New York State Learning Standards designed,
aligned and
supported by		    
 
 



Main Menu

About MPNY
Partners
Training
Resources
Aligned Lessons
Jump to a Strand

Algebra
Communication
Connections
Geometry
Measurement
Number Sense and Operations
Reasoning and Proof
Representation
Statistics and Probability
MST Standard 3 Math: Grade 5
Through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability, students will:
  • understand the concepts of and become proficient with the skills of mathematics;
  • communicate and reason mathematically;
  • become problem solvers by using appropriate tools and strategies;
Algebra
Students will represent and analyze algebraically a wide variety of problem solving situations.
Variables and Expressions
  5.A.2

Translate simple verbal expressions into algebraic expressions

  5.A.1

Define and use appropriate terminology when referring to constants, variables, and algebraic expressions 

       
Algebra
Students will perform algebraic procedures accurately.
Equations and Inequalities
  5.A.6

Evaluate the perimeter formula for given input values

  5.A.5

Solve and explain simple one-step equations using inverse operations involving whole numbers 

  5.A.4

Solve simple one-step equations using basic whole-number facts 

       
Algebra
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Patterns, Relations, and Functions
  5.A.8

Create algebraic or geometric patterns using concrete objects or visual drawings (e.g., rotate and shade geometric shapes)

  5.A.7

Create and explain patterns and algebraic relationships (e.g.,2,4,6,8...) algebraically: 2n (doubling)

       
Algebra
Students will perform algebraic procedures accurately.
Variables and Expressions
  5.A.3

Substitute assigned values into variable expressions and evaluate using order of operations

       
Communication
Students will organize and consolidate their mathematical thinking through communication.
  5.CM.3

Organize and accurately label work

  5.CM.2

Explain a rationale for strategy selection

  5.CM.1

Provide an organized thought process that is correct, complete, coherent, and clear

       
Communication
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
  5.CM.5

Answer clarifying questions from others

  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

       
Communication
Students will analyze and evaluate the mathematical thinking and strategies of others.
  5.CM.8

Consider strategies used and solutions found by others in relation  to their own work

  5.CM.6

Understand mathematical solutions shared by other students

  5.CM.7

Raise questions that elicit, extend, or challenge others' thinking

 
       
Communication
Students will use the language of mathematics to express mathematical ideas precisely.
  5.CM.11

Decode and comprehend mathematical visuals and symbols to construct meaning

 
  5.CM.10

Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale

  5.CM.9

Increase their use of mathematical vocabulary and language when communicating with others

       
Connections
Students will recognize and use connections among mathematical ideas.
  5.CN.3

Connect and apply mathematical information to solve problems

  5.CN.2

Explore and explain the relationship between mathematical ideas

  5.CN.1

Understand and make connections and conjectures in their everyday experiences to mathematical ideas

       
Connections
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
  5.CN.5

Model situations with objects and representations and be able to draw conclusions

  5.CN.4

Understand multiple representations and how they are related

       
Connections
Students will recognize and apply mathematics in contexts outside of mathematics.
  5.CN.9

Recognize and apply mathematics to other disciplines and areas of interest

  5.CN.8

Investigate the presence of mathematics in careers and areas of  interest

 
  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

       
Geometry
Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Shapes
  5.G.1

Calculate the perimeter of regular and irregular polygons

       
Geometry
Students will identify and justify geometric relationships, formally and informally.
Geometric Relationships
  5.G.9

Identify pairs of congruent triangles

  5.G.10

Identify corresponding parts of congruent triangles

  5.G.8

Find a missing angle when given two angles of a triangle

 
  5.G.7

Know that the sum of the interior angles of a triangle is 180 degrees

  5.G.6

Classify triangles by properties of their angles and sides

  5.G.5

Know that the sum of the interior angles of a quadrilateral is 360 degrees

  5.G.4

Classify quadrilaterals by properties of their angles and sides

  5.G.2

Identify pairs of similar triangles

  5.G.3

Identify the ratio of corresponding sides of similar triangles

       
Geometry
Students will apply transformations and symmetry to analyze problem solving situations.
Transformational Geometry
  5.G.11

Identify and draw lines of symmetry of basic geometric shapes

       
Geometry
Students will apply coordinate geometry to analyze problem solving situations.
Coordinate Geometry
  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)

  5.G.12

Identify and plot points in the first quadrant

       
Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
  5.M.3

Measure to the nearest centimeter

  5.M.4

Identify equivalent metric units of length

  5.M.5

Convert measurement within a given system

  5.M.1

Use a ruler to measure to the nearest inch, 1/2, 1/4, and 1/8 inch

  5.M.2

Identify customary equivalent units of length

       
Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Tools and Methods
  5.M.6

Determine the tool and technique to measure with an appropriate level of precision: lengths and angles

       
Measurement
Students will use units to give meaning to measurements.
Units
  5.M.7

Calculate elapsed time in hours and minutes

  5.M.8

Measure and draw angles using a protractor

 
       
Measurement
Students will develop strategies for estimating measurements.
Estimation
  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

       
Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
  5.N.6

Understand the concept of ratio

  5.N.1

Read and write whole numbers to millions

  5.N.2

Compare and order numbers to millions

  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

  5.N.4

Create equivalent fractions, given a fraction

  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.

  5.N.11

Understand that percent means part of 100, and write percents as fractions and decimals

  5.N.10

Compare decimals using <, >, or = 

  5.N.9

Compare fractions using <, >, or =

  5.N.8

Read, write, and order decimals to thousandths

  5.N.7

Express ratios in different forms

       
Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Theory
  5.N.15

Find the common factors and the greatest common factor of two numbers

  5.N.13

Calculate multiples of a whole number and the least common multiple of two numbers

  5.N.14

Identify the factors of a given number

  5.N.12

Recognize that some numbers are only divisible by one and themselves (prime) and others have multiple divisors (composite)

       
Number Sense and Operations
Students will understand meanings of operations and procedures, and how they relate to one another.
Operations
  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.

