Fourth Grade
Math
Report Card Guide
Here you'll find what fourth grade students are learning in Math during each of the three marking periods (trimesters).
First Trimester
 Number and Operations in Base Ten
 Operations and Algebraic Thinking
 Measurement and Data
 Mathematical Practices
Number and Operations in Base Ten
Applies place value concepts to show understanding of multidigit whole numbers
 Applies place value and numeration concepts to compare, find equivalencies, and round
 Demonstrates an understanding that in a multi digit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right
Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens place
 Compares two multidigit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols
 Reads and writes whole numbers in expanded, standard and word form (through 1,000,000)
 Rounds multidigit whole numbers (through 1,000,000) to any place
Uses place value understanding and properties of operations to perform multidigit arithmetic
 Uses operations to solve problems
 Adds and subtracts multidigit whole numbers (limit sums and subtrahends up to and including 1,000,000)
 Multiplies a whole number of up to four digits by a onedigit whole number and multiply 2 twodigit numbers
Operations and Algebraic Thinking
Represents and solves problems involving the four operations
 Uses numbers and symbols to model the concepts of expressions and equations
 Interprets a multiplication equation as a comparison
 Represents verbal statements of multiplicative comparisons as multiplication equations

Example: Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5

Example: Know that 24 is 3 times as many as 8 can be represented by the equation 24 = 3 x 8 or 24 = 8 x 3

 Multiplies or divides to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison
 Example: Know that 3 x 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects, and not just 3 more objects.
 Example: Know that 3 x 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects, and not just 3 more objects.
 Solves word problems (including multi step) posed with whole numbers using the four operations

Represents these problems using equations with a symbol or letter standing for the unknown quantity (includes order of operations with parentheses only)

 Interprets a multiplication equation as a comparison
Develops and/or applies number theory concepts to find factors and multiples
 Develops and applies number theory concepts to represent numbers in various ways
 Finds all factor pairs for a whole number in the interval 1 through 100
 Recognizes that a whole number is a multiple of each of its factors
 Identifies dimensions of an array as factors
 Determines whether a given whole number in the interval 1 through 100 is a multiple of a given onedigit number
 Determines whether a given whole number is prime, composite, and/or square
 Finds all factor pairs for a whole number in the interval 1 through 100
Generates and analyzes patterns using one rule
 Recognizes, describes, extends, creates, and replicates a variety of patterns
 Generates a number or shape pattern that follows a given rule and continue a given pattern
 Determines a rule for a function table or finds a missing element in a function table
 Generates a number or shape pattern that follows a given rule and continue a given pattern
Measurement and Data
Solves problems involving measurement and conversions from a larger unit to a smaller unit
 Solves problems involving time
 Uses the four operations to solve word problems involving intervals of time (such as elapsed time)
Organizes, represents and interprets data using a variety of graphs
 Represent and interpret data (whole number and fractions) found in tables, bar graphs, pictographs
 Translates information from one type of data display to another (ex: table to a bar graph or pictograph)
Mathematical Practices
Strategically applies concepts and processes to make sense of problems and solve them
 Makes sense of mathematical problems and perseveres in solving them
 Reasons abstractly and quantitatively
 Uses structures such as place value and properties of operations to solve problems
 Creates and uses mathematical models to represent a problem situation
 Uses appropriate tools strategically to solve problems
 Recognizes regularities and applies them when solving other related problems
 Uses math vocabulary to clearly explain and justify mathematical reasoning and critique the reasoning of others
 Calculates accurately and efficiently and uses clear and concise notation and vocabulary to record and explain work
Second Trimester
 Numbers and Operations in Base Ten
 Operations and Algebraic Thinking
 Geometry
 Measurement and Data
 Mathematical Practices
Numbers and Operations in Base Ten
Applies place value concepts to show understanding of multidigit whole numbers
 Applies place value and numeration concepts to compare, find equivalencies, and round
 Demonstrates an understanding that in a multi digit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right
Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens place
 Compares two multidigit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbol
 Reads and writes whole numbers in expanded, standard and word form (through 1,000,000)
 Rounds multidigit whole numbers (through 1,000,000) to any place
Uses place value understanding and properties of operations to perform multidigit arithmetic
 Uses operations to solve problems
 Multiplies two whole numbers using a variety of strategies, limited to problems involving:
 1 digit by 2 digit; 2 digit by 2 digit; 3 digit by 1 digit (multiples of 10 only)
 Understands the effect of multiplying by a multiple of 10
 Divides up to threedigit dividends by a onedigit divisor using a variety of strategies with answer written as whole number quotients and remainders
 1 digit by 2 digit; 2 digit by 2 digit; 3 digit by 1 digit (multiples of 10 only)
Operations and Algebraic Thinking
Represents and solves problems involving the four operations
 Uses numbers and symbols to model the concepts of expressions and equations
 Interprets a multiplication equation as a comparison
 Represents verbal statements of multiplicative comparisons as multiplication equations E

