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, compares, and orders whole numbers to 100.
2. Counts by 2’s to 30; counts by 5’s and 10’s to 100.
3. Counts backwards from 30 to 0.
4. Demonstrates an understanding of a 1 to 1 correspondence 0 to 100.
5. Demonstrates an understanding of ordinal numbers: first through tenth.
6. Begins at a number higher than one and counts on.
7. Demonstrates knowledge of simple/common fractions (½, 1/3, and ¼) at a concrete level.
8. Introduces place value concepts of ones, tens, and hundreds.
9. Has a knowledge of concepts more and less.
10. Understands the concepts of odd and even numbers.
11. Recognizes and interprets symbols: +, -, =.
12. Knows and uses physical models to demonstrate relationship between addition and subtraction.
13. Knows the strategies of: addition and subtraction, doubles, counting on, counting backwards, related facts—fact families.
14. Reads and demonstrates the ability to solve story problems by using mathematical vocabulary.
15. Has introductory knowledge of calculator use.
16. Understands mathematical vocabulary related to computations (ones, in all, are left).
17. Estimates quantities.
18. Uses estimation to determine if a solution is reasonable.
19. Given two sets of objects, each less than 20, determines sum or difference between the two sets.
20. Given three numbers between 1 and 100, orders them from smallest to largest.

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 height, size, length, volume, money, and time to describe, compare, and order objects.
2. Estimates and compares time and money.
3. Uses standard and non-standard units to measure length and volume.
4. Understands concepts of hour and half-hour.
5. Recognizes and identifies value of penny, nickel, dime, quarter, and dollar using cent notation.
6. Counts and compares pennies, nickels, and dimes.

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, sort, and draw simple geometric shapes: circles, squares, triangles, rectangles, diamonds, parallelograms, and ovals.
2. Identifies three-dimensional shapes: sphere, box, cube, cone, cylinder, and pyramid.
3. Understands and compares how geometric shapes and objects in the surrounding environment are related.
4. Uses informal geometric vocabulary to describe similarities and differences of physical objects.

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

1. Formulates questions for the purpose of gathering data.
2. Lists possible outcomes of simple experiments.
3. Collects, organizes, displays, and interprets data in numerical and graphical forms: tables, charts, pictographs, and bar graphs.
4. Predicts in real life and simple experimental situations.

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

1. Recognizes, creates, extends, and compares patterns of objects and numbers using a variety of materials to solve problems and make conjectures.
2. Symbolically represents number patterns.
3. Utilizes standard notations in reading and writing open sentences, for example: 1 + p = 5.
4. Manipulates objects to solve problems where an addend is unknown.
5. Uses physical objects and numerals to show the meaning of 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. Searches for patterns.
2. Uses a variety of strategies and approaches to solve problems.
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. Defines problems in familiar situations.
2. Identifies unknowns.

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 mathematical tools.
3. Applies and justifies appropriate strategies to solve real-life problems.

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/or relationships.

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

1. Makes and tests possible solutions based on collected data.

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 by reflecting, verbalizing, 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 examples (charts, tables, models, graphs, 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.

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.