Operations and Algebraic Thinking In preparation for the Expressions and Equations domain in grades 6-8, fifth graders begin to explore, interpret, and evaluate numerical expressions. Work with patterns that began in Grade 4 extends to generating patterns, forming ordered pairs, graphing on a coordinate plane, and then analyzing the graphical representations.

Numbers and Operations in Base Ten Fifth graders extend their work with place value to include decimal numbers to the thousandth place. They use efficient algorithms to multiply multi-digit whole numbers. They begin to divide whole numbers with two-digit divisors. They extend their understanding of whole number operations to adding, subtraction, multiplying, and dividing decimals to hundredths.

Numbers in Base Ten-Fractions Fifth graders build on previous experiences with fractions and use a variety of visual models and strategies to add and subtract fractions and mixed numbers with unlike denominators. Problem solving provides contexts for students to use mathematical reasoning to determine whether their answers makee sense. They extend their understanding of fractions as parts of a whole to interpret a fraction as a division representation of the numerator divided by the denominator. Students use this understanding in the context of dividing whole numbers with an answer in the form of a fraction or mixed number. They continue to build concpetual understanding of multiplication of fractions using visual models and connecting the meaning to the meaning of multiplication of whole numbers. Students use visual models and problem solving contexts to develop understanding of dividing a unit fraction by a whole number and a whole number by a unit fraction. Once conceptual understanding is established, students generalize efficient procedures for multiplying and dividing fractions.

Measurement and Data Fifth graders will convert like measurement units within a given measurement system and continue to represent and interpret data. In this domain, students will center their learning on geometric measurement with a spotlight on understanding the concept of volume.

Geometry In fifth grade, students will be thinking about the underlying structure of the coordinate system and learning how axes make it possible to locate points anywhere on a coordinate plane. At this grade level, students will also represent real-world and mathematical problems by graphing and interpreting points in the first quadrant of the coordinate plane. Students will also make a connection that attributes belonging to a category of two-dimensional shapes that belong to all subcategories of that category.

The Common Core Mathematics Companion: The Standards Decoded Grades 3-5 (2015). Authors: Linda M. Gojack and Ruth Harbin Miles