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, orders, and compares whole numbers through 999.
2. Identifies place value to ten thousands.
3. Reads and writes common fractions to represent models, real-life objects, and diagrams.
4. Orders fractions with like denominators using physical models, pictures, and symbols.
5. Reads and writes decimals to the tenths place to represent models, real-life objects, and diagrams.
6. Renames fractions with denominator 10 as decimal.
7. Recognizes money as a decimal notation.
8. Adds and subtracts multi-digit numbers with and without regrouping.
9. Increases and decreases numbers by multiples of 10, 100, and 1,000.
10. Demonstrates a conceptual understanding of multiplication and division.
11. Develops proficiency with multiplication and division facts through 10x10.
12. Multiplies three-digit whole number by one digit, including regrouping.
13. Uses inverse relationship of addition and subtraction, multiplication and division, to build fact families.
14. Demonstrates commutative property in addition and multiplication using physical models and equations.
15. Uses mental arithmetic, pencil and paper, or calculator as appropriate to computing task.
16. Understands there are situations where estimation is sufficient and computation is not necessary.
17. Uses a variety of strategies to estimate.
18. Develops skills in rounding to estimate.
19. Uses estimation to predict computation and determine 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. Uses directly measurable attributes such as length, perimeter, area, volume/capacity, weight/mass, money, temperature, and time to describe and compare objects.
2. Estimates,, measures, and records length, capacity, and weight in US and metric units.
3. Reads and records time to the nearest minute.
4. Understands measurement is approximate.
5. Estimates to predict and determine reasonableness of measurements.
6. Explores and describes area and perimeter of irregular two dimensional figures.
7. Explores volume of rectangular solids.
8. Understands the benefits of standard and non-standard units of measurement.
9. Uses appropriate tools for measuring length, perimeter, area, volume/capacity, weight/mass, money, temperature, and time.

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

1. Identifies plane and solid figures that are similar, congruent, or symmetrical and constructs examples of each.
2. Comprehends lines and line relationships, including parallel, perpendicular, diagonal, and angles.
3. Finds area of simple closed figures by counting grid squares.
4. Calculates perimeters of closed figures.
5. Identifies and constructs models of solid shapes.
6. Uses ordered pairs to locate points on a grid.
7. Predicts and verifies geometric transformations of a figure: slides, flips, turns.
8. Understands how geometric shapes and objects in the environment are related.

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

1. Understands difference between certain and uncertain events.
2. Lists all possible outcomes of simple experiments.
3. Understands and uses experiments to determine the probability of uncertain events.
4. Reads, discusses, and interprets pictographs, bar graphs, and tables.
5. Systematically collects data.
6. Organizes and displays data in numerical and graphic form: tallying, rank ordering, pictorgraphs, bar graphs, tables.
7. Predicts outcomes of simple activities and compares the prediction to experimental results.
8. Understands and makes inferences based on experimental results.

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

1. Recognizes, describes, extends, and creates a wide variety of patterns.
2. Uses standard notation to symbolically represent number patterns in open sentences.
3. Shows how one quantity determines another quantity in a functional relationship.
4. Solves simple open sentences at the symbolic level.

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.
2. Searches for patterns.
3. Recognizes when information is missing or extraneous.
4. Suggests a variety of strategies and approaches and chooses one.
5. Recognizes when an attempted approach is unproductive.
6. Tries another 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. Uses a variety of strategies.

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 in relatively familiar situations.
2. Compares and contrasts information.
3. 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 relatively familiar problem situations and justifies results.

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. Reflects on and evaluates procedures and reasonableness of results.
4. Checks for reasonableness of 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. Creates a plan for collecting information.
2. Uses appropriate mathematical vocabulary for concepts in content strands.
3. Uses reading, listening, and observation skills to access and extract mathematical information from a variety of sources such as, pictures, diagrams, physical models, classmates, oral narratives, and symbolic representation.
4. Uses technology to browse, select, and retrieve mathematical information from a variety of sources.

Component 4:2
Organizes and interprets information.

1. Organizes mathematical information.
2. Clarifies mathematical understandings by reflecting, discussing, 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 open sentences.
2. Expresses mathematical ideas using everyday language.
3. Justifies the use of one type of data collection and display over another.

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 between selected mathematical content areas in familiar situations.
2. Recognizes equivalent mathematical models and representations in familiar situations.
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. Recognizes mathematical patterns and ideas in familiar situations in other disciplines.
2. Uses mathematical thinking and modeling in familiar situations in other disciplines.
3. Describes examples of the contributions of different cultures to the historical development of number systems and patterns.
4. 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. Identifies examples of uses of mathematics in own daily life.
2. Identifies examples of uses of mathematics in situations that relate to society.