Grade Five Mathematics
Grade Five
In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2digit 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; and (3) developing understanding of volume.
 Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)
 Students develop understanding of why division procedures work based on the meaning of baseten numerals and properties of operations. They finalize fluency with multidigit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.
 Students recognize volume as an attribute of threedimensional space. They understand that volume can be measured by finding the total number of samesize units of volume required to fill the space without gaps or overlaps. They understand that a 1unit by 1unit by 1unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose threedimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.
Grade 5 Overview
Operations and Algebraic Thinking
 Write and interpret numerical expressions.
 Analyze patterns and relationships.
 http://www.corestandards.org/Math/Content/5/OA/
Number and Operations in Base Ten
 Understand the place value system.
 Perform operations with multidigit whole numbers and with decimals to hundredths.
 http://www.corestandards.org/Math/Content/5/NBT/
Number and Operationsâ€”Fractions
 Use equivalent fractions as a strategy to add and subtract fractions.
 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 http://www.corestandards.org/Math/Content/5/NF/
Measurement and Data
 Convert like measurement units within a given measurement system.
 Represent and interpret data.
 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
 http://www.corestandards.org/Math/Content/5/MD/
Geometry
 Graph points on the coordinate plane to solve realworld and mathematical problems.
 Classify twodimensional figures into categories based on their properties.
 http://www.corestandards.org/Math/Content/5/G/
*Information provided from: http://www.corestandards.org/
Grade Five Tentative Math Pacing Calendar
September 
Topic One 
Understand Place Value

September/October 
Topic Two 
Add and Subtract Decimals to Hundredths

October 
Topic Three 
Fluently Multiply MultiDigit Whole Numbers

October/November 
Topic Four 
Use Models and Strategies to Multiply Decimals

November 
Topic Five 
Use Models and Strategies to Divide Whole Numbers

December 
Topic Six 
Use Models and Strategies to Divide Decimals

December/January 
Topic Seven 
Use Equivalent Fractions to Add and Subtract Fractions

January 
Topic Eight 
Apply Understanding of Multiplication to Multiply Fractions

January/February 
Topic Nine 
Apply Understanding of Division to Divide Fractions

February 
Topic Ten 
Understand Volume Concepts

February/March 
Topic Eleven 
Convert Measurements

March 
Topic Twelve 
Represent and Interpret Data

March/April 
Topic Thirteen 
Write and Interpret Numerical Expressions

April 
Topic Fourteen 
Graph Points on the Coordinate

May 
Topic Fifteen 
Algebra: Analyze Patterns and Relationships

May/June 
Topic Sixteen 
Geometric Measurement: Classify TwoDimensional Figures 