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Core Content and Skills
Math Grade 2
2008-2009
BOE Approved 

Counting, Coins and Combinations  Content   Skills  Counting and Quantity - Developing strategies for accurately counting a set of objects by ones and groups   Counting sets of up to 60 objects Developing strategies for counting accurately Counting a quantity in more than one way Developing and analyzing visual images for quantities up to 10 Counting by groups of 10   Counting and Quantity - Developing an understanding of the magnitude and sequence of numbers up to 100   Using the number line to reason about, and keep track of information about, the magnitude and relationship of numbers Developing an understanding of the structure of the 100 chart Counting, writing, and reading numbers sequentially from 1 to 100 and beyond Identifying and using patterns in the structure of the number system   Whole-Number Operations - Making sense of and developing strategies to solve addition and subtraction problems with totals up to 45   Generating equivalent expressions for a number Comparing two amounts under 45 to find the difference Combining two quantities with totals up to 45 Visualizing, retelling, and modeling the action of addition and subtraction (as removal) situations Using known combinations (e.g., combinations that make 10) to compose, decompose, and combine numbers Subtracting a quantity from a whole of up to 30 Solving addition and subtraction (as removal) story problems Doubling a quantity   Computational Fluency - Knowing addition combinations 10 + 10   Developing fluency with the Make 10, Plus 1, and Plus 2 addition combinations Finding two addends that make 10 Finding the missing addend to make a total of 10 Doubling a quantity Developing fluency with the doubles combinations   Whole-Number Operations - Using manipulatives, drawings, tools, and notation to show strategies and solutions   Establishing use of tools, routines, and expectations for math class Using standard notation (>,<,+,-,=) to describe arrangements of cubes, to record expressions that equal a given number, to compare quantities, to represent addition and subtraction situations, and to represent doubling Using the number line to reason about, and keep track of information about, and keep track of information about, the magnitude and relationship of numbers Recording strategies for solving problems, including addition and subtraction story problems Using equations to record Connecting standard notation for addition and subtraction (+,-,=) to the quantities and actions that the signs and symbols represent Using a rectangular array to model doubling

Shapes, Blocks and Symmetry (2-D and 3-D Geometry)  Content   Skills  Features of Shape -Composing and Decomposing 2-D and 3-D Shapes   Combining shapes to make a new shape Covering a region, without gaps or overlaps, with a single shapes or multiple shapes Covering a region, without gaps or overlaps, using different shapes Combining shapes to make a 3-D whole Drawing 3-D shapes   Features of Shape -Describing, identifying, comparing and sorting 2-D and 3-D shapes   Describing attributes of and sorting 2-D and 3-D shapes Identifying names and attributes of 2-D and 3-D shapes Attending to features of 3-D shapes, particularly the number and shape of faces Identifying categories for 2-D shapes Identifying a 3-D shape by touch Sorting polygons by the number of sides Sorting quadrilaterals by angle Identifying quadrilaterals as shapes with 4 sides Identifying rectangles as 4-sided shapes with 4 right angles Identifying important features of a rectangle Defining biggest in different ways Ordering rectangles from biggest to smallest Recognizing that rectangular prisms have rectangular faces Recognizing which faces of a rectangular prism are the same size and shape Constructing a rectangular prism from rectangles Visualizing and describing rectangular prisms   Area Management -Visualizing the structure of arrays   Covering rectangles with arrays of tiles Arranging square tiles in rectangular arrays Constructing and describing rectangular arrays of tiles Making different rectangular arrays using the same number of tiles Drawing rectangles by attending to th lengths of sides   Features of Shape- Exploring mirror symmetry   Describing and identifying objects and designs that have mirror symmetry Constructing 2-D and 3-D symmetryical designs with mirror symmetry Reflecting a shape across a line of symmetry Exploring symmetry by folding and cutting paper patterns Identifying lines of symmetry Orienting shapes so that a line of symmetry aligns with a mirror (Shapes software) Determining what makes a line symmetrical   Computational Fluency- Knowing addition combinations to 10+10   Reviewing known addition combinations (combinations of 10, Plus 1, Plus 2) Developing fluency with the doubles combinations to 10+10 Achieving fluency with the doubles combinations

