Colorado Academic Standards Mathematics
The Colorado Academic Standards Mathematics, as developed by the Colorado Department of Education were revised in 2010.
The standards include:
- Number Sense, Properties, and Operations
- Patterns, Functions, and Algebraic Structures
- Data Analysis, Statistics, and Probability
- Shape, Dimension, and Geometric Relationships
The standards are then broken down by Grade Level Expectations (GLE), approximately seven per grade level (K-8) with 14 for high school. The standards also address 21st century and postsecondary workforce readiness skills, as well as the integration of Personal Financial Literacy (PFL) indicators. The standards are designed to build upon themselves, creating a vertical articulation among the grade levels.
Common Core State Standards Mathematics
The standards were drafted by experts and teachers from across the country to establish clear and consistent guidelines for what every student should know and be able to do. The Common Core State Standards Initiative has developed "What Parents Should Know" for further information about the development of the standards. The CCSSM calls for a shift in practice. The Publisher's Criteria K-8 and High School outlines the shift in practice breaking down and explaining focus, coherence, and the three elements of rigor: conceptual understanding, procedural skill and fluency, and application.
The standards are broken into 11 domains:
- Counting & Cardinality
- Operations & Algebraic Thinking
- Numbers & Operations in Base Ten
- Numbers & Operations - Fractions
- Measurement & Data
- Geometry - kindergarten
7. Ratios & Proportional Relationships
8. The Number System
9. Expressions & Equations
10. Functions - grade 8
11. Statistics & Probability - 6th grade
At the high school, there are six conceptual categories, listed below, with sub-domains, vertically culminating from the eleven present at the elementary and middle school levels.
- 1st Grade
- 2nd Grade
- 3rd Grade
- 4th Grade
- 5th Grade
- 6th Grade
- 7th Grade
- 8th Grade
By Conceptual Category
- Number and Quantity
- Functions - High School
- Geometry - High School
- Statistics & Probability - High School
- Algebra 1 (Appendix A: p 15-26)
- Geometry Standards (Appendix A: p 27-35)
- Algebra 2 (Appendix A: p 36-43)
In addition to the standards, the Common Core State Standards Initiative developed the Standards for Mathematical Practice. The Standards for Mathematical Practice are a standard for developing students.
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for an express regularity in repeated reasoning.