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Problem Solving Strand

Students will build new mathematical knowledge through problem solving

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

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 (e.g., as counting the number of children in the class or using the calendar to teach counting)

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

Use informal counting strategies to find solutions

Experience teacher-directed questioning process to understand problems

Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking

Use manipulatives (e.g., tiles, blocks) to model the action in problems

Use drawings/pictures to model the action in problems

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

Explain to others how a problem was solved, giving strategies and justifications

Reasoning and Proof Strand

Students will recognize reasoning and proof as fundamental aspects of mathematics

Understand that mathematical statements can be true or false

Recognize that mathematical ideas need to be supported by evidence

Students will make and investigate mathematical conjectures

Investigate the use of knowledgeable guessing as a mathematical tool

Explore guesses, using a variety of objects and manipulatives

Students will develop and evaluate mathematical arguments and proofs

Justify general claims, using manipulatives

Develop and explain an argument verbally or with objects

Listen to and discuss claims other students make

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

Use trial and error strategies to verify claims

Communication Strand

Students will organize and consolidate their mathematical thinking through communication

Understand how to organize their thought processes

Verbally support their reasoning and answer

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

Share mathematical ideas through the manipulation of objects, drawings, pictures, and verbal explanations

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

Listen to solutions shared by other students

Formulate mathematically relevant questions

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

Use appropriate mathematical terms, vocabulary, and language

Connections Strand

Students will recognize and use connections among mathematical ideas

Recognize the connections of patterns in their everyday experiences to mathematical ideas

Understand and use the connections between numbers and the quantities they represent to solve problems

Compare the similarities and differences of mathematical ideas

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

Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas

Understand meanings of operations and how they relate to one another

Understand how mathematical models represent quantitative relationships

Students will recognize and apply mathematics in contexts outside of mathematics

Recognize the presence of mathematics in their daily lives

Recognize and apply mathematics to solve problems

Recognize and apply mathematics to objects, pictures and symbols

Representation Strand

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

Use multiple representations, including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations

Share mental images of mathematical ideas and understandings

Use standard and nonstandard representations

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

Connect mathematical representations with problem solving

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., draw pictures to show a story problem, show number value using fingers on your hand)

Number Sense and Operations Strand

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

Skip count to 100 by 2s, 5s, 10s

Count back from 100 by 1s, 5s, 10s using a number chart

Skip count by 3s to 36 for multiplication readiness

Skip count by 4s to 48 for multiplication readiness

Compare and order numbers to 100

Develop an understanding of the base ten system: 10 ones = 1 ten; 10 tens = 1 hundred; 10 hundreds = 1 thousand

Use a variety of strategies to compose and decompose two-digit numbers

Understand and use the commutative property of addition

Name the number before and the number after a given number, and name the number(s) between two given numbers up to 100 (with and without the use of a number line or a hundreds chart)

Use and understand verbal ordinal terms

Read written ordinal terms (first through ninth) and use them to represent ordinal relations

Use zero as the identity element for addition

Recognize the meaning of zero in the place value system (0-100)

Use concrete materials to justify a number as odd or even

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

Determine sums and differences of number sentences by various means (e.g., families, related facts, inverse operations, addition doubles, and doubles plus one)

Use a variety of strategies to solve addition and subtraction problems with one- and two-digit numbers without regrouping

Demonstrate fluency and apply addition and subtraction facts up to and including 18

Use doubling to add 2-digit numbers

Use compensation to add 2-digit numbers

Develop readiness for multiplication by using repeated addition

Develop readiness for division by using repeated subtraction, dividing objects into groups (fair share)

Students will compute accurately and make reasonable estimates

Estimate the number in a collection to 100 and then compare by counting the actual items in the collection

Algebra Strand

Students will perform algebraic procedures accurately

Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100

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

Describe and extend increasing or decreasing (+,-) sequences and patterns (numbers or objects up to 100)

Geometry Strand

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

Experiment with slides, flips, and turns to compare two-dimensional shapes

Identify and appropriately name two-dimensional shapes: circle, square, rectangle, and triangle (both regular and irregular)

Compose (put together) and decompose (break apart) two-dimensional shapes

Students will identify and justify geometric relationships, formally and informally

Group objects by like properties

Students will apply transformations and symmetry to analyze problem solving situations

Explore and predict the outcome of slides, flips, and turns of two-dimensional shapes

Explore line symmetry

Measurement Strand

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

Use non-standard and standard units to measure both vertical and horizontal lengths

Use a ruler to measure standard units (including whole inches and whole feet)

Compare and order objects according to the attribute of length

Recognize mass as a qualitative measure (e.g., Which is heavier? Which is lighter?)

Compare and order objects, using lighter than and heavier than

Students will use units to give meaning to measurements

Know and recognize coins (penny, nickel, dime, quarter) and bills ($1, $5, $10, and $20)

Recognize the whole dollar notation as $1, etc

Identify equivalent combinations to make one dollar

Tell time to the half hour and five minutes using both digital and analog clocks

Students will develop strategies for estimating measurements

Select and use standard (customary) and non-standard units to estimate measurements

Statistics and Probability Strand

Students will collect, organize, display, and analyze data

Formulate questions about themselves and their surroundings

Collect and record data (using tallies) related to the question

Display data in pictographs and bar graphs using concrete objects or a representation of the object

Compare and interpret data in terms of describing quantity (similarity or differences)

Students will make predictions that are based upon data analysis

Discuss conclusions and make predictions from graphs

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