Stickers, Number Strings, and Story Problems  Content   Skills  Whole - Number Operation - Making sense of and developing strategies to slove additiion and subtraction problems with totals up to 45   Using known combinations to add two or more numbers Comparing a number to 20 to find the difference Visualizing, retelling, and modeling the action of a variety of addition and subtraction situations Developing strategies for solving a variety of addition and subtraction story problems with totals up to 45 and recording work Solving problems with an unknown change Combining coins to a total of 50 cents Solving an addition story problem by counting on or breaking numbers apart   Whole - Number Operations - (Understanding the properties of addition and subtraction)   Considering whether reordering three addends results in the same total Considering a generalization about reordering addends for all numbers Considering whether reordering the numbers in a subtraction problem results in the same total Considering the relationship between addition and subtraction   Counting and Quantity - (Counting by equal groups)   Investigating numbers that can and cannot be made into groups of two or two equal groups Understanding that any number that can be divided into groups of two can also be divided int two equal groups (and vice versa) Characterizing even and odd numbers as those that do or do not make groups of two (partners) and two equal groups (teams)   Counting and Quantity - (Develoing strategies for accurately counting a set of objects by ones and groups)   Looking at patterns and developing fluency with skip counting by 2s, 5s, and 10s Considering the relationship between skip counting and grouping Counting by groups of 2,5, and 10 Noticing and describing a 2:1 relationship (e.g., there are 2 legs for every 1 person) Solving problems that involve equal groups Knowing that the size of a group remains constant no matter how it is counted (by 1s, 2s, 5s, or 10s)   The Base-Ten Number System - Understanding the equivalence of one group and the discrete units that comprise it   Identifying coins and their values Indentifying and using coin equivalencies Recognizing that the first digit of a 2-digit number designates the number of groups of 10 and the second digit designates the number of ones Solving problems about 10s and 1s Using a place-value model to represent a number as 10s ans 1s Finding as many combinations of a number as possible, using only 10s and 1s Recognizing that different combinations of 10s and 1s for the same number are equivalent (e.g., 4 tens and 6 ones = 3 tens and 16 ones, etc.)   Whole-Number Computation (Using manipulatives, drawings, tools, and notation to sho strategies and solutions)   Using the calculator as a mathematical tool Using standard notation (+,-,=) to represent a variety of addition and subtractin situations Telling stories to match given equations Uaing tally marks to represent groups of 5   Computational Fluency (Knowing addition combinations to 10 + 10) Relating the doubles and near-doubles combinations Developing fluency with the near-doubles combinations Adding 10 to any number (or any number to 10) Developing fluency with the Plus 10 combinations Achieving fluency with the near-doubles combinations

Pockets, Teeth, and Favorite Things (Data Analysis)  Content   Skills  Data Analysis - Sorting and Classifying Data   Grouping data into categories based on similar attributes. Sorting the same set of data in different ways. Sorting a set of data by two attributes at one time.   Data Analysis (Representing data)   Representing a set of data sorted into categories. Comparing representations of a set of data. Using equations to shows how the sum of the responses in each category equals the total responsses collected Using a Venn diagram to represent a sorted set of data Ordering, representing, and describing a set of numnerical data Comparing ways of organizing data Representing data on a line plot   Data Analysis-Describing data   Describing what the data show about the group surveyed Interpreting a data representation including a line plot Describing important features of a data set Describing a set of numerical data Comparing two sets of data Developing a hypothesis based on a set of data   Data Analysis-Designing and carrying out a data investigation   Choosing a survey question Making a plan for collecting data Making predictions about data to be collected Collecting and recording data from a survey Interpreting and sharing results from a data investigation

How Many Floors? How Many Rooms? (Patterns, Functions, and Change)  Content   Skills  Linear Relationships - Describing and representing ratios   Describing the relationship between two quantities in a constant ratio situation Using tables to represent the ratio relationship between two quantities Finding the value of one quantity in a constant ratio situation, given the value of the other   Using Tables and Graphs - Using tables to represent change   Connecting numbers in a table to the situation they represent Using conventional language for a table and its parts: rows columns Describing the pattern in the numbers in a column and interpreting the pattern in terms of the situation the table represents Describing what is the same about situations that look different but can be represented by the same table Describing how the two numbers in the row of a table are connected to the situation the table represents Using information in a table to determine the relationship between two quantities   Number Sequences - Constructing, describing and extending number sequences with constant increments generated by various contexts   Extending a repeated pattern Identifying the unit of a repeating pattern Creating a repeating pattern that has the same structure as, but different elements than, another repeating pattern (e.g., a red-blue pattern and a clap-tap head pattern) Defining even and odd numbers Determining and describing the number sequence associated with one of the elements in an AB, ABC, ABCD, or AABBC repeating pattern (e.g.,2,4,6,8,...; 3,6,9,...;1,4,7,...) Determining the element of a repeating pattern associated with a particular counting number in AB, ABC, ABCD, or AABBC patterns (e.g.; what color is the 8th element in a red-blue repeating pattern?) Determining how and why the same number sequence can be generated by different contexts

