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 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.

Grade 5 Overview

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