nys common core math lesson 13 homework

Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

Looking for video lessons that will help you in your Common Core Grade 5 Math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Grade 5 students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. The Lesson Plans and Worksheets are divided into six modules.

Related Pages Common Core Math Resources, Lesson Plans And Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 5 Common Core Math Video Lessons, Math Worksheets and Games for all grades

Grade 5 Homework, Lesson Plans And Worksheets

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

• Board of Regents
• Business Portal

New York State Education Department

• Commissioner
• USNY Affiliates
• Organization Chart
• Building Tours
• Program Offices
• Rules & Regulations
• Office of Counsel
• Office of State Review
• Freedom of Information (FOIL)
• Governmental Relations
• Adult Education
• Bilingual Education
• Career & Technical Education
• Cultural Education
• Diversity, Equity, and Inclusion
• Early Learning
• Educator Quality
• Every Student Succeeds Act (ESSA)
• Graduation Measures
• Higher Education
• High School Equivalency
• My Brother's Keeper
• Indigenous Education
• P-12 Education
• Special Education
• Vocational Rehabilitation

Office of the Professions

• Next Generation Learning Standards: ELA and Math
• Office of Standards and Instruction
• Diploma Requirements
• Teaching in Remote/Hybrid Learning Environments (TRLE)
• Office of State Assessment
• Computer-Based Testing
• Exam Schedules
• Grades 3-8 Tests
• Regents Exams
• New York State Alternate Assessment (NYSAA)
• English as a Second Language Tests
• Test Security
• Teaching Assistants
• Pupil Personnel Services Staff
• School Administrators
• Professionals
• Career Schools
• Fingerprinting
• Accountability
• Audit Services
• Budget Coordination
• Chief Financial Office
• Child Nutrition
• Facilities Planning
• Ed Management Services
• Pupil Transportation Services
• Religious and Independent School Support
• SEDREF Query
• Public Data
• Data Privacy and Security
• Information & Reporting

Mathematics

• Mathematics Learning Standards
• Regents Diploma Requirements for Mathematics
• Regional Contest Winners
• Tournament Winners
• Curriculum Bridge
• Frequently Asked Questions
• Mathematics Related Links
• Presidential Awards for Excellence in Mathematics and Science Teaching

Additional Resources

• Awards and Scholarships
• EngageNY Resources
• General Education and Diploma Requirements
• Multiple Pathways
• Teacher Centers

Math Frequently Asked Questions

1.  What are Learning Standards?

Learning Standards are defined as the knowledge, skills, and understandings that individuals demonstrate over time when exposed to high-quality instructional environments and learning experiences.

In 1996, the New York State Board of Regents approved 28 learning standards in seven content areas, which included the Learning Standards for Mathematics, Science and Technology. In 2005, the Mathematics Core Curriculum (Revised 2005) was adopted.  In January 2011, the Board of Regents adopted the  NYS P-12 Common Core Learning Standards for Mathematics (NYS CCLSM). Starting in 2015, the Board of Regents asked for a review of the NYS CCLSM and the outcome of that review was the NYS Next Generation Mathematics Learning Standards which were adopted in September 2017.

​2.  Are the NYS P-12 Common Core Learning Standards for Mathematics still applicable to schools in New York State? When will the transition to the NYS Next Generation Mathematics Learning Standards occur?

Implementation of the New York State Next Generation Mathematics Learning Standards for grades Pk-8 will take place school year 2022-2023 with spring 2023 being the first administration of the new 3-8 grade level state assessments aligned to/measuring the NYS Next Generation Mathematics Learning Standards.  Information regarding implementation of the NYS Next Generation Mathematics Learning Standards at the high school level will be forthcoming, however, implementation of those standards will not be before the school year 2022-2023.

3.  The NYS Common Core Learning Standards for Mathematics (NYS CCLSM) contain content emphases.  Are there content emphases for the NYS Next Generation Mathematics Learning Standards?

No. The clusters of the NYS CCLSM are divided into three categories recommended for instructional and assessment emphasis.  These categories are major clusters, supporting clusters and additional clusters.  For the school year 2019-2020,   NYS’s grades 3-8 assessments aligned to the NYS P-12 CCLSM will reflect these content emphases.  When the NYS Next Generation Mathematics Learning Standards are implemented, which is school year 2022-2023 for grades 3-8, these content emphases will no longer be applicable. They will however, still be in effect for the High School courses until they transition over to the NYS Next Generation Mathematics Learning Standards. At that point, there will be no labels of Major, Supporting, and Additional. 

