Colorado State Standards for Mathematics: Kindergarten

CO.1. Number Sense, Properties, and Operations

1.1. Whole numbers can be used to name, count, represent, and order quantity. Students can:

1.1.a. Count and represent objects to 20

1.1.b. Identify, read, and write corresponding numerals

1.1.c. Compare sets up to 10 objects and use language to describe more, less, or same

1.1.d. Compare two sets of objects to at least 25 using language such as ''more,'' ''less,'' or ''the same''

1.1.e. Identify small groups of objects -fewer than five without counting, including zero as ''no objects''

1.1.f. Estimate quantities less than 20

1.2. Adding and subtracting to 10 involves composing and decomposing using a variety of strategies and representations. Students can:

1.2.a. Use objects including coins, and drawings to model addition and subtraction problems to 10 (PFL)

1.2.b. Identify numbers one more or one less than a given number up to 10

1.2.c. Determine if more than or less than is needed to change one quantity to another

CO.2. Patterns, Functions, and Algebraic Structures

2.1. Patterns can repeat. Students can:

2.1.a. Duplicate a simple pattern

2.1.b. Extend a repeating two-element pattern using a variety of materials such as numbers, letters, shapes, and manipulatives

2.2. Relationships exist between numbers. Students can:

2.2.a. Generalize the counting sequence pattern from counting all to knowing ''one more'' and ''one less''

2.2.b. Communicate the relationship between composing and decomposing numbers

CO.3. Data Analysis, Statistics, and Probability

3.1. Visual displays of information can used to answer questions. Students can:

3.1.a. Collect classroom data

3.1.b. Identify and compare own data to group's data

3.1.c. Describe bar graphs to answer questions such as more or less and simple trends

CO.4. Shape, Dimension, and Geometric Relationships

4.1. Shapes are described by their characteristics and position. Students can:

4.1.a. Recognize and informally describe two dimensional shapes with varying orientation, sizes, and shapes

4.1.b. Use relational vocabulary, such as above, below and next to, to describe spatial relationships

4.2. Measurement is used to compare and order objects. Students can:

4.2.a. Recognize and compare attributes of length, height, weight, capacity of objects

4.2.b. Use estimates of measurements from everyday experiences

4.2.c. Order several objects by length, height, weight, capacity, or price (PFL)

CO.5. Prepared Graduate Competencies in Mathematics: The prepared graduate competencies are the preschool through twelfth-grade concepts and skills that all students who complete the Colorado education system must master to ensure their success in a postsecondary and workforce setting.

5.1. Understand the structure and properties of our number system. At the most basic level numbers are abstract symbols that represent real-world quantities

5.2. Understand quantity through estimation, precision, order of magnitude, and comparison. The reasonableness of answers relies on the ability to judge appropriateness, compare, estimate, and analyze error

5.3. Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

5.4. Make both relative (multiplicative) and absolute (arithmetic) comparisons between quantities. Multiplicative thinking underlies proportional reasoning

5.5. Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts

5.6. Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

5.7. Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

5.8. Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data

5.9. Apply transformation to numbers, shapes, functional representations, and data

5.10. Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

5.11. Communicate effective logical arguments using mathematical justification and proof. Mathematical argumentation involves making and testing conjectures, drawing valid conclusions, and justifying thinking

5.12. Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions