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. Identifies, compares, and orders whole numbers to 1,000,000 and simple fractions.
2. Rounds numbers to the nearest tens, hundreds, and thousands.
3. Uses physical models and pictures to demonstrate relationships within fraction families (1/2, ¼, 1/8, 1/16, 1/3, 1/6, 1/12).
4. Identifies properties of addition and multiplication; uses objects, pictures, or symbols to illustrate the meanings of commutative and associative properties.
5. Uses physical models to solve problems involving a combination of any two whole number operations.
6. Adds, subtracts, multiplies, and divides whole numbers.
7. Writes number sentences representing addition, subtraction, multiplication, and division situations.
8. Solves relevant problems in other disciplines involving addition, subtraction, multiplication, and division of multi-digit whole numbers where the operations are not specified.
9. Uses mental arithmetic, pencil and paper, or calculator as appropriate to the task involving whole numbers.
10. Shows understanding of whole number operations (x, ö ) using a variety of manipulatives to solve problems containing one- to two-digit factors.
11. Estimates and solves realistic problems involving multiplication and division using the computation strategy most appropriate to the situation (mental math, paper and pencil, and calculator).
12. Identifies situations involving whole numbers in which estimation is useful.
13. Uses estimation to predict computation results and to determine the reasonableness of answers, for example, estimating a grocery bill.
14. Uses mental math to divide by 10’s and 100’s.

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

1. Uses language and symbols to compare attributes of perimeter, area, and volume.
2. Understands and uses the appropriate units of measure for time, money, length, area, volume, mass, angle, and temperature to describe and compare objects.
3. Estimates to predict and determine when measurements are reasonable, for example, estimating the length of the playground by pacing it off.
4. Uses a ruler, tape measure, scale, thermometer, and clock to measure accurately.
5. Determines and justifies whether exact or appropriate measures are needed when given a realistic situation.
6. Solves realistic problems involving measurement of perimeter, area, length, weight/mass, time, and temperature when given diagrams or objects.

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

1. Identifies and describes attributes of plane and solid geometrical figures using appropriate adjectives such as parallel, symmetric, congruent, similar, and perpendicular.
2. Draws or creates plane and solid geometric figures using appropriate tools.
3. Describes the relative position of figures located on a coordinate plane.
4. Understands and constructs simple geometric transformations using slides, flips, or turns.

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

1. Uses organized counting to determine the number of possible outcomes of an event.
2. Makes inferences based on experimental results using coins, random number generators, spinners, etc.
3. Poses simple questions and hypotheses in realistic situations in other disciplines, collects data and communicates results using graphs or tables supported by written or oral explanations.
4. Describes mean, median, and mode for specific data and associates them with measurement of central tendency.

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

1. Recognizes and creates sequential number patterns and generates rules for them.
2. Uses manipulatives and pictorial representations to illustrate processes maintaining equality in an equation.
3. Translates problem situations into mathematical equations using geometric symbols or letters to represent unknown quantities.
4. Represents number patterns symbolically.

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. Searches for patterns.
2. Uses a variety of strategies and approaches.
3. Recognizes when information is missing or extraneous.
4. Recognizes when an approach is unproductive and tries a new approach.

Component 2:2
Formulates questions and defines the problem.

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

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

1. Organizes relevant information.
2. Selects and uses appropriate tools.
3. Applies the appropriate methods, operations, and processes to construct a solution (mental math, paper and pencil, calculator).

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 and compares information in familiar situations.
2. Validates thinking using models, known facts, patterns, and relationships.

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 familiar problem situations.

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

1. Tests conjectures by finding examples to support or contradict them.
2. Supports arguments and justifies results based on own experiences.
3. Checks for reasonableness of results.
4. Reflects on and evaluates procedures and results in familiar situations.

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 and follows a plan for collecting information.
2. Uses reading, listening, and observation to extract mathematical information from a variety of sources (classmates, diagrams, etc.).
3. Uses available technology to browse and retrieve mathematical information from a variety of sources.

Component 4:2
Organizes and interprets information.

1. Organizes and clarifies mathematical information by reflecting, discussing, verbalizing, and writing.

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 using mathematical language and notation such as physical or pictorial models, tables, charts, graphs, or symbols.
2. Expresses mathematical ideas using everyday language.

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. Connects conceptual and procedural understandings among familiar mathematical content areas.
2. Recognizes equivalency between different representations and models of mathematics.
3. Recognizes relationships between mathematical ideas and topics.

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

1. Recognizes mathematical patterns and ideas in other disciplines.
2. Uses mathematical thinking and modeling in other disciplines.
3. Describes examples of contributions to the development of mathematics such as the contributions of women, men, and different cultures.

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. Gives examples of how mathematics is used in everyday life.
2. Identifies how mathematics is used in career settings.