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PK.CC.1 Count to 20.
PK.CC.2 Represent a number of objects with a written numeral 0–5 (with 0 representing a count of no objects).
PK.CC.3 Understand the relationship between numbers and quantities to 10; connect counting to cardinality.
PK.CC.4 Count to answer “how many?” questions about as many as 10 things arranged in a line, a rectangular array, or a circle, or as many as 5 things in a scattered configuration; given a number from 1–10, count out that many objects.
PK.OA.2 Duplicate and extend (e.g., What comes next?) simple patterns using concrete objects.
PK.MD.2 Sort objects into categories; count the numbers of objects in each category.
PK.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as top, bottom, up, down, in front of, behind, over, under, and next to.
PK.G.2 Correctly name shapes regardless of size.
PK.G.3 Analyze, compare, and sort two- and three-dimensional shapes and objects, in different sizes, using informal language to describe their similarities, differences, and other attributes (e.g., color, size, and shape).
PK.G.4 Create and build shapes from components (e.g., sticks and clay balls).
PK.CC.1 Count to 20.
PK.CC.2 Represent a number of objects with a written numeral 0–10.
PK.CC.3 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
PK.CC.4 Count to answer "how many?" questions about as many as 10 things.
PK.CC.5 Compare two numbers between 1 and 5 presented as written numerals.
PK.CC.6 Identify whether the number of objects in one group is more, less, or equal to the number of objects in another group.
PK.MD.1 Identify measurable attributes of objects, such as length and weight. Describe them using correct vocabulary (e.g., small, big, short, tall, empty, full, heavy, light).
PK.CC.1 Count to 20.
PK.CC.2 Represent a number of objects with a written numeral 0–5 (with 0 representing a count of no objects).
PK.OA.1 Demonstrate an understanding of addition and subtraction by using objects, fingers, and responding to practical situations (e.g., If we have 3 apples and add 2 more, how many apples do we have all together?).
PK.OA.2 Duplicate and extend (e.g., What comes next?) simple patterns using concrete objects.
K.CC.1 Count to 100 by ones and by tens.
K.CC.2 Count forward beginning from a given number within the known sequence.
K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20.
K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
K.CC.5 Count to answer "how many?" questions about as many as 20 things.
K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects.
K.G.2 Correctly name shapes regardless of their orientations or overall size.
K.G.3 Identify shapes as two-dimensional or three-dimensional.
K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations.
K.CC.6 Identify whether the number of objects in one group is more, less, or equal to the number of objects in another group.
K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.
K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
K.MD.2 Directly compare two objects with a measurable attribute in common,
to see which object has "more of"/"less of" the attribute, and describe the difference.
K.OA.1 Represent addition and subtraction with objects, fingers, drawings, etc.
K.OA.2 Solve addition and subtraction word problems within 10.
K.OA.3 Decompose numbers less than or equal to 10.
K.OA.4 Find the number that makes 10 when added to a given number.
K.OA.5 Fluently add and subtract within 5.
K.CC.1 Count to 100 by ones and by tens.
K.CC.2 Count forward beginning from a given number within the known sequence.
K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones.
K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.
K.G.4 Analyze and compare two- and three-dimensional shapes.
K.G.5 Model shapes in the world by building shapes from components and drawing shapes.
K.G.6 Compose simple shapes to form larger shapes.
1.OA.1 Use addition and subtraction within 20 to solve word problems.
1.OA.2 Solve word problems that call for addition of three whole numbers.
1.OA.3 Apply properties of operations as strategies to add and subtract.
1.OA.4 Understand subtraction as an unknown-addend problem.
1.OA.5 Relate counting to addition and subtraction.
1.OA.6 Add and subtract within 20.
1.OA.1 Use addition and subtraction within 20 to solve word problems.
1.OA.6 Add and subtract within 20.
1.NBT.1 Count to 120, starting at any number less than 120.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits.
1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.2 Express the length of an object as a whole number of length units.
1.MD.4 Organize, represent, and interpret data with up to three categories.
1.NBT.1 Count to 120, starting at any number less than 120.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits.
1.OA.1 Use addition and subtraction within 20 to solve word problems.
1.OA.6 Add and subtract within 20.
1.G.1 Distinguish between defining attributes versus non-defining attributes of shapes.
1.G.2 Compose two-dimensional shapes or three-dimensional shapes to create a composite shape.
1.G.3 Partition circles and rectangles into two and four equal shares.
1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.
1.NBT.1 Count to 120, starting at any number less than 120.
1.NBT.2 Understand place value.
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less.
1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10.
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems.
2.OA.2 Fluently add and subtract within 20 using mental strategies.
2.NBT.5 Fluently add and subtract within 100.
