Math Benchmarks

MATH – PROBLEM SOLVING

Uses strategies to solve word problems (Grade 1)

Comprehends problem situations; considers and uses strategies to solve addition and subtraction word problems, including: pencil and paper, concrete models, and pictorial representations.

Uses strategies to solve multi-step word problems (Grades 2-5)

Comprehends multi-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, and pictorial representations.

Explains thinking using numbers, objects, pictures, or words (Grades 1-5)

Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.

Makes sense of problems and perseveres while solving (Grades 2-5)

Explains to self the meaning of the problem; looks for entry points to problem situations; plans a solution pathway rather than simply jumping into a solution attempt; checks answers to problems; tries several approaches in finding a solution; struggles with various attempts over time and learns from previous solution attempts.

Attends to precision and accuracy (Grades 2-5)

Rarely submits work with computational errors, and is routinely able to find and correct errors when checking own work; uses appropriate units in problem solution; communicates thinking with precision using appropriate, learned mathematical language

Constructs viable arguments and critiques the reasoning of others (Grades 3-5)

Explains problem solving strategies and mathematical thinking for self using objects, drawings, diagrams, equations and/or actions; is able to converse about the mathematical thinking and ideas of classmates, decide whether they make sense, and identify strengths and weaknesses of others’ solutions.

Uses appropriate tools strategically (Grades 4-5)

Selects the appropriate tools to be used to help solve a problem and is able to explain the reasoning for the selection.

MATH – GRADE 5

Math Grade 5 Benchmarks

Operations and Algebraic Thinking	MP #1	MP #2	MP #3
Uses the four operations to solve problems	Solves problems involving all four operations with whole numbers and fractions/mixed numbers	Solves problems involving all four operations including whole numbers, decimals, and fractions	Solves problems involving all four operations including whole numbers, decimals, and fractions
Writes, interprets and evaluates numerical expressions and equations	Interprets and evaluates numerical expressions and equations following order of operations	Interprets and evaluates numerical expressions and equations following order of operations	Writes, interprets, and evaluates numerical expressions and equations following order of operations
Numbers and Operations Base Ten	MP #1	MP #2	MP #3
Understands place value of whole numbers and decimals	Reads, writes, rounds and compares whole numbers	Reads, writes, rounds and compares whole numbers	Reads, writes, rounds and compares whole numbers to thousandths
Performs operations with multi-digit whole numbers and decimals to hundredths	Adds, subtracts, multiplies and divides multi-digit whole numbers as presented	Adds, subtracts, multiplies and divides multi-digit whole numbers as presented	Adds, subtracts, multiplies and divides multi-digit whole numbers as presented and decimals to hundredths
Numbers and Operations - Fractions	MP #1	MP #2	MP #3
Performs operations with fractions and mixed numbers with like and unlike denominators	Adds and subtracts fractions and/or mixed numbers with like and unlike denominators	Adds, subtracts, multiplies and divides fractions and/or mixed numbers with like and unlike denominators	Performs all four operations with fractions and mixed numbers

Measurement and Data	MP #1	MP #2	MP #3
Converts units within given measurement systems			Converts measurements within one system to solve real world problems
Measures volume			Understands the concept of volume and accurately finds the volume of solid figures.
Represents and interprets data			Solves problems using all four operations and fractions by using data presented in a line plot
Geometry	MP #1	MP #2	MP #3
Graphs ordered pairs on a coordinate plane			Graphs ordered pairs on a coordinate plane to solve real world problems
Classifies two-dimensional figures based on their properties			Classifies two dimensional figures by their properties
Problem Solving	MP #1	MP #2	MP #3
Uses strategies to solve multi-step word problems	Comprehends multi-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, and pictorial representations.
Explains thinking using numbers, objects, pictures, or words	Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.
Makes sense of problems and perseveres while solving	Explains to self the meaning of the problem; looks for entry points to problem situations; plans a solution pathway rather than simply jumping into a solution attempt; checks answers to problems; tries several approaches in finding a solution; struggles with various attempts over time and learns from previous solution attempts.
Attends to precision and accuracy	Rarely submits work with computational errors, and is routinely able to find and correct errors when checking own work; uses appropriate units in problem solution; communicates thinking with precision using appropriate, learned mathematical language
Constructs viable arguments and critiques the reasoning of others	Explains problem solving strategies and mathematical thinking for self using objects, drawings, diagrams, equations and/or actions; is able to converse about the mathematical thinking and ideas of classmates, decide whether they make sense, and identify strengths and weaknesses of others’ solutions.
Uses appropriate tools strategically	Selects the appropriate tools to be used to help solve a problem and is able to explain the reasoning for the selection.

