**Math Topics**- Common Core
- Initiatives
- Methodology
- Resources
- Projects
- Manipulatives
- Software
**Learning Support**- Standardized Test Prep
- Technology Integration
- Assisting Readers
**Professionalism**- Associations
- Journals
- News
- Professional Development
- Education Standards
- Education Research
- CT4ME Publications

Educators across the country in states that have adopted the Common Core State Standards for Mathematics need teaching and learning resources that pair with the goals of the standards.

"Free" and low-cost with high quality are key words. The good news is that the Web has multiple sites from which to select resources. However, one needs to know where to look. That's where CT4ME comes in as a prime source.

CT4ME has taken on the challenge to identify specific resources that are aligned to or can be used to address each cluster of the CCSS high school math standards. Resources are intended to enhance instruction and to provide group and individual learning experiences for achieving the goals of the standards.

Within each cluster for number and quantity, algebra, functions, geometry, and statistics and probability you will find technology investigations, multiple choice and constructed response exercises, and performance tasks. The standards for mathematical practice, as they apply, are noted within many of those resources. Additionally, the 2013 book by Leslie Texas and Tammy Jones, Common Core Math Book Bundle: Strategies for Common Core Mathematics: Implementing the Standards for Mathematical Practice, 9-12 (Strategies for the Common Core Mathematics), will benefit math educators. It explains "each of the eight mathematical practices and gives high school educators specific instructional strategies that align with the Common Core State Standards for Mathematics."

Select the strand and then a domain within it to begin your exploration from this page:

**Tools and Plug-Ins**:

Some files in our collection are in pdf format. If needed, download Adobe Acrobat Reader, free software for viewing and printing PDF files.

You might need to download Java, a free plug-in to interact with virtual manipulative applets.

To interact with virtual manipulatives included within the Wolfram Demonstrations Project: Download the free Wolfram CDF player.

**General Resources**:

Achieve the Core: The section for mathematics includes Common Core exemplar tasks and assessments with explanations and supporting resources, and Common Core aligned exemplar lessons and units with supporting resources. There are also tools for planning, additional materials for understanding the math, and ready-to-use modules for professional development.

The CK-12 Math offers teacher and student versions. Students can master concepts through practice and using PLIX (play, learn, interact, explore). Teachers can find a standards-aligned flexbook. Math includes grades 1-5, Algebra, Geometry, Arithmetic, Statistics, Probability, Measurement, Trigonometry, Analysis, and Calculus. Videos, real world applications, and reading resources are included.

Curriculum Inspirations from the Mathematics Association of
America is "a collection of resources for Middle and High School
Math Teachers that demonstrate practical ways to engage students in
the lively exploration of mathematics and mathematical thinking
using problems from America’s longest-running and most successful
mathematics competition. Developed by James Tanton, these resources
include *Ten Problem Solving Strategy Essays*
and *Curriculum Bursts*." The problem solving essays
"relate specific AMC test questions to Common Core State Standards
Problem Solving Strategies. The Curriculum Bursts are "short
essays, paired with a * Curriculum Inspirations Video."*
These are found within individual content standards for each of the
Common Core high school and middle school math strands.

Desmos Online Graphing Calculator

EngageNY Common Core Curriculum includes grades preK-8, and high school algebra 1, algebra 2, geometry, precalculus and advanced topics. The site includes the "Common Core Standards, curriculum and instructional resources, bilingual resources, performance tasks and assessment guidelines and materials."

Khan Academy: Common Core aligned problems also feature step-by-step solutions and videos related to problems to support learning. Problems focus on conceptual understanding, procedural fluency, and real-world application.

Math Planet includes four courses: Pre-Algebra, Algebra 1, Algebra 2, and Geometry. Each comes with multiple chapters divided into several lesson topics. Under each lesson, you'll find theory, examples, and video lessons.

Mathematics Vision Project includes high school curriculum aligned to Common Core standards. There are student texts and teacher editions for Secondary I, II, and III. There are performance tasks and "ready-set-go assignments." The series takes a multi-tasking approach to learning. That is, each task addresses more than one standard and each standard is addressed in more than one task. Tasks are sequenced using the Comprehensive Mathematics Instruction framework: develop understanding, solidify understanding, and practice understanding.