2.NBT.6 Add up to four two-digit numbers.
2.NBT.7 Add and subtract within 1000.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work.
2.MD.1 Measure the length of an object by selecting and using appropriate tools.
2.MD.2 Measure the length of an object twice, using different units.
2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.4 Measure to determine how much longer one object is than another.
2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths.
2.MD.6 Represent whole numbers as lengths on a number line diagram.
2.NBT.1 Understand place value to 1000.
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits.
2.NBT.5 Fluently add and subtract within 100.
2.NBT.6 Add up to four two-digit numbers.
2.NBT.7 Add and subtract within 1000.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work.
2.NBT.7 Add and subtract within 1000.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work.
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members.
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays.
2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies.
2.MD.9 Generate measurement data by measuring lengths of several objects.
2.MD.10 Draw a picture graph and a bar graph to represent a data set with up to four categories.
2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes.
2.G.1 Recognize and draw shapes having specified attributes.
2.G.2 Partition a rectangle into rows and columns of same-size squares.
2.G.3 Partition circles and rectangles into equal shares.
3.OA.1 Interpret products of whole numbers.
3.OA.2 Interpret whole-number quotients of whole numbers.
3.OA.3 Use multiplication and division within 100 to solve word problems.
3.OA.4 Determine the unknown whole number in a multiplication or division equation.
3.OA.5 Apply properties of operations as strategies to multiply and divide.
3.OA.6 Understand division as an unknown-factor problem.
3.OA.7 Fluently multiply and divide within 100.
3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.2 Fluently add and subtract within 1000.
3.NBT.3 Multiply one-digit whole numbers by multiples of 10.
3.MD.1 Tell and write time to the nearest minute and measure time intervals.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units.
3.OA.7 Fluently multiply and divide within 100.
3.OA.8 Solve two-step word problems using the four operations.
3.OA.9 Identify arithmetic patterns and explain them using properties of operations.
3.NBT.3 Multiply one-digit whole numbers by multiples of 10.
3.MD.5 Recognize area as an attribute of plane figures.
3.MD.6 Measure areas by counting unit squares.
3.MD.7 Relate area to the operations of multiplication and addition.
3.OA.7 Fluently multiply and divide within 100.
3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
3.NF.2 Understand a fraction as a number on the number line.
3.NF.3 Explain equivalence of fractions and compare fractions by reasoning about their size.
3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set.
3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
3.MD.1 Tell and write time to the nearest minute and measure time intervals.
3.MD.2 Measure and estimate liquid volumes and masses of objects.
3.MD.1 Tell and write time to the nearest minute and measure time intervals.
3.MD.2 Measure and estimate liquid volumes and masses of objects.
3.MD.8 Solve real world and mathematical problems involving perimeters of polygons.
3.G.1 Understand that shapes in different categories may share attributes.
3.G.2 Partition shapes into parts with equal areas.
4.OA.1 Interpret a multiplication equation as a comparison.
4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison.
4.OA.3 Solve multi-step word problems using the four operations.
4.NBT.1 Recognize that in a multi-digit whole number, each digit represents ten times what it represents in the place to its right.
4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals.
4.NBT.3 Use place value understanding to round multi-digit whole numbers.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.MD.1 Know relative sizes of measurement units within one system of units.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
4.OA.5 Generate a number or shape pattern that follows a given rule.
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.
4.OA.4 Find all factor pairs for a whole number in the range 1–100.
4.OA.5 Generate a number or shape pattern that follows a given rule.
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint.
4.MD.6 Measure angles in whole-number degrees using a protractor.
4.MD.7 Recognize angle measure as additive.
4.G.1 Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines.
4.G.2 Classify two-dimensional figures based on parallel or perpendicular lines and angles.
4.G.3 Recognize a line of symmetry for a two-dimensional figure.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b).
4.NF.2 Compare two fractions with different numerators and different denominators.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100.
4.NF.6 Use decimal notation for fractions with denominators 10 or 100.
4.NF.7 Compare two decimals to hundredths by reasoning about their size.
4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100.
4.NF.6 Use decimal notation for fractions with denominators 10 or 100.
4.NF.7 Compare two decimals to hundredths by reasoning about their size.
4.MD.1 Know relative sizes of measurement units within one system of units.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
5.NBT.1 Recognize that in a multi-digit number, each digit represents 10 times what it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.2 Explain patterns in the number of zeros and in the placement of the decimal point when multiplying or dividing by powers of 10.
5.NBT.3 Read, write, and compare decimals to thousandths.
5.NBT.4 Use place value understanding to round decimals to any place.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths.
5.NF.1 Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.
5.NF.2 Solve word problems involving addition and subtraction of fractions.
5.NF.3 Interpret a fraction as division of the numerator by the denominator.