4.  Will there be Pre-Test and Post-Test Standards for the NYS Next Generation Mathematics Learning Standards?

Yes. In order to ensure a timely return of assessment results, the New York State Mathematics grades 3-8 assessments are given in April/May. Each question on a New York State Mathematics grades 3-8 grade level assessment is aligned only to a Pre-Test standard for the grade level or a Post-Test standard from the prior grade level. While the pre-post guidance provides a clear designation of when students are held accountable for understanding content at the proficiency/mastery level, it is not intended to serve as a directive as to when the content should be introduced or how instruction of content should occur. Teachers may choose to introduce post-test content at various points in the year and then reinforce and build upon that content in the remaining months of school. Pre-post guidance for the NYS P-12 Common Core Learning Standards for Mathematics can be found in the 2019 Educator Guides to the 3-8 Mathematics Tests .  The pre-post guidance can be found on the New York State Next Generation Mathematics Learning Standards webpage.  Teachers are encouraged to familiarize themselves with this document.

5.  How do the learning standards inform local curriculum?

It is the local school district’s responsibility to design and implement a curriculum which will provide students with the necessary experiences to achieve the NYS Learning Standards. During the school year 2012-2013, NYSED started providing  Curriculum Modules (EngageNY) aligned to the NYS P-12 Common Core Learning Standards for Mathematics for school districts to use. These modules are available for districts to adopt, adapt, or not use at all.  They are a voluntary curriculum that includes several resources such as curriculum maps, overviews, lesson plans, homework/problem sets, performance tasks and assessments.

6.  Will the EngageNY Curriculum Modules be re-written to align to the NYS Next Generation Mathematics Learning Standards?

Currently, there are no plans to re-write the curriculum modules.  However, the module mathematical content is applicable to much of the Next Generation Mathematics Learning Standards.  Districts who choose to use the modules in whole or in part  will need to align them to correspond with the Next Generation Mathematics Learning Standards and determine if there are gaps that will need to be filled.  

7.  Does the state have a list of recommended mathematics textbooks?

New York is a non-endorsing state and curricular materials are a local decision. Local educators are empowered to select textbooks, identify products, and use a rich array of instructional materials, strategies and activities to meet student needs.

8.  Are students expected to supply their own calculators for classroom and assessment use?

The State Education Department requires the use of calculators for intermediate and high school level mathematics and science assessments.  To the extent that calculators are a necessary part of the educational program, the school district must provide them.  Under no circumstances should students be charged for a calculator or otherwise required to purchase one in order to participate in an educational program.  Please see the following memo regarding charging students for calculators.

9.  Do the learning standards support all learners, including students with disabilities and English language learners (Multilingual learners)?

The standards set grade-specific learning targets, but do not define the intervention methods or materials necessary to support students who are below or above grade-level expectations. It is beyond the scope of the standards to define the full range of supports appropriate for English Language Learners (ELLs)/Multilingual Learners (MLLs) and Students with Disabilities. However, the department ensured that teachers of English Language Learners (ELLs)/Multilingual Learners (MLLs) and Students with Disabilities participated in the revision of the standards. The New York State Education Department (NYSED) has created two statewide frameworks, the Blueprint for Improved Results for Students with Disabilities and the Blueprint for English Language Learner Success , aimed to clarify expectations and to provide guidance for administrators, policymakers, and practitioners to prepare ELLs/MLLs and Students with Disabilities for success. These principles therein the frameworks are intended to enhance programming and improve instruction that would allow for students within these populations to reach the same standards as all students and leave school prepared to successfully transition to post school learning, living and working.

10.  Where can additional information be found about education services for students with disabilities?

The  Office of P-12 Special Education  is the best source of information regarding New York State law, regulation, and policy governing the education of students with disabilities.

11.  Where can additional information be found about education services for English Language Learners?

The  Office of Bilingual Education and World Languages  provides support and technical assistance to Districts, Charter Schools, Non-Public Schools and other organizations (Universities, State Educational Organizations, etc.) in the development, implementation, and evaluation of programs for English language learners (ELLs), as well as to world language (WL) students within the State’s P-16 initiative.

