The National Council of Teachers of Mathematics calls them "Curriculum Focal Points," and the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) named them "Common Core Standards." Regardless of the terminology, educators have identified critical math concepts students should learn at each grade level. Though there is a wide variety of specific skills and tasks, critical concepts for fifth-grade math are separated into three main areas.
The Common Core Standards require instructional time to include "developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases." Students apply previous knowledge of fractions and of multiplication and division to more advanced uses of fractions. The Math Worksheet Center web site stresses that fifth-grade students "recognize parts of fractions as units of whole numbers, along with finding fraction locations on a number line."
As students increase fluency with fractions and functions, the Common Core Standards state that fifth-graders will expand their fluency with division by "extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations." The National Council of Teachers of Mathematics emphasizes this application of previous knowledge to expand fluency as a way for students to develop their skills of "problem solving, reasoning, and critical thinking skills, which are important to all mathematics learning." The Math Worksheet Center emphasizes an understanding of division and other functions that requires students to "be able to mentally compute multiplication and division problems" as they "develop fluency in arithmetic computations" using whole numbers, fractions and decimals.
According to the Common Core Standards, fifth-grade students will "recognize volume as an attribute of three-dimensional space" that "can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps." Students begin to use geometry to "understand concepts of volume and relate volume to multiplication and to addition." The Math Worksheet Center directs that fifth-grade students "learn how to construct geometric shapes to find their area and volume, using mathematical formulas." Fifth-graders apply geometry and concepts about volume to real world situations. As fifth-grade students apply previous knowledge to combine interrelated critical math skills, they use concepts such as understanding of volume to address the Common Core Standards and "make sense of problems and persevere in solving them and reason abstractly and quantitatively."