NY-7.RP 1

Compute unit rates associated with ratios of fractions

NY-7.RP 2  a, b, c, & d

Recognize and represent proportional relationships between quantities

NY-7.RP 3

Use proportional relationships to solve multistep ratio and percent problems

NY-7.NS 1 a, b, c, & d

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.  Represent addition on a horizontal or vertical number line

NY-7.NS 3

Solve real-world and mathematical problems involving the four operations with rational numbers

NY-7.NS 2 a, b, c, & d

Apply and extend previous understanding of multiplication and division of fractions to multiply and divide rational numbers.

NY-7.NS 3

Solve real-world and mathematical problems involving the four operations with rational numbers

NY-7.EE 1

Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations

NY-7.EE 2

Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related.

NY-7.EE 3

Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form using tools strategically.  Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.  Assess the reasonableness of answers using mental computation and estimation strategies.

NY-7.EE 4 a & b

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

NY-7.EE 3

Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form using tools strategically. 

Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. 

Assess the reasonableness of answers using mental computation and estimation strategies.

NY-7.EE 4 a & b

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

NY-8.EE 7 A & B

Solve linear equations in one variable.

NY-8.EF 2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

NY-8.EF 4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.

Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

NY-8.G 1 A, B, & C

Verify experimentally the properties of rotations, reflections, and translations.

NY-8.G 2

Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent.

Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations.

Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.

NY-8.G 3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

NY-8.G 4

Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion.

Equivalently, two, two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations.

Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.

NY-8.G 5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

NY-8.G 6

Understand a proof of the Pythagorean Theorem and its converse.

NY-8.G 7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

NY-8.G 8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

NY-8.G 9

Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems.

NY-8.EE 3

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

NY-8.EE 3

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

NY-8.EE 4

Perform multiplication and division with numbers expressed in scientific notation, including problems where both standard decimal form and scientific notation are used.

Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.