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Core Ideas
- Core Idea 1: Number and Operation
- Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
- Understand fractions, decimals, and percents as parts of whole units and as parts of a collection.
- Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
- Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.
- Understand the meaning and effects of operations with fractions and decimals.
- Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
- Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators, and paper-and-pencil, depending on the situation, and apply selected methods.
- Develop and analyze algorithms for operations on fractions and decimals, and develop fluency in their use.
- Understand and use proportional reasoning to represent quantitative relationships.
- Understand and use the associative and commutative properties of addition to simplify computations with fractions, decimals, and whole numbers.
- Core Idea 2: Probability
- Demonstrate understanding and use of probability in problem situations.
- Determine theoretical and experimental probabilities and use these to make predictions about events.
- Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.
- Represent probabilities as ratios, proportions, decimals, or percents.
- Represent the sample space for a given event in an organized way (e.g. table, diagram, organized list, and tree diagram).
- Core Idea 3: Algebra and Functions
- Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change.
- Represent, analyze, and generalize a variety of relations and functions with tables, graphs, and words.
- Use symbolic algebra to represent situations and to solve linear equations.
- Model and solve contextualized problems using various representations, such as graphs, tables, and equations.
- Core Idea 4: Geometry and Measurement
- Analyze characteristics and properties of two- and three-dimensional geometric shapes; use symmetry to predict and describe the results of sliding, flipping and turning two-dimensional shapes; and apply the appropriate techniques, tools, and formulas to determine measurements.
- Describe, classify, and understand relationships among types of two- and three-dimensional objects, using their defining properties.
- Develop, understand, and use formulas to determine the area of triangles, quadrilaterals, and the circumference and area of circles.
- Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes.
- Understand line and rotational symmetry and predict the results of these transformations.
- Select and apply techniques and tools to accurately find length, area, and angle measures to appropriate levels of precision.
- Core Idea 5: Statistics
- Select and use appropriate statistical methods to display, analyze, compare, and interpret different data sets.
- Compare data sets using measures of center and spread (mean, median, mode, range, outlier, and difference from the mean) to understand what each indicates about the data sets.
- Represent and analyze data in the form of graphs including circle graphs.
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Tools for Educators