## Math Curriculum Standards

Looking to adopt a new textbook series? Please visit the website below or download the documents below:

High School Criteria for reviewing curricular materials

http://www.mathedleadership.org/ccss/materials.html

**COMMON CORE STATE STANDARDS IMPLEMENTATION TOOLS AND RESOURCES**

"Kid-Friendly" Mathematics Practice Standards Placemat

Common Core Resources for Mathematics

Common Core: http://www.corestandards.org/

CCSSO has developed this preliminary list of tools and resources to point states to some promising practices and products to help them as they implement the Common Core State Standards. This document primarily lists resources developed by CCSSO and the lead writers of the standards and is not intended to be a comprehensive list of all the quality resources available.

Math Common Core Resource Materials from MAISA

http://gomaisa.org/math-ccrs-materials

Website Resources for the Common Core:

http://www.nctm.org/standards/mathcommoncore/

**Communications and Outreach**

**PTA Parent Guides**Provide grade-by-grade parent guides that reflect the Common Core State Standards. Individual guides were created for grades K-8 and two were created for grades 9-12 (one for English language arts/literacy and one for mathematics). Eleven Guides were created in all.*Purpose:*http://www.pta.org/4446.htm State education agencies, school districts, state boards of education, and state/local PTAs may co-brand the Guides. The modifiable Guides are available online at: http://www.globalprinting.com/national-pta/ (Username: pta_user, Password: global).*Website:*PTA and Common Core State Standards writers Who to Contact: National PTA at parentsguide@pta.org*Creators:*Complete*Status:*

**MATHEMATICS COMMON CORE STATE STANDARDS**

**Classroom examples and tools for mathematics instruction**Inside Mathematics is a professional resource for educators that features classroom examples of innovative teaching methods and insights into student learning, tools for mathematics instruction that teachers can use immediately, and video tours of the ideas and materials on the website. Inside Mathematics will be aligning its tools and examples to the Common Core.*Purpose:*www.insidemathematics.org/*Website:*To be notified when the resources are available, visit: http://insidemathematics.org/index.php/about-inside-mathematics/common-core-standards*Timeline:*

**Hyperlinked version of the math standards**Provide a version of the math standards that has hyperlinks within the document so a reader can electronically navigate the standards with fluidity.*Purpose:*Bill McCallum, lead math standards writer*Creator/Lead Author:*http://commoncoretools.files.w...*Website:*

**Illustrative Mathematics Project**Guide the work of states, assessment consortia, and testing companies by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the standards.*Purpose:*Bill McCallum, lead math standards writer*Creator/Lead Author:*http://www.illustrativemathematics.org/*Website:*Under development; projected completion in fall 2011*Timeline:*

**Lead writer Bill McCallum's blog**Math Common Core lead writer Bill McCallum keeps a blog of math Common Core implementation projects that he hears of through his work.*Purpose:*http://commoncoretools.wordpress.com/*Website:*

**Math curricular analysis tool**Help educators analyze curricular materials as they implement the math Common Core. There will be three tools produced: one looking at the treatment of key content areas in each of four grade bands (K-2, 3-5, 6-8, 9-12); one analyzing how well the standards for mathematical practice are integrated into the materials; and one assessing pedagogical aspects of the materials.*Purpose:*Bill Bush, University of Louisville*Creator/Lead Author:*Projected completion in June 2011*Timeline:*

**Progressions documents for the Common Core Math Standards**Produce a final version of the math progressions, which are 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. The original math Common Core writing team will finalize and publish these documents.*Purpose:*Bill McCallum, lead math standards writer*Creator/Lead Author:*http://ime.math.arizona.edu/progressions/*Website:*Under development. First draft can be found at http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_nbt_2011_04_07.pdf*Timeline:*