12.  Is there a set of literacy standards for mathematics, in addition to the learning standards for literacy in History/Social Studies, Science and Technical Subjects?

Each discipline has its own literacy, including mathematics. The Standards for Mathematical Practice, which can be found starting on page 7 of the NYS Next Generation Mathematics Learning Standards document , reinforce the mathematical literacy skills that are needed in our students. Mathematical language/literacy is developed through opportunities that allow for the merging of content and practice. There is further information regarding advanced literacies that can be found in the presentation on this topic, NYS Next Generation Learning Standards: Leading Advanced Literacies Instruction For the 21st Century , that was given during our Supporting All Learners Conferences last year. The four hallmarks discussed tie directly to the mathematical practices, as well as the modeling cycle.

13.  What tools are appropriate to support instruction aligned to the NYS P-12 CCLSM or the NYS Next Generation Mathematics Learning Standards?  

The fifth Standard for Mathematical practice reads, “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 web site, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.”   It is up to the student to decide when it will be helpful to use the mathematics tools to answer a question.

When various mathematical tools (e.g., manipulatives, rulers, protractors, compasses, reference sheets, and technology) are appropriately incorporated into classroom instruction, these tools can:

• enhance learning;
• increase motivation;
• help students visualize concepts and ideas; and
• help teachers engage students across various learning styles through multiple representations.

Specifications for the allowable tools on the NYS 3-8 assessments can be found in the 2019 School Administrator’s Manual , Appendix E. Specifications for allowable tools on the Regents Examinations can be found in the Guidelines for Graphing Calculator Use for Commencement-Level Mathematics .

14.  Where is there additional information regarding the scope and sequence of mathematics instruction aligned to the NYS P-12 CCLSM or the NYS Next Generation Mathematics Learning Standards?  

The following recommended sources help explain the coherency between the grade levels and the progression of mathematical concepts P-12.

• Progression Documents for the Common Core Math Standards
• Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report
• Illustrative Mathematics
• Achieve the Core - Coherence Map

15.  What are the unpacking documents?

The unpacking documents that are available on our website are a set of exemplars Pk-Algebra II that demonstrate one process a teacher or team of educators can engage in to help identify the visible learning of a standard. As stated on our website, 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.  The intent was to provide teachers with an initial template that could serve as a platform for collaborative conversations about what they want their students to know and be able to do. The unpacking guide outlines the process that was used by the group of NYS educators that created the exemplars. It is important to keep in mind that the unpacking documents outline instructional strategies that could be used to support learning of the content.  They are not assessment items or directed lesson plans.

16. Where can previously adopted standards documents be found?

1996 Learning Standards for MST

Standards 1 and 2 Standard 3 (Math) Standards 6 and 7

Mathematics Core Curriculum (Revised 2005)

17 .  Are course outlines still available for Sequential Course I, II and III, as well as Math A/B?

Sequential Course I, II and III outlines Math A and Math B outlines key ideas and performance indicators

1.  What are the mathematics requirements for a Regents Diploma?

According to the Part 100 (100.5(a)(3)(iv)) of the Regulations of the Commissioner of Education, to receive a Regents Diploma a student must earn three commencement-level mathematics credits (more advanced than grade eight and must meet the commencement-level mathematics learning standards as determined by the commissioner) and achieve a passing score on one Mathematics Regents Examination or Department Approved Alternative mathematics examination.  

2.  What are the mathematics requirements for a Regents Diploma with Advanced Designation?

In order to earn a Regents Diploma with Advanced Designation Students must earn 3 commencement level Mathematics credits  and pass the Regents examinations in Algebra I, Geometry and Algebra II or the Department Approved Alternative for the examination requirements.  Further information regarding diploma requirements and the STEM pathway can be found on the C/I website .

3.  Can a student earn two credits for Algebra I?

According to the Part 100 (100.5(a)(3)(iv)) of the Regulations of the Commissioner of Education  … no more than two credits shall be earned for any Algebra I, Geometry, or Algebra II commencement level mathematics course . Algebra I is designed to be a one-unit course, however, the content of Algebra I (Geometry or Algebra II) may be spread out over two years with each year culminating in one credit.

