- Core Idea 1: Number Properties
- Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
- Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
- Develop understanding of the relative magnitude of whole numbers and the concepts of sequence, quantity, and the relative positions of numbers.
- Understand the place-value structure of the base-ten number system including being able to represent and compare whole numbers and decimals (in the context of dollars and cents).
- Core Idea 2: Number Operations
- Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
- Understand different meanings of addition and subtraction of whole numbers and the relationship between the two operations.
- Understand the effects of adding and subtracting whole numbers.
- Understand multiplication as repeated addition, an area model, an array, and an operation on scale.
- Develop fluency in adding and subtracting whole numbers.
- Develop and use strategies to estimate and judge the reasonableness of results.
- Solve problems involving dollars and cents.
- Core Idea 3: Patterns, Functions, and Algebra
- Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships.
- Describe and extend geometric and numeric patterns.
- Represent and analyze patterns using words and/or tables.
- Illustrate general principles and properties of operations, such as commutativity, using specific numbers.
- Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
- Model problem situations with objects and use representations such as graphs and tables to draw conclusions.
- Describe qualitative change (such as students growing taller).
- Describe quantitative change (such as a student's growing two inches in one year).
- Solve simple problems involving a functional relationship (two quantities which vary together, like finding the total cost of multiple items when you know the cost of one).
- Core Idea 4: Geometry and Measurement
- Recognize and use characteristics, properties, and relationships of two-dimensional geometric shapes and apply appropriate techniques to determine measurements.
- Choose appropriate units and tools for particular tasks and use these units and tools to estimate and measure (length, weight, temperature, time, and capacity).
- Identify and compare attributes of two-dimensional shapes and develop vocabulary to describe the attributes.
- Calculate perimeter and area and be able to distinguish between the two measures. (Area may be measured by covering a figure with squares.)
- Use visualization, spatial reasoning, and geometric modeling to solve problems.
- Recognize geometric ideas and relationships and apply them to problems.
- Core Idea 5: Data Analysis
- Collect, organize, display, and interpret data about themselves and their surroundings.
- Describe important features of a set of data (maximum, minimum, increasing, decreasing, most, least, and comparison).
- Represent data using tables, line plots, bar graphs, and pictographs.