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New York Math Standards - 5th Grade
MathScore aligns to the New York Math Standards for 5th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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Problem Solving
5.PS.1 Know the difference between relevant and irrelevant information when solving problems5.PS.2 Understand that some ways of representing a problem are more efficient than others
5.PS.3 Interpret information correctly, identify the problem, and generate possible strategies and solutions (Arithmetic Word Problems , Word Problems With Remainders )
5.PS.4 Act out or model with manipulatives activities involving mathematical content from literature
5.PS.5 Formulate problems and solutions from everyday situations (Making Change )
5.PS.6 Translate from a picture/diagram to a numeric expression (Percentage Pictures )
5.PS.7 Represent problem situations verbally, numerically, algebraically, and/or graphically (Algebraic Sentences )
5.PS.8 Select an appropriate representation of a problem
5.PS.9 Understand the basic language of logic in mathematical situations (and, or, not)
5.PS.10 Work in collaboration with others to solve problems
5.PS.11 Translate from a picture/diagram to a number or symbolic expression.
5.PS.12 Use trial and error and the process of elimination to solve problems
5.PS.13 Model problems with pictures/diagrams or physical objects
5.PS.14 Analyze problems by observing patterns (Function Tables , Function Tables 2 )
5.PS.15 Make organized lists or charts to solve numerical problems
5.PS.16 Discuss with peers to understand a problem situation
5.PS.17 Determine what information is needed to solve problems
5.PS.18 Determine the efficiency of different representations of a problem
5.PS.19 Differentiate between valid and invalid approaches
5.PS.20 Understand valid counterexamples
5.PS.21 Explain the methods and reasoning behind the problem solving strategies used
5.PS.22 Discuss whether a solution is reasonable in the context of the original problem
5.PS.23 Verify results of a problem
Reasoning and Proof
5.RP.1 Recognize that mathematical ideas can be supported using a variety of strategies5.RP.2 Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking
5.RP.3 Investigate conjectures, using arguments and appropriate mathematical terms
5.RP.4 Make and evaluate conjectures, using a variety of strategies
5.RP.5 Justify general claims or conjectures, using manipulatives, models, expressions, and mathematical relationships
5.RP.6 Develop and explain an argument verbally, numerically, and/or graphically
5.RP.7 Verify claims other students make, using examples and counterexamples when appropriate
5.RP.8 Support an argument through examples/counterexamples and special cases
Communication
5.CM.1 Provide an organized thought process that is correct, complete, coherent, and clear5.CM.2 Explain a rationale for strategy selection
5.CM.3 Organize and accurately label work
5.CM.4 Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form
5.CM.5 Answer clarifying questions from others
5.CM.6 Understand mathematical solutions shared by other students
5.CM.7 Raise questions that elicit, extend, or challenge others' thinking
5.CM.8 Consider strategies used and solutions found by others in relation to their own work
5.CM.9 Increase their use of mathematical vocabulary and language when communicating with others (Algebraic Terms )
5.CM.10 Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale
5.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning (Line Graphs , Function Tables , Function Tables 2 )
Connections
5.CN.1 Understand and make connections and conjectures in their everyday experiences to mathematical ideas (Making Change )5.CN.2 Explore and explain the relationship between mathematical ideas (Variable Substitution )
5.CN.3 Connect and apply mathematical information to solve problems (Algebraic Word Problems )
5.CN.4 Understand multiple representations and how they are related (Basic Fraction Simplification , Fraction Simplification , Fractions to Decimals , Decimals To Fractions , Percentages , Percentage Pictures )
5.CN.5 Model situations with objects and representations and be able to draw conclusions
5.CN.6 Recognize and provide examples of the presence of mathematics in their daily lives
5.CN.7 Apply mathematics to problem situations that develop outside of mathematics
5.CN.8 Investigate the presence of mathematics in careers and areas of interest
5.CN.9 Recognize and apply mathematics to other disciplines and areas of interest
Representation
5.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations5.R.2 Explain, describe, and defend mathematical ideas using representations
5.R.3 Read, interpret, and extend external models (Line Graphs )
5.R.4 Use standard and nonstandard representations with accuracy and detail
5.R.5 Use representations to explore problem situations
5.R.6 Investigate relationships between different representations and their impact on a given problem
5.R.7 Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)
5.R.8 Use mathematics to show and understand social phenomena (e.g., construct tables to organize data showing book sales)
5.R.9 Use mathematics to show and understand mathematical phenomena (e.g., find the missing value that makes the equation true: (3 + 4) + 5 = 3 + (4 + ___ )
Number Sense and Operations
5.N.1 Read and write whole numbers to millions5.N.2 Compare and order numbers to millions (Order Numbers , Order Large Numbers )
5.N.3 Understand the place value structure of the base ten number system 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand, 10 thousands = 1 ten thousand, 10 ten thousands = 1 hundred thousand, 10 hundred thousands = 1 million (Order Numbers , Order Large Numbers )
5.N.4 Create equivalent fractions, given a fraction (Basic Fraction Simplification , Fraction Simplification )
5.N.5 Compare and order fractions including unlike denominators (with and without the use of a number line) Note: Commonly used fractions such as those that might be indicated on ruler, measuring cup, etc. (Fraction Comparison )
5.N.6 Understand the concept of ratio (Ratios )
