In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

1. Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.
2. Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.
3. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.

Operations and Algebraic Thinking

Number and Operations in Base Ten

Number and Operations—Fractions

• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.
• http://www.corestandards.org/Math/Content/4/NF/

Measurement and Data

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
• Represent and interpret data.
• Geometric measurement: understand concepts of angle and measure angles.
• http://www.corestandards.org/Math/Content/4/MD/

Geometry

*Information provided from: http://www.corestandards.org/

Grade Four Tentative Math Pacing Calendar

 September Topic One Generalize Place Value Understanding September Topic Two Fluently Add and Subtract Multi-Digit Whole Numbers October Topic Three Use Strategies and Properties to Multiply by 1-Digit Numbers October/November Topic Four Use Strategies and Properties to Multiply by 2-Digit Numbers November Topic Five Use Strategies and Properties to Divide by 1-Digit Numbers December Topic Six Use Operations with Whole Numbers to Solve Problems December Topic Seven Factors and Multiples January Topic Eight Extend Understanding of Fraction Equivalence and Ordering January Topic Nine Understand Addition and Subtraction of Fractions January/February Topic Ten Extend Multiplication Concepts to Fractions February Topic Eleven Represent and interpret Data on Line Plots February Topic Thirteen (only some lessons) Measurement: Find Equivalence in Units of Measure March Topic Fourteen Algebra: Generate and Analyze Patterns March/April Topic Fifteen Geometric Measurement: Understand Concepts of Angles and Angle Measurement April Topic Sixteen Lines, Angles and Shapes May Topic Twelve Understand and Compare Decimals June Topic Thirteen (remaining lessons) Measurement: Find Equivalence in Units of Measurement