4.  If a student takes a 1 year Algebra I course and passes however does not pass the Regents examination in Algebra 1, can they repeat the course and earn an additional credit?

No.  In order to earn 2 credits in a commencement level math course that culminates in a Regents examination, the course must be designed in such a way as that one half of the course content is delivered in year one and the second half of the content is delivered in year 2.  Each year should explore different mathematical concepts in greater depth/breadth, building a progression of skills.

5.  What is Credit by Examination and can it be used to earn Mathematics credit?

A student may earn a maximum of 6½ units of credit for either a Regents or local diploma without completing units of study.  In certain circumstances, students may have already mastered the learning outcomes of a Regents level course without having taken the course in the high school.  In such instances, the student may make a request to the superintendent to earn credit by exam.  If the superintendent decides to allow this, the student must earn a score of 85 on the Regents examination and complete a special project or oral examination.  In such cases where the student is successful, s/he would earn course credit without having to sit for the course of study. For more information on this option, please see section 100.5(d)(1) of the Part 100 of the Regulations of the Commissioner of Education,  Credit by Examination.

6.  Can Technology Education courses be used to fulfill mathematics credit?

A commencement level course in technology education may be used as the third unit of credit in science or mathematics but not both. For further information, see Using Technology Education Courses as the Third Unit of Math or Science under the Revised Graduation Requirements from the CTE Webpage.

7.  Can students at the middle level earn high school mathematics credit?

Students in grade eight shall have the opportunity to earn diploma credit in mathematics. The superintendent, or his or her designee, shall determine whether a student has demonstrated readiness in each subject, including mathematics, in which he or she asks to begin high school courses in the eighth grade leading to a diploma. A student shall be awarded high school credit for such courses only if such student passes the course and the associated Regents Examination. For additional information, please refer to  Section 100.4  (d) of the Part 100 Regulations of the Commissioner of Education. Further clarification about these regulations was given in the December 20, 2007 P-16 News and Notes that stated

• This provision was put in place to provide opportunities for individual students rather than as a vehicle for accelerating entire cohorts of students into high school courses.
• Superintendents or their designees shall determine whether an eighth-grade student has demonstrated readiness to take high school courses. School districts are encouraged to develop and use a written set of criteria to determine each student's readiness for acceleration.
• Grade eight students who are accelerated for diploma credit must have been provided instruction designed to facilitate their attainment of, by the end of grade seven, the State intermediate learning standards in each subject area in which they are accelerated.
• Part 100 Regulations of the Commissioner of Education allow only grade eight students the opportunity to be accelerated into high school courses in the eighth grade and to receive credit for use in satisfying diploma requirements. This provision does not extend to grade seven students.​ 

8.  Can students in grades earlier than 8 take high school math courses for credit?

Students in grades earlier than 8 can be placed into high school courses if their scholarship warrants and they may sit for the corresponding Regents examination.  If the student successfully passes the course and the Regents examination, s/he has met an assessment requirement toward a high school diploma, but does not earn a unit of math credit.  

9.  What is AIS-Academic Intervention Services and where can I find guidance regarding the program?

AIS is supplemental  instruction intended to assist students who are at risk of not achieving the State Learning Standards in ELA, mathematics, social studies, and/or science. Information about AIS can be found in the Part 100 Regulations of the Commissioner of Education, specifically:

• Definition of Academic Intervention Services
• Requirements of Academic Intervention Services
• Guidelines for Implementing Academic Intervention Services Q&A

1.  Which mathematics assessments are required by New York State?

In New York State, Every Student Succeeds Act (ESSA) requires students in grades 3-8 to be scheduled to take a New York State assessment for their grade level.  These assessments take place in the spring of each school year. At the high school level, successfully passing a Regents Examination in Mathematics is a graduation requirement for earning a Regents diploma. The  Educator Guides to the 3-8 Mathematics Tests  and the Educator Test Guides for Algebra I, Geometry and Algebra II provide helpful guidance around the content and design of these assessments. To learn more about New York State assessments, please visit the  Office of State Assessment website .

