North Carolina Middle School Mathematics Standard Course of Study (2010 Standards)

The Middle Grades Standards

0

K-8 Math Standards Overview and Critical Area Learning Description Continuums

These documents show a progression of the domains and clusters for the elementary and middle school math standards. This can help districts and teachers see the progressions between the content domains in each grade level. This can also be a reference for planning intervention and extension strategies within and across different grade levels.

Not all of the content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis than others based on the depth of the ideas, the time it takes to master, and/or their importance to future mathematics. Some things have greater emphasis is not to say that anything in the standards can safely be neglected in instruction. These documents are to help teachers and districts to organize their curriculum and resources based on priority and to assist in the integration of domains within and across grade levels.

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

The Unpacking Documents are designed to help North Carolina educators teach the State Standards. NCDPI staff are continually updating and improving these tools to be helpful and specific. We believe that as this document is used, teachers and educators will find ways in which the unpacking can be improved and made ever more useful. Based on your feedback, revisions to this document are made on a continual basis. In order to determine if you have the most current version, please refer to the date located on the first page of the Unpacking Document.

Illustrative Mathematics This site contains illustrations and explanations of content standards for mathematics and the standards for mathematical practice. Teachers are encouraged to use the illustrations during implementation of the tasks and provide constructive feedback. www.illustrativemathematics.org

Mathematics Progressions Documents The standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. This work is being undertaken by members of the original work team of the progressions and also by mathematicians and educators not involved in the initial writing. For additional information about this work please visithttp://ime.math.arizona.edu/progressions

SUDDS Digital Learning System (DLS) for middle grades is comprised of a learning map, links to free web-based resources, and a diagnostic assessment system. The map is built around nine big ideas that organize the content for grades 6-8 into clusters and constructs. Each construct is undergirded by research-based learning trajectories of observable student behaviors.

The GISMO research team at North Carolina State University has developed 18 learning trajectories that unpack the K-8 State Standards for Mathematics from the standpoint of student learning, and elaborate the underlying scientific research in mathematics education. The hexagon map illustrates these learning trajectories, standard by standard. Clicking on a hexagon or a trajectory takes you to detailed descriptors that articulate students' progression from prior knowledge and naïve conceptions to more sophisticated mathematical concepts and reasoning. TurnOnCCMath is a comprehensive resource to support teachers, teacher educators, professional development providers, and district and state-level curriculum experts in interpreting the Standards for instructional implementation. Documented throughout with citations from research and practitioner journals, TurnOnCCMath will also support educational researchers in identifying fruitful areas for further research on student learning.

Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

EDC – Implementing the Practices Implementing the Mathematical Practice Standards is an EDC project funded by the National Science Foundation to develop Illustrations of the Mathematical Practices and a professional development curriculum for teachers in grades 5–10. Each Illustration of the Standards for Mathematical Practice (SMP) consists of a mathematics task; a student dialogue based on that task; information about grade level, standards, and the context for the dialogue; teacher reflection questions; a mathematical overview; and optional student materials. While the primary use of Illustrations is for teacher learning about the SMP, some components are designed for classroom use with students.

Achieve, Inc. Achieve has developed materials to help states, districts, and others understand the organization and content of the standards and the content and evidence base used to support the standards.

Building the Language of Mathematics for Students (Vocabulary)

Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. The terms students should learn to use at each grade level with increasing precision are included in this document.

Selected tasks from the DPI Week-by-Week and Strategies Document rewritten to align to Standards. This document was created by selecting high leverage tasks from the DPI Week-by-Week and Strategies for Instruction Documents and rewritten to align to Standards. These lessons incorporate the Standards for Mathematical Practice to support teachers with the implementation of the content standards.The intent of this document is not to replace teachers’ resources but be used to support teachers’current resources. Because of the high demand for support materials, a first draft has been posted on the wiki. More of these lessons will be forthcoming. Once additional lessons are written and the documents complete then the documents will be finalized (table of contents, etc…). Thank you for your patience as we continue to work on support materials.

Middle School AIG-IRP Resources AIG~IRP Resources developed for Grades 6-8 advanced math learners. Each lesson has principle standards addressed listed in the template.

Additional Math Resources While not directly aligned to the State Standards, these resources contain high leverage tasks that could be used to supplement your existing resources.

Internet Resources A variety of resources are available on the internet. This is a compilation of resources that may be useful in lesson planning and instruction.

