K-12 Enduring Understandings

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GIPS K-12 Mathematics Program
Enduring Understandings

 

Number and Operations

• Abstraction is what makes mathematics work.
• The problem in front of you is a member of a family of problems.
• Numerical representations can be used to describe quantitative relationships.
• The ability to express the relationship amongst sets of numbers provides the foundations for the rules that govern arithmetic and algebra.
• The type of representation used depends upon the nature of the question to be answered.
• Estimating the answer to a problem helps mathematicians predict the reasonableness of a solution.

Algebraic Concepts

• Algebraic representations generalize patterns and relationships that help solve specific problems.
• Functions and relations help us formulate potential solutions for real-life problems involving two variables.
• The formulation of an equation or functional relationship reflects the mathematician's clarity about the problem or pattern.
• Mathematicians formulate equations or functional relationships to communicate generalizations so that specific problems can be solved more efficiently.
• Mathematicians communicate fluently using numerical, symbolic, and graphical representation.
• Sophisticated mathematicians naturally move from one representation to another (and back again).

Geometry

• The language of geometry allows us to communicate in a precise and efficient manner.
• Relationships exist among the angles, sides, lengths, perimeters, areas and volumes of geometric figures.
• The properties of geometric figures determine the construction of man-made objects and explains the structure of objects found in nature.
• Geometric figures can change size and/or position while maintaining proportional attributes.
• What we measure influences how we measure.
• Standard units of measure allow us to describe objects, interpret events and make comparisons in a way that can be universally understood.
• The best mathematical solution is not always the most functional solution in the real world.

Data Analysis

• The quality of the questions used has a significant impact on the collection of data and the validity of the results.
• Data illustrate relationships so inferences and predictions can be made and actions can be taken.
• Choices in dataP collection and representation affect their interpretation and use.
• Organization of data creates context so that what seems random may be quite predictable.
• The probability of an event occurring can be described numerically and used to make predictions about other events.