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A.RP.06.08 Understand that graphs and tables can suggest relationships between quantities.

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A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs and formulas, and translate among these representations.

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A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inverse functions (y = k/x), cubics (y = ax³), roots (y = √x), and exponentials (y = a^x, a > 0), using tables, graphs, and equations.

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A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs and formulas, and translate among these representations.

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A.PA.08.02 For basic functions, e.g. simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.

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D.RE.05.01 Read and interpret line graphs, and solve problems based on line graphs, e.g., distance – time graphs, and problems with two or three line graphs on same axes, comparing different data.

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N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.

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N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.

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A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.

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A.RP.06.10 Represent simple relationships between quantities, using verbal descriptions, formulas or equations, tables, and graphs, e.g. perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches.

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A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs and formulas, and translate among these representations.

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A.RP.07.10 Know that the graph of y = k/x is not a line; know its shape, and know that it crosses neither the x nor the y-axis.

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A.PA.08.03 Recognize basic functions in problem context, e.g. area of a circle is r², volume of a sphere is 4/3 r³, and represent them using tables, graphs, and formulas.

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A.PA.06.09 Graph and write equations for linear functions of the form y = mx and solve related problems, e.g., given n chairs, the "leg function" is f (n) = 4n: if you have 5 chairs, how many legs?; if you have 12 legs, how many chairs?

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G.GS.05.06 Understand why the sum of the interior angles of a triangle is 180º and the sum of the interior angles of a quadrilateral is 360º, and use these properties to solve problems.

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G.SR.08.07 Understand the concept of surface area and find the surface area of prisms, cones, spheres, pyramids, and cylinders.

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M.TE.05.08 Build solids with unit cubes and state their volumes.

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G.SR.06.05 Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors, and justify informally.

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G.SR.07.01 Use a ruler and other tools to draw squares, rectangles, triangles and parallelograms with specified dimensions.

G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids, including orthogonal views (top, front, and side), picture views (projective or isometric) and nets, and use such two-dimensional representations to help solve problems.

G.TR.06.04 Understand and use simple compositions of basic rigid transformations, e.g., a translation followed by a reflection.

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G.SR.07.02 Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand informal justifications.

G.SR.08.04 Find area and perimeter of complex figures by subdividing them into basic shapes (quadrilaterals, triangles, circles).

G.GS.06.02 Understand that for polygons, congruence means corresponding sides and angles have equal measures.

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G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems.

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A.PA.07.05 Understand and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity.

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G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids, including: orthogonal views (top, front, and side), picture views (projective or isometric) and nets, and use such two-dimensional representations to help solve problems.

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G.SR.06.05 Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors, and justify informally.

G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems.

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G.TR.05.01 Associate an angle with a certain amount of turning; know that angles are measured in degrees; understand that 90º, 180º, 270º, and 360º are associated, respectively, with ¼, ½, ¾ and full turns.

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G.TR.06.04 Understand and use simple compositions of basic rigid transformations, e.g., a translation followed by a reflection.

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G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems.

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A.RP.06.02 Plot ordered pairs of integers and use ordered pairs of integers to identify points in all four quadrants of the coordinate plane.

G.LO.08.02 Find the distance between two points on the coordinate plane, using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem.

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G.TR.06.03 Understand the basic rigid motions in the plane (reflections, rotations, translations), relate these to congruence, and apply them to solve problems.

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G.GS.05.02 Measure angles with a protractor and classify them as acute, right, obtuse or straight.

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G.SR.07.02 Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand informal justifications.

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M.UN.05.03 Compare the relative sizes of one cubic inch to one cubic foot, and one cubic centimeter to one cubic meter.

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M.PS.05.05 Represent relationships between areas of rectangles, triangles and parallelograms using models.

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G.TR.07.06 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r².

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G.GS.05.07 Find unknown angles using the properties of: triangles, including right, isosceles, and equilateral triangles; parallelograms, including rectangles and rhombuses; and trapezoids.

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M.TE.06.03 Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides, using formulas.

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N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.

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G.SR.08.06 Know the volume formulas for generalized cylinders ((area of base) x height), generalized cones and pyramids (1/3 (area of base) x height) and spheres (4/3 π (radius)³), and apply them to solve problems.

G.SR.08.07 Understand the concept of surface area and find the surface area of prisms, cones, spheres, pyramids, and cylinders.

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M.PS.05.10 Solve applied problems about the volumes of rectangular prisms using multiplication and division and using the appropriate units.

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D.RE.05.02 Construct line graphs from tables of data; include axis labels and scale.

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D.AN.07.02 Create and interpret scatter plots and use an estimated line of best fit to answer questions about the data.

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D.RE.05.02 Construct line graphs from tables of data; include axis labels and scale.

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A.RP.06.10 Represent simple relationships between quantities, using verbal descriptions, formulas or equations, tables, and graphs, e.g. perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches.

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D.AN.07.02 Create and interpret scatter plots and use an estimated line of best fit to answer questions about the data.

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D.AN.05.03 Given a set of data, find and interpret the mean (using the concept of fair share) and mode.

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D.AN.07.04 Find and interpret the median, quartiles, and interquartile range of a given set of data.

D.AN.08.01 Determine which measure of central tendency (mean, median, mode) best represents a data set, e.g. salaries, home prices for answering certain questions, and justify the choice made.

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D.AN.05.04 Solve multi-step problems involving means.

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D.AN.07.02 Create and interpret scatter plots and use an estimated line of best fit to answer questions about the data.

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D.RE.05.01 Read and interpret line graphs, and solve problems based on line graphs, e.g., distance – time graphs, and problems with two or three line graphs on same axes, comparing different data.

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D.AN.08.02 Recognize practices of collecting and displaying data that may bias the presentation or analysis.

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N.ME.05.10 Understand a fraction as a statement of division, e.g., 2 ÷ 3 = ⅔, using simple fractions and pictures to represent.

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N.ME.06.18 Understand that rational numbers are quotients of integers (nonzero denominators), e.g., a rational number is either a fraction or a negative fraction.

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N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g. 0.¯1=1/9; 0.¯3 = 1/3.

N.ME.06.16 Understand and use integer exponents, excluding powers of negative numbers; express numbers in scientific notation.

N.MR.07.06 Understand the concept of square root and cube root, and estimate using calculators.

N.ME.08.02 Understand meanings for zero and negative integer exponents.

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A.FO.06.13 Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solutions.

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A.FO.07.12 Add, subtract and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) – 5x + y, or -2x (5x – 4), and justify using properties of real numbers.

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N.ME.05.10 Understand a fraction as a statement of division, e.g., 2 ÷ 3 = 2/3, using simple fractions and pictures to represent.

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N.ME.06.05 Order rational numbers and place them on the number line.

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N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g. 0.¯1=1/9; 0.¯3 = 1/3.

N.ME.05.23 Express ratios in several ways, given applied situations, e.g., 3 cups to 5 people, 3:5, 3/5; recognize and find equivalent ratios.

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N.ME.06.06 Represent rational numbers as fractions or terminating decimals when possible, and translate between these representations.

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N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g. 0.¯1=1/9; 0.¯3 = 1/3.

N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness; use examples involving money.

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N.FL.06.14 For applied situations, estimate the answers to calculations involving operations with rational numbers.

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N.FL.07.09 Estimate results of computations with rational numbers.

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N.FL.08.06 Find square roots of perfect squares and approximate the square roots of non-perfect squares by locating between consecutive integers, e.g., √130 is between 11 and 12.

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N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness; use examples involving money.

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N.FL.06.14 For applied situations, estimate the answers to calculations involving operations with rational numbers.

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N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.

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N.MR.08.11 Solve problems involving ratio units such as miles per hour, dollars per pound, or persons per square mile.

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N.ME.05.08 Understand the relative magnitude of ones, tenths, and hundredths and the relationship of each place value to the place to its right, e.g., 1 is 10 tenths, one tenth is 10 hundredths.

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N.ME.06.17 Locate negative rational numbers (including integers) on the number line; know that numbers and their negatives add to 0, and are on opposites sides and at equal distance from 0 on a number line.

N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g. 0.¯1=1/9; 0.¯3 = 1/3.

N.ME.08.04 Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, e.g. √2, √3, on the number line.

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N.ME.05.23 Express ratios in several ways, given applied situations, e.g., 3 cups to 5 people, 3:5, ³; recognize and find equivalent ratios.

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A.PA.06.01 Solve applied problems involving rates, including speed, e.g., if a car is going 50 mph, how far will it go in 3-1/2 hours?

A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.

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A.PA.08.02 For basic functions, e.g. simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.

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N.MR.05.07 Find the prime factorization of numbers between 1 and 50, express in exponential notation, e.g., 24 = 2³ x 3¹, and understand that every whole number can be expressed as a product of primes.

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N.ME.08.02 Understand meanings for zero and negative integer exponents.

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N.MR.05.15 Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, and 1000; identify patterns.

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N.ME.06.16 Understand and use integer exponents, excluding powers of negative numbers; express numbers in scientific notation.

N.MR.07.06 Understand the concept of square root and cube root, and estimate using calculators.

A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inverse functions (y = k/x), cubics (y = ax³), roots (y = √x), and exponentials (y = a^x, a > 0), using tables, graphs, and equations.

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A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations; e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed.

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N.MR.08.11 Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile.

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N.MR.05.02 Relate division of whole numbers with remainders to the form a = bq + r, e.g., 34 ÷ 5 = 6 r 4, so 5 · 6 + 4 = 34; note remainder (4) is less than divisor (5).

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N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness; use examples involving money.

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N.FL.06.14 For applied situations, estimate the answers to calculations involving operations with rational numbers.

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N.Fl.07.09 Estimate results of computations with rational numbers.

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A.PA.07.11 Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition.

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N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness; use examples involving money.

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N.FL.06.15 Solve applied problems that use the four operations with appropriate decimal numbers.

N.FL.07.09 Estimate results of computations with rational numbers.

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N.MR.05.21 Solve for the unknown in such equations as: ¼ + x = 7/12

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