5th grade

Students investigate numbers, ways of representing numbers, relationships among numbers, and number systems.

Students perform mathematical operations and determine how they relate to one another

Students investigate patterns, functions, and quantitative relationships and apply that knowledge to modeling, analyzing, or solving mathematical and real-world problems.

Students use symbolic forms, operations, and properties to represent, model, solve, and analyze mathematical situations and structures.

Students explore properties, relationships, and transformations of shapes and space using coordinate geometry and other representational systems.

Students explore concepts and practical applications of units, geometrical constructions, and measurements of plane and geometric shapes and space.

Students demonstrate statistical thinking and apply statistical methods to collect, organize, analyze, display, and make inferences based on data.

Students use concepts of chance and probability to explain outcomes of real-life situations.

Recognize and categorize the place value system, and use it to compare and round decimals

Explore properties and patterns in using powers of 10

Perform operations with multidigit whole numbers and with decimals (to hundredths)

Apply and extend previous understandings of multiplication to multiply fractions and division to divide fractions or whole numbers by a fraction

Use equivalent fractions as a strategy to add and subtract fractions

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions

Generate and analyze a pair of patterns, and graph them on a coordinate plane

Solve real-world mathematical problems by graphing points on the coordinate plane

Use variables to explain how one quantity changes as a function of another

Write and interpret numerical expressions

Draw and identify lines and angles, and classify shapes by properties of their lines and angles

Identify and draw lines of symmetries, and classify 2-D figures into categories based on their properties

Convert like measurement units within a given measurement system

Recognize area and perimeter as attributes of plane figures and volume as an attribute of solid figures, and explain concepts of area, perimeter, and volume measurements

Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume

Collect, organize, read, and display a data set of measurements in charts, graphs, and tables

Conduct simple experiments where probabilities of all outcomes are equal