# Standards Alignment

## Pennsylvania Academic Standards

#### 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

Region | Standard | Description | Level |
---|---|---|---|

Pennsylvania | CC.2.2.PreK.A.1 | Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. | Prekindergarten |

Pennsylvania | CC.2.3.PreK.A.1 | Identify and describe shapes. | Prekindergarten |

Pennsylvania | CC.2.3.PreK.A.2 | Analyze, compare, create, and compose shapes. | Prekindergarten |

Pennsylvania | CC.2.4.PreK.A.1 | Describe and compare measurable attributes of length and weight of everyday objects. | Prekindergarten |

Pennsylvania | CC.2.4.PreK.A.4 | Classify objects and count the number of objects in each category. | Prekindergarten |

Pennsylvania | CC.2.1.PreK.A.1 | Know number names and the count sequence. | Prekindergarten |

Pennsylvania | CC.2.1.PreK.A.2 | Count to tell the number of objects. | Prekindergarten |

Pennsylvania | CC.2.1.PreK.A.3 | Compare numbers. | Prekindergarten |

Pennsylvania | CC.2.2.K.A.1 | Extend the concepts of putting together and taking apart to add and subtract within 10. | Kindergarten |

Pennsylvania | CC.2.3.K.A.1 | Identify and describe two- and three-dimensional shapes. | Kindergarten |

Pennsylvania | CC.2.3.K.A.2 | Analyze, compare, create, and compose two- and three-dimensional shapes. | Kindergarten |

Pennsylvania | CC.2.4.K.A.1 | Describe and compare attributes of length, area, weight, and capacity of everyday objects. | Kindergarten |

Pennsylvania | CC.2.4.K.A.4 | Classify objects and count the number of objects in each category. | Kindergarten |

Pennsylvania | CC.2.1.K.A.1 | Know number names and write and recite the count sequence. | Kindergarten |

Pennsylvania | CC.2.1.K.A.2 | Apply one-to-one correspondence to count the number of objects. | Kindergarten |

Pennsylvania | CC.2.1.K.A.3 | Apply the concept of magnitude to compare numbers and quantities. | Kindergarten |

Pennsylvania | CC.2.1.K.B.1 | Use place value to compose and decompose numbers within 19. | Kindergarten |

Pennsylvania | CC.2.2.1.A.1 | Represent and solve problems involving addition and subtraction within 20. | Grade 1 |

Pennsylvania | CC.2.2.1.A.2 | Understand and apply properties of operations and the relationship between addition and subtraction. | Grade 1 |

Pennsylvania | CC.2.3.1.A.1 | Compose and distinguish between two- and three-dimensional shapes based on their attributes. | Grade 1 |

Pennsylvania | CC.2.3.1.A.2 | Use the understanding of fractions to partition shapes into halves and quarters. | Grade 1 |

Pennsylvania | CC.2.4.1.A.1 | Order lengths and measure them both indirectly and by repeating length units. | Grade 1 |

Pennsylvania | CC.2.4.1.A.2 | Tell and write time to the nearest half hour using both analog and digital clocks. | Grade 1 |

Pennsylvania | CC.2.4.1.A.4 | Represent and interpret data using tables/charts. | Grade 1 |

Pennsylvania | CC.2.1.1.B.1 | Extend the counting sequence to read and write numerals to represent objects. | Grade 1 |

Pennsylvania | CC.2.1.1.B.2 | Use place-value concepts to represent amounts of tens and ones and to compare two digit numbers. | Grade 1 |

Pennsylvania | CC.2.1.1.B.3 | Use place-value concepts and properties of operations to add and subtract within 100. | Grade 1 |

Pennsylvania | CC.2.2.2.A.1 | Represent and solve problems involving addition and subtraction within 100. | Grade 2 |

Pennsylvania | CC.2.2.2.A.2 | Use mental strategies to add and subtract within 20. | Grade 2 |

Pennsylvania | CC.2.2.2.A.3 | Work with equal groups of objects to gain foundations for multiplication. | Grade 2 |

