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

 

 


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 and decimals to thousandths

Reads, writes, rounds and compares whole numbers and decimals 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 and decimals to hundredths

Adds, subtracts, multiplies and divides multi-digit whole numbers 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

 

 


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

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

Measures and compares areas and perimeters using addition and multiplication, as presented in this marking period

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

 

 


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

 

 


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.





 

 

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