**Research-based professional development for math Common Core implementation**Research study entitled "Articulating Research Ideas that Support the Implementation of the Professional Development Needed for Making the Common Core State Standards in Mathematics Reality for K-12 Teachers"*Description:*This National Science Foundation (NSF) funded project will coordinate knowledge from different fields to develop recommendations for the design, implementation, and assessment of large-scale professional development systems consistent with the mathematics of the Common Core State Standards. Research results from diverse perspectives (e.g., mathematics education, organizational theory, professional development) will be articulated into a coherent framework and a set of recommendations for successful large-scale, system-level implementation of mathematics professional development initiatives. The recommendations will be disseminated through the National Council of Teachers of Mathematics.*Purpose:*North Carolina State University researchers*Creators/Lead Authors:*Project director and principal investigator Paola Sztajn, paola_sztajn@ncsu.edu*Contact:*Grant expires on 2/29/12*Timeline:*

**Visual depiction of the mathematical practices**Display some higher-order structure to the mathematical practice standards, just as the clusters and domains provide higher order structure to the content standards.*Purpose:*Bill McCallum*Creator/Lead Author:*http://commoncoretools.files.wordpress.com/2011/03/practices.pdf*Website:*Complete*Status:*

**THE STANDARDS FOR MATHEMATICAL PRACTICE**

Bulleted Mathematical Practices

Poster of the Eight Mathematical Practices of the Common Core (For a copy of the poster for your mathematics classroom, please contact Libby Pizzo at pizzol@resa.net)

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).

*Learn more about the Eight Mathematical Practices by clicking on the drop-downs below!*

**Common Core Charts per Standard**

**Instructional Resources**

These activities will help teachers understand and incorporate the instructional strategies imbedded in the Common Core State Standards.

Links to video-taped lessons that incorporate effective instructional strategies:

Lessons of Effective Instruction

**Assessment Resources**

Tools to help assess student mastery of Common Core State Standards

The SMARTER Balanced Assessment Consortium (SBAC) brings together 30 states, including Michigan, to create a common, innovative assessment system for Mathematics and English Lanugage Arts that is aligned with the Common Core State Standards.

Smarter Balanced Assessment Slide

SBAC Content Specifications with Content Mapping for the Summative Assessment of the CCSS for Mathematics

In an effort to help ease the transition to new technology-driven assessments planned for nationwide implementation in 2014, the State Educational Technology Directors Association (SETDA) has launched Assess4ed.net, a new online resource and community for state and district education leaders. Assess4ed.net is a community of practice site designed to help prepare leaders for the shift to assessments that are being developed under a United States Department of Education program and that are targeted for delivery beginning in the 2014-2015 school year.

**Curriculum Resources**

- Everyday Math
- Common Core Alignment Document
- Connected Math
- Core Plus
- Carnegie Learning
- The K - 12 Mathematics Curriculum Center
- The What Works Clearinghouse
- Exemplary Mathematics Programs
- Investigations in Number, Data and Space Report

**THIS NCSM WEBSITE HAS A NUMBER OF USEFUL RESOURCES INCLUDING TWO IN PARTICULAR:**

- A tool kit for educators beginning a mathematics textbook adoption and looking to see how well various instructional materials (aka textbooks) align with the new CCSS standards. Download two files, Curriculum Materials Analysis Project (DOC) and Professional Development for CCSSM Curriculum Analysis Reviewers (PPT)
- Three professional development modules designed to help educators understand and use the CCSS Practices. The materials for each module can be found under the header on this same page.

**NCSM Illustrating Mathematical Practices**

Look for additional modules to be added early next year!

##### 1. Make sense of problems and persevere in solving them

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

##### 2. Reason abstractly and quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

##### 3. Construct viable arguments and critique the reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

##### 4. Model with mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

##### 5. Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. 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. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. 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.

##### 6. 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, express 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.

##### 7. Look for and make use of structure

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 7 × 3, in preparation for learning about the distributive property. In the expression x2 9x 14, older students can see the 14 as 2 × 7 and the 9 as 2 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

##### 8. Look for and express regularity in repeated reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x 1), (x - 1)(x2 x 1), and (x - 1)(x3 x2 x 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

##### Connecting Mathematical Practice and Mathematical Content Standards

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word "understand" are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.

In this respect, those content standards which set an expectation of understanding are potential "points of intersection" between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.