Math Warehouse has numerous animations, lessons, and interactive practice problems for algebra, geometry, trigonometry, and calculus.

Mathispower4u by James Sousa contains a collection of over 4000 mini-lessons and videos organized by course and topic: number sense, arithmetic/prealgebra, algebra 1, algebra 2, geometry, math for liberal arts, trigonometry, calculus 1, calculus 2, calculus 3, linear algebra, differential equations. The site also includes problem solving activities with video solutions. Multiple Common Core topics are addressed in these.

**HOT!**:
National Science Digital Library at Ohio State University
emphasizes STEM resources for K-12 and beyond. You will find over 3000
resources related to the Common Core Math Standards and can refine your
search by grade level, learning domain, and alignment. In general,
search options include by education level, resource type, subject,
standards, and an advanced search option to further narrow what you are
looking for. Most are open educational resources.

OpenEd has videos, quizzes, lesson plans and assessments aligned to the Common Core math standards. You can search by standard. OpenEd has a free app, Common Core Quest, for iPad and iPhone. It contains SBAC and PARCC style questions within quizzes covering math and language arts standards for grades 6 and up with some coverage of the elementary standards. Among resources, are "lesson plans aligned to most of the popular textbooks in the USA. They are paced by chapter, and include videos, formative assessments, homework assignments, games for the exact chapter of the textbook" that educators are teaching.

Virtual Nerd from Pearson Education is an online, self-guided video tutorial site for math. There are over 1,500 video lessons covering grades 6-8 math, pre-Algebra, Algebra I, Algebra 2, and Geometry. Pearson has made these videos available for free. You can also select Virtual Nerd videos based on alignments to Common Core standards.

See additional Common Core Content Resources on CT4ME within our math methodology curriculum resources.

**Vocabulary Building:**

CT4ME recommends that learners develop math vocabulary by creating their own vocabulary cards to include the word, its definition in their own words, examples and non-examples of the word, and characteristics and facts about the word, such as would be found using the Frayer Model.

Frayer Model |
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Definition |
Characteristics Facts |
||

Word or Concept |
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Examples |
Non-Examples |

Vocabulary for the Common Core by Robert Marzano and Julie Simms (2013) will help educators to incorporate CCSS vocabulary into teaching and learning. Among its goals is for readers to be able to make general academic and domain specific language from the CCSS relevant to students.

CCSS Math Vocabulary Cards for All Grade Levels (K-7 and Secondary) are posted by the North Central Educational Service District. They will help learners with math content vocabulary, including ELL, and gifted-talented, special education, and regular education learners. Vocabulary is listed alphabetically with three levels: the word only; the word and a graphic; and the word, a graphic, and definition. For the secondary level, select the following:

- CCSS Math Vocabulary Secondary A-L
- CCSS Math Vocabulary Secondary M-Z

Mathwords.com features "terms and formulas from beginning algebra to calculus." Terms include appropriate pictures, diagrams, tables, and examples and are indexed by subject area: numbers and symbols; sets, logic, proof; geometry, algebra, trigonometry, advanced algebra and precalculus, calculus, advanced topics, probability and statistics, real world applications. Entries that feature multimedia are noted.

Stat Trek: Statistics and Probability Dictionary

**Are your students ready for the Common Core math exams?**

You can find out by using Benchmark Now!, a free online tool from Naiku for Grades 3-High School. It is designed to help identify students' knowledge and skills with professionally developed assessments using questions from Houghton Mifflin Harcourt’s Assess2Know® Benchmark Item Bank. Questions in the item bank are aligned to Common Core State Standards. There are beginning-of-year assessments help identify students’ readiness by domain and multiple interim assessments for each grade. Domain specific assessments provide teachers insight into student performance by standard.

For testing in your state and sample test items, see our CT4ME section for Standardized Test Preparation.

**Do you want to make parents more aware of the Common Core
standards and how they can help their children?**

The Council of the Great City Schools produced Parent Roadmaps to the Common Core Standards- Mathematics in 2012 and 2013 for grades K-8 and high school to help provide guidance to parents about what their children will be learning and how they can support that learning. The publications also include three-year snapshots showing how selected standards progress from year to year so that students will be college and career ready upon their graduation from high school.

ASCD Policy Points (2013, October) dispels rumors and myths surrounding the CCSS, so that parents, educators, policymakers, and the general public have a better understanding of what the standards are and are not. Read Common Core State Standards--Myths and Facts.

**
PARCC Assessments and Practice Tests**:

The Partnership for Assessment of Readiness for College and Careers (PARCC) includes a series of common policies related to assessment administration, scoring and the reporting of Common Core test results. There is also a section that addresses accessibility and test accommodations for learners with disabilities and English language learners. You'll also find released test items.

See PARCC.Pearson for Pearson Access, your technology set-up requirements, manuals and training, test preparation (sample items, tutorials, practice tests), bulletins, and support. The math practice tests are available in computer based and print formats for each grade 3-8, algebra 1, algebra 2, geometry, and integrated pathway.

PARCC Test Administration Portal lists Mathematics Guidance and Policies, including the following:

- The
**PARCC Calculator Policy**indicates for high school that a student may use "Graphing calculators with functionalities consistent with TI-84 or similar models. (Student may also bring a scientific calculator or a four-function with square root and percentage functions.)" (2012, 2016 update, p. 1). [Note: TI Math includes multiple activities for using the TI-84 calculator with learners. Activities are grouped by content area: Algebra I, Geometry, Algebra 2, Precalculus, Calculus, and Statistics.] - PARCC's
**High School Assessment Reference Sheet**(2016) will also be helpful to learners, as it contains key measurements and algebra and geometry formulas.

Learners who will take the PARCC assessment should be aware of how their performance will be reported. In July 2013, the Partnership for Assessment of Readiness for College and Careers (PARCC) released its Contents of the Grade- and Subject-Specific Performance Level Descriptors (PLDs) in Mathematics. The PLDs can be downloaded by grade level, course, grade band, all high school courses, or as a complete package. A PowerPoint presentation is also available to explain the structure of the PLDs. The PLDs are rubrics indicating the broad categories that will be used to report learner performance on an assessment. Five levels of command include 5: Distinguished, 4: Strong, 3: Moderate, 2: Partial Command, or Level 1 indicating a range from no work shown to Minimal command."

Technology Guidelines for PARCC Assessments (updated January 2015) "provides minimum and recommended specifications for computer hardware, input devices, and security requirements; and suggests recommended levels of bandwidth that will support schools instructional and assessment needs" (PARCC description).

Teacher Chris Aviles (2015, February 3) posted an informative video at Tech & Learning that introduces teachers to their role in administering the PARCC online on test day: PARCC: Won't Somebody Please Think of the Teachers.

The Smarter Balanced Assessment Consortium (SBAC) assessments will include summative assessments for accountability purposes and optional interim assessments for instructional use and will use computer adaptive testing to the greatest extent possible. Assessments will go beyond multiple-choice questions to include extended response and technology enhanced items, as well as performance tasks that allow students to demonstrate critical-thinking and problem-solving skills. See SBAC Practice and Training Tests.

Read the SBAC Usability, Accessibility, and Accommodations Guidelines that outline the kinds of testing supports and tools that will be made available to all students, and particularly those with disabilities and English-language learners for the Common Core assessments.

SBAC Testing Technology Information

Also see the SBAC Calculator Availability for Operational Assessments (2015), which notes calculators that students use for SBAC assessments.

**Domains**: Click on a domain to find technology
investigations, multiple choice and constructed response exercises, and
performance tasks.

- RN: The Real Number System
- Q: Quantities
- CN: The Complex Number System
- VM: Vectors and Matrix Quantities

**General**:

- CCSS Initiative: Number and Quantity Introduction
- Annenberg Learner: Learning Math: Number and Operations: Session 2: Number Sets, Infinity, and Zero. Exploration of the number sets that make up the real number system and on the concept of infinity and the importance of zero. Videos and homework are included.
- EngageNY/Common Core Curriculum for Precalculus and Advanced Topics includes modules on complex numbers and matrices.
- Illustrative Mathematics: Performance tasks for Number and Quantity
- Khan Academy: Common Core aligned problems:
- LearnZillion: lesson sets for Number and Quantity strand.
- MathsIsFun.com: Resources related to each of the Common Core standards for High School Number and Quantity. Each contains a tutorial and examples. Learners then complete problems for each section, most of which are multiple choice.
- Virtual Nerd: CCSS aligned Math Video Lessons from Pearson Education, Inc.: Select the section for High School: Number and Quantity.

