Algebra I Educator Guide 2023 (October 2023)

New York State

Testing Program

Educator Guide to the

Regents Examination in

Algebra I

Next Generation Mathematics Learning Standards

Updated: October 2023

THE UNIVERSITY OF THE STATE OF NEW YORK

Regents of The University

LESTER W. YOUNG, JR., Chancellor, B.S., M.S., Ed.D. ......................................

J

OSEPHINE VICTORIA FINN, Vice Chancellor B.A., J.D. .....................................

R

OGER TILLES, B.A., J.D. ....................................................................................

C

HRISTINE D. CEA, B.A., M.A., Ph.D. ..............................................................

W

ADE S. NORWOOD, B.A. .................................................................................

K

ATHLEEN M. CASHIN, B.S., M.S., Ed.D. ........................................................

J

AMES E. COTTRELL, B.S., M.D. .........................................................................

J

UDITH CHIN, B.S., M.S. in Ed. ..........................................................................

C

ATHERINE COLLINS, R.N., N.P., B.S., M.S. in Ed., Ed.D. ..............................

E

LIZABETH S. HAKANSON, A.S., B.A., M.A., C.A.S. ........................................

L

UIS O. REYES, B.A., M.A., Ph.D. ......................................................................

S

USAN W. MITTLER, B.S., M.S. ..........................................................................

F

RANCES G. WILLS, B.A., M.A., M.Ed., C.A.S., Ph.D. .....................................

A

RAMINA VEGA FERRER, B.A., M.S. in Ed., Ph.D. ..........................................

S

HINO TANIKAWA, B.A., M.S. ...........................................................................

R

OGER P. CATANIA, B.A., M.A., M.S., C.A.S., Ph.D. ......................................

A

DRIAN I. HALE, A.S., B.A. ...............................................................................

Commissioner of Education and President of The University

B

ETTY A. ROSA, B.A., M.S. in Ed., M.S. in Ed., M.Ed., Ed.D.

Senior Deputy Commissioner, Office of Education Policy

JAMES N. BALDWIN

Deputy Commissioner, P-12 Operational Support

JASON HARMON

Assistant Commissioner, Office of State Assessment

ZACHARY WARNER

Beechhurst

Monticello

Manhasset

Staten Island

Rochester

Brooklyn

New York

Little Neck

Buffalo

Syracuse

New York

Ithaca

Ossining

Bronx

Manhattan

Saranac Lake

Rochester

The State Education Department does not discriminate on the basis of race, creed, color, national origin, religion,

age, sex, military, marital status, familial status, domestic violence victim status, carrier status, disability,

genetic predisposition, sexual orientation and criminal record in its recruitment, educational programs,

services, and activities. NYSED has adopted a web accessibility policy, and publications designed for

distribution can be made available in an accessible format upon request. Inquiries regarding this policy of

nondiscrimination should be directed to the Office of Human Resources Management, Room 528 EB, Education

Building, Albany, New York 12234.

Revision Date

Revision

October 2023

p.11, the reference sheet section was revised

to provide a link to a stand-alone, printable

reference sheet with an updated Annual

Compound Interest formula

Table of Contents

Foreword............................................................................................................................................................. 1

New York State High School Mathematics Testing Program ....................................................................... 2

New York State Educators’ Involvement in Test Development.............................................................. 2

The Next Generation Mathematics Learning Standards...............................................................................3

Standards for Mathematical Practice ....................................................................................................... 3

Conceptual Categories, Domains, Clusters, Standards, and Assessment.....................................................4

Regents Examination in Algebra I Blueprint........................................................................................... 5

Algebra I Examination: Time, Format, Design, and Scoring........................................................................7

Testing Session and Time ........................................................................................................................ 7

Question Formats.....................................................................................................................................7

Algebra I Examination Design................................................................................................................. 8

Algebra I Scoring Policies ....................................................................................................................... 8

Policy Definitions ............................................................................................................................................... 9

Performance Level Descriptions.............................................................................................................. 9

Mathematics Tools for the Regents Examination in Algebra I.................................................................... 10

Reference Sheet ................................................................................................................................................ 11

Appendix A: Sample Questions for the Regents Examination in Algebra I .............................................. 12

Foreword

The information contained in this Educator Guide is designed to raise educator awareness of the

structure of the New York State Regents Examination in Algebra I measuring the New York State Next

Generation Mathematics Learning Standards.

