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, and orders whole numbers to 999.
2. Understands place value concepts through 999.
3. Demonstrates knowledge of simple/common fractions at a pictorial level.
4. Knows addition and subtraction facts to 18.
5. Adds and subtracts two and three-digit numbers with one regrouping, progressing from the concrete through the symbolic.
6. Uses mental arithmetic, pencil and paper, or calculator as appropriate to task.
7. Describes and justifies own methods of estimation involving realistic measurement situations (time, money, length, etc.).
8. Uses physical models and patterns to describe the difference between odd and even numbers.
9. Uses a variety of strategies to describe and solve situations involving multiplication and division.

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, volume, money, and time to describe and compare objects.
2. Estimates to predict and to determine when measurements are reasonable.
3. Understands the benefits of standard and non-standard units of measurement.
4. Knows appropriate units of measure for length, perimeter, area, weight/mass, money, temperature, and time.
5. Knows and uses appropriate tools for measuring length, perimeter, weight/mass, money, temperature, and time.
6. Measures to the nearest whole unit.

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

1. Uses attributes of shape and size to identify, name, and sort three-dimensional figures such as cubes, cones, and cylinders.
2. Determines, by counting, the number of faces, corners, and edges of three-dimensional objects.
3. Produces symmetrical designs.
4. Identifies lines of symmetry in shapes.
5. Combines and sub-divides shapes to form other shapes.
6. Understands and compares how geometric shapes and objects in the surrounding environment are related.
7. Graphs and describes location of objects on a coordinate grid.
8. Describes the relationship between triangle and quadrilaterals.
9. Understands and constructs symmetric, congruent, and similar figures.
10. Understands simple geometric transformations.
11. Uses appropriate vocabulary to describe geometric figures.
12. Draws and uses geometric figures in order to solve problems in real life two-dimensional settings.

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

1. Understands the difference between certain and uncertain events.
2. Knows how to list possible outcomes of simple experiments.
3. Uses experiments to investigate uncertain events.
4. Knows that data can consist of tabulations of events, objects, or occurrences.
5. Systematically collects data.
6. Organizes and displays data in numerical and graphical form.
7. Predicts outcomes and compares the predictions 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, creates, and extends patterns of objects and numbers.
2. Understands the use of guess and check in the search for patterns.
3. Symbolically represents number patterns.
4. Uses the symbols > (greater than), < (less than), and = (equal) to indicate numerical relationships.
5. Uses standard notation in reading and writing open sentences.
6. Represents and records different combinations of numbers which equal the same total.
7. Demonstrates and records the inverse relation of addition and subtraction.
8. Solves equations at the concrete, pictorial, and 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. Searches for patterns.
2. Uses a variety of strategies and approaches.
3. Recognizes when information is missing or extraneous.
4. Recognizes when an attempted 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 to solve a problem.
2. Selects and uses appropriate tools to measure length, mass, and capacity.
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 problems.

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 experiences.
3. Checks for reasonableness of results using concepts and procedures.
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. Creates a plan for collecting information.
2. 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 representations.
3. 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 orally and in writing.
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.

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 concepts and procedures between mathematical content areas in familiar situations.

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

1. Uses mathematical thinking and modeling in familiar situations in other disciplines.
2. Describes examples of contributions of different cultures to the development of number systems and patterns.

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.