Example: 24 is 3 times as many as 8 can be represented as: 24 = 3 x 8 or 24 = 8 x 3
 Solves single and multistep word problems using the four operations

Involving addition and subtraction of whole numbers

Involving multiplication of whole numbers and multiplicative comparison

Involving division of whole numbers with answers as whole numbers or having remainders that must be interpreted based on the story context

 Multiplies or divides to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison
 Example: Know that 3 x 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects, and not just 3 more objects
 Example: Know that 3 x 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects, and not just 3 more objects
 Represents word problems using equations with a symbol or letter standing for an unknown quantity including application of order of operations (with parentheses only)
 Interprets a multiplication equation as a comparison
Generates and analyzes patterns using one rule
 Recognizes, describes, extends, creates, and replicates a variety of patterns
 Generates a number or shape pattern that follows a given rule and continue a given pattern
 Determines a rule for a function table or finds a missing element in a function table
 Generates a number or shape pattern that follows a given rule and continue a given pattern
Geometry
Draws lines and angles and identifies these in twodimensional figures
 Lists properties, classifies, draws, and identifies geometric figures in two dimensions
 Draws points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines
 Identifies these in twodimensional figures
 Draws points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines
Classifies twodimensional figures by properties of their lines and angles and by the absence or presence of lines of symmetry
 Classifies twodimensional figures based on:
 Presence or absence of parallel or perpendicular lines
 Presence or absence of angles of a specific size (right, acute, obtuse)
 recognizes right triangles as a category, and identify right triangles
 recognizes right triangles as a category, and identify right triangles
 Attributes including number and length of sides
 recognizes attributes of quadrilaterals
 recognizes attributes of quadrilaterals
 Presence or absence of parallel or perpendicular lines
 Draws, recognizes and names points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines
 Recognizes 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 mirroring parts
 Identifies linesymmetric figures
 Draw lines of symmetry on a two dimensional figure (up to two lines of symmetry)
 Identifies linesymmetric figures
Measurement and Data
Solves problems involving measurements, conversions and measuring angles
 Solves problems involving length, weight, liquid volume, time, area and perimeter
 Converts linear measurements using a table of equivalencies
 Solves word problems involving linear conversions
 Tells time and calculates elapsed time
 Understands the concepts of area and perimeter and the realworld applications of each
 Applies formulas to determine the area and perimeter of rectangles in realworld mathematical problems
 Finds missing side length when one side length and the area and/or perimeter is given
 Converts linear measurements using a table of equivalencies
 Measures angles and uses properties of adjacent angles to solve problems
 Uses appropriate tools and units to sketch an angle and determine angle measurements
 Measures angles in wholenumber degrees using a protractor and sketches angles of specified measure
 Solves addition and subtraction problems to find unknown angles on a diagram in realworld and mathematical problems.
 Uses appropriate tools and units to sketch an angle and determine angle measurements
Organizes, represents and interprets data using a variety of graphs
 Represent and interpret data (whole number and fractions) found in tables, bar graphs, pictographs, line plots
 Translates information from one type of data display to another (ex: table to a line plot marked in fractional units, bar graph, pictograph)
 Make a line plot to display a data set of measurements in fraction of a unit (halves, fourths and eighths)
 Solve problems involving addition and subtraction of fractions by using information presented in the line plots
 Translates information from one type of data display to another (ex: table to a line plot marked in fractional units, bar graph, pictograph)
Mathematical Practices
Strategically applies concepts and processes to make sense of problems and solve them
 Makes sense of mathematical problems and perseveres in solving them
 Reasons abstractly and quantitatively
 Uses structures such as place value and properties of operations to solve problems
 Creates and uses mathematical models to represent a problem situation
 Uses appropriate tools strategically to solve problems
 Recognizes regularities and applies them when solving other related problems
 Uses math vocabulary to clearly explain and justify mathematical reasoning and critique the reasoning of others
 Calculates accurately and efficiently and uses clear and concise notation and vocabulary to record and explain work
Third Trimester
 Number and Operations in Base Ten
 Numbers and Operations: Fractions
 Operations and Algebraic Thinking
 Measurement and Data
 Mathematical Practices
Number and Operations in Base Ten
Applies place value concepts to show understanding of multidigit whole numbers
 Applies place value and numeration concepts to compare, find equivalencies, and round
 Demonstrates an understanding that in a multidigit whole number (through 1,000,000) a digit in one place represents ten times what it represents in the place to its right
