Pennsylvania: CC Math Standards

CC.2

• CC.2.1.1.B.1 Extend the counting sequence to read and write numerals to represent objects.
• CC.2.1.1.B.2 Use place-value concepts to represent amounts of tens and ones and to compare two digit numbers.
• CC.2.1.1.B.3 Use place-value concepts and properties of operations to add and subtract within 100.
• CC.2.1.2.B.1 Use place-value concepts to represent amounts of tens and ones and to compare three digit numbers.
• CC.2.1.2.B.2 Use place-value concepts to read, write, and skip count to 1000.
• CC.2.1.2.B.3 Use place-value understanding and properties of operations to add and subtract within 1000.
• CC.2.1.3.B.1 Apply place-value understanding and properties of operations to perform multi-digit arithmetic.
• CC.2.1.3.C.1 Explore and develop an understanding of fractions as numbers.
• CC.2.1.4.B.1 Apply place-value concepts to show an understanding of multi-digit whole numbers.
• CC.2.1.4.B.2 Use place-value understanding and properties of operations to perform multi-digit arithmetic.
• CC.2.1.4.C.1 Extend the understanding of fractions to show equivalence and ordering.
• CC.2.1.4.C.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• CC.2.1.4.C.3 Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100).
• CC.2.1.5.B.1 Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.
• CC.2.1.5.B.2 Extend an understanding of operations with whole numbers to perform operations including decimals.
• CC.2.1.5.C.1 Use the understanding of equivalency to add and subtract fractions.
• CC.2.1.5.C.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
• CC.2.1.6.D.1 Understand ratio concepts and use ratio reasoning to solve problems.
• CC.2.1.6.E.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• CC.2.1.6.E.2 Identify and choose appropriate processes to compute fluently with multi-digit numbers.
• CC.2.1.6.E.3 Develop and/or apply number theory concepts to find common factors and multiples.
• CC.2.1.6.E.4 Apply and extend previous understandings of numbers to the system of rational numbers.
• CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solve real-world and mathematical problems.
• CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers.
• CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.
• CC.2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers.
• CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.
• CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems.
• CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.
• CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems.
• CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
• CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers.
• CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.
• CC.2.1.K.A.1 Know number names and write and recite the count sequence.
• CC.2.1.K.A.2 Apply one-to-one correspondence to count the number of objects.
• CC.2.1.K.A.3 Apply the concept of magnitude to compare numbers and quantities.
• CC.2.1.K.B.1 Use place value to compose and decompose numbers within 19.
• CC.2.2.1.A.1 Represent and solve problems involving addition and subtraction within 20.
• CC.2.2.1.A.2 Understand and apply properties of operations and the relationship between addition and subtraction.
• CC.2.2.2.A.1 Represent and solve problems involving addition and subtraction within 100.
• CC.2.2.2.A.2 Use mental strategies to add and subtract within 20.
• CC.2.2.2.A.3 Work with equal groups of objects to gain foundations for multiplication.
• CC.2.2.3.A.1 Represent and solve problems involving multiplication and division.
• CC.2.2.3.A.2 Understand properties of multiplication and the relationship between multiplication and division.
• CC.2.2.3.A.3 Demonstrate multiplication and division fluency.
• CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.
• CC.2.2.4.A.1 Represent and solve problems involving the four operations.
• CC.2.2.4.A.2 Develop and/or apply number theory concepts to find factors and multiples.
• CC.2.2.4.A.4 Generate and analyze patterns using one rule.
• CC.2.2.5.A.1 Interpret and evaluate numerical expressions using order of operations.
• CC.2.2.5.A.4 Analyze patterns and relationships using two rules.
• CC.2.2.6.B.1 Apply and extend previous understandings of arithmetic to algebraic expressions.
• CC.2.2.6.B.2 Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems.
• CC.2.2.6.B.3 Represent and analyze quantitative relationships between dependent and independent variables.
• CC.2.2.7.B.1 Apply properties of operations to generate equivalent expressions.
• CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
• CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.
• CC.2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations.
• CC.2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations.
• CC.2.2.8.C.1 Define, evaluate, and compare functions.
• CC.2.2.8.C.2 Use concepts of functions to model relationships between quantities.
• CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context.
• CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations.
• CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities.
• CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions.
• CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems.
• CC.2.2.HS.C.6 Interpret functions in terms of the situations they model.
• CC.2.2.HS.C.7 Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.
• CC.2.2.HS.C.8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.
• CC.2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate trigonometric ratios.
• CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context.
• CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
• CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.
• CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.
• CC.2.2.HS.D.5 Use polynomial identities to solve problems.
• CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.
• CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships.
• CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.
• CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.
• CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
• CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.
• CC.2.3.1.A.1 Compose and distinguish between two- and three-dimensional shapes based on their attributes.
• CC.2.3.1.A.2 Use the understanding of fractions to partition shapes into halves and quarters.
• CC.2.3.2.A.1 Analyze and draw two- and three-dimensional shapes having specified attributes.
• CC.2.3.2.A.2 Use the understanding of fractions to partition shapes into halves, quarters, and thirds.
• CC.2.3.3.A.1 Identify, compare, and classify shapes and their attributes.
• CC.2.3.3.A.2 Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.
• CC.2.3.4.A.1 Draw lines and angles and identify these in two-dimensional figures.
• CC.2.3.4.A.2 Classify two-dimensional figures by properties of their lines and angles.
• CC.2.3.4.A.3 Recognize symmetric shapes and draw lines of symmetry.
• CC.2.3.5.A.1 Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.
• CC.2.3.5.A.2 Classify two-dimensional figures into categories based on an understanding of their properties.
• CC.2.3.6.A.1 Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.
• CC.2.3.7.A.1 Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
• CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them.
• CC.2.3.8.A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
• CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools.
• CC.2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems.
• CC.2.3.HS.A.1 Use geometric figures and their properties to represent transformations in the plane.
• CC.2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.
• CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
• CC.2.3.HS.A.4 Apply the concept of congruence to create geometric constructions.
• CC.2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.
• CC.2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
• CC.2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.
• CC.2.3.HS.A.8 Apply geometric theorems to verify properties of circles.
• CC.2.3.HS.A.9 Extend the concept of similarity to determine arc lengths and areas of sectors of circles.
• CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section.
• CC.2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.
• CC.2.3.HS.A.12 Explain volume formulas and use them to solve problems.
• CC.2.3.HS.A.13 Analyze relationships between two-dimensional and three-dimensional objects.
• CC.2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.
• CC.2.3.K.A.1 Identify and describe two- and three-dimensional shapes.
• CC.2.3.K.A.2 Analyze, compare, create, and compose two- and three-dimensional shapes.
• CC.2.4.1.A.1 Order lengths and measure them both indirectly and by repeating length units.
• CC.2.4.1.A.2 Tell and write time to the nearest half hour using both analog and digital clocks.
• CC.2.4.1.A.4 Represent and interpret data using tables/charts.
• CC.2.4.2.A.1 Measure and estimate lengths in standard units using appropriate tools.
• CC.2.4.2.A.2 Tell and write time to the nearest five minutes using both analog and digital clocks.
• CC.2.4.2.A.3 Solve problems and make change using coins and paper currency with appropriate symbols.
• CC.2.4.2.A.4 Represent and interpret data using line plots, picture graphs, and bar graphs.
• CC.2.4.2.A.6 Extend the concepts of addition and subtraction to problems involving length.
• CC.2.4.3.A.1 Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length.
• CC.2.4.3.A.2 Tell and write time to the nearest minute and solve problems by calculating time intervals.
• CC.2.4.3.A.3 Solve problems and make change involving money using a combination of coins and bills.
• CC.2.4.3.A.4 Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs.
• CC.2.4.3.A.5 Determine the area of a rectangle and apply the concept to multiplication and to addition.
• CC.2.4.3.A.6 Solve problems involving perimeters of polygons and distinguish between linear and area measures.
• CC.2.4.4.A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit.
• CC.2.4.4.A.2 Translate information from one type of data display to another.
• CC.2.4.4.A.4 Represent and interpret data involving fractions using information provided in a line plot.
• CC.2.4.4.A.6 Measure angles and use properties of adjacent angles to solve problems.
• CC.2.4.5.A.1 Solve problems using conversions within a given measurement system.
• CC.2.4.5.A.2 Represent and interpret data using appropriate scale.
• CC.2.4.5.A.4 Solve problems involving computation of fractions using information provided in a line plot.
• CC.2.4.5.A.5 Apply concepts of volume to solve problems and relate volume to multiplication and to addition.
• CC.2.4.6.B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions.
• CC.2.4.7.B.1 Draw inferences about populations based on random sampling concepts.
• CC.2.4.7.B.2 Draw informal comparative inferences about two populations.
• CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models.
• CC.2.4.8.B.1 Analyze and/or interpret bivariate data displayed in multiple representations.
• CC.2.4.8.B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies.
• CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.
• CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.
• CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data.
• CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments.
• CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
• CC.2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data.
• CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.
• CC.2.4.K.A.1 Describe and compare attributes of length, area, weight, and capacity of everyday objects.
• CC.2.4.K.A.4 Classify objects and count the number of objects in each category.