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2.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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2.PS.1
Explore, examine, and make observations about a social problem or mathematical situation
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2.PS.2
Interpret information correctly, identify the problem, and generate possible solutions
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Students will solve problems that arise in mathematics and in other contexts.
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2.PS.3
Act out or model with manipulatives activities involving mathematical content from literature and/or story telling
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2.PS.4
Formulate problems and solutions from everyday situations (e.g., counting the number of children in the class, using the calendar to teach counting).
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Students will apply and adapt a variety of appropriate strategies to solve problems.
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2.PS.5
Use informal counting strategies to find solutions
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2.PS.6
Experience teacher-directed questioning process to understand problems
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2.PS.7
Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking
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2.PS.8
Use manipulatives (e.g., tiles, blocks) to model the action in problems
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2.PS.9
Use drawings/pictures to model the action in problems
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Students will monitor and reflect on the process of mathematical problem solving.
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2.PS.10
Explain to others how a problem was solved, giving strategies and justifications
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2.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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2.RP.1
Understand that mathematical statements can be true or false
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2.RP.2
Recognize that mathematical ideas need to be supported by evidence
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Students will make and investigate mathematical conjectures.
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2.RP.3
Investigate the use of knowledgeable guessing as a mathematical tool
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2.RP.4
Explore guesses, using a variety of objects and manipulatives
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Students will develop and evaluate mathematical arguments and proofs.
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2.RP.5
Justify general claims, using manipulatives
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2.RP.6
Develop and explain an argument verbally or with objects
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2.RP.7
Listen to and discuss claims other students make
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Students will select and use various types of reasoning and methods of proof.
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2.RP.8
Use trial and error strategies to verify claims
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2.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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2.CM.1
Understand how to organize their thought processes
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2.CM.2
Verbally support their reasoning and answer
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Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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2.CM.3
Share mathematical ideas through the manipulation of objects, drawings, pictures, charts, and symbols in both written and verbal explanations
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Students will analyze and evaluate the mathematical thinking and strategies of others.
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2.CM.4
Listen to solutions shared by other students
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2.CM.5
Formulate mathematically relevant questions
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Students will use the language of mathematics to express mathematical ideas precisely.
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2.CM.6
Use appropriate mathematical terms, vocabulary, and language
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2.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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2.CN.1
Recognize the connections of patterns in their everyday experiences to mathematical ideas
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2.CN.2
Understand and use the connections between numbers and the quantities they represent to solve problems
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2.CN.3
Compare the similarities and differences of mathematical ideas
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Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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2.CN.4
Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas
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2.CN.5
Understand meanings of operations and how they relate to one another
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2.CN.6
Understand how mathematical models represent quantitative relationships
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Students will recognize and apply mathematics in contexts outside of mathematics.
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2.CN.7
Recognize the presence of mathematics in their daily lives
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2.CN.8
Recognize and apply mathematics to solve problems
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2.CN.9
Recognize and apply mathematics to objects, pictures and symbols
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2.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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2.R.1
Use multiple representations, including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations
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2.R.2
Share mental images of mathematical ideas and understandings
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2.R.3
Use standard and nonstandard representations
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Students will select, apply, and translate among mathematical representations to solve problems.
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2.R.4
Connect mathematical representations with problem solving
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Students will use representations to model and interpret physical, social, and mathematical phenomena.
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2.R.5
Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)
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2.R.6
Use mathematics to show and understand social phenomena (e.g., count and represent sharing cookies between friends)
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2.R.7
Use mathematics to show and understand mathematical phenomena (e.g., draw pictures to show a story problem or show number value using fingers on your hand)
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2.N
Number Sense and Operations
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Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
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Number Systems
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2.N.1
Skip count to 100 by 2's, 5's, 10's
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2.N.2
Count back from 100 by 1's, 5's, 10's using a number chart
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2.N.3
Skip count by 3's to 36 for multiplication readiness
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2.N.4
Skip count by 4's to 48 for multiplication readiness
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2.N.5
Compare and order numbers to 100
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2.N.6
Develop an understanding of the base ten system:
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2.N.6.a
10 ones = 1 ten
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2.N.6.b
10 tens = 1 hundred
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2.N.6.c
10 hundreds = 1 thousand
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2.N.7
Use a variety of strategies to compose and decompose two-digit numbers
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2.N.8
Understand and use the commutative property of addition
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2.N.9
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)
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2.N.10
Use and understand verbal ordinal terms
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2.N.11
Read written ordinal terms (first through ninth) and use them to represent ordinal relations
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2.N.12
Use zero as the identity element for addition
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2.N.13
Recognize the meaning of zero in the place value system (0-100)
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Number Theory
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2.N.14
Use concrete materials to justify a number as odd or even
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Students will understand meanings of operations and procedures, and how they relate to one another.