  5.N.23

Use a variety of strategies to add, subtract, multiply, and divide decimals to thousandths

  5.N.22

Add and subtract mixed numbers with like denominators

  5.N.21

Use a variety of strategies to add and subtract fractions with like denominators

  5.N.20

Convert improper fractions to mixed numbers, and mixed numbers to improper fractions

 
  5.N.19

Simplify fractions to lowest terms

  5.N.18

Evaluate an arithmetic expression using order of operations including multiplication, division, addition, subtraction and parentheses

  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.

       
Number Sense and Operations
Students will compute accurately and make reasonable estimates.
Estimation
  5.N.27

Justify the reasonableness of answers using estimation

  5.N.25

Estimate sums and differences of fractions with like denominators

  5.N.26

Estimate sums, differences, products, and quotients of decimals

  5.N.24

Round numbers to the nearest hundredth and up to 10,000

       
Problem Solving
Students will build new mathematical knowledge through problem solving.
  5.PS.3

Interpret information correctly, identify the problem, and generate possible strategies and solutions

  5.PS.2

Understand that some ways of representing a problem are more efficient than others

  5.PS.1

Know the difference between relevant and irrelevant information when solving problems

 
       
Problem Solving
Students will solve problems that arise in mathematics and in other contexts.
  5.PS.9

Understand the basic language of logic in mathematical situations (and, or, not)

  5.PS.7

Represent problem situations verbally, numerically, algebraically, and/or graphically

  5.PS.8

Select an appropriate representation of a problem

  5.PS.6

Translate from a picture/diagram to a numeric expression

  5.PS.5

Formulate problems and solutions from everyday situations

  5.PS.4

Act out or model with manipulatives activities involving mathematical content from literature

       
Problem Solving
Students will apply and adapt a variety of appropriate strategies to solve problems.
  5.PS.15

Make organized lists or charts to solve numerical problems

  5.PS.13

Model problems with pictures/diagrams or physical objects

  5.PS.14

Analyze problems by observing patterns

  5.PS.12

Use trial and error and the process of elimination to solve  problems

  5.PS.11

Translate from a picture/diagram to a number or symbolic expression

  5.PS.10

Work in collaboration with others to solve problems

       
Problem Solving
Students will monitor and reflect on the process of mathematical problem solving.
  5.PS.23

Verify results of a problem

  5.PS.22

Discuss whether a solution is reasonable in the context of the original problem

  5.PS.21

Explain the methods and reasoning behind the problem solving strategies used

  5.PS.20

Understand valid counterexamples

 
  5.PS.19

Differentiate between valid and invalid approaches

  5.PS.18

Determine the efficiency of different representations of a problem

  5.PS.16

Discuss with peers to understand a problem situation

  5.PS.17

Determine what information is needed to solve problem

       
Reasoning and Proof
Students will recognize reasoning and proof as fundamental aspects of mathematics.
  5.RP.2

Understand that mathematical statements can be supported, using  models, facts, and relationships to explain their thinking

  5.RP.1

Recognize that mathematical ideas can be supported using a  variety of strategies

       
Reasoning and Proof
Students will make and investigate mathematical conjectures.
  5.RP.4

Make and evaluate conjectures, using a variety of strategies

  5.RP.3

Investigate conjectures, using arguments and appropriate mathematical terms

       
Reasoning and Proof
Students will develop and evaluate mathematical arguments and proofs.
  5.RP.6

Develop and explain an argument verbally, numerically, and/or graphically

  5.RP.5

Justify general claims or conjectures, using manipulatives,  models, expressions, and mathematical relationships

       
Reasoning and Proof
Students will select and use various types of reasoning and methods of proof.
  5.RP.8

Support an argument through examples/counterexamples and special cases

 
  5.RP.7

Verify claims other students make, using examples and  counterexamples when appropriate

       
Representation
Students will create and use representations to organize, record, and communicate mathematical ideas.
  5.R.3

Read, interpret, and extend external models

 
  5.R.4

Use standard and nonstandard representations with accuracy and detail

  5.R.2

Explain, describe, and defend mathematical ideas using representations

  5.R.1

Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations

       
Representation
Students will select, apply, and translate among mathematical representations to solve problems.
  5.R.5

Use representations to explore problem situations

  5.R.6

Investigate relationships between different representations and their impact on a given problem

       
Representation
Students will use representations to model and interpret physical, social, and mathematical phenomena.
  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 + ___ )

  5.R.7

Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)

       
Statistics and Probability
Students will collect, organize, display, and analyze data.
Collection of Data
  5.S.1

Collect and record data from a variety of sources (e.g., newspapers, magazines, polls, charts, and surveys)

       
Statistics and Probability
Students will collect, organize, display, and analyze data.
Organization and Display of Data
  5.S.2

Display data in a line graph to show an increase or decrease over time

       
Statistics and Probability
Students will collect, organize, display, and analyze data.
Analysis of Data
  5.S.3

Calculate the mean for a given set of data and use to describe a set of data

       
Statistics and Probability
Students will make predictions that are based upon data analysis.
Predictions from Data
  5.S.4

Formulate conclusions and make predictions from graphs

       
Statistics and Probability
Students will understand and apply concepts of probability.
Probability
  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)

  5.S.5

List the possible outcomes for a single-event experiment 

  5.S.6

Record experiment results using fractions/ratios 

       
 
  ©2005-10 New York State Teacher Centers and the New York Institute of Technology.  All rights reserved.