Core Ideas
  • Core Idea 1: Number Properties
    • Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
    • Develop an understanding of fractions as a part of a whole unit, as part of a collection, and as a location on a number line.
    • Use models, benchmarks, and equivalent forms to judge the size of friendly fractions.
    • Recognize and generate equivalent forms of commonly used fractions.
  • Core Idea 2: Number Operations
    • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
    • Understand division as the inverse operation of multiplication, the operation of sharing (partitive), partitioning (measurement), repeated subtraction, and an operation to determine rates.
    • Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems.
    • Develop fluency in multiplying whole numbers.
  • Core Idea 3: Patterns, Functions, and Algebra
    • Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships.
    • Represent and analyze patterns and functions using words, tables, and graphs.
    • Find the results of a rule for a specific value.
    • Use inverse operations to solve multi-step problems.
    • Use concrete, pictorial, and verbal representations to solve problems involving unknowns.
    • Understand and use the concept of equality.
  • Core Idea 4: Geometry and Measurement
    • Use characteristics, properties, and relationships of two-dimensional geometric shapes and apply appropriate techniques to determine measurements. Examine, compare, and analyze attributes of geometric figures.
    • Classify two-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles.
    • Understand line symmetry and predict the results of sliding, flipping, or turning two-dimensional figures.
    • Investigate, describe, and reason about the results of combining and subdividing figures.
    • Understand and use appropriate techniques to determine measurement.
  • Core Idea 5: Data Analysis
    • Collect, organize, represent, and interpret numerical and categorical data, and clearly communicate their findings. Understand and apply basic concepts of probability.
    • Represent data using tables, charts, line plots, and bar graphs.
    • Interpret data to answer questions about a situation.
    • Describe the shape and important features of a set of data.
    • Describe events as likely or unlikely and discuss the degree of likelihood (using such words as certain, equally likely, and impossible).
    • Predict the probability of simple experiments and express the results numerically (e.g. 3 out of 4).
 


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