Math Focal Points Grade 5

Introduction

The National Council of Teachers of Mathematics (NCTM), in an effort to highlight the most important mathematical topics at each grade level, has developed Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics. Rather than a discrete topic to be checked off a list, NCTM emphasizes that a “focal point” is a “cluster of related knowledge, skills, and concepts.” These focal points, three at each grade level, specify “the mathematical content that a student needs to understand deeply and thoroughly for future mathematics learning.”

With this publication, the Middle School Portal begins a series on resources that support the teaching of the Curriculum Focal Points for grades 5 through 8. We begin with grade 5.

NCTM foresees that students at the fifth-grade level would work on developing understanding and mastery of division of whole numbers. To support this area, we feature online interactive activities that model the connection between multiplication and division of whole numbers, plus lessons that give direct instruction on the process of division.

Students at this level would also be developing an understanding and mastery of addition and subtraction of fractions and decimals. Resources in the fractions and decimals section concentrate on basic concepts, such as equivalent fractions and decimal place value, as well as visual demonstrations of addition and subtraction and opportunities for practice.

In grade 5, students would also learn to describe three-dimensional shapes and analyze their properties, including volume and surface area. Through the activities online and offline in the three-dimensional section, students can explore the properties of solids and go on to consider the rules that determine surface area and volume.

In Background Information for Teachers, you will find professional learning resources. Finally, we discuss the focal points as they are related to the NCTM Principles and Standards for School Mathematics.

Future publications in this series will look at the focal points for grades 6, 7, and 8. We hope the resources in the Math Focal Points series open your classes to a wider view of mathematics!

For a complete statement of the NCTM Curriculum Focal Points for grade 5 see below.

NCTM Curriculum Focal Points for Grade 5

Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers.
Students apply their understanding of models for division, place value, properties, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends. They select appropriate methods and apply them accurately to estimate quotients or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for dividing whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems. They consider the context in which a problem is situated to select the most useful form of the quotient for the solution, and they interpret it appropriately.

Number and Operations: Developing an understanding of and fluency with addition and subtraction of fractions and decimals.
Students apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They apply their understandings of decimal models, place value, and properties to add and subtract decimals. They develop fluency with standard procedures for adding and subtracting fractions and decimals. They make reasonable estimates of fraction and decimal sums and differences. Students add and subtract fractions and decimals to solve problems, including problems involving measurement.

Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their properties, including volume and surface area.
Students relate two-dimensional shapes to three-dimensional shapes and analyze properties of polyhedral solids, describing them by the number of edges, faces, or vertices as well as the types of faces. Students recognize volume as an attribute of three-dimensional space. They understand that they can quantify volume by finding the total number of same-sized units of volume that they need to fill the space without gaps or overlaps. They understand that a cube that is 1 unit on an edge is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume. They decompose three-dimensional shapes and find surface areas and volumes of prisms. As they work with surface area, they find and justify relationships among the formulas for the areas of different polygons. They measure necessary attributes of shapes to use area formulas to solve problems.

Reprinted with permission from Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, copyright 2006 by the National Council of Teachers of Mathematics. All rights reserved.

by Terese Herrera

Terry Herrera taught math several years at middle and high school levels, then earned a Ph.D. in mathematics education. She is a resource specialist for the Middle School Portal. Please email any comments to: msp@msteacher.org

There's More! You'll know when new math or science publications are posted on the NSDL Middle School Portal by requesting free email notices at http://msteacher.org/registration.aspx. Don't forget to browse the Math Pathway every once in a while to find a wealth of resources for your teaching.

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Copyright March 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
This work is licensed under a Creative Commons License. Creative Commons License
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