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.5 Interpret multiplication as scaling (resizing).
5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.
5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5.MD.4 Measure volumes by counting unit cubes.
5.MD.5 Relate volume to the operations of multiplication and addition.
5.MD.1 Convert among different-sized standard measurement units within a given measurement system.
5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit.
5.G.1 Use a pair of perpendicular number lines (axes) to define a coordinate system.
5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant.
5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories.
5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.
6.NS.4 Find the greatest common factor and least common multiple.
6.NS.5 Understand that positive and negative numbers describe quantities having opposite directions or values.
6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes to represent negative numbers.
6.NS.7 Understand ordering and absolute value of rational numbers.
6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.3 Apply the properties of operations to generate equivalent expressions.
6.EE.4 Identify when two expressions are equivalent.
6.EE.5 Understand solving an equation or inequality as a process of answering a question.
6.EE.6 Use variables to represent numbers and write expressions.
6.EE.7 Solve real-world and mathematical problems by writing and solving equations.
6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition.
6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons.
6.G.2 Find the volume of a right rectangular prism with fractional edge lengths.
6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices.
6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles.
6.SP.1 Recognize a statistical question as one that anticipates variability in the data.
6.SP.2 Understand that a set of data has a distribution which can be described by its center, spread, and overall shape.
6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.5 Summarize numerical data sets in relation to their context.
7.RP.1 Compute unit rates associated with ratios of fractions.
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of multiplication and division to multiply and divide rational numbers.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions.
7.EE.2 Understand that rewriting an expression in different forms can shed light on the problem.
7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers.
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem.
7.RP.1 Compute unit rates associated with ratios of fractions.
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.
7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population.
7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions.
7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
7.SP.5 Understand that the probability of a chance event is a number between 0 and 1.
7.SP.6 Approximate the probability of a chance event by collecting data on the chance process.
7.SP.7 Develop a probability model and use it to find probabilities of events.
7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
7.G.1 Solve problems involving scale drawings of geometric figures.
7.G.2 Draw geometric shapes with given conditions.
7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures.
7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems.
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects.
8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.2 Use square root and cube root symbols to represent solutions to equations.
8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10.
8.EE.4 Perform operations with numbers expressed in scientific notation.
8.G.1 Verify experimentally the properties of rotations, reflections, and translations.
8.G.2 Understand that a two-dimensional figure is congruent to another if one can be obtained from the other by a sequence of rotations, reflections, and translations.
8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.4 Understand that a two-dimensional figure is similar to another if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations.
8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.4 Understand that a two-dimensional figure is similar to another if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations.
8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
8.EE.7 Solve linear equations in one variable.
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
8.F.4 Construct a function to model a linear relationship between two quantities.
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph.
8.F.1 Understand that a function is a rule that assigns to each input exactly one output.
8.F.2 Compare properties of two functions represented in different ways.
8.F.3 Interpret the equation y = mx + b as defining a linear function.
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths.
8.G.8 Apply the Pythagorean Theorem to find the distance between two points.
N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems.
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
N.Q.3 Choose a level of accuracy appropriate to limitations on measurement.
A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
S.ID.1 Represent data with plots on the real number line.
S.ID.2 Use statistics appropriate to the shape of the data distribution.
S.ID.3 Interpret differences in shape, center, and spread.
F.IF.1 Understand that a function assigns to each element of one set exactly one element of another set.
F.IF.2 Use function notation, evaluate functions for inputs.
F.IF.3 Recognize that sequences are functions.
F.IF.4 Interpret key features of graphs and tables.
F.IF.5 Relate the domain of a function to its graph.
F.IF.6 Calculate and interpret the average rate of change of a function.
F.BF.1 Write a function that describes a relationship between two quantities.
F.BF.2 Write arithmetic and geometric sequences.
F.BF.3 Identify the effect of transformations on graphs.
G.CO.1-5 Transform shapes in the coordinate plane.
G.SRT.1-3 Verify similarity criteria for triangles.
G.GMD.1-4 Calculate volumes and surface areas.
G.GPE.1-7 Use coordinates to solve geometric problems.
G.C.1-5 Apply theorems about circles.
A.APR.1-7 Perform operations on polynomials.
F.TF.1-9 Model periodic phenomena with trigonometric functions.
F.LE.1-4 Construct and compare exponential models.
S.IC.1-6 Understand and evaluate random processes.
N.CN.1-9 Perform operations with complex numbers.
N.VM.1-12 Perform operations on vectors and matrices.
F.BF.3-5 Build and analyze rational and exponential functions.
F.TF.9-11 Work with advanced trigonometric concepts.
S.CP.1-9 Work with conditional probability and statistical processes.