# Standards Alignment

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#### Innovative lessons for key K-8 math concepts and skills

The Pennsylvania Academic Standards work together to enable all students to develop the world-class knowledge, skills, and life and career characteristics identified in the Profile of the Pennsylvania Graduate. Because manipulatives and technology are integral to the development of mathematical understanding in all grade levels and courses, Pennsylvania Academic Standards recommends that the curriculum should support, and instructional approaches should include, the use of a variety of concrete materials and technological tools in order to help students explore connections, make conjectures, formulate generalizations, draw conclusions, and discover new mathematical ideas. DreamBox provides rigorous lessons and easy-to-use reporting that supports the
Pennsylvania Academic Standards, teachers, and students. You can track progress with Insight Reports that surface student performance by each standard and even create personalized assignments aligned with specific Pennsylvania Academic Standards Course of Study.

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#### Lessons by Standards

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