EALR: 1. The student understands and applies the concepts and procedures of mathematics.

Component 1:1
Understands and applies concepts and procedures from number sense (number and numeration, computation, and estimation).

1. Reads, writes, compares, sequences, and identifies place value of whole numbers and decimals from 1,000,000,000 to hundred thousandths (.00001).
2. Compares and renames simple/common fractions, decimals, and percents.
3. Comprehends concepts involving prime, composite, square numbers, and divisibility at the concrete level.
4. Multiplies and divides multi-digit numbers by three-digit numbers.
5. Adds, subtracts, multiplies, and divides decimal numbers.
6. Adds and subtracts fractional numbers with and without like denominators.
7. Models multiplication and division of fractions and decimals at concrete level.
8. Uses appropriate mathematical tools to complete tasks.
9. Identifies situations where estimation is sufficient and computation is not required.
10. Uses estimation to predict computation results.
11. Uses estimation to check work through determining reasonableness of answers.

Component 1:2
Understands and applies concepts and procedures from measurement (attributes and dimensions, approximation and precision, and systems and tools).

1. Understands and uses different systems to measure objects and angles directly and indirectly.
2. Understands how dimensional changes affect perimeter, area, and/or volume at the concrete level.
3. Uses estimation to obtain reasonable approximations (linear and volume).
4. Understands benefits of standard and non-standard units of measure.
5. Knows relationships among units within each system (US/metric).
6. Selects and uses tools that will provide an appropriate degree of precision required to solve the problem.

Component 1:3
Understands and applies concepts and procedures from geometric sense (shape and dimension, and relationships and transformations).

1. Identifies attributes of points, lines, rays, angles, parallel lines, perpendicular lines.
2. Identifies, classifies, and compares plane figures and solid figures.
3. Describes types of triangles both by sides and angles.
4. Identifies similar and congruent figures.
5. Measures angles using protractor.
6. Estimates angle measurement.
7. Constructs simple plane shapes using compass and ruler.
8. Identifies lines of symmetry.
9. Identifies center, radius, diameter, arcs, chords, and circumference of circles.
10. Performs/identifies transformations (slides, flips, turns).
11. Uses ordered pairs to locate points on a coordinate grid.

Component 1:4
Understands and applies concepts and procedures from probability and statistics (probability, statistics, and prediction and inference).

1. Creates a data analysis investigation: considers the problem, collects and records data (i.e., random sampling, tallying, line graphs, bar graphs, pie graphs), organizes and interprets data to develop hypothesis and theories based on the data.
2. Calculates probability of uncertainty for simple events.
3. Conducts experiments and simulations to compare results with mathematical expectations.
4. Develops understanding of the meaning of probability and its usefulness by predicting, comparing, and inferring experimental results.

Component 1:5
Understands and applies concepts and procedures from algebraic sense (relations and representations, and operations).

1. Looks for, recognizes, and uses patterns as a strategy to solve problems.
2. Recognizes, creates, and extends series and sequences.
3. Understands and represents number patterns with tables and graphs.
4. Demonstrates an understanding of ratio.
5. Symbolically represents equalities and inequalities.
6. Understands the relationship between the basic arithmetic operations.
7. Organizes and solves single-variable equations.

EALR: 2. The student uses mathematics to define and solve problems.

Component 2:1
Investigates situations (by searching for patterns and exploring a variety of approaches).

1. Conducts explorations using a variety of strategies and approaches.
2. Systematically searches for patterns.
3. Recognizes and identifies information which is missing or extraneous.
4. Recognizes when an attempted approach is unproductive and tries to modify it or tries a new approach.

Component 2:2
Formulates questions and defines the problem.

1. Identifies questions to be answered.
2. Defines problems in familiar situations.
3. Identifies the unknowns in new situations.

Component 2:3
Constructs solutions (by choosing the necessary information and using the appropriate mathematical tools).

1. Organizes relevant information collected from a variety of sources and plans a sequence of steps to effectively meet a goal.
2. Uses appropriate strategies.
3. Analyzes her/his own thinking process to determine effectiveness.

EALR: 3. The student uses mathematical reasoning.

Component 3:1
Analyzes information (from a variety of sources; uses models, known facts, patterns and relationships to validate thinking).

1. Interprets information from a variety of sources.
2. Compares and contrasts information accessed from different sources.
3. Validates thinking and mathematical ideas using models, known facts, patterns, relationships, and proportional reasoning in familiar situations.

Component 3:2
Predicts results and makes inferences (and makes conjectures based on analysis of problem situations).

1. Makes conjectures and inferences based on analysis of problem situations.

Component 3:3
Draws conclusions and verifies results (supports mathematical arguments, justifies results, and checks for reasonableness of solutions).

1. Tests conjectures and inferences and discusses why they are true or not true.
2. Supports arguments and justifies results using inductive reasoning.
3. Reflects on and evaluates procedures and results.

EALR: 4. The student communicates knowledge and understanding in both everyday and mathematical language.

Component 4:1
Gathers information (reads, listens, and observes to access and extract mathematical information).

1. Develops a system for collecting information.
2. Gathers information from a variety of sources (observations, polling, diagrams, etc.).

Component 4:2
Organizes and interprets information.

1. Organizes information (which has been provided) in a useful way.
2. Interprets given information.
3. Draws conclusions from charts, graphs, etc.

Component 4:3
Represents and shares information (shares, explains, and defends mathematical ideas using terms, language, charts, and graphs that can be clearly understood by a variety of audiences).

1. Expresses ideas in a variety of ways using pictures, models, graphs, charts, number sentences, and written sentence format.
2. Orally communicates mathematical ideas in a manner appropriate for audience.
3. Defends mathematical ideas, concepts, and procedures using appropriate vocabulary.

EALR: 5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to                          real-life situations.

Component 5:1
Relates concepts and procedures within mathematics (recognizes relationships among mathematical ideas and topics).

1. Links conceptual and procedural understandings among a variety of mathematical content areas.
2. Uses equivalent mathematical models and representations.
3. Sees relationships between selected parts of mathematics.

Component 5:2
Relates mathematical concepts and procedures to other disciplines (identifies and applies mathematical thinking and notation in other subject areas).

1. Identifies mathematical patterns and ideas in other disciplines.
2. Describes examples of the contributions of various cultures to the historical development of number systems, measurement, and patterns.
3. Describes examples of the contributions of both women and men to the development of mathematics.

Component 5:3
Relates mathematical concepts and procedures to real-life situations (understands the connections between mathematics and problem-solving skills used every day at work and at home).

1. Recognizes the widespread use of mathematics in daily life.
2. Recognizes the extensive use of mathematics in situations that relate to society.
3. Understands that mathematically related careers are open to all students.
4. Understands that access to many diverse career opportunities is dependent upon mathematical understanding of the Auburn stands in mathematics.