Math Scope and Sequence
Key Topics in Fourth Grade Math:
Operations and Algebraic Thinking  Numbers and Operations (Base 10) 


Number & Operations  Fractions  
 
Measurement and Data  Geometry 


Math Units
4th Grade
Topic  Category  Standard  Quarter 
UNIT 1: Number & Operations in Base Ten, Part 1  
Review of Third Grade Skills  1st  
L1: Understand Place Value  Numbers & Operations in Base Ten  Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right.  1st 
L2: Compare Whole Numbers  Numbers & Operations in Base Ten  Read & Write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of the comparisons.  1st 
L3: Add and Subtract Whole Numbers  Numbers & Operations in Base Ten  Fluently add and subtract multidigit whole numbers to any place.  1st 
L4: Round Whole Numbers  Numbers & Operations in Base Ten  Use place value understanding to round multidigit whole numbers to any place.  1st 
UNIT 1 Test : Number and Operations Base 10, Part 1  
UNIT 2: Operations and Algebraic Thinking  
L5: Understand Multiplication  Operations & Algebraic Thinking  Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.  1st 
L6: Multiplication & Division with Word Problems  Operations & Algebraic Thinking  Multiply or Divide to solve word problems involving multiplicative comparison.  1st 
L7: Multiples and Factors  Operations & Algebraic Thinking  Find all factor pairs for a whole number in the range 1  100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1  100 is a multiple of a given onedigit number. Determine whether a given whole number is in the range 1  100 is prime or composite.  1st 
L8: Number & Shape Patterns  Operations & Algebraic Thinking  Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.  1st 
L9: Model MultiStep Problems  Operations & Algebraic Thinking  Solve multistep word problems with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  1st 
L10: Solve MultiStep Problems  Operations & Algebraic Thinking  Solve multistep word problems with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  1st 
UNIT 2 Test : Operations & Algebraic Thinking  
UNIT 3 : Numbers & Operations in Base Ten, Part 2  
L11: Multiply Whole Numbers  Number & Operations in Base Ten  Multiply a whole number up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.  2nd 
L12: Division with Whole Numbers  Number & Operations in Base Ten  Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculations by using equations, rectangular arrays and/or area models.  2nd 
UNIT 3 Test : Numbers & Operations in Base Ten, Part 2  
UNIT 4 : Number & Operations  Fractions  
L13: Understand Equivalent Fractions  Number & Operations  Fractions  Explain why a fraction a/b is equivalent to a fraction (n X a)/ (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.  2nd 
L14: Compare Fractions  Number & Operations  Fractions  Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.  2nd 
L15: Understand Fraction Addition and Subtraction  Number & Operations  Fractions  Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions.  2nd 
L16: Add and Subtract Fractions  Number & Operations  Fractions  Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.  2nd 
L17: Add and Subtract Mixed Numbers  Number & Operations  Fractions  Decompose a fraction into a sum of fractions with the same denominator in more that one way, recording each decomposition by an equation. Justify decompositions. Add and Subtract mixed numbers with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.  2nd 
L18: Understand Fraction Multiplication  Number & Operations  Fractions  Understand a fraction a/b as a multiple of 1/b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.  3rd 
L19: Multiply Fractions  Numbers & Operations  Fractions  Solve word problems involving multiplication of a fraction by a whole number.  3rd 
L20: Fractions as Tenths and Hundredths  Numbers & Operations  Fractions  Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.  3rd 
L21: Relate Decimals and Fractions  Numbers & Operations  Fractions  Use decimal notation for fractions with denominators 10 or 100.  3rd 
L22: Compare Decimals  Numbers & Operations  Fractions  Compare two decimals to hundreths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole number. Record the results of comparisons with the symbols <. =, or >, and justify the conclusion.  3rd 
Unit 4 Test : Number & Operations  Fractions  
Unit 5 : Measurement & Data  
L23: Convert Measurements  Measurement & Data  Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l , ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table.  3rd 
L24: Time and Money  Measurement & Data  Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.  3rd 
L25: Length, Liquid Volume, and Mass  Measurement & Data  Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.  3rd 
L26: Perimeter and Area  Measurement & Data  Apply the area and perimeter formulas for rectangles in real world and mathematical problems.  3rd 
L27: Line Plots  Measurement & Data  Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, ⅛). Solve problems involving addition and subtraction of fractions by using information presented in line plots.  3rd 
L28: Understand Angles  Measurement & Data  An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through n onedegree angles is said to have an angle measure of n degrees.  4th 
L29: Measure and Draw Angles  Measurement & Data  Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure.  4th 
L30: Add and Subtract with Angles  Measurement & Data  Recognize angle measures as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.  4th 
Unit 5 Test : Measurement & Data  
Unit 6 : Geometry  
L31: Points, Lines, Rays and Angles  Geometry  Draw points, lines, and line segments, rays and angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.  4th 
L32: Classify TwoDimensional Figures  Geometry  Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.  4th 
L33: Symmetry  Geometry  Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.  4th 
Unit 6 Test : Geometry 