**Domains**: Click on a domain to find technology
investigations, multiple choice and constructed response exercises, and
performance tasks.

- SSE: Seeing Structure in Expressions
- APR: Arithmetic with Polynomials and Rational Expressions
- CED: Creating Equations
- REI: Reasoning with Equations and Inequalities

**General**:

- CCSS Initiative: Algebra Introduction
- CK-12 FlexBooks:
- Algebra 1--2nd edition: "This revised and reorganized edition of CK-12 Algebra I is a complete high school course covering equations and functions, properties of real numbers, using linear functions and systems of equations, introducing higher order equations and functions, and including new material on probability and statistics. This edition is here aligned by chapter in support of state implementation of Common Core State Standards for High School Math."
- Algebra II with Trigonometry
- Texas Instruments Algebra I Student Edition

- CK-12: Browse Algebra has multiple resources for algebra listed by concepts developed and additional Algebra FlexBooks.
- Common Core Mathematics, A Story of Functions: Algebra I, Module I: Relationships Between Quantities and Reasoning with Equations and Their Graphs by Common Core (2013) contains lessons combining conceptual understanding, fluency, and application. Formative assessments are included. Content in Module 1 addresses standards: N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-SSE.2, A-APR.1, A-CED.1, A-CED.2, A-CED.3, A-CED.4, A-REI.1, A-REI.3, A-REI.5, A-REI.6, A-REI.10, A-REI.12.
- Curriki Algebra 1 Aligned to the CCSS-M Standards is designed for grade 9 learners with resources organized by Common Core math standards. Per its description, "Both teacher facing and student facing assets are included and are of various forms, e.g. text, video, and animations."
- A. Dendane: Analyze Math: Free online tutorials for algebra and functions, many of which include applets for learner technology investigations.
- EngageNY/Common Core Curriculum for Algebra I and Algebra II: a full-year curriculum with lessons organized in modules.
- Geogebra: free, open-source, dynamic mathematics software that joins geometry, algebra and calculus.
- Illustrative Mathematics: Performance tasks for Algebra
- Khan Academy: Common Core aligned problems:
- Kuta Software: Free Content Worksheets: Choose from Algebra 1 and Algebra 2.
- LearnZillion: lesson sets for Algebra strand.
- Mathguide.com: Lessons and Interactive Quizzes for Algebra, Geometry, and College Algebra. Many include videos.
- MathsIsFun.com: Resources related to each of the Common Core standards for High School Algebra. Each contains a tutorial and examples. Learners then complete problems for each section, most of which are multiple choice.
- Purplemath has multiple content modules for beginning, intermediate, and advanced algebra that also include function topics, plus sections for word problems and an introduction to trigonometry.
- Virtual Nerd: CCSS aligned Math Video Lessons from Pearson Education, Inc. Select the section for High School: Algebra.

**Domains**: Click on a domain to find technology
investigations, multiple choice and constructed response exercises, and
performance tasks.

- IF: Interpreting Functions
- BF: Building Functions
- LE: Linear, Quadratic, and Exponential Models
- TF: Trigonometric Functions

**General**::

- CCSS Initiative: Functions Introduction
- CK-12 FlexBooks:
- Algebra 1--2nd edition: "This revised and reorganized edition of CK-12 Algebra I is a complete high school course covering equations and functions, properties of real numbers, using linear functions and systems of equations, introducing higher order equations and functions, and including new material on probability and statistics. This edition is here aligned by chapter in support of state implementation of Common Core State Standards for High School Math."
- Algebra II with Trigonometry
- Texas Instruments Algebra I Student Edition
- Trigonometry Concepts: This text provides an introduction to trig, and delves into trig graphs, trig identities, inverse trig functions, triangles and vectors, and the polar system.

