Principles And Standards For School Mathematics

Front 1

Equity Principle

Back 1

Excellence in mathematics requires high expectations and strong support for all students

Front 2

Curriculum Principle

Back 2

A curriculum is more than a collection of activities, it must be coherent (big ideas) , focused on important mathematics (help develop other ideas, link one idea to another), and well articulated

Front 3

Teaching Principle

Back 3

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well

Front 4

Learning Principle

Back 4

Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge

Front 5

Assessment Principle

Back 5

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students, it should be done for students to guide and enhance their learning

Front 6

Technology Principle

Back 6

Technology is essential in teaching and learning mathematics, it influences the mathematics that is taught and enhances students' learning

Front 7

Five Content Standards

Back 7

Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability

Front 8

Five Process Standards

Back 8

Problem Solving (build mathematical knowledge through problem solving, solve problems, apply and adapt strategies to solve problems, monitor and reflection) Reasoning and Proof (reasoning and proof as fundamental aspects, investigate, develop and evaluate proofs, select and use various reasoning and methods of proof), Communication (consolidate mathematical thinking through communication, coherently to peers, teachers, evaluate thinking of others, use language of mathematics to express ideas), Connection (use connection among math ideas, apply math in real world, understand how ideas interconnect and build on one another to produce a coherent whole) Representation (create and use representation to organize, record, and communication math ideas, select apply and translate among mathematical representations to solve problems, use representations to model phenomena)

Front 9

Operations and Algebraic Thinking

Back 9

K-5

Front 10

Numbers and Operations in Base 10

Back 10

K-5

Front 11

Measurement and Data

Back 11

K-5

Front 12

Geometry

Back 12

K-8

Front 13

Numbers and Operations-Fractions

Back 13

3-5

Front 14

Counting and Cardinality

Back 14

K

Front 15

Expressions and Equations

Back 15

6-8

Front 16

The Number System

Back 16

6-8

Front 17

Statistics and Probability

Back 17

6-8

Front 18

Rations and Proportional Relationships

Back 18

6-7

Front 19

Functions

Back 19

8

Front 20

Standards for Mathematical Practice: Make Sense of problems and persevere in solving them

Back 20

Explain meaning of problem, possible approaches to solution, consider similar problems to gain insights, use concrete objects to think about problems, monitor and evaluate progress/change strategy if need be, check answers using different method

Front 21

Standards for Mathematical Practice: Reason Abstractly and quantitatively

Back 21

Explain relationship between quantities in problem situations, represent situations using symbols, create representations that fit problem, use flexibly the different properties of operations and objects

Front 22

Standards for Mathematical Practice: Construct viable arguments and critique the reasoning of others

Back 22

Understand and use assumptions, definitions and previous results to explain or justify solutions, analyze situations and use counterexamples, justify conclusions in a way that is understandable, compare two possible arguments for strengths and weaknesses

Front 23

Standards for Mathematical Practice: Model With Mathematics

Back 23

Apply mathematics to solve problems in every day life, make assumptions to simplify a problem, identify important quantities and use tools to map relationships, reflect on reasonableness of answer based on context of problem

Front 24

Standards for Mathematics Practice: Use appropriate tools strategically

Back 24

Consider a variety of tools and choose the appropriate tool to support problem solving, use estimation to detect possible errors, use technology to help visualize, explore/compare info

Front 25

Standards for Mathematics Practice: Attend to Precision

Back 25

Communicate precisely using clear definitions and appropriate mat language, state meaning of symbols, specify appropriate units of measure and labels of axes, use a degree of precision appropriate for the problem context

Front 26

Standards for Mathematics Practice: Look for and make use of structure

Back 26

Explain mathematical patterns or structures, shift perspective and see things as single objects or as compose of several objects, explain why and when properties of operations are true in a context

Front 27

Standards for Mathematics Practice: Look for and express regularity in repeated reasoning

Back 27

Notice if calculations are repeated and use info to solve problems, use and justify the use of general methods or shortcuts, self-assess to see whether a strategy makes sense as they work, checking for reasonableness prior to getting the answer