MATH – GRADE 4

Operations and Algebraic Thinking	MP #1	MP #2	MP #3
Uses the four operations with whole numbers to solve problems	Solves problems involving all four operations as presented	Solves problems involving all four operations including interpreting remainders	Solves problems involving all four operations including interpreting remainders
Identifies factor pairs and multiples for all whole numbers to 100	Identifies all factor pairs and multiples for all whole numbers to 100; determines prime and composite	Identifies and uses all factor pairs and multiples for all whole numbers to 100; determines prime and composite	Identifies and uses all factor pairs and multiples for all whole numbers to 100; determines prime and composite
Numbers and Operations Base Ten	MP #1	MP #2	MP #3
Performs operations with multi-digit whole numbers	Fluently adds and subtracts multi-digit whole numbers using the standard algorithm. Multiplies multi-digit numbers (4 digits by 1 digit and 2 digits by 2 digits)	Fluently adds and subtracts multi-digit whole numbers using the standard algorithm. Multiplies and divides multi-digit numbers.	Fluently adds and subtracts multi-digit whole numbers. Multiplies and divides multi-digit numbers using the standard algorithm
Uses place value understanding to round and compare multi-digit whole numbers	Uses place value understanding to round and compare multi-digit whole numbers	Uses place value understanding to round and compare multi-digit whole numbers	Uses place value understanding to round and compare multi-digit whole numbers
Numbers and Operations - Fractions	MP #1	MP #2	MP #3
Generates, compares, and explains fractions and their equivalents		Begins to generate, compare and explain equivalent fractions using fraction models	Generates, compares, and explains equivalent fractions using fraction models
Adds, subtracts and multiplies fractions with like denominators		Adds, subtracts and multiplies fractions and/or mixed numbers with like denominators	Adds, subtracts and multiplies fractions and/or mixed numbers with like denominators
Compares, converts and adds decimal fractions		Compares and converts decimals (tenths and hundredths)	Compares, converts and adds decimals (tenths and hundredths)
Measurement and Data	MP #1	MP #2	MP #3
Solves problems involving measurement and conversion of measurements			Converts measurements within one system: distance, liquid volume, mass, time and money; Applies formulas for area and perimeter
Represents and interprets data			Solves problems involving addition and subtraction of fractions by using data presented in a line plot
Geometry	MP #1	MP #2	MP #3
Draws, measures and identifies lines and angles			Draws, measures and identifies lines and angles
Classifies shapes by properties of lines and angles			Classifies two dimensional shapes by properties of lines, angles and symmetry
Problem Solving	MP #1	MP #2	MP #3
Uses strategies to solve multi-step word problems	Comprehends multi-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, or pictorial representations.
Explains thinking using numbers, objects, pictures, or words	Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.
Makes sense of problems and perseveres while solving	Self-monitors for comprehension of the problem; looks for entry points to each problem; plans a solution; checks answers to problems; tries several approaches in finding a solution; struggles with various attempts over time and learns from previous solution attempts.
Attends to precision and accuracy	Rarely submits work with computational errors, and is routinely able to find and correct errors when checking own work; uses appropriate units in problem solution; communicates thinking with precision using appropriate, learned mathematical language
Constructs viable arguments and critiques the reasoning of others	Explains problem solving strategies and mathematical thinking using objects, drawings, diagrams, equations and/or models; is able to converse about the mathematical thinking and ideas of classmates, decide whether they make sense, and identify strengths and weaknesses of others’ solutions.
Uses appropriate tools strategically	Selects the appropriate tools to be used to help solve a problem and is able to explain the reasoning for the selection.

