Colorado State Standards for Mathematics: Grade 3

CO.1. Number Sense, Properties, and Operations

1.1. The whole number system describes place value relationships from ones to 10,000 and forms the foundation for efficient algorithms. Students can:

1.1.a. Read and write numbers from one to 10,000 and explain place value for four-digit numbers

1.1.b. Generalize the change represented when moving from one place to another place in a number

1.1.c. Compose and decompose multi-digit numbers based on place value

1.2. Parts of a whole can be modeled and represented in different ways. Students can:

1.2.a. Use drawings, models, and numerals to represent fractions (halves, thirds, fourths, sixths, eighths) based on a whole shape, number set, or number line

1.2.b. Estimate and justify the reasonableness of solutions to problems involving representations of fractions

1.2.c. Describe why equivalent fractions are two ways of modeling the same quantity using a model or drawing

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

1.3.a. Use number sense to estimate and justify the reasonableness of solutions to problems

1.3.b. Use flexible methods of computing, including student-generated strategies and standard algorithms

1.3.c. Estimate using strategies such as front-end estimation or landmark numbers

1.4. Multiplying and dividing are inverse operations modeled in a variety of ways. Students can:

1.4.a. Demonstrate fluency with multiplication and division facts with single-digit factors

1.4.b. Describe relationships between related facts and between multiplication and division

1.4.c. Represent multiplication and division problems with drawings, models, number sentences, and stories

1.4.d. Model strategies to achieve a personal financial goal using arithmetic operations (PFL)

CO.2. Patterns, Functions, and Algebraic Structures

2.1. Number patterns are based on operations and relationships. Students can:

2.1.a. Extend simple arithmetic and geometric sequences

2.1.b. Count by and analyze patterns in multiples of 2, 3, 5, 9, 10, 11, 25, 50 and 100

2.1.c. Use known multiplication facts to solve unknown multiplication problems

2.2. Number properties can be used to solve problems. Students can:

2.2.a. Use the commutative property to solve addition and multiplication problems

2.2.b. Use the associative property to solve addition problems

2.2.c. Use the relationship between addition and multiplication to solve problems

CO.3. Data Analysis, Statistics, and Probability

3.1. Visual displays of data can be used to answer questions of interest. Students can:

3.1.a. Compose questions to generate data

3.1.b. Collect and organize data from simple experiments or surveys in class

3.1.c. Create picture graphs, bar graphs, dot plots, and frequency tables from a data set

3.1.d. Describe data using the concepts of mode, clusters and gaps

3.2. Mathematical models are used to explore and describe fairness. Students can:

3.2.a. Investigate chance devices such as coins, spinners, and number cubes

3.2.b. Apply the concepts of impossible, unlikely and likely

3.2.c. Determine if a chance device is fair or unfair

CO.4. Shape, Dimension, and Geometric Relationships

4.1. Geometric figures are described by their attributes and position in the plane. Students can:

4.1.a. Construct and describe two-dimensional shapes by attributes and properties such as sides, angles, and symmetry

4.1.b. Recognize and demonstrate transformations - reflections, translations, and rotations - of basic shapes or designs

4.1.c. Use geometric properties of points and line segments to describe figures

4.2. Objects have distinct attributes that can be measured with appropriate tools. Students can:

4.2.a. Use standard units to measure to the nearest 1/2 or whole inch or centimeter

4.2.b. Estimate and measure distance and perimeter

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