- CK-12: Browse Algebra has multiple resources for algebra listed by concepts developed and additional Algebra FlexBooks.
*Common Core Mathematics, A Story of Functions: Algebra I*, Module 3, Module 4, and Module 5 by Common Core (2014) contain lessons combining conceptual understanding, fluency, and application. Formative assessments are included:- Module 3: Linear and Exponential Functions addresses standards: A-SSE.3, A-CED.1, A.REI.11, F-IF.1, F-IF.2, F-IF.3, F-IF.4, F-IF.5, F-IF.6, F-IF.7, F-IF.9, F-BF.1, F-BF.3, F-LE.1, F-LE.2, F-LE.3, F-LE.5.
- Module 4: Polynomial and Quadratic Expressions, Equations and Functions addresses standards: N-RN.3, A-SSE.1, A-SSE.2, A-SSE.3, A-APR.1, A-APR.3, A-CED.1, A-CED.2, A-REI.4, A-REI.11, F-IF.4, F-IF.5, F-IF.6, F-IF.7, F-IF.8, F-IF.9, F-BF.3.
- Module 5: A Synthesis of Modeling with Equations and Functions addresses standards: N-Q.3, A-CED.1, A-CED.2, F-IF.4, F-IF.5, F-IF.6, F-BF.1, F-LE.1, F-LE.2.

- EngageNY/Common Core Curriculum for Precalculus and Advanced Topics
- Khan Academy: Common Core aligned problems:
- LearnZillion: lesson sets for Functions strand.
- PARCC: Assessments: Administration: High School Math Assessment Reference Sheet
- Purplemath has multiple content modules for beginning, intermediate, and advanced algebra that also include function topics, plus sections for word problems and an introduction to trigonometry.
- A. Dendane: Analyze Math: Free online tutorials for algebra and functions, many of which include applets for learner technology investigations.
- Geogebra: free, open-source, dynamic mathematics software that joins geometry, algebra and calculus.
- Illustrative Mathematics: Performance tasks for Functions
- Kuta Software: Free Content Worksheets: http://www.kutasoftware.com/freemain.html Choose from Algebra 1 and Algebra 2.
- MathsIsFun.com: Resources related to each of the Common Core standards for High School Functions. Each contains a tutorial and examples. Learners then complete problems for each section, most of which are multiple choice.
- Virtual Nerd: CCSS aligned Math Video Lessons from Pearson Education, Inc.: Select the section for High School: Functions.

**Domains**: Click on a domain to find technology
investigations, multiple choice and constructed response exercises, and
performance tasks.

- CO: Congruence
- SRT: Similarity, Right Triangles, and Trigonometry
- C: Circles
- GPE: Expressing Geometric Properties with Equations
- GMD: Geometric Measurement and Dimension
- MG: Modeling with Geometry

**General**:

- CCSS Initiative: Geometry Introduction
- CK-12 FlexBook: Geometry-Second Edition: "This revised edition of CK-12 Geometry is a complete high school course covering the essentials of geometry, logic and proof, congruent triangles, quadrilaterals, similarity, perimeter, area, volume, and transformations, here aligned by chapter in support of state implementation of Common Core State Standards for High School Math."
- CK-12: Browse Geometry has multiple resources for geometry listed by concepts developed and additional Geometry FlexBooks.
*Common Core Mathematics, A Story of Functions, Geometry*by Common Core (2013, 2014) is available in five separate modules, each with lessons combining conceptual understanding, fluency, and application. Formative assessments are included:- Curriki Geometry Aligned to the CCSS-M Standards "is a collection of resources for a high school course in Geometry. The resources are organized by Common Core State Standards for Mathematics and reflect a ninth or tenth grade course. Both teacher facing and student facing assets are included and are of various forms, e.g. text, video, and animations" (Content section description).
- Curriki PBL Geometry uses a project-based approach to teach geometry. There are several Common Core State Standards (CCSS)- aligned projects from which to choose. They can be taught in any order. Each focuses on two or more of the eight CCSS mathematical practices and includes technology and Web 2.0 resources. Quizzes, exam suggestions, and project assessment rubrics are provided. You'll find:
- Selling Geometry
- Designing a Winner
- What’s Your Angle, Pythagoras?
- TED Talk: House of the Future
- The Art of Triangles
- How Random is My Life?
- EngageNY/Common Core Curriculum for Geometry: a full-year curriculum map with lessons organized in modules.
- Geogebra: free, open-source, dynamic mathematics software that joins geometry, algebra and calculus.
- Illustrative Mathematics: Performance tasks for Geometry
- Khan Academy: Common Core aligned problems:
- Kuta Software: Free Content Worksheets: Choose from Geometry.
- LearnZillion: lesson sets for Geometry strand.
- Mathguide.com: Lessons and Interactive Quizzes for Algebra, Geometry, and College Algebra. Many include videos.
- MathsIsFun.com: Resources related to each of the Common Core standards for High School Geometry. Each contains a tutorial and examples. Learners then complete problems for each section, most of which are multiple choice.
- Math Open Reference is a free geometry textbook for high school learners by John Page. There are topics in plane geometry, coordinate geometry, and solid geometry (e.g., cylinders, cubes). Its focus is on using interactive materials and animations to develop concepts. Students can manipulate numerous interactive applets with at least one accompanying nearly every concept that is presented.
- PARCC: Assessments: Administration: High School Math Assessment Reference Sheet
- Virtual Nerd: CCSS aligned Math Video Lessons from Pearson Education, Inc.: Select the section for High School: Geometry.