5.N.7 Express ratios in different forms (Ratios )
5.N.8 Read, write, and order decimals to thousandths (Decimal Place Value , Order Decimals )
5.N.9 Compare fractions using <, >, or = (Fraction Comparison )
5.N.10 Compare decimals using <, >, or = (Compare Decimals )
5.N.11 Understand that percent means part of 100, and write percents as fractions and decimals (Percentage Pictures )
5.N.12 Recognize that some numbers are only divisible by one and themselves (prime) and others have multiple divisors (composite) (Prime Numbers )
5.N.13 Calculate multiples of a whole number and the least common multiple of two numbers (Least Common Multiple )
5.N.14 Identify the factors of a given number (Factoring )
5.N.15 Find the common factors and the greatest common factor of two numbers (Greatest Common Factor )
5.N.16 Use a variety of strategies to multiply three-digit by three-digit numbers Note: Multiplication by anything greater than a three-digit multiplier/ multiplicand should be done using technology. (Long Multiplication )
5.N.17 Use a variety of strategies to divide three-digit numbers by one- and two-digit numbers Note: Division by anything greater than a two-digit divisor should be done using technology. (Long Division By One Digit , Long Division , Division with Remainders , Long Division with Remainders )
5.N.18 Evaluate an arithmetic expression using order of operations including multiplication, division, addition, subtraction and parentheses (Using Parentheses , Order Of Operations )
5.N.19 Simplify fractions to lowest terms (Basic Fraction Simplification , Fraction Simplification )
5.N.20 Convert improper fractions to mixed numbers, and mixed numbers to improper fractions (Fraction Simplification )
5.N.21 Use a variety of strategies to add and subtract fractions with like denominators (Basic Fraction Addition , Basic Fraction Subtraction )
5.N.22 Add and subtract mixed numbers with like denominators (Basic Fraction Addition , Basic Fraction Subtraction )
5.N.23 Use a variety of strategies to add, subtract, multiply, and divide decimals to thousandths (Small Decimal Division , Money Multiplication , Money Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division )
5.N.24 Round numbers to the nearest hundredth and up to 10,000 (Rounding Numbers , Decimal Rounding to .01 , Decimal Rounding )
5.N.25 Estimate sums and differences of fractions with like denominators .
5.N.26 Estimate sums, differences, products, and quotients of decimals (Money Addition , Money Subtraction )
5.N.27 Justify the reasonableness of answers using estimation
Algebra
5.A.1 Define and use appropriate terminology when referring to constants, variables, and algebraic expressions (Algebraic Terms )5.A.2 Translate simple verbal expressions into algebraic expressions (Phrases to Algebraic Expressions , Algebraic Sentences )
5.A.3 Substitute assigned values into variable expressions and evaluate using order of operations (Variable Substitution )
5.A.4 Solve simple one-step equations using basic whole-number facts (Single Variable Equations )
5.A.5 Solve and explain simple one-step equations using inverse operations involving whole numbers (Single Variable Equations )
5.A.6 Evaluate the perimeter formula for given input values
5.A.7 Create and explain patterns and algebraic relationships (e,g.,2,4,6,8...) algebraically: 2n (doubling) (Function Tables , Function Tables 2 )
5.A.8 Create algebraic or geometric patterns using concrete objects or visual drawings (e.g., rotate and shade geometric shapes)
Geometry
5.G.1 Calculate the perimeter of regular and irregular polygons (Perimeter )5.G.2 Identify pairs of similar triangles (Congruent And Similar Triangles )
5.G.3 Identify the ratio of corresponding sides of similar triangles
5.G.4 Classify quadrilaterals by properties of their angles and sides (Quadrilateral Types )
5.G.5 Know that the sum of the interior angles of a quadrilateral is 360 degrees (Quadrilateral Angles )
5.G.6 Classify triangles by properties of their angles and sides (Triangle Types )
5.G.7 Know that the sum of the interior angles of a triangle is 180 degrees (Triangle Angles )
5.G.8 Find a missing angle when given two angles of a triangle (Triangle Angles )
5.G.9 Identify pairs of congruent triangles (Congruent And Similar Triangles )
5.G.10 Identify corresponding parts of congruent triangles
5.G.11 Identify and draw lines of symmetry of basic geometric shapes
5.G.12 Identify and plot points in the first quadrant
5.G.13 Plot points to form basic geometric shapes (identify and classify)
5.G.14 Calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths and parallel to the axes) (Line Segments )
Measurement
5.M.1 Use a ruler to measure to the nearest inch,1/2, 1/4, and 1/8 inch5.M.2 Identify customary equivalent units of length (Distance Conversion )
5.M.3 Measure to the nearest centimeter
5.M.4 Identify equivalent metric units of length (Distance Conversion )
5.M.5 Convert measurement within a given system (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
5.M.6 Determine the tool and technique to measure with an appropriate level of precision: lengths and angles
5.M.7 Calculate elapsed time in hours and minutes (Time Intervals )
5.M.8 Measure and draw angles using a protractor
5.M.9 Determine personal references for customary units of length (e.g., your pace is approximately 3 feet, your height is approximately 5 feet, etc.)
5.M.10 Determine personal references for metric units of length
5.M.11 Justify the reasonableness of estimates
Statistics and Probability
5.S.1 Collect and record data from a variety of sources (e.g., newspapers, magazines, polls, charts, and surveys)5.S.2 Display data in a line graph to show an increase or decrease over time
5.S.3 Calculate the mean for a given set of data and use to describe a set of data
5.S.4 Formulate conclusions and make predictions from graphs
5.S.5 List the possible outcomes for a single-event experiment
5.S.6 Record experiment results using fractions/ratios
5.S.7 Create a sample space and determine the probability of a single event, given a simple experiment (e.g., rolling a number cube) (Probability )
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