MATH – GRADE 3

Math Grade 3 Benchmarks

Operations and Algebraic Thinking	MP#1	MP#2	MP#3
Demonstrates fluency and accuracy with addition and subtraction math facts	Knows from memory all sums of two one-digit numbers	Knows from memory all sums of two one-digit numbers	Knows from memory all sums of two one-digit numbers
Demonstrates fluency and accuracy with multiplication and division math facts		Multiplies within 100, using strategies such as the relationship between multiplication and division or decomposing unknown facts into two known facts	Knows from memory all products of two one-digit numbers
Numbers and Operations Base Ten	MP#1	MP#2	MP#3
Uses place value understanding and properties to perform multi-digit arithmetic	Adds, subtracts, and rounds numbers within 1000	Fluently adds, subtracts, and rounds numbers within 1000	Fluently adds, subtracts, and multiplies numbers within 1000 (one digit numbers by multiples of 10 with a range 10-90)
Numbers and Operations - Fractions	MP#1	MP#2	MP#3
Represents and explains fractions on a number line		Accurately plots fractions on a number line using equal intervals	Accurately plots fractions on a number line using equal intervals
Explains and compares fractions and their equivalents		Accurately expresses, compares, and generates equivalent fractions	Accurately expresses, compares, and generates equivalent fractions
Measurement and Data	MP#1	MP#2	MP#3
Reads, writes and solves problems involving time			Accurately reads and writes time to the minute and solves problems involving elapsed time
Solves problems using metric measure involving liquid volume and mass			Accurately measures, estimates and solve problems in metric units involving liquid volume and mass
Represents and interprets data using graphs and line plots			Accurately generates and interprets data on line plots, picture graphs and bar graphs
Understands concepts of perimeter and area			Accurately measures and compares areas and perimeters using addition and multiplication
Geometry	MP#1	MP#2	MP#3
Categorizes shapes by their attributes			Accurately describes, compares, and classifies shapes into multiple categories (ex. trapezoid = quadrilateral)
Problem Solving	MP #1	MP #2	MP #3
Uses strategies to solve multi-step word problems	Comprehends multi-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, and pictorial representations.
Explains thinking using numbers, objects, pictures, or words	Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.
Makes sense of problems and perseveres while solving	Explains to self the meaning of the problem; looks for entry points to problem situations; plans a solution pathway rather than simply jumping into a solution attempt; checks answers to problems; tries several approaches in finding a solution; struggles with various attempts over time and learns from previous solution attempts.
Attends to precision and accuracy	Rarely submits work with computational errors, and is routinely able to find and correct errors when checking own work; uses appropriate units in problem solution; communicates thinking with precision using appropriate, learned mathematical language
Constructs viable arguments and critiques the reasoning of others	Explains problem solving strategies and mathematical thinking for self using objects, drawings, diagrams, equations and/or actions; is able to converse about the mathematical thinking and ideas of classmates, decide whether they make sense, and identify strengths and weaknesses of others’ solutions.

MATH – GRADE 2

Math Grade 2 Benchmarks

Operations and Algebraic Thinking	MP#1	MP#2	MP#3
Adds fluently within 20	Adds within 20 using mental strategies, including counting on, making ten, using the relationship between addition and subtraction, and decomposing facts to create easier, known sums	Adds within 20 using mental strategies, including counting on, making ten, using the relationship between addition and subtraction, and decomposing facts to create easier, known sums	Knows from memory all addition facts within 20 (all sums of two one-digit numbers)
Subtracts fluently within 20	Subtracts within 20 using mental strategies, including decomposing a number leading to a ten, using the relationship between addition and subtraction	Subtracts within 20 using mental strategies, including decomposing a number leading to a ten, using the relationship between addition and subtraction	Knows from memory all subtraction facts within 20
Numbers and Operations Base Ten	MP#1	MP#2	MP#3
Uses place-value to read, write, and count numbers to 1000	Reads, writes, counts and compares numbers to 1000	Reads, writes, counts, and compares numbers to 1000	Accurately reads, writes, counts, and compares numbers to 1000
Uses strategies to add and subtract within 1000	Uses place value to regroup in addition and subtraction within 1000 using concrete models or drawings	Uses place value to regroup in addition and subtraction within 1000	Accurately uses place value to regroup in addition and subtraction within 1000
Skip counts with equal groups as foundation for multiplication	Skip count by 10s, and 100s, within 1000	Skip count by 2s, 5s, 10s, and 100s, within 1000	Accurately adds equal groups of objects arranged in rectangular arrays
Measurement and Data	MP#1	MP#2	MP#3
Estimates and measures length	Skills not assessed at this time	Accurately measures, compares, and estimates lengths in centimeters and meters	Accurately measures, compares, and estimates lengths in inches, feet, centimeters, and meters
Reads and writes time to the nearest 5 minutes	Skills not assessed at this time	Accurately reads and writes time to the nearest 5 minutes	Accurately reads and writes time to the nearest 5 minutes
Counts and solves problems using money	Skills not assessed at this time	Counts and compares coins and bills; solves multi-step word problems involving money.	Accurately solves multi-step word problems involving money
Represents and interprets data	Skills not assessed at this time	Skills not assessed at this time	Accurately draws picture graphs and bar graphs to represent and solve problems using data
Geometry	MP#1	MP#2	MP#3
Understands fractions as halves, thirds, and fourths	Skills not assessed at this time	Partitions circles and rectangles into two, three, and four equal parts	Accurately partitions circles and rectangles into two, three, and four equal parts
Identifies and draws shapes with specified attributes	Skills not assessed at this time	Skills not assessed at this time	Accurately identifies and draws triangles, quadrilaterals, pentagons, hexagons, and cubes
Problem Solving	MP#1	MP#2	MP#3
Uses strategies to solve two-step word problems	Comprehends one-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, and pictorial representations.	Comprehends two-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, and pictorial representations.
Explains thinking using numbers, objects, pictures, or words	Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.
Makes sense of problems and perseveres while solving	Explains to self the meaning of the problem; looks for entry points to problem situations; plans a solution pathway rather than simply jumping into a solution attempt; checks answers to problems; tries several approaches in finding a solution; struggles with various attempts over time and learns from previous solution attempts.
Attends to precision and accuracy	Rarely submits work with computational errors, and is routinely able to find and correct errors when checking own work; uses appropriate units in problem solution; communicates thinking with precision using appropriate, learned mathematical language

