NYC StudentsNYC ParentsNYC Teachers Math NYC


Problem Solving Strand

Students will build new mathematical knowledge through problem solving

Explore, examine, and make observations about a social problem or mathematical situation

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

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

Students will solve problems that arise in mathematics and in other contexts

Act out or model with manipulatives activities involving mathematical content from literature and/or story telling

Formulate problems and solutions from everyday situations

Translate from a picture/diagram to a numeric expression

Represent problem situations in oral, written, concrete, pictorial, and graphical forms

Select an appropriate representation of a problem

Students will apply and adapt a variety of appropriate strategies to solve problems

Use trial and error to solve problems

Use process of elimination to solve problems

Make pictures/diagrams of problems

Use physical objects to model problems

Work in collaboration with others to solve problems

Make organized lists to solve numerical problems

Make charts to solve numerical problems

Analyze problems by identifying relationships

Analyze problems by identifying relevant versus irrelevant information

Analyze problems by observing patterns

State a problem in their own words

Students will monitor and reflect on the process of mathematical problem solving

Determine what information is needed to solve a problem

Discuss with peers to understand a problem situation

Discuss the efficiency of different representations of a problem

Verify results of a problem

Recognize invalid approaches

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

Reasoning and Proof Strand

Students will recognize reasoning and proof as fundamental aspects of mathematics

Use representations to support mathematical ideas

Determine whether a mathematical statement is true or false and explain why

Students will make and investigate mathematical conjectures

Investigate the use of knowledgeable guessing by generalizing mathematical ideas

Make conjectures from a variety of representations

Students will develop and evalute mathematical arguments and proofs

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

Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms

Discuss, listen, and make comments that support or reject claims made by other students

Students will select and use various types of reasoning and methods of proof

Support an argument by trying many cases

Disprove an argument by finding counterexamples

Communication Strand

Students will organize and consolidate their mathematical thinking through communication

Understand and explain how to organize their thought process

Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Verbally explain their rationale for strategy selection

Provide reasoning both in written and verbal form

Organize and accurately label work

Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form models, symbols, and expressions in written and verbal form

Answer clarifying questions from others

Students will analyze and evaluate the mathematical thinking and strategies of others

Restate mathematical solutions shared by other students

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

Students will use the language of mathematics to express mathematical ideas precisely

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

Describe objects, relationships, solutions, and rationale using appropriate vocabulary

Decode and comprehend mathematical visuals and symbols to construct meaning

Connections Strand

Students will recognize and use connections among mathematical ideas

Recognize, understand, and make connections in their everyday experiences to mathematical ideas

Compare and contrast mathematical ideas

Connect and apply mathematical information to solve problems

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

Understand multiple representations and how they are related

Model situations with objects and representations and be able to make observations

Students will recognize and apply mathematics in contexts outside of mathematics

Recognize the presence of mathematics in their daily lives

Apply mathematics to solve problems that develop outside of mathematics

Recognize and apply mathematics to other disciplines

Representation Strand

Students will create and use representations to organize, record, and communicate mathematical ideas

Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations

Share mental images of mathematical ideas and understandings

Recognize and use external mathematical representations

Use standard and nonstandard representations with accuracy and detail

Students will select, apply, and translate among mathematical representations to solve problems

Understand similarities and differences in representations

Connect mathematical representations with problem solving

Construct effective representations to solve problems

Students will use representations to model and interpret physical, social, and mathematical phenomena

Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)

Use mathematics to show and understand social phenomena (e.g., count and represent sharing cookies between friends)

Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)

Number Sense and Operations Strand

Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems

Skip count by 1,000s

Read and write whole numbers to 10,000

Compare and order numbers to 10,000

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

Recognize equivalent representations for numbers up to four digits and generate them by decomposing and composing numbers

Understand, use, and explain the associative property of multiplication

Develop an understanding of fractions as locations on number lines and as divisions of whole numbers

Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and tenths) using manipulatives, visual models, and illustrations

Use concrete materials and visual models to compare and order unit fractions or fractions with the same denominator (with and without the use of a number line)

Develop an understanding of decimals as part of a whole

Read and write decimals to hundredths, using money as a context

Use concrete materials and visual models to compare and order decimals (less than 1) to the hundredths place in the context of money

Develop an understanding of the properties of odd/even numbers as a result of multiplication

Students will understand meanings of operations and procedures, and how they relate to one another

Use a variety of strategies to add and subtract numbers up to 10,000

Select appropriate computational and operational methods to solve problems

Understand various meanings of multiplication and division

Use multiplication and division as inverse operations to solve problems

Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with and without regrouping)

Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with and without regrouping)

Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000

Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and without remainders)

Interpret the meaning of remainders

Add and subtract proper fractions with common denominators

Express decimals as an equivalent form of fractions to tenths and hundredths

Add and subtract decimals to tenths and hundredths using a hundreds chart

Students will compute accurately and make reasonable estimates

Round numbers less than 1,000 to the nearest tens and hundreds

Check reasonableness of an answer by using estimation

Algebra Strand

Students will represent and analyze algebraically a wide variety of problem solving situations

Evaluate and express relationships using open sentences with one operation

Students will perform algebraic procedures accurately

Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare whole numbers and unit fractions and decimals (up to hundredths)

Find the value or values that will make an open sentence true, if it contains < or >

Students will recognize, use, and represent algebraically patterns, relations, and functions

Describe, extend, and make generalizations about numeric ( +,−,×,÷ ) and geometric patterns

Analyze a pattern or a whole-number function and state the rule, given a table or an input/output box

Geometry Strand

Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes

Identify and name polygons, recognizing that their names are related to the number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon)

Identify points and line segments when drawing a plane figure

Find perimeter of polygons by adding sides

Find the area of a rectangle by counting the number of squares needed to cover the rectangle

Define and identify vertices, faces, and edges of three-dimensional shapes

Students will identify and justify geometric relationships, formally and informally

Draw and identify intersecting, perpendicular, and parallel lines

Identify points and rays when drawing angles

Classify angles as acute, obtuse, right, and straight

Measurement Strand

Students will determine what can be measured and how, using appropriate methods and formulas

Select tools and units (customary and metric) appropriate for the length being measured

Use a ruler to measure to the nearest standard unit (whole, 1/2 and 1/4 inches, whole feet, whole yards, whole centimeters, and whole meters)

Know and understand equivalent standard units of length: 12 inches = 1 foot; 3 feet = 1 yard

Select tools and units appropriate to the mass of the object being measured (grams and kilograms)

Measure mass, using grams

Select tools and units appropriate to the capacity being measured (milliliters and liters)

Measure capacity, using milliliters and liters

Students will use units to give meaning to measurements

Make change, using combined coins and dollar amounts

Calculate elapsed time in hours and half hours, not crossing A.M./P.M.

Calculate elapsed time in days and weeks, using a calendar

Statistics and Probability Strand

Students will collect, organize, display, and analyze data

Design investigations to address a question from given data

Collect data using observations, surveys, and experiments and record appropriately

Represent data using tables, bar graphs, and pictographs

Read and interpret line graphs

Students will make predictions that are based upon data analysis

Develop and make predictions that are based on data

Formulate conclusions and make predictions from graphs

Information Source: NYSED.GOV CS&IT (standards pdf)