2020 Colorado State Mathematics Standards at Animas High School
Purpose of Mathematics
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​The 2020 Colorado State Mathematics Standards begin with an outline of the following three primary purposes of mathematics, as developed by the The National Council of Teachers of Mathematics (2018). AHS uses these purposes as guiding principles when supporting students to learn and apply mathematical thinking skills.
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  1. To Expand Professional Opportunity. Just as the ability to read and write was critical for workers when the early 20th-century economy shifted from agriculture to manufacturing, the ability to do mathematics is critical for workers in the 21st century as the economy has shifted from manufacturing to information technology. Workers with a robust understanding of mathematics are in demand by employers, and job growth in STEM (science, technology, engineering, and mathematics) fields is forecast to accelerate over the next decade.
  2. Understand and Critique the World. A consequence of living in a technological society is the need to interpret and understand the mathematics behind our social, scientific, commercial, and political systems. Much of this mathematics appears in the way of statistics, tables, and graphs, but this need to understand and critique the world extends to the application of mathematical models, attention given to precision, bias in data collection, and the soundness of mathematical claims and arguments. Learners of mathematics should feel empowered to make sense of the world around them and to better participate as an informed member of a democratic society. ​
  3. Experience Wonder, Joy, and Beauty. Just as human forms and movement can be beautiful in dance, or sounds can make beautiful music, the patterns, shapes, and reasoning of mathematics can also be beautiful. On a personal level, mathematical problem solving can be an authentic act of individual creativity, while on a societal level, mathematics both informs and is informed by the culture of those who use and develop it, just as art or language is used and developed.​
The Colorado State Standards for Mathematical Practice
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These standards are addressed within each unit via everyday IMP unit content, including regularly assigned and explored Problems of the Week (POWs), and map to the Animas High School “Habits of a Mathematician.” The Standards for Mathematical Practice in summary:
  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.    
The Colorado State Standards for Mathematical Content
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​The Colorado academic standards in mathematics are the topical organization of the concepts and skills every Colorado student should know and be able to do throughout their preschool through twelfth-grade experience. At AHS, each content area is explored within each grade level, within the context of real-world problems.
  1. Number and Quantity: From preschool through high school, students are continually extending their concept of numbers as they build understanding of whole numbers, rational numbers, real numbers, and complex numbers. As they engage in real-world mathematical problems, they conceive of quantities, numbers with associated units. Students learn that numbers are governed by properties and understand these properties lead to fluency with operations.
  2. Algebra and Functions: Algebraic thinking is about understanding and using numbers, and students’ work in this area helps them extend the arithmetic of early grades to expressions, equations, and functions in later grades. This mathematics is applied to real-world problems as students use numbers, expressions, and equations to model the world. The mathematics of this standard is closely related to that of Number and Quantity.
  3. Data Analysis, Statistics, and Probability: From the early grades, students gather, display, summarize, examine, and interpret data to discover patterns and deviations from patterns. Measurement is used to generate, represent and analyze data. Working with data and an understanding of the principles of probability lead to a formal study of statistics in middle in high school. Statistics provides tools for describing variability in data and for making informed decisions that take variability into account.
  4. Geometry: Students’ study of geometry allows them to comprehend space and shape. Students analyze the characteristics and relationships of shapes and structures, and engage in logical reasoning. Students learn that geometry is useful in representing, modeling, and solving problems in the real world as well as in mathematics.