The guide provides educators with pertinent information about the test development process, the learning

standards that the test design is set to measure, the format of the testing session, including which types of

questions will be asked, and which mathematics tools are allowed during testing. Links to additional

resources are provided to further enhance educators’ understanding of the structure of the Regents

Examination in Algebra I. Educators are encouraged to review the guide prior to the test administration to

gain familiarity with the test format. The information presented can also be used as a platform for educator

discussion on how student assessment results can guide future instruction.

The High School Regents Examination testing schedule for the June 2024 administration can be found on

the New York State Education Department’s website. Questions regarding the New York State Testing

Program and test design may be addressed to the Office of State Assessment at [email protected].

Questions regarding the New York State Learning Standards may be addressed to the Office of Standards and

Instruction at [email protected].

Algebra I Educator Guide

1

New York State High School Mathematics Testing Program

In September 2017, the Board of Regents adopted the New York State Next Generation Mathematics

Learning Standards, which were implemented at the beginning of the 2022-2023 school year. The New York

State High School Mathematics Testing Program is designed to measure student progress on the Next

Generation Mathematics Learning Standards following the implementation timeline for the Regents

Examinations as follows:

• June 2024: Algebra I

• June 2025: Geometry

• June 2026: Algebra II

New York State Educators’ Involvement in Test Development

Many steps in the test development process for the Regents Examination in Algebra I involve New York

State-certified classroom teachers. For example, teachers write and revise all test questions and scoring

rubrics. The New York State Education Department (NYSED) continues to expand the number of

opportunities for New York State educators to become involved. New York State educators provide the critical

input necessary to ensure that the tests are fair, valid, and appropriate for students through their participation

in many test-development activities.

The test development process includes the development, review, and approval of test questions, construction

of field and operational test forms, final approval of test forms prior to administration, and the development

of scoring materials. NYSED remains committed to improving the quality of the State’s assessments and the

experiences that students have taking these tests. For more information on opportunities to participate in the

test development process, please visit Test Development Participation.

Algebra I Educator Guide

2

The Next Generation Mathematics Learning Standards

The NYS Next Generation Mathematics Learning Standards define the knowledge and skills that individuals

can and do habitually demonstrate over time when exposed to high-quality instructional environments and

learning experiences. The Learning Standards, defined through the integration of the Standards for

Mathematical Content and the Standards for Mathematical Practice, collectively, are focused and cohesive

— designed to support student access to the knowledge and understanding of the mathematical concepts that

are necessary to function in a world very dependent upon the application of mathematics. Students are

expected to understand math conceptually, use procedural skills, and solve math problems rooted in the real

world, deciding for themselves which strategies, formulas, and grade-appropriate tools (e.g., calculator,

straightedge, or compass) to use.

Curriculum and instruction that support the content of the learning standards and the unique learning needs

of students are locally determined by each individual district in New York State. Teacher preference and

flexibility in planning units of study continue to play vital roles to both meet the needs of the students and

align with the expectations of the learning standards. For additional guidance with instructional planning

surrounding the Next Generation Mathematics Learning Standards, please see the Next Generation

Mathematics Learning Standards.

Standards for Mathematical Practice

The Learning Standards for each grade level (and high school course) begin with the eight Standards for

Mathematical Practice. The Standards for Mathematical Practice describe the ways in which developing

practitioners increasingly should engage with the subject matter as they grow in mathematical maturity and

expertise throughout the elementary, middle, and high school years. References to the integration of the

Standards for Mathematical Content and the Standards for Mathematical Practice are provided throughout

the Next Generation Mathematics Learning Standards.

