Third Grade Mathematics
Grade Three
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing twodimensional shapes.
 Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equalsized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equalsized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving singledigit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.
 Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
 Students recognize area as an attribute of twodimensional regions. They measure the area of a shape by finding the total number of samesize units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.
 Students describe, analyze, and compare properties of twodimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.
Grade 3 Overview
Operations and Algebraic Thinking
 Represent and solve problems involving multiplication and division.
 Understand properties of multiplication and the relationship between multiplication and division.
 Multiply and divide within 100.
 Solve problems involving the four operations, and identify and explain patterns in arithmetic.
 http://www.corestandards.org/Math/Content/3/OA/
Number and Operations in Base Ten
 Use place value understanding and properties of operations to perform multidigit arithmetic.
 http://www.corestandards.org/Math/Content/3/NBT/
Number and Operationsâ€”Fractions
 Develop understanding of fractions as numbers.
 http://www.corestandards.org/Math/Content/3/NF/
Measurement and Data
 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
 Represent and interpret data.
 Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
 http://www.corestandards.org/Math/Content/3/MD/
Geometry
 Reason with shapes and their attributes.
 http://www.corestandards.org/Math/Content/3/G/
*Information provided from: http://www.corestandards.org/
Grade Three Tentative Math Pacing Calendar
September 
Topic One/Two 
Understand Multiplication and Multiplication Facts: Use Patterns

October 
Topic Three 
Apply Properties: Multiplication Facts for 3, 4, 5, 6, 7, 8

November 
Topic Four 
Use Multiplication to Divide: Division Facts

November/December 
Topic Five 
Fluently Multiply and Divide Within 100

December 
Topic Six 
Connect Area to Multiplication and Addition

January 
Topic Seven 
Represent and Interpret Data

January 
Topic Eight 
Use Subtraction and Properties to Add and Subtract

February 
Topic Nine 
Fluently Add and Subtract Within 1,000

February/March 
Topic Ten 
Multiply by Multiples of 10

March 
Topic Eleven 
Use Operations with Whole Numbers to Solve Problems

March/April 
Topic Twelve 
Understand Fractions as Numbers

April 
Topic Thirteen 
Fraction Equivalence and Comparison

April 
Topic Sixteen 
Solve Perimeter Problems

May 
Topic Fourteen 
Solve Time, Capacity and Mass Problems

May/June 
Topic Fifteen 
Attributes of TwoDimensional Shapes