MATH – GRADE 1

Math Grade 1 Benchmarks

Operations and Algebraic Thinking	December - MP#1	March - MP#2	June - MP#3
Adds fluently within 20	Adds within 10 using manipulatives	Adds within 10, using strategies such as counting on, making ten, using the relationship between addition and subtraction, and decomposing facts to create easier, known sums	Adds within 20, using strategies such as manipulatives, counting on, making ten, using the relationship between addition and subtraction, and decomposing facts to create easier, known sums
Subtracts fluently within 20	Subtracts within 10 using manipulatives	Subtracts within 10, using strategies such as decomposing a number leading to a ten, and using the relationship between addition and subtraction	Subtracts within 20, using strategies such as manipulatives, decomposing a number leading to a ten, and using the relationship between addition and subtraction
Numbers and Operations Base Ten	December - MP#1	March - MP#2	June - MP#3
Reads, writes, and counts numbers to 120	Reads, writes, and counts numbers to 31	Reads, writes, and counts numbers to 100	Accurately reads, writes, and counts numbers to 120
Uses place value to add and subtract within 100	Skills not assessed at this time	Uses place value to add within 20 and subtracts multiples of 10 within 20	Accurately uses place value to add within 100 and subtract multiples of 10 within 100
Measurement and Data	December - MP#1	March - MP#2	June - MP#3
Measures and compares length	Skills not assessed at this time	Measures and orders lengths of three objects	Accurately measures and orders lengths of three objects
Reads and writes time to the half-hour	Skills not assessed at this time	Skills not assessed at this time	Accurately reads and writes time to the half-hour
Represents and interprets data	Skills not assessed at this time	Collects, organizes, and interprets data to make a pictograph, bar graph or tally chart	Accurately collects, organizes, and interprets data to make a pictograph, bar graph or tally chart
Geometry	December - MP#1	March - MP#2	June - MP#3
Identifies and composes 2 and 3 dimensional shapes	Skills not assessed at this time	Compares, composes and distinguishes two and three-dimensional shapes by their attributes	Accurately compares, composes and distinguishes two and three-dimensional shapes by their attributes
Understands equal parts (halves and fourths)	Skills not assessed at this time	Partitions circles and rectangles into halves and fourths/quarters	Accurately partitions circles and rectangles into halves and fourths/quarters
Problem Solving	December - MP#1	March - MP#2	June - MP#3
Uses strategies to solve word problems	Comprehends problem situations; considers and uses strategies to solve addition and subtraction word problems, including: pencil and paper, concrete models, and pictorial representations.
Explains thinking using numbers, objects, pictures, or words	Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.

Math Benchmarks

Wyckoff

WyckoffSchool District

Uses strategies to solve word problems (Grade 1)	Comprehends problem situations; considers and uses strategies to solve addition and subtraction word problems, including: pencil and paper, concrete models, and pictorial representations.
Uses strategies to solve multi-step word problems (Grades 2-5)	Comprehends multi-step problem situations; considers and uses strategies to solve word problems, including: pencil and paper, concrete models, and pictorial representations.
Explains thinking using numbers, objects, pictures, or words (Grades 1-5)	Uses objects, drawings, words, and/or equations to communicate thinking so that others understand methods and solutions with minimal prompting.
Makes sense of problems and perseveres while solving (Grades 2-5)	Explains to self the meaning of the problem; looks for entry points to problem situations; plans a solution pathway rather than simply jumping into a solution attempt; checks answers to problems; tries several approaches in finding a solution; struggles with various attempts over time and learns from previous solution attempts.
Attends to precision and accuracy (Grades 2-5)	Rarely submits work with computational errors, and is routinely able to find and correct errors when checking own work; uses appropriate units in problem solution; communicates thinking with precision using appropriate, learned mathematical language
Constructs viable arguments and critiques the reasoning of others (Grades 3-5)	Explains problem solving strategies and mathematical thinking for self using objects, drawings, diagrams, equations and/or actions; is able to converse about the mathematical thinking and ideas of classmates, decide whether they make sense, and identify strengths and weaknesses of others’ solutions.
Uses appropriate tools strategically (Grades 4-5)	Selects the appropriate tools to be used to help solve a problem and is able to explain the reasoning for the selection.