How Many Tens? How Many Ones?  Content   Skills  Whole-Number Operation-Making sense of and developing strategies to solve addition and subtraction problems with totals up to 100   Developing efficient methods for adding and subtracting 2-digit numbers Adding tens and ones to combine 2-digit numbers Noticing what happens to the tens place when a multiple of 10 is added or subtracted Adding 2-digit numbers by keeping one number whole Naming and comparing strategies for adding and subtracting 2-digit numbers Determining the difference between a number and a multiple of 10 up to 100 Adding 2-digit numbers Adding multiples of 5 and 10, up to 100 Adding coin amounts, up to $1.00 Determining the difference between a given amount and $1.00 Adding and subtracting 10 and multiples of 10 to/from any number Subtracting amounts from 100 or $1.00, down to 0 Organizing cubes into 10s and 1s Using a place-value model to represent a number as 10s and 1s Using coin equivalencies Working with the relationship between 1, 10, and 100   Counting and Quality-developing an understanding of the magnitude and sequence of numbers up to 100   Becoming familiar with the structure of the 100 chart Developing fluency with the sequence of numbers from 1 to 100 Finding and using patterns in the sequence of numbers Using the 100 chart to reason about, and keep track of, information about the magnitude and relationship of numbers   Counting and Quantity-Counting by equal groups   Skip counting by 2s, 5s, and 10s Thinking about the structure of 100 in terms of groups of 5 and 10 Identifying patterns in the multiples of 2, 5, and 10 Using the relationship between 5 and 10, and between nickels and dimes, to solve problems   The Base-ten Number System-Understanding the equivalence of one group and the discreteunits that comprise it   Organizing cubes into 10s and 1s Using a place-value model to represent a number as 10s and 1s Using coin equivalencies Working with the relationship between 1, 10, and 100   Whole-Number Computation-Using manipulatives, drawings, tools, and notation to show strategies and solutions   Writing an equation that represents a problem Developing efficient methods for notating addition and subtraction strategies Visualizing and making jumps of multiples of 5 on the 100 chart Using coins to model adding by 5s and 10s Using the 100 chart and the number line to model addition

Parts of a Whole, Parts of a Group (Fractions)  Content   Skills  Rational Numbers - Understanding fractions as equal parts of a whole   Finding equal parts of a whole and naming them with fractions (e.g., 1/2 is one of two equal parts; 1/3 is one of three equal parts, and so on) Showing one half of an object Determing whether a block is half of another block Determining whether a region is half of a given rectangle Seeing different ways to make fourths of a square Recognizing the equivalence of different fourths of the same object Identifying halves, thirds, and fourths of regions Identifying and naming fractional parts that have numerators greater than 1 (e.g., 2/3, 2/4, 3/4)   Rational Numbers - Understanding fractions as equal parts of a group   Finding equal parts of a group and naming them with fractions (e.g., 1/2 is one of two equal parts; 1/3 is one of three equal parts, and so on Finding one half of a set Solving problems about finding halves of quantities in different contexts Solving problems that result in mixed numbers Finding thirds and fourths of sets Finding fractions of sets   Rational Numbers - Using terms and notation   Learning the term one half and the notaion 1/2 Learning the terms and notation for mixed numbers (e.g., one and a half and 1 1/2 Learning the term one fourth and the notation 1/4 Learning the term one third and the notation 1/3 Learning the terms and notation for fractions that contain more than one part (e.g., 2/3, 2/4 and 3/4)

Partners, Teams and Paper Clips  Content   Skills  Whole-Number Operations- Adding even and odd numbers   Characrterizing even and odd numbers as those that do or do not make groups of two (partners) and two equal groups (teams) Investigating what happens with partners and teams when two groups are combined Making and testing conjectures about adding even and odd numbers Finding combinations of odd and even numbers that make given numbers or determining that these combinations are not possible Making and justifying generalizations about adding even and odd numbers   Computational Fluency- Knowing addition combinations to 10 + 10   Relating unknown combinations to known combinations Developing and achieving fluency with the plus 9 and remaining combinations   Whole-Number Operations- Making sense of and devloping strategies to solve addition and subtraction problems with totals to 100   Subtracting amounts from 100 Visualizing, retelling and modeling the action of addition and subtraction strategies Developing efficient methods for adding, subtracting and notating strategies Solving subtraction problems by subtracting in parts Solving subtraction problems by adding up or subtracting back to find the difference Comparing problems in which the amount subtracted differs by 1 Adding 2-digit numbers by keeping one number whole Adding 2-digit numbers by adding tens and ones Noticing what happens to place value when two 2-digit numbers with a sum over 100 are combined   Whole-Number Computation- Using manipulatives, drawings, tools and notation to show strategies and solutions   Using cubes and the number line to show how addition combinations are related Representing the action of subtraction and addition situations using notation (-, +, =)

Measuring Length and Time  Content   Skills  Linear Measurement - Understanding length   Comparing two lengths Using direct and indirect comparison to identify equal lengths Identifying length and width as different dimensions of an object   Linear Measurement - Using linear units   Iterating units to measure length Estimating and calculating length using units that are related by a 2:1 ratio Identifying strategies for accurate measurement Considering sources of measurement error Understanding that different-sized units yield different counts (the smaller the unit, the higher the count) Establishing the need for and using a common unit in order to compare measurements Identifying and labeling partial units Recognizing that, given equal counts of two different units, the larger unit marks off a longer length   Linear Measurement - Measuring with standard units   Establishing the need for and using a standard unit of measure Creating and using a 12-inch measuring tool Iterating a 12-inch measuring tool Measuring lengths that are longer than 12 inches Using a ruler as a standard measuring tool Comparing a variety of measuring tools