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 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; and (3) developing understanding of volume.

1. 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.)
2. Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit 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.
3. Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit 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 three-dimensional 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.

Operations and Algebraic Thinking

Number and Operations in Base Ten

Number and Operations—Fractions

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

*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 Multi-Digit 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 Two-Dimensional Figures