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## 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.

 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.