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. Counts, recognizes, writes, and orders numbers to 20.
2. Rote counts from 1 to 100.
3. Demonstrates 1-1 correspondence to 20.
4. Demonstrates and understands more and less.
5. Demonstrates understanding of ordinal numbers (first through tenth).
6. Demonstrates understanding of addition and subtraction through manipulatives, acting out stories, and other strategies.
7. Uses vocabulary such as shorter, higher, longer, over, etc.
8. Understands equal parts.
9. Counts by 5s and 10s.
10. Counts backwards from 10.
11. Begins to develop system for keeping track when counting objects.
12. Exposure to calculator use.
13. Begins at a number higher than one and counts from there.
14. Develops basic understanding of addition and subtraction using manipulatives.
15. Recognizes +, -, =.
16. Uses estimation to determine if a solution is reasonable.
17. Begins to estimate quantities.
18. Determines the cardinal number of a set of objects through 30.
19. When given three groups of objects (1-20), orders them from smallest to largest.
20. Uses a known quantity to estimate an unknown quantity (sets of objects to 30) using a variety of strategies and approaches.

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

1. Begins to use direct measurable attributes such as length, money, temperature, and time to describe and compare objects.
2. Begins to estimate and compare attributes.
3. Uses standard and non-standard units of measurement.
4. Introduced to hour and half hour.
5. Recognizes and identifies value of penny, nickel, and dime.
6. Begins to count and compare pennies, nickels, and dimes.
7. Uses comparative words (longer, shorter, heavier, lighter) to compare objects relative to weight or length.

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 simple geometric shapes: circles, squares, triangles, rectangles, diamonds, and ovals.
2. Identifies dimensional shapes: ball, box, can, and cone.
3. Describes and compares geometric figures and objects using spatial vocabulary, such as corners, curves, inside, outside, right, left, below, and above.

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

1. Collects, organizes, and displays data in numerical and graphical forms.
2. Predicts and compares data in familiar situations.
3. Expresses the likelihood of an event in a real world context by using vocabulary such as, impossible, probable, and certain.
4. Sorts and classifies objects in order to draw conclusions.

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 using a variety of materials.
2. Solves equations at the concrete level to show equality and inequality.

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. Uses a variety of strategies and approaches to investigate and solve problems.
2. Recognizes when information is missing or extraneous.
3. Recognizes when an attempted approach is unproductive and tries a new approach.

Component 2:2
Formulates questions and defines the problem.

1. Defines problems.
2. Identifies unknowns.
3. Formulates questions.

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

1. Selects appropriate tools and organizes relevant information to solve a problem.

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.
2. Validates thinking using models, facts, patterns, and relationships.

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

1. Identifies possible solutions and predicts results.

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

1. Tests and evaluates possible solutions.
2. Checks for reasonable 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. 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 technology to browse and retrieve mathematical information.

Component 4:2
Organizes and interprets information.

1. Organizes and clarifies mathematical information through the use of objects, models, and pictures.

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 examples (charts, tables, etc.).
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 concepts and procedures within math content areas.
2. Recognizes equivalent mathematical models (i.e., 5 cubes, 5 boys, 5 chairs).

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 in other disciplines.

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. Recognizes that math is used in careers.