Released test forms may be used by school systems to help acquaint students with valuable test taking strategies in summative assessment situations. These strategies may include managing time, following directions, understanding reading selections, and thinking through how to select the correct answer. Released test forms may be used by parents and the general public in gaining a greater understanding of how the State Standards for Mathematics are measured.

Balanced Assessment This site is the result of a National Science Foundation funded mathematics assessment task development project called Balanced Assessment for the Mathematics Curriculum. In addition to the project team at the Harvard Graduate School of Education there were groups at the University of California, Michigan State University, and the University of Nottingham. At Harvard, they designed balanced collections of assessment tasks for both elementary and secondary mathematics.

Mathematics Assessment Project MAP is a collaboration between the University of California, Berkeley and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. The site includes a collection of formative and summative assessment tasks for secondary (6-12) mathematics organized by complexity level (expert, apprentice and novice).

Smarter Balanced (SBAC) and PARRCC The K-12 Assessment Center by ETS has been contracted by the US Department of Education to provide information about next generation assessments aligned to the common core state standards. The two comprehensive assessment consortia (SBAC and PARCC) have released sample assessment items that are computer interactive and/or computer adaptive.

## For resources aligned to the new mathematics standards, please visit the Tools 4 Teachers website: http://tools4ncteachers.com/ and the DPI Math Standard Course of Study website: www.ncpublicschools.org/curriculum/mathematics/scos.

## North Carolina Middle School Mathematics Standard Course of Study (2010 Standards)

## The Middle Grades Standards

## K-8 Math Standards Overview and Critical Area Learning Description Continuums

These documents show a progression of the domains and clusters for the elementary and middle school math standards. This can help districts and teachers see the progressions between the content domains in each grade level. This can also be a reference for planning intervention and extension strategies within and across different grade levels.K-8 Math Standards Critical Area Learning Continuum

6th Grade Math Standard Course of Study7th Grade Math Standard Course of Study8th Grade Math Standard Course of Study8th Grade Horizontal Layout (PDF)

## Major Work of the Grade

Not all of the content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis than others based on the depth of the ideas, the time it takes to master, and/or their importance to future mathematics. Some things have greater emphasis is not to say that anything in the standards can safely be neglected in instruction. These documents are to help teachers and districts to organize their curriculum and resources based on priority and to assist in the integration of domains within and across grade levels.## Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).Commentary of the Standards for Mathematical PracticeBack to Middle School Resources

## Middle School Unpacking Documents

## Unpacking Document

The Unpacking Documents are designed to help North Carolina educators teach the State Standards. NCDPI staff are continually updating and improving these tools to be helpful and specific. We believe that as this document is used, teachers and educators will find ways in which the unpacking can be improved and made ever more useful. Based on your feedback, revisions to this document are made on a continual basis. In order to determine if you have the most current version, please refer to the date located on the first page of the Unpacking Document.6th Grade Unpacked (Word)

6th Grade Unpacked (PDF)

7th Grade Unpacked (PDF)

8th Grade Unpacked (PDF)

00000000000000000000000000000000000000000000000000000000000

ADDITIONAL RESOURCES:Understanding the StandardsIllustrative MathematicsThis site contains illustrations and explanations of content standards for mathematics and the standards for mathematical practice. Teachers are encouraged to use the illustrations during implementation of the tasks and provide constructive feedback. www.illustrativemathematics.org

Illustrative Mathematics-HS Standards

Mathematics Progressions DocumentsThe standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. This work is being undertaken by members of the original work team of the progressions and also by mathematicians and educators not involved in the initial writing. For additional information about this work please visithttp://ime.math.arizona.edu/progressions

Draft K-5 Progression on Counting and Cardinality and Operations and Algebraic Thinking

Draft K-6 Progession on Geometry

7th Grade-HS Geometry

Draft 6-7 Progression on Ratios and Proportional Relationships

Draft 6–8 Progression on The Number System; High School, Number

Draft 6-8 Progression on Statistics and Probability

Draft 6-8 Progression on Expressions and Equations

## SUDDS

SUDDS Digital Learning System (DLS) for middle grades is comprised of a learning map, links to free web-based resources, and a diagnostic assessment system. The map is built around nine big ideas that organize the content for grades 6-8 into clusters and constructs. Each construct is undergirded by research-based learning trajectories of observable student behaviors.Scaling Up Digital Design Studies

