Department Big Ideas Enduring Understandings EQ

Mathematics Department Big Ideas / Enduring Understandings / EQ

Doing and understanding mathematics fosters growth in the following fundamental processes:

Big Ideas Problem Solving

Enduring Understandings Tools and strategies are strategically selected and used to solve particular applications.

Essential Questions How do I know where to begin when solving a problem?

Reflection on the process and reasonableness of the solution moves students from the symbolic to the practical.

What are the characteristics of a successful problem solver?

What is the best method or technique for working toward a solution?

Connections

Connections exist within mathematical concepts and can broaden understanding of the world.

What is the meaning of the solution and does it make sense? Where do mathematical ideas surface in the world?

Mathematical ideas interconnect and build on one How can I use mathematical knowledge

another to produce a coherent whole.

in different contexts?

How is mathematics a coherent discipline that contains internal structure and interconnectedness?

Reasoning

Abstract and quantitative reasoning are required to process mathematical information and solve problems.

Mathematical conjectures are developed and investigated through observing patterns.

Sound reasoning requires the ability to distinguish between valid and invalid arguments and to critique the reasoning of others.

How do I select appropriate reasoning tools to progress mathematically?

What is a possible approach? What happens if I follow that approach?

Is my / their reasoning sound? What does a well-reasoned argument entail?

What constitutes proof?

Communication

Mathematical ideas must be communicated clearly How do I communicate mathematical

in written, visual, or oral form.

ideas clearly?

Communication of mathematical thinking should demonstrate clear and concise organization.

How can I organize and consolidate my thinking through communication?

Mathematical language can be used to express ideas symbolically, numerically, and graphically.

How can mathematics be perceived as a language? What terms, notations, and representations most accurately and succinctly convey my ideas?

Representation

Symbols, graphs, pictures, and tables can be used to What representation best illuminates

represent real situations.

this relationship?

Flexibility in one's ability to read and interpret various forms is important in understanding problems and solutions.

How do I move between mathematical abstraction and physical reality?

Various mathematical representations are useful for problem solving and communicating a solution.

Mathematics Department Big Ideas / Enduring Understandings/ EQ

The content of mathematics is valuable and important for students to learn.

Big Ideas Number and Operations

Enduring Understandings Understanding numbers, their representations, properties, and relationships assist in higher level thinking.

Essential Questions How does the context of a problem dictate the number system that should be used?

What operation is most appropriate given the context of the problem?

When is a rough estimate, an approximation, or an exact answer suitable for a solution to a problem?

Algebraic Understanding

Patterns, relations, and functions are mathematical How can I generalize patterns, describe ways to describe connectedness and dependence. relationships, and analyze functions?

Mathematical situations and structures can be

How do I use the tools of symbolic

represented and analyzed using symbols to advance algebra to judge the reasonableness of

algebraic thinking.

mathematical representations?

Mathematical models can be used to represent and How is the idea of change analyzed? understand quantitative relationships.

Change can be modeled in a variety of mathematically ways.

Geometric Understanding and Measurement

Two and three dimensional shapes have properties and relationships similar to each other.

Coordinate geometry can be used to describe spatial relationships and location.

How do the tools of geometry such as definitions, theorems, and properties foster an increasing ability to spatially visualize and logically deduce conclusions?

The study of transformations and symmetry provides a deeper understanding of physical change.

What is the relationship between units and physical quantity?

Visualization, spatial reasoning, and geometric modeling are strategies to enhance problem solving.

In order to assign numerical values to spatial and physical attributes, objects can be measured using appropriate systems, units, and processes.

Data Analysis and Probability

Data collection and its organization helps formulate relevant questions that can be answered using mathematical tools.

Selection of the appropriate statistical method to analyze data will progress students toward solutions and subsequent inferences.

A study of probability helps illuminate the randomness of our everyday world.

What types of questions can be answered by analyzing data?

When is data analysis valid and what is its purpose?

How can I become a critical interpreter of data?

How does probability relate to the real world?

Revised 4/24/13.

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