Pennsylvania | CC.2.3.2.A.1 | Analyze and draw two- and three-dimensional shapes having specified attributes. | Grade 2 |

Pennsylvania | CC.2.3.2.A.2 | Use the understanding of fractions to partition shapes into halves, quarters, and thirds. | Grade 2 |

Pennsylvania | CC.2.4.2.A.1 | Measure and estimate lengths in standard units using appropriate tools. | Grade 2 |

Pennsylvania | CC.2.4.2.A.2 | Tell and write time to the nearest five minutes using both analog and digital clocks. | Grade 2 |

Pennsylvania | CC.2.4.2.A.3 | Solve problems and make change using coins and paper currency with appropriate symbols. | Grade 2 |

Pennsylvania | CC.2.4.2.A.4 | Represent and interpret data using line plots, picture graphs, and bar graphs. | Grade 2 |

Pennsylvania | CC.2.4.2.A.6 | Extend the concepts of addition and subtraction to problems involving length. | Grade 2 |

Pennsylvania | CC.2.1.2.B.1 | Use place-value concepts to represent amounts of tens and ones and to compare three digit numbers. | Grade 2 |

Pennsylvania | CC.2.1.2.B.2 | Use place-value concepts to read, write and skip count to 1000. | Grade 2 |

Pennsylvania | CC.2.1.2.B.3 | Use place-value understanding and properties of operations to add and subtract within 1000. | Grade 2 |

Pennsylvania | CC.2.2.3.A.1 | Represent and solve problems involving multiplication and division. | Grade 3 |

Pennsylvania | CC.2.2.3.A.2 | Understand properties of multiplication and the relationship between multiplication and division. | Grade 3 |

Pennsylvania | CC.2.2.3.A.3 | Demonstrate multiplication and division fluency. | Grade 3 |

Pennsylvania | CC.2.2.3.A.4 | Solve problems involving the four operations, and identify and explain patterns in arithmetic. | Grade 3 |

Pennsylvania | CC.2.3.3.A.1 | Identify, compare, and classify shapes and their attributes. | Grade 3 |

Pennsylvania | 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. | Grade 3 |

Pennsylvania | CC.2.4.3.A.1 | Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length. | Grade 3 |

Pennsylvania | CC.2.4.3.A.2 | Tell and write time to the nearest minute and solve problems by calculating time intervals. | Grade 3 |

Pennsylvania | CC.2.4.3.A.3 | Solve problems and make change involving money using a combination of coins and bills. | Grade 3 |

Pennsylvania | CC.2.4.3.A.4 | Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs. | Grade 3 |

Pennsylvania | CC.2.4.3.A.5 | Determine the area of a rectangle and apply the concept to multiplication and to addition. | Grade 3 |

Pennsylvania | CC.2.4.3.A.6 | Solve problems involving perimeters of polygons and distinguish between linear and area measures. | Grade 3 |

Pennsylvania | CC.2.1.3.C.1 | Explore and develop an understanding of fractions as numbers. | Grade 3 |

Pennsylvania | CC.2.1.3.B.1 | Apply place-value understanding and properties of operations to perform multi-digit arithmetic. | Grade 3 |

Pennsylvania | CC.2.2.4.A.1 | Represent and solve problems involving the four operations. | Grade 4 |

Pennsylvania | CC.2.2.4.A.2 | Develop and/or apply number theory concepts to find factors and multiples. | Grade 4 |

Pennsylvania | CC.2.2.4.A.4 | Generate and analyze patterns using one rule. | Grade 4 |

Pennsylvania | CC.2.3.4.A.1 | Draw lines and angles and identify these in two-dimensional figures. | Grade 4 |

Pennsylvania | CC.2.3.4.A.2 | Classify two-dimensional figures by properties of their lines and angles. | Grade 4 |

Pennsylvania | CC.2.3.4.A.3 | Recognize symmetric shapes and draw lines of symmetry. | Grade 4 |

Pennsylvania | CC.2.4.4.A.1 | Solve problems involving measurement and conversions from a larger unit to a smaller unit. | Grade 4 |

