• District Curriculum Overview
  • Introduction to Curriculum Guides
  • Professional Teaching Standards
  • Professional Development Guiding Principles
  • Social Justice Commitment
  • Curriculum Guide Glossary of Terms
• Teaching Standards
  • Knowledge of Students
  • Planning and Teaching for Learning
  • A Culture and Environment for Learning
  • Monitoring Progress
  • Professional Growth
• Subject Areas
  • English/Language Arts
  • Mathematics
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K-12 Curriculum Standards
Overarching Big Ideas

[Note: See Principles and Standards for School Mathematics published in 2000 by The National Council of Teachers of Mathematics, Inc., Chapter Three: "Standards for School Mathematics Prekindergarten through Grade 12." The "Overarching Big Ideas" presented here are excerpted from this chapter. NCTM provides us with clear and coherent descriptions of critical skills and content competencies for each of their articulated standards: Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability, Problem Solving, Reasoning and Proof, Communications, Connections, Representation. See also http://www.nctm.org/standards/ for the NCTM standards and http://www.doe.mass.edu/frameworks/current.html for complete Massachusetts Curriculum Framework for Mathematics.]

Mathematics Process Standards
That Are Universal to All Grades and Strands

1. Problem Solving—Students will engage in tasks for which the solution method is not known in advance—formulating, grappling with, and solving complex problems that require a significant amount of effort. Students will acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that will extend outside the mathematics classroom. Students will—

   • build new mathematical knowledge through problem solving;

   • solve problems that arise in mathematics and in other contexts;

   • apply and adapt a variety of appropriate strategies to solve problems; and

   • monitor and reflect on the process of mathematical problem solving.

2. Reasoning & Proof—By developing ideas, exploring phenomena, justifying results, and using mathematical conjectures at all grade levels, students will see and expect that mathematics makes sense. Students will reason and think analytically—noting patterns, structure, and/or regularities in both real-world situations and symbolic object; asking if those patterns are accidental or if they occur for a reason, and making conjectures and proofs. Students will—

   • recognize reasoning and proof as fundamental aspects of mathematics;

   • make and investigate mathematical conjectures;

   • develop and evaluate mathematical arguments and proofs; and

   • select and use various types of reasoning and methods of proof;

3. Communication—Students will be able to express their understanding orally, in writing, and with models—a critical aspect of having a deep understanding of math. Students will be able to demonstrate proficiency by explaining how they solved a problem and by explaining the concept behind a mathematical skill. Students will-

   • organize and consolidate their mathematical thinking;

   • communicate their mathematical thinking coherently and clearly to peers, teachers, and others; and

   • analyze and evaluate the mathematical thinking and strategies of others; and

   • use the language of mathematics to express mathematical ideas precisely.

4. Connections—Students will deepen their understanding by connecting mathematical ideas to each other and to real world applications of those ideas. Students will —

   • recognize and use connections among mathematical ideas;

   • understand how mathematical ideas interconnect and build on one another to produce a coherent whole; and

   • recognize and apply mathematics in contexts outside of mathematics.

5. Representations—Students will learn to use representation to understand and communicate mathematical ideas. Using multiple representations, students will look at mathematical concepts or problems in a variety of ways. Student will —

   • create and use representations to organize, record, and communicate mathematical ideas and strategies;

   • select, apply, and translate among mathematical representations to solve problems; and

   • use representations to model and interpret physical, social, and mathematical phenomena.

Mathematics Content Standards
That Are Universal to All Grades and Strands

6. Number and Operations - Students will develop a deep and fundamental understanding of, and proficiency with, counting, numbers, and arithmetic, as well as an understanding of number systems and their structures. Students will-

   • understand numbers, ways of representing numbers, relationships among numbers, and number systems

   • understand meanings of operations and how they relate to one another

   • compute fluently through efficient and accurate methods that are supported by an understanding of numbers and operations

   • make reasonable estimates

7. Algebra – from kindergarten on, students will engage in experiences that build a solid foundation of understanding patterns, functions, relationships, variable, and mathematical modeling. Students will-

   • understand patterns, relations, and functions

   • represent and analyze mathematical situations and structures using algebraic symbols

   • use mathematical models to represent and understand quantitative relationships

   • analyze change in various contexts

8. Geometry – Through the study of geometry students learn about geometric shapes and structures and how to analyze their characteristics and relationships. Students will -

   • analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

   • specify locations and describe spatial relationships using coordinate geometry and other representational systems

   • apply transformations and use symmetry to analyze mathematical situations

   • use visualization, spatial reasoning, and geometric modeling to solve problems

9. Measurement – Measurement is the assignment of a numerical value to an attribute of an object, such as the length of a pencil. At more sophisticated levels, measurement involves assigning a number to a characteristic of a situation, as is done by the consumer price index. Students will come to understand what a measurable attribute is and become familiar with the units and processes that are used in measuring attributes. They will become proficient in using measurement tools, techniques, and formulas in a range of situations. In studying measurement, students will learn and apply other mathematics and explore connections to other subject areas. Students will-

   • understand measurable attributes of objects and units, systems, and processes of measurement

   • apply appropriate techniques, tools, and formulas to determine measurements

   • learn how to choose an appropriate unit of measure

   • develop an understanding that all measurements are approximations

10. Data Analysis and Probability – Throughout the grades students will engage with posing questions; collecting, organizing, analyzing, and displaying data; and basic probability in ways that grow in sophistication from grade to grade. Developing understanding of these elements of the curriculum is essential to being an informed citizen and intelligent consumer. Students will -

    • formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

    • select and use appropriate statistical methods to analyze data

    • develop and evaluate inferences and predictions that are based on data

    • understand and apply basic concepts of probability

We welcome your feedback to the Mathematics Curriculum Guide. Please send comments to Mathematics@arps.org.