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.