Pennsylvania | CC.2.4.4.A.2 | Translate information from one type of data display to another. | Grade 4 |

Pennsylvania | CC.2.4.4.A.4 | Represent and interpret data involving fractions using information provided in a line plot. | Grade 4 |

Pennsylvania | CC.2.4.4.A.6 | Measure angles and use properties of adjacent angles to solve problems. | Grade 4 |

Pennsylvania | CC.2.1.4.C.1 | Extend the understanding of fractions to show equivalence and ordering. | Grade 4 |

Pennsylvania | CC.2.1.4.C.2 | Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. | Grade 4 |

Pennsylvania | CC.2.1.4.C.3 | Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). | Grade 4 |

Pennsylvania | CC.2.1.4.B.1 | Apply place-value concepts to show an understanding of multi-digit whole numbers. | Grade 4 |

Pennsylvania | CC.2.1.4.B.2 | Use place-value understanding and properties of operations to perform multi-digit arithmetic. | Grade 4 |

Pennsylvania | CC.2.2.5.A.1 | Interpret and evaluate numerical expressions using order of operations. | Grade 5 |

Pennsylvania | CC.2.2.5.A.4 | Analyze patterns and relationships using two rules. | Grade 5 |

Pennsylvania | 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. | Grade 5 |

Pennsylvania | CC.2.3.5.A.2 | Classify two-dimensional figures into categories based on an understanding of their properties. | Grade 5 |

Pennsylvania | CC.2.4.5.A.1 | Solve problems using conversions within a given measurement system. | Grade 5 |

Pennsylvania | CC.2.4.5.A.2 | Represent and interpret data using appropriate scale. | Grade 5 |

Pennsylvania | CC.2.4.5.A.4 | Solve problems involving computation of fractions using information provided in a line plot. | Grade 5 |

Pennsylvania | CC.2.4.5.A.5 | Apply concepts of volume to solve problems and relate volume to multiplication and to addition. | Grade 5 |

Pennsylvania | CC.2.1.5.C.1 | Use the understanding of equivalency to add and subtract fractions. | Grade 5 |

Pennsylvania | CC.2.1.5.C.2 | Apply and extend previous understandings of multiplication and division to multiply and divide fractions. | Grade 5 |

Pennsylvania | 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. | Grade 5 |

Pennsylvania | CC.2.1.5.B.2 | Extend an understanding of operations with whole numbers to perform operations including decimals. | Grade 5 |

Pennsylvania | CC.2.2.6.B.1 | Apply and extend previous understandings of arithmetic to algebraic expressions. | Grade 6 |

Pennsylvania | CC.2.2.6.B.2 | Understand the process of solving a one-variable equation or inequality and apply to real-world and mathematical problems. | Grade 6 |

Pennsylvania | CC.2.2.6.B.3 | Represent and analyze quantitative relationships between dependent and independent variables. | Grade 6 |

Pennsylvania | CC.2.3.6.A.1 | Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume. | Grade 6 |

Pennsylvania | CC.2.4.6.B.1 | Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions. | Grade 6 |

Pennsylvania | CC.2.1.6.D.1 | Understand ratio concepts and use ratio reasoning to solve problems. | Grade 6 |

Pennsylvania | CC.2.1.6.E.1 | Apply and extend previous understandings of multiplication and division to divide fractions by fractions. | Grade 6 |

Pennsylvania | CC.2.1.6.E.2 | Identify and choose appropriate processes to compute fluently with multi-digit numbers. | Grade 6 |

Pennsylvania | CC.2.1.6.E.3 | Develop and/or apply number theory concepts to find common factors and multiples. | Grade 6 |

Pennsylvania | CC.2.1.6.E.4 | Apply and extend previous understandings of numbers to the system of rational numbers. | Grade 6 |

Pennsylvania | CC.2.2.7.B.1 | Apply properties of operations to generate equivalent expressions. | Grade 7 |

Pennsylvania | CC.2.2.7.B.3 | Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. | Grade 7 |

Pennsylvania | CC.2.3.7.A.1 | Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume. | Grade 7 |

