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.
01The 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.
Students will learn to read and write decimals to the thousandths place using base-ten numerals, number names, and expanded form.
Students will compare two decimals to thousandths based on the meaning of the digits in each place and round decimals to any place.
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.
Students will fluently add and subtract decimals to hundredths using concrete models or drawings and strategies based on place value.
Students will multiply decimals to hundredths using concrete models or drawings and strategies based on place value.
Students will divide decimals to hundredths using concrete models or drawings and strategies based on place value.
02Fractions 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.
Students will solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Students will interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
Students will apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Students will find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths.
Understanding that multiplying by a fraction less than one results in a smaller product.
Students will solve real-world problems involving multiplication of fractions and mixed numbers.
Exploring the relationship between division and multiplication through fractional parts.
Students will divide whole numbers by unit fractions using visual fraction models and equations.
Students will solve real-world problems involving division of unit fractions by non-zero whole numbers and whole numbers by unit fractions.
03Algebraic 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.
Students will write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Generating and comparing two numerical patterns using given rules.
Students will form ordered pairs from corresponding terms of two numerical patterns and graph them on a coordinate plane.
Understanding the structure of the coordinate system to represent real world problems.
Students will represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values.
04Volume 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.
Students will measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Students will relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
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.
Students will solve multi-step word problems involving conversions of measurement units.
05Classifying Shapes and Analyzing Data
Organizing geometric figures based on properties and interpreting complex data sets.
Classifying polygons based on their properties and understanding subcategories.
Students will understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Creating and interpreting line plots that include fractional measurements.
Students will use information from line plots to solve problems involving addition and subtraction of fractions.
Applying geometric principles to architectural and design challenges.