Please note that the Algebra I overview does not include every standard/topic that should be included

in instruction. Further information about the entire scope of the learning expectations for each grade level,

as well as additional instructional considerations that include the within-grade connections, grade-level

fluencies, and connecting the Standards for Mathematical Practice to Mathematical Content can be found in

the Next Generation Mathematics Learning Standards and the associated grade-level crosswalks/snapshots.

Algebra I Educator Guide

3

Conceptual Categories, Domains, Clusters, Standards, and Assessment

The Algebra I Examination will measure the NYS Next Generation Mathematics Learning Standards. The

NYS Next Generation Mathematics Learning Standards are divided into conceptual categories, domains,

clusters, and standards.

•

Conceptual Categories are the highest organizing level in the standards and portray a coherent view

of high school mathematics.

•

Domains are larger groups of related clusters and standards. Standards from different domains may

be closely related.

•

Clusters are groups of related standards. Note that standards from different clusters may sometimes

be closely related, because mathematics is a connected subject.

•

Standards define what students should understand and be able to do. In some cases, standards are

further articulated into lettered components.

Algebra I is associated with the high school content standards within four conceptual categories:

Number & Quantity, Algebra, Functions, and Statistics & Probability. The conceptual category of

Modeling is also included in Algebra I, but is best interpreted not as a collection of isolated topics but

rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice,

and specific modeling standards appear throughout the high school standards. Modeling links classroom

mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of

choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand

them better, and to improve decisions.

While all questions on the Regents Examination are linked to a primary standard, some questions measure

more than one standard and one or more of the Standards for Mathematical Practice. Similarly, some

questions measure cluster-level understandings. As a result of the alignment to standards, clusters, and

Standards for Mathematical Practice, the test assesses students’ conceptual understanding, procedural

fluency, and problem-solving abilities, rather than assessing their knowledge of isolated skills and facts.

Algebra I Educator Guide

4

Regents Examination in Algebra I Blueprint

The test blueprint for the Regents Examination in Algebra I demonstrates NYSED’s commitment

to ensuring that educators are able to focus their instruction on the most critical elements of the

Algebra I course.

The following chart shows the percent of test by credit, as well as the domains included in Algebra I for each

conceptual category.

Conceptual

Category

Domain Cluster

Cluster

Code

Standard

Number &

Quantity

4% - 10%

The Real Number System

Use properties of rational and irrational numbers.

N-RN.

B

N

-RN.3(a,b

)

Q

uantities

Reason quantitatively and use units to solve

problems.

N-Q.

A

N-Q.1

N-Q.3

Algebra

48% - 61%

Seeing Structure in

Expressions

Interpret the structure of expressions. A-SSE.

A

A-SSE.1(a,b)

A-SSE.2

Write expressions in equivalent forms to reveal

their characteristics.

A-SSE.B A-SSE.3(c)

Arithmetic with

Polynomials

and Rational

Expressions

Perform arithmetic operations on polynomials.

A-APR.

A A

-APR.

1

Understand the relationship between zeros and

factors of polynomials.

A-APR.B A-APR.3

C

reating

Equations

Create equations that describe numbers or

relationships.

A-CED.A

A-CED.1

A-CED.2

A-CED.3

A-CED.4

Reasoning with Equations

and Inequalities

Understand solving equations as a process of

reasoning and explain the reasoning.

A-REI.

A

-REI.1

a

S

olve equations and inequalities in one

variable.

A-REI.

B

A-REI.3

A-REI.4(a,b)

Solve systems of equations.

A-REI.C

A-REI.6a

A-REI.7a

Represent and solve equations and inequalities

graphically.

A-REI.

D

A-REI.10

A-REI.11

A-REI.12

Functions

24% - 32%

Interpreting

Functions

Understand the concept of a function and use

function notation.

F-IF.

A

F-IF.1

F-IF.2

F-IF.3

Interpret functions that arise in applications in

terms of the context.

F-IF.

B

F-IF.4

F-IF.5

F-IF.6

Analyze functions using different

representations.

F-IF.C

F-IF.7(a,b)

F-IF.8(a)

F-IF.9

Building

Functions

Build a function that models a relationship

between two quantities.

F-BF.A

F

-BF.1

a

Build new functions from existing functions.

F-BF.B

F-BF.3a

Linear, Quadratic and

Exponential Models

Construct and compare linear, quadratic, and

exponential models and solve problems.

F-LE.A

F-LE.1(a,b,c)

F-LE.2

F-LE.3

Interpret expressions for functions in terms of

the situation they model.

F-LE.B

F

-LE.

5

S

tatistics &

Probability

7% - 15%

Interpreting Categorical

and Quantitative Data

Summarize, represent, and interpret data on a

single count or measurement variable.

S-ID.

A

S-ID.1

S-ID.2

S-ID.3

Summarize, represent, and interpret data on two

categorical and quantitative variables.

S-ID.B

S-ID.5

S-ID.6(a)

Interpret linear models.

S-ID.

C

S-ID.7

S-ID.8

S-ID.9

Algebra I Educator Guide

6

Algebra I Examination: Time, Format, Design, and Scoring

Testing Session and Time

The Regents Examination in Algebra I will consist of one booklet that is administered during the designated

time determined by NYSED. Students are permitted three hours to complete the Regents Examination in

Algebra I. While it is likely that most students will complete the test in less than three hours, students may

not leave the testing location prior to the Uniform Admission Deadline. This design provides ample time for

students who work at different paces.

Question Formats

The Regents Examination in Algebra I contains multiple-choice and constructed-response questions. For

multiple-choice questions, students select the correct response from four answer choices. For constructed-

response questions, students are required to clearly indicate the necessary steps, including appropriate

formula substitutions, diagrams, graphs, charts, etc. In some cases, they may be required to explain, in words,

how they arrived at their answers. Students must also have the exclusive use of a graphing calculator for the

full duration of the examination. For more information about calculator use please refer to page 10 of this

document.

Multiple-choice questions will be used to assess procedural fluency and conceptual understanding. Multiple-

choice questions measure the Standards for Mathematical Content and may incorporate Standards for

Mathematical Practices and real-world applications. Some multiple-choice questions require students to

complete multiple steps. Likewise, questions may measure more than one cluster, drawing on the

simultaneous application of multiple skills and concepts. Within answer choices, distractors

1

will be based

on plausible missteps.

Constructed-response questions will require students to show a deep understanding of mathematical

procedures, concepts, and applications. The Regents Examination in Algebra I contains 2-, 4-, and 6-credit

constructed-response questions.

The 2-credit constructed-response questions require students to complete a task and show their work. These

questions may involve multiple steps, the application of multiple mathematics skills, and real-world

applications. These questions may ask students to explain or justify their solutions and/or show their process

of problem solving.

The 4-credit and 6-credit constructed-response questions require students to show their work in completing

more extensive problems that may involve multiple tasks. Students may be asked to make sense of

mathematical and real-world problems in order to demonstrate procedural and conceptual understanding.

These questions may ask students to explain or justify their solutions and/or show their process of problem

solving.

1

A distractor is an incorrect response that may appear to be a plausible correct response to a student who has not mastered the

skill or concept being tested.

Algebra I Educator Guide

7

Algebra I Examination Design

Test

Component

Number of

Questions

Credits per

Question

Credits per

Section

Part I

24

2

48

Part II

6

2

12

Part III

4

16

Part IV

1

6

Total

35

-

82

Algebra I Scoring Policies

The general procedures to be followed in scoring Regents Examinations are provided in the publications

Directions for Administering Regents Examinations (DET 541) and the School Administrator’s Manual.