Pennsylvania | CC.2.3.7.A.2 | Visualize and represent geometric figures and describe the relationships between them. | Grade 7 |

Pennsylvania | CC.2.4.7.B.1 | Draw inferences about populations based on random sampling concepts. | Grade 7 |

Pennsylvania | CC.2.4.7.B.2 | Draw informal comparative inferences about two populations. | Grade 7 |

Pennsylvania | CC.2.4.7.B.3 | Investigate chance processes and develop, use, and evaluate probability models. | Grade 7 |

Pennsylvania | CC.2.1.7.D.1 | Analyze proportional relationships and use them to model and solve real-world and mathematical problems. | Grade 7 |

Pennsylvania | CC.2.1.7.E.1 | Apply and extend previous understandings of operations with fractions to operations with rational numbers. | Grade 7 |

Pennsylvania | CC.2.2.8.B.1 | Apply concepts of radicals and integer exponents to generate equivalent expressions. | Grade 8 |

Pennsylvania | CC.2.2.8.B.2 | Understand the connections between proportional relationships, lines, and linear equations. | Grade 8 |

Pennsylvania | CC.2.2.8.B.3 | Analyze and solve linear equations and pairs of simultaneous linear equations. | Grade 8 |

Pennsylvania | CC.2.2.8.C.1 | Define, evaluate, and compare functions. | Grade 8 |

Pennsylvania | CC.2.2.8.C.2 | Use concepts of functions to model relationships between quantities. | Grade 8 |

Pennsylvania | CC.2.3.8.A.1 | Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems. | Grade 8 |

Pennsylvania | CC.2.3.8.A.2 | Understand and apply congruence, similarity, and geometric transformations using various tools. | Grade 8 |

Pennsylvania | CC.2.3.8.A.3 | Understand and apply the Pythagorean Theorem to solve problems. | Grade 8 |

Pennsylvania | CC.2.4.8.B.1 | Analyze and/or interpret bivariate data displayed in multiple representations. | Grade 8 |

Pennsylvania | CC.2.4.8.B.2 | Understand that patterns of association can be seen in bivariate data utilizing frequencies. | Grade 8 |

Pennsylvania | CC.2.1.8.E.1 | Distinguish between rational and irrational numbers using their properties. | Grade 8 |

Pennsylvania | CC.2.1.8.E.4 | Estimate irrational numbers by comparing them to rational numbers. | Grade 8 |

Pennsylvania | CC.2.2.HS.D.1 | Interpret the structure of expressions to represent a quantity in terms of its context. | High School |

Pennsylvania | CC.2.2.HS.D.2 | Write expressions in equivalent forms to solve problems. | High School |

Pennsylvania | CC.2.2.HS.D.3 | Extend the knowledge of arithmetic operations and apply to polynomials. | High School |

Pennsylvania | CC.2.2.HS.D.4 | Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. | High School |

Pennsylvania | CC.2.2.HS.D.5 | Use polynomial identities to solve problems. | High School |

Pennsylvania | CC.2.2.HS.D.6 | Extend the knowledge of rational functions to rewrite in equivalent forms. | High School |

Pennsylvania | CC.2.2.HS.D.7 | Create and graph equations or inequalities to describe numbers or relationships. | High School |

Pennsylvania | CC.2.2.HS.D.8 | Apply inverse operations to solve equations or formulas for a given variable. | High School |

Pennsylvania | CC.2.2.HS.D.9 | Use reasoning to solve equations and justify the solution method. | High School |

Pennsylvania | CC.2.2.HS.D.10 | Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. | High School |

Pennsylvania | CC.2.2.HS.C.1 | Use the concept and notation of functions to interpret and apply them in terms of their context. | High School |

Pennsylvania | CC.2.2.HS.C.2 | Graph and analyze functions and use their properties to make connections between the different representations. | High School |

Pennsylvania | CC.2.2.HS.C.3 | Write functions or sequences that model relationships between two quantities. | High School |

Pennsylvania | CC.2.2.HS.C.4 | Interpret the effects transformations have on functions and find the inverses of functions. | High School |

