Mathematics Standards by Grade

Count to 100 by ones and by tens.

Understand the relationship between numbers and quantities.

Count to answer "how many?" questions about up to 20 objects.

Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.

Compare two numbers between 1 and 10 presented as written numerals.

Correctly name shapes regardless of orientation or overall size.

Analyze and compare two- and three-dimensional shapes by attributes.

Model shapes in the world by building and drawing shapes.

Classify objects into given categories, count the number of objects in each category, and sort the categories by count.

Compose and decompose numbers from 11 to 19 into ten ones and some further ones.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Order objects by length and compare the lengths of two objects indirectly.

Express the length of an object as a whole number of length units.

Organize, represent, and interpret data with up to three categories.

Understand that the two digits of a two-digit number represent amounts of tens and ones.

Compare two two-digit numbers based on meanings of the tens and ones digits.

Use addition and subtraction within 20 to solve word problems.

Understand subtraction as an unknown-addend problem.

Add and subtract within 20 using strategies such as counting on and making ten.

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

Recognize and draw shapes having specified attributes.

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

Tell and write time from analog and digital clocks to the nearest five minutes.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols.

Count within 1000; skip-count by 5s, 10s, and 100s.

Fluently add and subtract within 100 using strategies based on place value and properties of operations.

Explain why addition and subtraction strategies work using place value and operation properties.

Determine whether a group of objects has an odd or even number of members.

Recognize area as an attribute of plane figures and understand concepts of area measurement.

Measure areas by counting unit squares.

Solve real-world and mathematical problems involving perimeters of polygons.

Use place value understanding to round whole numbers to the nearest 10 or 100.

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.

Understand a fraction as a number on the number line and represent fractions on a number line diagram.

Interpret products of whole numbers as equal groups.

Interpret whole-number quotients of whole numbers using equal shares and equal groups.

Use multiplication within 100 to solve word problems in situations involving equal groups and arrays.

Apply properties of operations as strategies to multiply.

Understand division as an unknown-factor problem.

Look for and make use of structure.

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form, and compare them.

Use place value understanding to round multi-digit whole numbers to any place.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using place value strategies and the properties of operations.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value and the properties of operations.

Explain why a fraction is equivalent to another fraction by using visual fraction models and attention to the number and size of the parts.

Compare two fractions with different numerators and different denominators and record the comparisons with symbols.

Solve multistep word problems posed with whole numbers using the four operations.

Use a pair of perpendicular number lines, called axes, to define a coordinate system and locate points by ordered pairs.

Represent real world and mathematical problems by graphing points in the first quadrant and interpret coordinate values.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

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

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Explain patterns in the number of zeros of the product when multiplying by powers of 10, and explain patterns in the placement of the decimal point.

Read, write, and compare decimals to thousandths.

Add, subtract, multiply, and divide decimals to hundredths using place value strategies and properties of operations.

Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.

Solve word problems involving addition and subtraction of fractions referring to the same whole.

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

Interpret multiplication as scaling by comparing the size of a product to the size of one factor.

Solve real world problems involving multiplication of fractions and mixed numbers.

Generate two numerical patterns using two given rules and identify apparent relationships between corresponding terms.

Write, read, and evaluate expressions in which letters stand for numbers.

Understand solving an equation or inequality as a process of answering a question.

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

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q.

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

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as multiplying the edge lengths of the prism.

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

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

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.

Understand rational numbers as points on the number line and extend coordinate axes to represent points in the plane with negative number coordinates.

Understand ordering and absolute value of rational numbers.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0.

Use ratio and rate reasoning to solve real-world and mathematical problems.

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

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

Summarize numerical data sets in relation to their context by describing center, spread, and overall pattern.

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems.

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle.

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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

Recognize and represent proportional relationships between quantities.

Use proportional relationships to solve multistep ratio and percent problems.

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

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

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

Develop a probability model and use it to find probabilities of events, comparing probabilities from a model to observed frequencies.

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Graph proportional relationships, interpreting the unit rate as the slope of the graph and comparing two different proportional relationships represented in different ways.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.

Solve linear equations in one variable.

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions and collecting like terms.

Analyze and solve pairs of simultaneous linear equations.

Understand that a function is a rule that assigns to each input exactly one output.

Compare properties of two functions each represented in a different way.

Interpret the equation y = mx + b as defining a linear function whose graph is a straight line.

Construct a function to model a linear relationship between two quantities and determine the rate of change and initial value from a description, table, or graph.

Verify experimentally the properties of rotations, reflections, and translations.

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

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

Explain a proof of the Pythagorean Theorem and its converse.

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

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.