| EALR #1:
The student understands and applies the concepts and procedures of
mathematics. |
| 1.1 Number Sense |
- Understands and uses properties and symbolic representations of real
numbers.
- Explains the magnitude of numbers by comparing and ordering real
numbers.
- Understands concepts of and uses processes involving prime and
composite numbers, factors and multiples, and divisibility.
- Understands and applies the concepts of ratio and both direct and
indirect proportion.
- Computes with real numbers, powers, and roots.
- Uses mental arithmetic, pencil and paper, calculator, or computer as
appropriate to the task involving real numbers.
- Identifies situations involving real numbers in which estimation is
sufficient and computation is not required.
- Uses estimation to predict computation results and to determine the
reasonableness of answers involving real numbers.
|
| 1.2 Measurement |
- Understands how changes in dimension affect perimeter, area, and
volume.
- Measures objects and events directly or uses indirect methods.
- Understands that the precision and accuracy of measurement is
affected by the measurement tools and calculating procedures.
- Uses estimation to obtain reasonable approximations.
- Understands the benefits of standard units of measurement and the
advantages of the metric system.
- Compares, contrasts, and uses both the U.S. and metric systems.
- Selects and uses tools that will provide an appropriate degree of
precision.
- Calculates the length and midpoint of a line segment.
|
| 1.3 Geometric Sense |
- Compares, describes, and classifies 2- and 3-dimensional geometric
figures.
- Constructs geometric models and scale drawings using tools as
appropriate.
- Understands and uses coordinate grids.
- Identifies simple differences between geometric properties of a plane
and a sphere.
- Understands and uses properties of symmetry, similarity, and
congruence.
- Understands and constructs multiple geometric transformations using
combinations of translation, reflection, or rotation.
- Uses variety of tools and technologies to perform geometric
constructions.
- Develops understanding of the differences between Euclidean and
non-Euclidean geometries through discussions, manipulative use, and written products.
- Recognizes corresponding parts of congruent or similar figures.
- Explores angle relationships associated with parallel and
perpendicular lines.
- Applies connections between geometric figures and theorems with
written products.
|
| 1.4 Probability and Statistics |
- Understands the properties of dependent and independent events.
- Understands and uses appropriate counting procedures to determine
probabilities.
- Uses statistics to support different points of view.
- Collects data using appropriate methods and technology.
- Organizes and displays data in appropriate forms.
- Calculates and uses the different measures of central tendency,
variability, and range as appropriate in describing sets of data.
- Designs and conducts experiments to verify or disprove predictions.
- Understands and makes inferences based on the analysis of
experimental results.
|
| 1.5 Algebraic Sense |
- Recognizes, creates, extends, and generalizes patterns, sequences,
and series.
- Understands, develops, and expresses rules describing patterns.
- Translates among tabular, symbolic, and graphical representations of
relations.
- Represents situations that involve variable quantities with
expressions, formulas and equations, and inequalities.
- Creates and solves equations and inequalities.
- Evaluates and simplifies expressions.
|
| EALR #2: The student uses
mathematics to define and solve problems. |
| 2.1 Investigate Situations |
- Searches systematically for patterns in complex situations.
- Analyzes and uses multiple strategies.
- Identifies what information is missing or extraneous and compensates
for it.
- Analyzes an unproductive approach and attempts to modify it or try a
new approach.
- Explores right triangle trigonometry.
|
| 2.2 Formulate Questions |
- Identifies questions to be answered in complex situations.
- Defines problems in complex situations.
- Identifies the unknowns in complex situations.
|
| 2.3 Construct Solutions |
- Organizes and synthesizes information from multiple sources.
- Selects and uses appropriate mathematical tools.
- Applies appropriate methods, operations, and processes to construct a
solution.
|
| EALR #3: The student uses
mathematical reasoning. |
| 3.1 Analyze Information |
- Tests conjectures and inferences by formulating a proof or by
constructing a counter example.
- Supports arguments and justifies results using inductive and
deductive reasoning.
- Checks for reasonableness of results.
- Reflects on and evaluates procedures and results and makes necessary
revisions.
|
| 3.2 Predict and Infer |
- Makes and explains conjectures and inferences based on analysis of
problem situations.
- Predicts future outcomes by using statistical methods.
|
| 3.3 Draw Conclusions and Verify |
- Interprets and integrates information from multiple sources.
- Validates thinking and mathematical ideas using models, known facts,
patterns, relationships, counter-examples, and proportional reasoning.
- Develops geometric postulates.
- Develops formulas for geometric formulas.
- Demonstrates an understanding of the Pythagorean Theorem and its
converse through applications.
|
| EALR #4: The student
communicates knowledge and understanding in both everyday and mathematical language. |
| 4.1 Gather Information |
- Develops or selects an efficient system for collecting information.
- Uses reading, listening, and observation skills to access and extract
mathematical information from multiple, self-selected sources.
- Integrates the use of variety of available technologies to browse,
select, and retrieve mathematical information from multiple sources.
|
| 4.2 Organize and Interpret |
- Organizes, clarifies, and refines mathematical information in
multiple ways – reflecting, verbalizing, discussing, or writing.
- Determines the reasonableness of an answer by critiquing a given
solution through discussion or in writing.
|
| 4.3 Represent and Share |
- Expresses complex ideas and situations using mathematical language
and notation in appropriate and efficient forms.
- Expresses or presents mathematical ideas clearly and effectively
using both everyday and mathematical language appropriate to audience.
- Compares the linear relationships parallel and perpendicular by
calculating and comparing slopes.
- Demonstrates knowledge of lines, circles, and their equations on
graphical displays, written products, and/or appropriate technology.
|
| EALR #5: The student
understands how mathematical ideas connect to other subject areas and real-life
situations. |
| 5.1 Relate Concepts and Procedures Within
Mathematics |
- Identifies situations in which mathematics can by used to solve
problems with local, national, or international implications.
- Investigates the mathematical knowledge and training requirements for
occupational/career areas of interest.
- Demonstrates the connection between geometric concepts and the
Cartesian Coordinate System.
- Develops the connections between geometric figures and theorems
through written products current technology use, and/or discussions and demonstrations.
- Develops relationships between central and inscribed angles and the
arcs related to these angles, and the concept of tangent as it applies to circles.
|
| 5.2 Relate Concepts and Procedures
to Other Disciplines |
- Relates and uses conceptual and procedural understandings among
multiple mathematical content areas.
- Relates and uses multiple equivalent mathematical models and
representations.
- Applies an understanding of algebraic and geometric relationships
through the use of manipulatives, written solutions, and group discussion.
|
| 5.3 Relate Concepts and Procedures to
Real-Life |
- Extends mathematical patterns and ideas to other disciplines.
- Applies mathematical thinking and modeling in other disciplines.
- Describes examples of contributions to the development of mathematics
such as the contributions of women, men, and different cultures.
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