Grade 5 Math Curriculum in North America: What Children Learn

Grade 5 is the last year of the elementary arithmetic arc. Children finish learning operations with fractions and decimals, meet volume as a three-dimensional concept, and start working with a coordinate plane. By the end of Grade 5 most of the pure computation is in place — Grade 6 and beyond shift toward reasoning.

Fractions

• Adding and subtracting fractions with unlike denominators.
• Multiplying fractions by fractions and by whole numbers.
• Dividing whole numbers by unit fractions and unit fractions by whole numbers.
• Solving fraction word problems including mixed numbers.

Decimals

• Reading, writing, and comparing decimals to thousandths.
• Adding, subtracting, multiplying, and dividing decimals.
• Rounding decimals to any place.

Volume

• Understanding volume as the number of unit cubes in a solid.
• Finding volumes of right rectangular prisms using V = l × w × h or V = B × h.
• Solving real-world volume problems.

Coordinate plane and geometry

• Graphing points on the coordinate plane in the first quadrant.
• Classifying two-dimensional figures into a hierarchy based on properties.

Expressions and patterns

• Writing and interpreting simple numerical expressions with grouping symbols.
• Order of operations.
• Generating and analyzing patterns from rules.

A note about fractions

Fraction division is the single topic in Grade 5 most likely to cause frustration. The rule "keep, change, flip" is easy to memorize and impossible to understand without more concrete work first. Before your child tries to memorize the rule, make sure they can answer questions like "how many halves are in three?" That is the conceptual foundation the rule sits on.