 Compares two multidigit numbers through 1,000,000 based on meanings of the digits in each place, using >, <, and = symbols
 Demonstrates an understanding that in a multidigit whole number (through 1,000,000) a digit in one place represents ten times what it represents in the place to its right
Uses place value understanding and properties of operations to perform multidigit arithmetic
 Uses operations to solve problems
 Multiplies two whole numbers using a variety of strategies, limited to problems involving:1 digit by 2 digit; 2 digit by 2 digit; 3 digit by 1 digit, and 4 digit by 1 digit
 Divides up to fourdigit dividends by a one or twodigit divisor using a variety of strategies (including the application of the multiplication/division relationship) with answer written as whole number quotients and remainders
 Multiplies two whole numbers using a variety of strategies, limited to problems involving:1 digit by 2 digit; 2 digit by 2 digit; 3 digit by 1 digit, and 4 digit by 1 digit
Numbers and Operations: Fractions
Generates equivalencies and compares fractions
 Recognizes equivalent fractions
 Creates a set of fractions which are equivalent to a given fraction, i.e. 2/4 = ½
 Compares two fractions using symbols: <, >, =
 Orders fractions on a number line
Solves problems involving fractions and whole numbers
 Adds and subtracts fractions and mixed numbers with common denominators (straight computation and word problems)
 Multiplies a whole number by a fraction (straight computation and word problems)
Connects decimal notation to fractions and compares decimal fractions
 Writes fractions with denominators of 10 or 100 as a decimal
 Compares two decimals using >, <, = symbols and justifies the conclusions
 Adds two fractions with respective denominators 10 and 100
 Example: add 3/10 + 4/100 = ___ by renaming 3/10 as 30/100; 30/10 + 4/100 = 34/100
Operations and Algebraic Thinking
Represents and solves problems involving the four operations
 Uses numbers and symbols to model the concepts of expressions and equations
 Interprets a multiplication equation as a comparison
 Represents verbal statements of multiplicative comparisons as multiplication equations
 Example: Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5
 Example: Know that 24 is 3 times as many as 8 can be represented by the equation 24 = 3 x 8 or 24 = 8 x 3
 Example: Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5
 Solves single and multistep word problems using the four operations
 Involving addition and subtraction of whole numbers
 Involving multiplicative comparison
 Involving multiplication of whole numbers
 Involving division of whole numbers with answers as whole numbers or having remainders that must be interpreted based on the story context
 Involving addition and subtraction of whole numbers
 Represents word problems using equations with a symbol or letter standing for an unknown quantity, including application of order of operations (with parentheses only)
 Interprets a multiplication equation as a comparison
Develops and/or applies number theory concepts to find factors and multiples
 Develops and applies number theory concepts to represent numbers in various ways
 Knows multiplication combinations up to 12 x 12
 Knows division combinations related to multiplication combinations
 Knows multiplication combinations up to 12 x 12
 Applies understanding of factors and multiples to develop strategies for solving multiplication and division problems=
Generates and analyzes patterns using one rule
 Recognizes, describes, extends, creates, and replicates a variety of patterns
 Generates a number or shape pattern that follows a given rule and continue a given pattern
 Determines a rule for a function table or finds a missing element in a function table
 Generates a number or shape pattern that follows a given rule and continue a given pattern
Measurement and Data
Solves problems involving measurements, conversions and measuring angles
 Solves problems involving length, weight, liquid volume, time, area and perimeter
 Converts measurements using a table of equivalencies to solve word problems
 Uses the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving simple fractions or decimals; and problems that require expressing measurements given in a larger unit in terms of a smaller unit
 Converts measurements using a table of equivalencies to solve word problems
Organizes, represents and interprets data using a variety of graphs
 Represent and interpret data (whole number and fractions) found in tables, bar graphs, pictographs, line plots
 Translates information from one type of data display to another (ex: table to a line plot marked in fractional units, bar graph, pictograph)
 Make a line plot to display a data set of measurements in fraction of a unit (halves, fourths and eighths)
 Solve problems involving addition and subtraction of fractions by using information presented in the line plots
 Translates information from one type of data display to another (ex: table to a line plot marked in fractional units, bar graph, pictograph)
Mathematical Practices
Strategically applies concepts and processes to make sense of problems and solve them
 Makes sense of mathematical problems and perseveres in solving them
 Uses structures such as place value and properties of operations to solve problems
 Creates and uses mathematical models to represent a problem situation
 Uses appropriate tools strategically to solve problems
 Recognizes regularities and applies them when solving other related problems
 Uses math vocabulary to clearly explain and justify mathematical reasoning and critique the reasoning of others
 Calculates accurately and efficiently and uses clear and concise notation and vocabulary to record and explain work