Colorado State Standards for Mathematics: Grade 4

CO.1. Number Sense, Properties, and Operations

1.1. The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms. Students can:

1.1.a. Read and write numbers from one to 100,000 and explain place value for five-digit numbers

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

1.1.c. Read and write numbers to the hundredths place

1.1.d. Identify the value of any given digit in a number with decimals to the hundredths place

1.2. Formulate, represent, and use algorithms to multiply and divide with flexibility, accuracy, and efficiency. Students can:

1.2.a. Use flexible and efficient methods of computing including standard algorithms to solve three- or four-digit by one-digit multiplication or division problems

1.2.b. Estimate using strategies such as front end or rounding to justify the reasonableness of solutions to problems

1.2.c. Demonstrate fluency with multiplication facts and their related division facts 0 to 12

1.2.d. Explain why multi-digit multiplication and division procedures work based on place value properties and use them to solve problems

1.3. Different models and representations can be used to compare fractional parts. Students can:

1.3.a. Solve comparison problems using models of fractions with like and unlike denominators through 10

1.3.b. Estimate and justify the reasonableness of solutions to problems involving comparison of fractions

1.3.c. Demonstrate equivalent fractions, decimals, and percents using drawings and models

CO.2. Patterns, Functions, and Algebraic Structures

2.1. Number patterns and relationships can be represented by symbols. Students can:

2.1.a. Use number relationships to find the missing number in a sequence

2.1.b. Use a symbol to represent and find an unknown quantity in a problem situation

2.1.c. Complete input/output tables

2.1.d. Find the unknown in simple equations

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

2.2.a. Use and describe number patterns for counting by 2, 5, 9, 10, and 11 from a given starting number

2.2.b. Communicate the inverse relationship between multiplication and division, and use this relationship to efficiently solve and check problems

2.2.c. Use the commutative and associative properties of multiplication to solve problems

CO.3. Data Analysis, Statistics, and Probability

3.1. Visual displays of classroom data can be used to summarize information across the content areas. Students can:

3.1.a. Compose questions to generate data related to grade level areas of study

3.1.b. Collect data from class experiments or multi-classroom surveys

3.1.c. Create data displays appropriate to data collected

3.1.d. Describe data using the concept of shape of the distribution

3.2. Mathematical models are used to test predictions about the likelihood of events. Students can:

3.2.a. Formulate a question to test a prediction, and conduct an experiment using chance devices, such as coins, spinners, and number cubes, to test predictions

3.2.b. Represent the outcomes of experiments with fractions, and describe using the concepts of impossible, unlikely, likely, and certain

3.2.c. Describe the likelihood of real-life situations using the concepts of impossible, unlikely, likely and certain (PFL)

CO.4. Shape, Dimension, and Geometric Relationships

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

4.1.a. Identify parallel, perpendicular, and intersecting line segments in the plane and within geometric shapes

4.1.b. Create geometric designs using transformations: reflections, translations, and rotations

4.1.c. Compare geometric figures according to the attributes of congruence, symmetry, and angle size

4.1.d. Name and locate points specified by ordered number pairs on a coordinate grid

4.2. Appropriate measurement tools, units, and systems are used to measure different attributes of objects and time. Students can:

4.2.a. Model area using square units

4.2.b. Distinguish between area and perimeter

4.2.c. Convert using unit equivalencies within the standard measurement system (yards to feet and feet to inches, pounds to ounces, gallons to quarts)

4.2.d. Convert using unit equivalencies within the metric measuring system (meters to centimeters, kilometers to meters, and liters to milliliters)

4.2.e. Estimate and measure elapsed time to the nearest quarter hour

4.2.f. Select an appropriate tool and unit for measuring length, weight, and capacity

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