Both of these documents are available on the Department’s website. For more information see the

Information Booklet for Scoring the Regents Examination in Algebra I, the Directions for Administering

Regents Examinations, the Scoring Key and Rating Guides, and the Model Response Set for the appropriate

examination.

Algebra I Educator Guide

8

Policy Definitions

For each subject area, students perform along a continuum of the knowledge and skills necessary to meet

the demands of the Learning Standards for Mathematics. Regents Examinations are designed to classify

student performance into one of five levels based on the knowledge and skills the student has demonstrated.

Due to the need to identify student proficiency, the State tests must provide students at each performance

level opportunities to demonstrate their knowledge and skills in the Next Generation Mathematics Learning

Standards.

These performance levels are defined as:

NYS Level 5

Students performing at this level meet with distinction grade-level expectations of learning standards.

NYS Level 4

Students performing at this level fully meet grade-level expectations of learning standards (likely prepared

to succeed in the next level of coursework).

NYS Level 3

Students performing at this level minimally meet grade-level expectations of learning standards (meet the

content area requirements for a Regents diploma but may need additional support to succeed in the next level

of coursework).

NYS Level 2 (Safety Net)

Students performing at this level partially meet grade-level expectations of learning standards (sufficient

for Local Diploma purposes).

NYS Level 1

Students performing at this level demonstrate knowledge and skills below Level 2.

Performance Level Descriptions

Performance Level Descriptions exemplify the knowledge and skills that students at each performance level

demonstrate and describe the progression of learning within a subject area. The Performance Level

Descriptions play a central role in the test development process, specifically question-writing and standard-

setting. For more information about the Next Generation Mathematics Learning Standards Performance

Level Descriptions for Algebra I, please see the Algebra I webpage.

Algebra I Educator Guide

9

Mathematics Tools for the Regents Examination in Algebra I

Calculators and Straightedges (rulers)

A graphing calculator and straightedge (ruler) must be available to all students taking the Regents Examination

in Algebra I. No students may use calculators that are capable of symbol manipulation or that can communicate

with other calculators through infrared sensors, nor may students use operating manuals, instruction or formula

cards, or other information concerning the operation of calculators during the test. For more information

regarding calculators see The Guidelines for Graphing Calculator Use and the Directions for Administering

Regents Examinations.

Note: Schools are responsible for supplying the appropriate tools for use with the Regents Examination in

Algebra I.

Value of Pi

Students should use the π symbol and its corresponding value (i.e. pi key on the calculator) when applicable

on the Regents Examination in Algebra I. Unless otherwise specified, use of the approximate values of π, such

as 3.1416, 3.14, or

22

are unacceptable.

7

Mathematics Tools

The use of tools is necessary for students to meet the Standards for Mathematical Practice in the Next

Generation Mathematics Learning Standards for Mathematics. For example:

Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem.

Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound

decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their

limitations. Mathematically proficient students at various grade levels are able to identify relevant external

mathematical resources, such as digital content located on a website, and use them to pose or solve problems.

They are able to use technological tools to explore and deepen their understanding of concepts.

Attend to precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in

discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including

using the equal sign consistently and appropriately. They are careful about specifying units of measure and

labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and

efficiently, expressing numerical answers with a degree of precision appropriate for the problem context. In

the elementary grades, students give carefully formulated explanations to each other. By the time they reach

high school, they have learned to examine claims and make explicit use of definitions.

Algebra I Educator Guide

10

Algebra I Educator Guide

11

Reference Sheet

A detachable reference sheet will be included at the end of the Regents Examination in Algebra I test booklet.

It contains information that students are expected to apply, but not necessarily memorize. Teachers should use

this reference sheet in instruction throughout the Algebra I course t o familiarize students with its content.