## Turn on Common Core Math

The GISMO research team at North Carolina State University has developed 18 learning trajectories that unpack the K-8 State Standards for Mathematics from the standpoint of student learning, and elaborate the underlying scientific research in mathematics education. The hexagon map illustrates these learning trajectories, standard by standard. Clicking on a hexagon or a trajectory takes you to detailed descriptors that articulate students' progression from prior knowledge and naïve conceptions to more sophisticated mathematical concepts and reasoning. TurnOnCCMath is a comprehensive resource to support teachers, teacher educators, professional development providers, and district and state-level curriculum experts in interpreting the Standards for instructional implementation. Documented throughout with citations from research and practitioner journals, TurnOnCCMath will also support educational researchers in identifying fruitful areas for further research on student learning.http://www.turnonccmath.com/

Standards for Mathematical PracticeThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

SMP Teacher Planning Guide

Standards for Math Practice

SMP_Poster_Chart

SMP_Poster_Notebook

EDC – Implementing the PracticesImplementing the Mathematical Practice Standards is an EDC project funded by the National Science Foundation to develop Illustrations of the Mathematical Practices and a professional development curriculum for teachers in grades 5–10. Each Illustration of the Standards for Mathematical Practice (SMP) consists of a mathematics task; a student dialogue based on that task; information about grade level, standards, and the context for the dialogue; teacher reflection questions; a mathematical overview; and optional student materials. While the primary use of Illustrations is for teacher learning about the SMP, some components are designed for classroom use with students.

Educational Development Center

Achieve, Inc.Achieve has developed materials to help states, districts, and others understand the organization and content of the standards and the content and evidence base used to support the standards.

Achieve

Instructional Resources## Building the Language of Mathematics for Students (Vocabulary)

Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. The terms students should learn to use at each grade level with increasing precision are included in this document.Building Vocabulary (Word)

## Lessons for Learning

Selected tasks from the DPI Week-by-Week and Strategies Document rewritten to align to Standards. This document was created by selecting high leverage tasks from the DPI Week-by-Week and Strategies for Instruction Documents and rewritten to align to Standards. These lessons incorporate the Standards for Mathematical Practice to support teachers with the implementation of the content standards.The intent of this document is not to replace teachers’ resources but be used to support teachers’current resources. Because of the high demand for support materials, a first draft has been posted on the wiki. More of these lessons will be forthcoming. Once additional lessons are written and the documents complete then the documents will be finalized (table of contents, etc…). Thank you for your patience as we continue to work on support materials.Middle School AIG-IRP ResourcesAIG~IRP Resources developed for Grades 6-8 advanced math learners. Each lesson has principle standards addressed listed in the template.

Additional Math ResourcesWhile not directly aligned to the State Standards, these resources contain high leverage tasks that could be used to supplement your existing resources.

Superstars

Problem Solving Deck

Internet ResourcesA variety of resources are available on the internet. This is a compilation of resources that may be useful in lesson planning and instruction.

Back to Middle School Resources

Assessment Resources## North Carolina End-Of Grade Assessments (EOG)

Released test forms may be used by school systems to help acquaint students with valuable test taking strategies in summative assessment situations. These strategies may include managing time, following directions, understanding reading selections, and thinking through how to select the correct answer. Released test forms may be used by parents and the general public in gaining a greater understanding of how the State Standards for Mathematics are measured.NC EOG Information

## Released Forms

Gridded Response SheetBalanced AssessmentThis site is the result of a National Science Foundation funded mathematics assessment task development project called Balanced Assessment for the Mathematics Curriculum. In addition to the project team at the Harvard Graduate School of Education there were groups at the University of California, Michigan State University, and the University of Nottingham. At Harvard, they designed balanced collections of assessment tasks for both elementary and secondary mathematics.

Mathematics Assessment ProjectMAP is a collaboration between the University of California, Berkeley and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. The site includes a collection of formative and summative assessment tasks for secondary (6-12) mathematics organized by complexity level (expert, apprentice and novice).

Mathematics Assessment Project

Smarter Balanced (SBAC) and PARRCCThe K-12 Assessment Center by ETS has been contracted by the US Department of Education to provide information about next generation assessments aligned to the common core state standards. The two comprehensive assessment consortia (SBAC and PARCC) have released sample assessment items that are computer interactive and/or computer adaptive.

K-12 Center at ETS

SBAC

PARCC