United States · Common Core State Standards
5th Grade Mathematics
This course builds deep conceptual understanding of the base ten system, fraction operations, and coordinate geometry. Students transition from concrete arithmetic to abstract algebraic reasoning through rigorous problem solving and mathematical modeling.
The Power of Ten and Multi-Digit Operations
Students explore the structure of the place value system and master multi-digit multiplication and division using various strategies.
Investigating how a digit's value changes as it moves left or right in a multi-digit number.
Moving beyond the standard algorithm to understand the distributive property in large scale multiplication.
Exploring division as the inverse of multiplication using partial quotients and area models.
Fractions as Relationships and Operations
Developing a deep understanding of fraction equivalence and performing all four operations with fractions and mixed numbers.
Finding common ground to combine fractional parts of different sizes.
Understanding that multiplying by a fraction less than one results in a smaller product.
Exploring the relationship between division and multiplication through fractional parts.
Algebraic Thinking and Coordinate Geometry
Analyzing patterns and relationships while learning to graph points on a coordinate plane.
Using parentheses and brackets to communicate mathematical logic.
Generating and comparing two numerical patterns using given rules.
Understanding the structure of the coordinate system to represent real world problems.
Volume and Measurement Systems
Mastering the concept of volume as an attribute of 3D space and converting between measurement units.
Developing the understanding that volume is the amount of space an object occupies.
Calculating the volume of complex shapes by decomposing them into rectangular prisms.
Using multiplication and division to convert between different sizes of units within a system.
Classifying Shapes and Analyzing Data
Organizing geometric figures based on properties and interpreting complex data sets.
Classifying polygons based on their properties and understanding subcategories.
Creating and interpreting line plots that include fractional measurements.
Applying geometric principles to architectural and design challenges.