an expression for the inverse of a simple, invertible function f(x). Understand that an inverse function can be ob...

Graph exponential and logarithmic functions, showing intercepts and end behavior.

Verify that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal...

Construct linear and exponential functions using a graph, a description of a relationship, or two input-output pairs (in...

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base ang...

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses paral...

Use a function to describe data trends to solve problems in the context of the data. Use given functions or choose a fun...