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 multi-digit 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 multi-digit 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 multi-digit whole numbers (through 1,000,000) to any place
Uses place value understanding and properties of operations to perform multi-digit arithmetic
- Uses operations to solve problems
- Adds and subtracts multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000)
- Multiplies a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit 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
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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
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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
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- 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
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Represents these problems using equations with a symbol or letter standing for the unknown quantity (includes order of operations with parentheses only)
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- 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 one-digit 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 multi-digit 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 multi-digit 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 multi-digit whole numbers (through 1,000,000) to any place
Uses place value understanding and properties of operations to perform multi-digit 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 three-digit dividends by a one-digit 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
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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 multi-step word problems using the four operations
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Involving addition and subtraction of whole numbers
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Involving multiplication of whole numbers and multiplicative comparison
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Involving division of whole numbers with answers as whole numbers or having remainders that must be interpreted based on the story context
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- 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 two-dimensional 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 two-dimensional figures
- Draws points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines
Classifies two-dimensional figures by properties of their lines and angles and by the absence or presence of lines of symmetry
- Classifies two-dimensional 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 two-dimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts
- Identifies line-symmetric figures
- Draw lines of symmetry on a two dimensional figure (up to two lines of symmetry)
- Identifies line-symmetric 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 real-world applications of each
- Applies formulas to determine the area and perimeter of rectangles in real-world 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 whole-number degrees using a protractor and sketches angles of specified measure
- Solves addition and subtraction problems to find unknown angles on a diagram in real-world 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 multi-digit 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
- Compares two multi-digit numbers through 1,000,000 based on meanings of the digits in each place, using >, <, and = symbols
- 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
Uses place value understanding and properties of operations to perform multi-digit 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 four-digit dividends by a one or two-digit 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 multi-step 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