Number & Operations (N)
7.N.1 Read, write, represent, and compare rational numbers, expressed as
integers, fractions, and decimals.
7.N.1.1 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.
7.N.1.2 Compare and order rational numbers expressed in various forms using the symbols <, >, and =.
7.N.1.3 Recognize and generate equivalent representations of rational numbers, including equivalent fractions.
7.N.2 Calculate with integers and rational numbers, with and without positive integer exponents, to solve realworld and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero.
7.N.2.1 Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results.
7.N.2.2 Illustrate multiplication and division of integers using a variety of representations.
7.N.2.3 Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms.
7.N.2.4 Raise integers to positive integer exponents.
7.N.2.5 Solve real-world and mathematical problems involving calculations with rational numbers and positive integer exponents.
7.N.2.6 Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value.

Algebraic Reasoning & Algebra (A)
7.A.1 Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.
7.A.1.1 Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x= k or y = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships ( xy = k or y = k/x).
7.A.1.2 Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where both r and the slope are the unit rate (constant of proportionality, k).

7.A.2 Recognize proportionalrelationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols, and graphs; solve problems involving proportional relationships and interpret results in the original context.
7.A.2.1 Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.
7.A.2.2 Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations.
7.A.2.3 Use proportional reasoning to solve real-world and mathematical problems involving ratios.
7.A.2.4 Use proportional reasoning to assess the reasonableness of solutions.
7.A.3 Represent and solve linear equations and inequalities.
7.A.3.1 Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x+ q) = r, where p, q, and r are rational numbers.
7.A.3.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p, and q are nonnegative rational numbers.
7.A.3.3 Represent real-world or mathematical situations using equations and inequalities involving variables and rational numbers.
7.A.4 Use order of operations and properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols; evaluate such expressions.
7.A.4.1 Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.
7.A.4.2 Apply understanding of order of operations and grouping symbols when using calculators and other technologies.

Geometry & Measurement (GM)
7.GM.1 Develop and understand the concept of surface area and volume of rectangular prisms.
7.GM.1.1 Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism with rational-valued edge lengths can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements such as cm2.
7.GM.1.2 Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms with rational-valued edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements such as cm3.
7.GM.2 Determine the area of trapezoids and area and perimeter of composite figures.
7.GM.2.1 Develop and use the formula to determine the area of a trapezoid to solve problems.

7.GM.2.2 Find the area and perimeter of composite figures to solve real-world and mathematical problems.
7.GM.3 Use reasoning with proportions and ratios to determine measurements, justify formulas, and solve real-world and
mathematical problems involving circles and related geometric figures.
7.GM.3.1 Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is
π and can be approximated by rational numbers such as 22/7
and 3.14.
7.GM.3.2 Calculate the circumference and area of circles to solve problems in various contexts, in terms of
π and using approximations for π. and can be approximated by rational numbers such as 22/7 and 3.14.
7.GM.3.2 Calculate the circumference and area of circles to solve problems in various contexts, in terms of ! and using approximations for
π.

7.GM.4 Analyze the effect of dilations, translations, and reflections on the attributes of two-dimensional figures on
and off the coordinate plane.
7.GM.4.1 Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.
7.GM.4.2 Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar triangles and rectangles.
7.GM.4.3 Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation.

Data & Probability (D)
7.D.1 Display and analyze data in a variety of ways.
7.D.1.1 Design simple experiments, collect data and calculate measures of central tendency (mean, median, and mode) and spread (range). Use these quantities to draw conclusions about the data collected and make predictions.
7.D.1.2 Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.
7.D.2 Calculate probabilities and reason about probabilities using proportions to
solve real-world and mathematical problems.
7.D.2.1 Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1.
7.D.2.2 Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.
7.D.2.3 Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.

Number & Operations (N)
PA.N.1 Read, write, compare, classify, and represent real numbers and use them to solve problems in various
contexts.
PA.N.1.1 Develop and apply the properties of integer exponents, including !! = 1 (with ! ≠ 0), to generate equivalent numerical and algebraic expressions.
PA.N.1.2 Express and compare approximations of very large and very small numbers using scientific notation.
PA.N.1.3 Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.
PA.N.1.4 Classify real numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational number and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational.
PA.N.1.5 Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Algebraic Reasoning & Algebra (A)
PA.A.1 Understand the concept of function in real-world and mathematical situations, and distinguish between linear and nonlinear functions.
PA.A.1.1 Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable.
PA.A.1.2 Use linear functions to represent and explain real-world and mathematical situations.
PA.A.1.3 Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line.
PA.A.2 Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret results in the original context.
PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.
PA.A.2.2 Identify, describe, and analyze linear relationships between two variables.
PA.A.2.3 Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the yintercept is zero when the function represents a proportional relationship.
PA.A.2.4 Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects.
PA.A.2.5 Solve problems involving linear functions and interpret results in the original context.

PA.A.3 Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.
PA.A.3.1 Use substitution to simplify and evaluate algebraic expressions.
PA.A.3.2 Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations, including grouping symbols.
PA.A.4 Represent real-world and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context.
PA.A.4.1 Illustrate, write, and solve mathematical and real-world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret solutions in the original context.
PA.A.4.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p, and q are rational numbers.
PA.A.4.3 Represent real-world situations using equations and inequalities involving one variable.

Geometry & Measurement (GM)
PA.GM.1 Solve problems involving right triangles using the Pythagorean Theorem.
PA.GM.1.1 Informally justify the Pythagorean Theorem using measurements, diagrams, or dynamic software and use the Pythagorean Theorem to solve problems in two and three dimensions involving right triangles.
PA.GM.1.2 Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.
PA.GM.2 Calculate surface area and volume of three-dimensional figures.
PA.GM.2.1 Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as cm2.
PA.GM.2.2 Calculate the surface area of a cylinder, in terms of
π and using approximations for !, using decomposition or nets. Use appropriate measurements such as cm2.
PA.GM.2.3 Develop and use the formulas V = lwℎ and V = Bh to determine the volume of rectangular prisms. Justify why base area (B) and height (h) are multiplied to find the volume of a rectangular prism. Use appropriate measurements such as cm3.
PA.GM.2.4 Develop and use the formulas V =
πr2ℎ and V = Bh to determine the volume of right cylinders, in terms of ! and using approximations for !. Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate measurements such as cm3.

Data & Probability (D)

PA.D.1 Display and interpret data in a variety of ways, including using scatterplots and approximate lines of best fit. Use line of best fit and average rate of change to make predictions and draw conclusions about data.
PA.D.1.1 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact.
PA.D.1.2 Explain how outliers affect measures of central tendency.
PA.D.1.3 Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units.
PA.D.2 Calculate experimental probabilities and reason about probabilities to solve real-world and
mathematical problems.
PA.D.2.1 Calculate experimental probabilities and represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.
PA.D.2.2 Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.
PA.D.2.3 Compare and contrast dependent and independent events.