This reference sheet is available at

https://www.nysed.gov/sites/default/files/programs/state-assessment/a1-next-gen-reference-sheet.pdf

Appendix A: Sample Questions for the Regents Examination in Algebra I

To aid in the implementation of the Next Generation Mathematics Learning Standards, a limited number of

sample questions are being provided to help students, parents, and educators better understand the shifts of the

NGMLS. The five questions below illustrate these shifts for Algebra I.

While educators from around the state have helped craft these sample questions, they have not undergone the

same extensive review, vetting, and field testing that occurs with actual questions used on the State exams. The

sample questions were designed to help educators think about content, NOT to show how operational exams

look exactly or to provide information about how teachers should administer the test.

1. N-RN.3a

What is the sum of 3

√

7 + 2

√

7?

(1) 5

√

7

(2) 5

2

√

7

(3) 5

√

14

(4) 5

2

√

14

2. A-REI.10

What is an equation of the line that passes through the points (2,7) and (-1,3)?

3

(1)  − 2 = ( − 7)

4

(2)  − 2 = ( − 7)

3

(3)  − 7 = ( − 2)

4

(4)  − 7 = ( − 2)

3

Algebra I Educator Guide

12

3. N-RN.3a

3

Rationalize:

2

√

6

4. A-REI.4b

Use the method of completing the square to determine the exact values of x for the equation



2

+ 6 − 41 = 0. Express your answer in simplest radical form.

5. A-REI.7a

Solve the following systems of equations algebraically for all values of x and y:

 = 

2

+ 5 − 17

 −  = 5

Answer Key to Algebra I Sample Items

1. Choice 1

2. Choice 4

3. Rubric

[2]

3

√

6

or an equivalent answer with no radical in the denominator, and correct work is shown.

12

[1] Appropriate work is shown, but one computational error is made.

or

[1] Appropriate work is shown, but one conceptual error is made.

or

[1]

3

√

6

, but no work is shown.

12

[0] A zero response does not contain enough relevant course-level work to receive any credit, does not

satisfy the criteria for one or more credits, or is a correct response that was obtained by an obviously

incorrect procedure.

Algebra I Educator Guide

13

4. Rubric

[4] −3 ± 5

√

2, and correct work is shown.

[3] Appropriate work is shown, but one computational or simplification error is made.

or

[3] Appropriate work is shown, but only one solution is stated.

[2] Appropriate work is shown, but two or more computational or simplification errors are made.

or

[2] Appropriate work is shown to find −3 ±

√

50, but no further correct work is shown.

or

[2] −3 ± 5

√

2, but a method other than completing the square is used.

[1] −3 ± 5

√

2, but no work is shown.

[0] A zero response does not contain enough relevant course-level work to receive any credit, does not

satisfy the criteria for one or more credits, or is a response that was obtained by an obviously incorrect

procedure.

5. Rubric

[4]  = −6,  = −11 and  = 2,  = −3 or (−6, −11) and ( 2, −3), and correct algebraic work is

shown.

[3] Appropriate work is shown, but one computational or factoring error is made.

or

[3] Appropriate work is shown to find  = −6 and  = 2, but no further correct work is shown.

or

[3] Appropriate work is shown to find either (−6, −11) or (2, −3), but no further correct work is

shown.

[2] Appropriate work is shown, but two or more computational or factoring errors are made.

or

[2] Appropriate work is shown to find

(

 + 6

)(

 − 2

)

= 0, but no further correct work is shown.

or

[2] A correct substitution is made into the quadratic formula, but no further correct work is shown.

or

[2]  = −6,  = −11 and  = 2,  = −3, but a method other than algebraic is used.

[1] A correct quadratic equation in standard form is written, but no further correct work is shown.

or

[1]  = −6,  = −11 and  = 2,  = −3 are stated, but no work is shown.

[0] A zero response does not contain enough relevant course-level work to receive any credit, does not

satisfy the criteria for one or more credits, or is a response that was obtained by an obviously

incorrect procedure.

Algebra I Educator Guide

14