Pennsylvania | CC.2.2.HS.C.5 | Construct and compare linear, quadratic and exponential models to solve problems. | High School |

Pennsylvania | CC.2.2.HS.C.6 | Interpret functions in terms of the situations they model. | High School |

Pennsylvania | CC.2.2.HS.C.7 | Apply radian measure of an angle and the unit circle to analyze the trigonometric functions. | High School |

Pennsylvania | CC.2.2.HS.C.8 | Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs. | High School |

Pennsylvania | CC.2.2.HS.C.9 | Prove the Pythagorean identity and use it to calculate trigonometric ratios. | High School |

Pennsylvania | CC.2.3.HS.A.1 | Use geometric figures and their properties to represent transformations in the plane. | High School |

Pennsylvania | CC.2.3.HS.A.2 | Apply rigid transformations to determine and explain congruence. | High School |

Pennsylvania | CC.2.3.HS.A.3 | Verify and apply geometric theorems as they relate to geometric figures. | High School |

Pennsylvania | CC.2.3.HS.A.4 | Apply the concept of congruence to create geometric constructions. | High School |

Pennsylvania | CC.2.3.HS.A.5 | Create justifications based on transformations to establish similarity of plane figures. | High School |

Pennsylvania | CC.2.3.HS.A.6 | Verify and apply theorems involving similarity as they relate to plane figures. | High School |

Pennsylvania | CC.2.3.HS.A.7 | Apply trigonometric ratios to solve problems involving right triangles. | High School |

Pennsylvania | CC.2.3.HS.A.8 | Apply geometric theorems to verify properties of circles. | High School |

Pennsylvania | CC.2.3.HS.A.9 | Extend the concept of similarity to determine arc lengths and areas of sectors of circles. | High School |

Pennsylvania | CC.2.3.HS.A.10 | Translate between the geometric description and the equation for a conic section. | High School |

Pennsylvania | CC.2.3.HS.A.11 | Apply coordinate geometry to prove simple geometric theorems algebraically. | High School |

Pennsylvania | CC.2.3.HS.A.12 | Explain volume formulas and use them to solve problems. | High School |

Pennsylvania | CC.2.3.HS.A.13 | Analyze relationships between two-dimensional and three-dimensional objects. | High School |

Pennsylvania | CC.2.3.HS.A.14 | Apply geometric concepts to model and solve real world problems. | High School |

Pennsylvania | CC.2.4.HS.B.1 | Summarize, represent, and interpret data on a single count or measurement variable. | High School |

Pennsylvania | CC.2.4.HS.B.2 | Summarize, represent, and interpret data on two categorical and quantitative variables. | High School |

Pennsylvania | CC.2.4.HS.B.3 | Analyze linear models to make interpretations based on the data. | High School |

Pennsylvania | CC.2.4.HS.B.4 | Recognize and evaluate random processes underlying statistical experiments. | High School |

Pennsylvania | CC.2.4.HS.B.5 | Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. | High School |

Pennsylvania | CC.2.4.HS.B.6 | Use the concepts of independence and conditional probability to interpret data. | High School |

Pennsylvania | CC.2.4.HS.B.7 | Apply the rules of probability to compute probabilities of compound events in a uniform probability model. | High School |

Pennsylvania | CC.2.1.HS.F.1 | Apply and extend the properties of exponents to solve problems with rational exponents. | High School |

Pennsylvania | CC.2.1.HS.F.2 | Apply properties of rational and irrational numbers to solve real world or mathematical problems. | High School |

Pennsylvania | CC.2.1.HS.F.3 | Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. | High School |

Pennsylvania | CC.2.1.HS.F.4 | Use units as a way to understand problems and to guide the solution of multi-step problems. | High School |

Pennsylvania | CC.2.1.HS.F.5 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | High School |

Pennsylvania | CC.2.1.HS.F.6 | Extend the knowledge of arithmetic operations and apply to complex numbers. | High School |

Pennsylvania | CC.2.1.HS.F.7 | Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. | High School |