**Domains**: Click on a domain to find technology
investigations, multiple choice and constructed response exercises, and
performance tasks.

- ID: Interpreting Categorical and Quantitative Data
- IC: Making Inferences and Justifying Conclusions
- CP: Conditional Probability and the Rules of Probability
- MD: Using Probability to Make Decisions

**General**:

- CCSS Initiative: Statistics and Probability Introduction
- CK-12 FlexBook: Basic Probability and Statistics – a Full Course
- CK-12: Browse Statistics or Browse Probability have multiple resources for each listed by concepts developed and additional Statistics and Probability FlexBooks.
- Common Core Mathematics, A Story of Functions: Algebra 1, Module 2: Descriptive Statistics by Common Core (2013) contains lessons combining conceptual understanding, fluency, and application. Formative assessments are included. Content in Module 2 addresses standards: S-ID.1, S-ID.2, S-ID.3, S-ID.5, S-ID.6, S-ID.7, S-ID.8, S-ID.9.
- American Statistical Association: Guidelines for Assessment and Instruction in Statistics Education (GAISE): Report for preK-12. This report contains examples that learners can do to investigate concepts in both statistics and probability with focus on real world applications.
- EngageNY/Common Core Curriculum for Precalculus and Advanced Topics: Module 5 includes 19 lessons on probability, random variables and discrete probability distributions, and using probability to make decisions.
- Illustrative Mathematics: Performance tasks for Statistics and Probability
- Khan Academy: Common Core aligned problems:
- LearnZillion: lesson sets for Statistics and Probability strand.
- MathsIsFun.com: Resources related to each of the Common Core standards for High School Statistics and Probability. Each contains a tutorial and examples. Learners then complete problems for each section, most of which are multiple choice.
- Stattrek.com: Statistics tutorials, also includes probability.
- Virtual Nerd: CCSS aligned Math Video Lessons from Pearson Education, Inc.: Select the section for High School: Statistics & Probability.

**Maximize your opportunities to use
technology in instruction.**

In *Technology Readiness for College and Career Ready Teaching,
Learning and Assessment*, the State Educational Technology Directors
Association (2012) reminded educators that:

"

Digital testing requires digital learning.Students using technology to take high--stakes tests must have significant opportunities to develop and demonstrate master of tested knowledge, skills and abilities via substantially similar technology prior to being tested. Teachers must be prepared to support this shift in instruction" (p. 1).

CT4ME has multiple resources to help with this endeavor.

Common Core State Standards (2010). *Mathematics Standards*.
Washington, DC: National Governors Association Center for Best Practices,
Council of Chief State School Officers. Retrieved from
http://www.corestandards.org/Math/

State Educational Technology Directors Association (2012). *Technology
Readiness for College and Career Ready Teaching, Learning and Assessment*. Retrieved
from
http://www.setda.org/priorities/online-assessment/