2.  When can a student take a Regents Examination in mathematics?

The admission requirement for taking the Regents Examination in mathematics is the completion of the course of study. Please see the  2019 Edition School Administrator's Manual, Regents Examinations  for more information. Each local school district determines when a student has completed the course of study. Please note that there is no provision in the Part 100 Regulations that allows a student to take a Regents examination before he/she has completed the necessary course of study in which he or she is enrolled.

3.  What are the New York State approved Alternative Examinations for meeting the requirements for a local or Regents diploma?

The New York State Department of Education Assessment Panel meets periodically to review proposals for alternative assessments to the Regents examinations and to make recommendations to the Commissioner of Education about whether the proposed alternatives should be approved. Several examinations have been approved, and the minimum acceptable scores have been set. Reference the  Department-Approved Alternative Examinations  memo for approved alternatives.

4.  Do students who are accelerated for diploma credit in grade eight need to take both the NYS Grade 8 Mathematics Test and the Regents examination associated with the unit of study?

The  Department has secured a waiver from the United States Department of Education (USDE) that relieves students, teachers, and schools from having to prepare students in seventh and eighth grade who are receiving instruction in Algebra I for multiple end of year assessments. This provision would also apply to students in grades 7 and 8 who receive instruction in Geometry and who take the Regents Examination in Geometry.   Grade eight students who have been accelerated into a high school mathematics course must take the corresponding Regents examination in order to earn a unit of diploma credit.  The district may choose to have the students in grades 7 and 8 who are taking Regents courses in mathematics,  take just the Regents examination or take both the grade level examination and the Regents examination.  If the student takes both examinations, the grade level examination score will be used for school and district accountability.  If the student takes only the Regents examination, the score earned on the Regents examination will be used for school and district accountability.  

5.  What are Testing Accommodations?

Some students require testing accommodations in order to participate in testing programs. Such accommodations provide students with the ability to demonstrate mastery of skills and attainment of knowledge without being limited or unfairly restricted because of a disability. The Office of State Assessment's  Accommodations for Testing website relays information on testing accommodations for students.

6.  Are computer based assessments an option for schools?

Computer-based administration of the NYS 3-8 mathematics assessments and stand-alone field testing is available for those schools or districts choosing that option.  Computer-based assessment resources , including practice questions and video tutorials, are available. 

7.  Is there an approved list of tools/calculators that can be used on the 3-8 state assessments and the Regents Examinations?

Specifications for the allowable tools on the NYS 3-8 assessments can be found in the 2019 School Administrator’s Manual , Appendix E. Specifications for allowable tools on the Regents Examinations can be found in the Guidelines for Graphing Calculator Use for Commencement-Level Mathematics  .

Get the Latest Updates!

Subscribe to receive news and updates from the New York State Education Department.

Popular Topics

• Charter Schools
• High School Equivalency Test
• Next Generation Learning Standards
• Professional Licenses & Certification
• Reports & Data
• School Climate
• School Report Cards
• Teacher Certification
• Vocational Services
• Find a school report card
• Find assessment results
• Find high school graduation rates
• Find information about grants
• Get information about learning standards
• Get information about my teacher certification
• Obtain vocational services
• Serve legal papers
• Verify a licensed professional
• File an appeal to the Commissioner

Quick Links

• About the New York State Education Department
• About the University of the State of New York (USNY)
• Business Portal for School Administrators
• Employment Opportunities
• FOIL (Freedom of Information Law)
• Incorporation for Education Corporations
• NYS Archives
• NYS Library
• NYSED Online Services
• Public Broadcasting

Media Center

• Newsletters
• Video Gallery
• X (Formerly Twitter)

New York State Education Building

89 Washington Avenue

Albany, NY 12234

CONTACT US  

NYSED General Information: (518) 474-3852

ACCES-VR: 1-800-222-JOBS (5627)

High School Equivalency: (518) 474-5906

New York State Archives: (518) 474-6926

New York State Library: (518) 474-5355

New York State Museum: (518) 474-5877

Office of Higher Education: (518) 486-3633

Office of the Professions: (518) 474-3817

P-12 Education: (518) 474-3862

EMAIL CONTACTS  

Adult Education & Vocational Services 

New York State Archives 

New York State Library 

New York State Museum 

Office of Higher Education 

Office of Education Policy (P-20)

© 2015 - 2024 New York State Education Department

Diversity & Access | Accessibility | Internet Privacy Policy | Disclaimer  |  Terms of Use