Colorado State Standards for Mathematics: Grade 2

CO.1. Number Sense, Properties, and Operations

1.1. The whole number system describes place value relationships from ones to 1,000 and forms the foundation for efficient algorithms. Students can:

1.1.a. Read and write numbers to 1,000 and identify place value for three-digit numbers

1.1.b. Describe relationships between ones, tens, and hundreds

1.1.c. Explain the value of a digit in a three-digit number

1.1.d. Order a collection of whole numbers

1.2. Formulate, represent, and use algorithms to add and subtract two-digit whole numbers with flexibility, accuracy, and efficiency. Students can:

1.2.a. Demonstrate fluency with basic addition and subtraction facts to sums of 20

1.2.b. Find the value of a collection of coins and choose coins to have a given value

1.2.c. Create stories and models, including linear and difference, to illustrate addition and subtraction

1.2.d. Select and use appropriate methods to estimate sums and differences or calculate them mentally depending on the context and numbers involved

1.2.e. Apply addition and subtraction concepts to financial decision-making (PFL)

1.3. Fractions represent parts of a whole object or set. Students can:

1.3.a. Partition basic shapes, using common fractions such as 1/2, 1/3, and 1/4

1.3.b. Partition sets using common fractions such as 1/2, 1/3, 1/4

CO.2. Patterns, Functions, and Algebraic Structures

2.1. Patterns are based on rules. Students can:

2.1.a. Count objects by groups of 2, 5, and 10

2.1.b. Identify a missing number in a sequence, and describe a rule

2.1.c. Create and extend repeating patterns of 3-5 elements using a variety of materials such as numbers, letters, shapes, and manipulatives

2.2. Number relationships can be used to develop computation strategies. Students can:

2.2.a. Use ten-based strategies to solve addition and subtraction facts to 20

2.2.b. Demonstrate the structure of numbers as tens and ones in addition and subtraction

2.2.c. Communicate the inverse relationship between addition and subtraction, and use this relationship to efficiently solve and check problems

CO.3. Data Analysis, Statistics, and Probability

3.1. Visual displays of data can be constructed in a variety of formats. Students can:

3.1.a. Construct picture graphs and bar graphs from a data set

3.1.b. Read and explain information in picture graphs and bar graphs

3.1.c. Describe data using concepts of median and range

3.2. Mathematical models are used to describe the likelihood of an outcome or event. Students can:

3.2.a. Collect data using chance devices, such as spinners and describe outcomes as likely or unlikely

3.2.b. Apply the concepts of likely or not likely to decisions from daily life (PFL)

CO.4. Shape, Dimension, and Geometric Relationships

4.1. Shapes can be created and described by quantifiable attributes. Students can:

4.1.a. Recognize, describe, and create geometric figures according to given quantifiable attributes such as number of sides and size

4.1.b. Identify symmetry in two-dimensional figures

4.1.c. Use quantifiable attributes to describe and estimate size of objects

4.2. Some attributes of objects are measurable and can be quantified using different tools. Students can:

4.2.a. Identify the measurable attribute and appropriate unit of measure for an object

4.2.b. Use common objects as non-standard units

4.2.c. Use standard linear measuring tools to measure to the nearest whole unit

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