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Operations
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2.N.15
Determine sums and differences of number sentences by various means (e.g., families, related facts, inverse operations, addition doubles, and doubles plus one)
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2.N.16
Use a variety of strategies to solve addition and subtraction problems using one- and two-digit numbers with and without regrouping
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2.N.17
Demonstrate fluency and apply addition and subtraction facts up to and including 18
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2.N.18
Use doubling to add 2-digit numbers
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2.N.19
Use compensation to add 2-digit numbers
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2.N.20
Develop readiness for multiplication by using repeated addition
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2.N.21
Develop readiness for division by using repeated subtraction, dividing objects into groups (fair share)
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Students will compute accurately and make reasonable estimates.
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Estimation
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2.N.22
Estimate the number in a collection to 100 and then compare by counting the actual items in the collection
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2.A
Algebra
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Students will perform algebraic procedures accurately.
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Equations and Inequalities
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2.A.1
Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100
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Students will recognize, use, and represent algebraically patterns, relations, and functions.
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Patterns, Relations, and Functions
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2.A.2
Describe and extend increasing or decreasing (+,-) sequences and patterns (numbers or objects up to 100)
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2.G
Geometry
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Shapes
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2.G.1
Experiment with slides, flips, and turns to compare two-dimensional shapes
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2.G.2
Identify and appropriately name two-dimensional shapes: circle, square, rectangle, and triangle (both regular and irregular)
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2.G.3
Compose (put together) and decompose (break apart) two-dimensional shapes
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Students will identify and justify geometric relationships, formally and informally.
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Geometric Relationships
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2.G.4
Group objects by like properties
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Students will apply transformations and symmetry to analyze problem solving situations.
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Transformational Geometry
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2.G.5
Explore and predict the outcome of slides, flips, and turns of two-dimensional shapes
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2.G.6
Explore line symmetry
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2.M
Measurement
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Students will determine what can be measured and how, using appropriate methods and formulas.
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Units of Measurement
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2.M.1
Use non-standard and standard units to measure both vertical and horizontal lengths
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2.M.2
Use a ruler to measure standard units (including whole inches and whole feet)
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2.M.3
Compare and order objects according to the attribute of length
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2.M.4
Recognize mass as a qualitative measure (e.g., Which is heavier? Which is lighter?)
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2.M.5
Compare and order objects, using lighter than and heavier than
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Students will use units to give meaning to measurements.
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Units
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2.M.6
Know and recognize coins (penny, nickel, dime, quarter) and bills ($1, $5, $10, and $20)
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2.M.7
Recognize the whole dollar notation as $1, etc.
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2.M.8
Identify equivalent combinations to make one dollar
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2.M.9
Tell time to the half hour and five minutes using both digital and analog clocks
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Students will develop strategies for estimating measurements.
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Estimation
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2.M.10
Select and use standard (customary) and non-standard units to estimate measurements
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2.S
Statistics and Probability
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Students will collect, organize, display, and analyze data.
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Collection of Data
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2.S.1
Formulate questions about themselves and their surroundings
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2.S.2
Collect and record data (using tallies) related to the question
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Organization and Display of Data
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2.S.3
Display data in pictographs and bar graphs using concrete objects or a representation of the object
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Analysis of Data
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2.S.4
Compare and interpret data in terms of describing quantity (similarity or differences)
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Students will make predictions that are based upon data analysis.
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Predictions from Data
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2.S.5
Discuss conclusions and make predictions from graphs
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