- Core Idea 1: Number Properties
- Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
- Use models, benchmarks, and equivalent forms to judge the size of fractions.
- Recognize and generate equivalent forms of commonly used fractions and decimals.
- Understand the place-value structure of the base-ten number system including being able to represent and compare rational numbers.
- Describe classes of numbers according to characteristics such as the nature of their factors.
- Core Idea 2: Number Operations
- Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
- Develop fluency in dividing whole numbers.
- Understand the meaning of remainders by modeling division problems.
- Reason about and solve problem situations that involve more than one operation in multi-step problems.
- Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.
- Develop and use strategies to solve problems involving number operations with fractions and decimals relevant to students’ experience.
- Core Idea 3: Patterns, Functions, and Algebra
- Understand patterns and use mathematical models such as algebraic symbols and graphs to represent and understand quantitative relationships.
- Represent the idea of a variable as an unknown quantity using a letter or a symbol.
- Express mathematical relationships using equations and graph them on a coordinate grid.
- Investigate how a change in one variable relates to a change in a second variable.
- Identify and describe situations with constant and varying rates of change and compare them.
- Understand and use properties of operations, such as the distributive property of multiplication over addition.
- Core Idea 4: Geometry and Measurement
- Analyze characteristics and properties of two- and three-dimensional geometric shapes, understand attributes, and apply appropriate techniques, tools, and formulas to determine measurements.
- Understand such attributes as length, area, weight, volume, and angle size and select the appropriate type of unit for measuring each attribute. (Volume may be measured by filling an object.)
- Develop, understand, and use methods to find the area of rectangles and use that understanding of rectangles to find areas of triangles and parallelograms.
- Develop strategies for estimating or calculating the perimeters and areas of irregular shapes.
- Identify, compare, and analyze attributes of two- and three-dimensional shapes, and develop vocabulary to describe the attributes.
- Explore and determine what happens to perimeter and area of a two-dimensional figure when its shape is changed in some way.
- Core Idea 5: Data Analysis
- Display, analyze, compare, and interpret different data sets.
- Compare different sets of data.
- Use measures of center (mean, median, and mode) and understand what each does and does not indicate about the data set.
- Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.
- Organize and display data in appropriate graphs and representations (e.g., histograms and line graphs) and explain which types of graphs are appropriate for different kinds of data sets.)
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Tools for Educators