# NYS Next Generation Mathematics Learning Standards Unpacking Documents

In 2015, New York State (NYS) began a process of review and revision of the NYS P-12 Common Core Learning Standards for Mathematics. Through numerous phases of public comment, virtual and face-to-face meetings with committees consisting of NYS educators (including Special Education, Bilingual Education and English as a New Language teachers), parents, curriculum specialists, school administrators, college professors, and experts in cognitive research, the NYS Next Generation Mathematics Learning Standards (2017) were developed. These standards reflect the collaborative efforts and expertise of all constituents involved and were adopted by the Board of Regents in September 2017. The Next Generation Learning Standards Roadmap and Implementation Timeline provides a suggested plan designed to assist educators as they transition to the NYS Next Generation Learning Standards.

Learning standards are defined as the knowledge, skills and understanding that individuals can habitually demonstrate over time because of instruction and learning experiences. To assist with the transition to the Next Generation Mathematics Learning Standards, a team of NYS educators developed a series of unpacking documents that demonstrate one method of analyzing a specific standard designed to help illustrate what student learning might look like with regard to that standard.

The ideas presented in these documents can be utilized in conjunction with current local curriculum and instruction. Educators are encouraged to add on to these documents and adapt them to best fit the needs of their learners, as well as work through the process of unpacking other grade-level standards, which will provide an opportunity for reflective practice and aid in lesson planning. Further information on the process utilized in developing the unpacking documents listed below can be found in *A Guide for Unpacking the New York State Next Generation Mathematics Learning Standards*.

The list of standards below contain some unpacking exemplars for each of the grade-levels Prekindergarten-Grade 8. A blank unpacking template is also provided. Any suggestions and/or additions on how to make the exemplars more useful can be addressed to the Office of Curriculum and Instruction, emscurric@nysed.gov.

#### Unpacking Template

#### Unpacking Guide

## Grade Level Unpacking Documents for Pk-8 Domains:

**Prekindergarten **

*Counting and Cardinality*

- NY-PK.CC.2 Represent a number of objects, with a written numeral.
- NY-PK.CC.3 Understand the relationship between numbers and quantities to 10; connect counting to cardinality.

**Kindergarten **

*Operations and Algebraic Thinking*

- NY-K.OA.1 Represent addition and subtraction using objects, fingers, pennies, drawings, sounds acting out situations, verbal explanations, expressions, equations, or other strategies.

**Counting and Cardinality**

- NY-K.CC.4 Understand the relationship between numbers and quantities up to 20; connect counting to cardinality.

**Grade 1 **

**Operations and Algebraic Thinking**

- NY-1.OA.2 Solve word problems that call for addtition of three whole numbers whose sum is less than or equal to 20.

**Measurement and Data**

- NY-1.MD.3 Tell and write time in hours and half-hours. Recognize and identify coins. Count a mixed collection of dimes and pennies.

**Grade 2 **

**Operations and Algebraic Thinking**

- NY-2.OA.1a and 1b
- NY-2.OA.2a and 2b Fluently add and subtract within 20 using mental strategies. Know from memory all sums within 20 of two one-digit numbers.

**Grade 3 **

**Operations and Algebraic Thinking**

- NY-3.OA.8 Solve two-step word problems posed with whole numbers and having whole number answers using the found operations.
- NY-3.OA.9 Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).

**Grade 4 **

**Operations and Algebraic Thinking**

- NY-4.OA.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.
- NY-4.OA.3 Solve multi-step problems posed with whole numbers and having whole-number answers using the four operations; including problems in which remainders must be interpreted.

**Grade 5 **

*Numbers and Operations in Base Ten*

- NY-5.NBT
**.**3 Read, write and compare decimals to the thousandths.

**Number and Operations - Fractions**

- NY-5.NF.4 Appy and extend previous understandings of multiplication to multiply a fraction by a whole number or fraction.
- NY-5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

**Grade 6 **

**The Number System**

- NY-6.NS.1 Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions.

**Expressions and Equations (Inequalities)**

- NY-6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
- NY-6.EE.2 Write, read and evaluate expressions in which letters stand for numbers.

**Grade 7**

*Ratio and Proportional Reasoning*

- NY-7.RP.1 Compute the unit rates associated with ratios of fractions.
- NY-7.RP.2 Recognize and represent proportional relationships between quantities.

**Grade 8 **

**Expressions and Equations (Inequalities)**

- NY-8.EE.6 Use similar triangles to explain why the slope,
*m*is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation of*y=mx*for a line through the origin and the equations*y=mx+b*for a line intercepting the vertical axis at*b*.

**Functions**

- NY-8.F.3 Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line. Recognize examples of fucntions that are linear and non-linear.

## Unpacking Documents for High School Course Domains:

**High School Geometry**

*Congruence*

- GEO-G.CO.2 Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.
- GEO-G.CO.4 Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.
- GEO-G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

**Similarity, Right Triangles, and Trigonometry**

- GEO-G.SRT.9 Justify and apply the formula A=1/2
*ab*sin (C) to find the area of any triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

**High School Algebra I**

*Number and Quantity- The Real Number System*

- AI-N.RN.3a Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.

**Algebra - Seeing Structure in Expressions**

- AI-A.SSE.1 Interpret expressions that represent a quantity in terms of context.
- AI-A.SSE.3c Use the properties of exponents to rewrite exponential expressions.

**High School Algebra II**

**Number and Quantity - The Complex Number System**

- AII-N.CN. 1 and 2 Know there is a complex number
*i*such that*i*^{2}=-1 and every complex number has the form*a+bi*with*a*and*b*real. Use the relation i^{2}=-1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

**Algebra - Seeing Structure in Expressions **

- AII-A.SSE.3c Use the properties of exponents to rewrite exponential expressions.

**Functions - Trigonometric Functions**

- AII-F.TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.