| NCTM
Standards |
PreK-2 |
3-5 |
6-8 |
9-12 |
| Numbers
and Operations |
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Understand
numbers, ways of representing numbers, relationships
among numbers, and number systems; |
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Understand
meanings of operations and how they relate to
one another; |
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Compute
fluently and make reasonable estimate |
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| Algebra |
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Understand
patterns, relations, and functions |
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Represent
and analyze mathematical situations and structures
using algebraic symbols |
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Use
mathematical models to represent and understand
quantitative relationships |
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Analyze
change in various contexts |
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| Geometry |
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Analyze
characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments
about geometric relationships |
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Specify
locations and describe spatial relationships using
coordinate geometry and other representational
systems |
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Apply
transformations and use symmetry to analyze mathematical
situations |
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Use
visualization, spatial reasoning, and geometric
modeling to solve problems |
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| Measurement |
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Understand
measurable attributes of objects and the units,
systems, and processes of measurement |
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Apply
appropriate techniques, tools, and formulas to
determine measurements |
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| Data
Analysis & Probability |
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Formulate
questions that can be addresses with data and
collect, organize, and display relevant data to
answer them |
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Select
and use appropriate statistical methods to analyze
data |
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Develop
and evaluate inferences and predictions that are
based on data |
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Understand
and apply basic concepts of probability |
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| Problem
Solving |
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Build
new mathematical knowledge through problem solving |
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Solve
problems that arise in mathematics and in other
contexts |
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Apply
and adapt a variety of appropriate strategies
to solve problems |
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Monitor
and reflect on the process of mathematical problem
solving |
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| Reasoning
& Proof |
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Recognize
reasoning and proof as fundamental aspects of
mathematics |
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Make
and investigate mathematical conjectures |
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Develop
and evaluate mathematical arguments and proofs |
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Select
and use various types of reasoning and methods
of proof |
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| Communication |
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Organize
and consolidate their mathematical thinking through
communication |
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Communicate
their mathematical thinking coherently and clearly
to peers, teachers, and others |
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Analyze
and evaluate the mathematical thinking and strategies
of others |
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Use
the language of mathematics to express mathematical
ideas precisely |
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| Connections |
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Recognize
and use connections among mathematical ideas |
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Understand
how mathematical ideas interconnect and build
on one another to produce a coherent whole |
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Recognize
and apply mathematics in context outside of mathematics |
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| Representation |
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Create
and use representations to organize, record, and
communicate mathematical ideas |
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Select,
apply, and translate among mathematical representations
to solve problems |
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Use
representations to model and interpret physical,
social, and mathematical phenomena |
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