Math Curriculum for Grade 2

All schools in the Diocese of Albany now use the latest edition of the Archdiocesan Essential Learnings for Mathematics.

At St. Thomas we have math textbooks to use as a resource, but they won't dictate what we teach or when we teach it.

**All information is quoted from The latest edition of the Archdiocesan Essential Learnings for Mathematics. It was revised in accordance with the 2005 NYS Mathematics standards. The goal of mathematics instruction is to provide students with the knowledge and understanding of the mathematics necessary to function in a world that is dependent on the application of mathematics. Instructionally, this goal translates into three components:

* conceptual understanding

* procedural fluency

* problem solving

As students progress from pre-K through grade 8, conceptual understanding, procedural fluency, and problem solving are represented as process strands and content strands. These strands help to define what students should know and be able to do as a result of their engagement in the study of mathematics.

The content strands explicitly describe the content that students should learn. This content should be taught in an integrated fashion, allowing students to see how mathematical knowledge is related, not only within mathematics, but also to other disciplines and the real world as well.

This year second grade will again be using the suggested **Enhanced Content Curriculum** to determine the sequence of instruction as opposed to the order of content that is in our textbook. I will keep families updated through e-mail about what we are currently studying. The index to the Second Grade site also will have updated information.

Unit Plans - 2007

- divided into four quarters

2.N.1Skip count to 100 by 2's, 5's, 10's

2.N.2Count back from 100 by 1's, 5's, 10's using a number chart

2.N.5Compare and order numbers to 100

2.N.8Understand and use the commutative property of addition

NB:The commutative property of addition states that the sum of two terms is unaffected by the order in which the terms are added; i.e., the sum remains the same.

For example, 3 + 5 = 5 + 3

2.N.9Name 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)

2N.10 Use and understand verbal ordinal terms

2.N.12 Use zero as the identity element for addition

2.N.14 Use concrete materials to justify a number as odd or even

2.N.16 Use a variety of strategies to solve addition and subtraction problems using one-digit #s

2.N.17 Demonstrate fluency and apply addition and subtraction facts up to and including 20

2.N.22 Estimate the number in a collection to 100 and then compare by counting the actual items in the collection

2.A.1Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 50

2.A.2Describe and extend increasing or decreasing (+,-) sequences and patterns (numbers or objects up to 50)

2.G.2Identify and appropriately name two-dimensional shapes: circle, square, rectangle, and triangle (both regular and irregular)

2.G.4Group objects by like properties

2.M.9 Tell time to the nearest hour using both digital and analog clocks

2.S.1 Formulate questions about themselves and their surroundings

2.S.4Compare and interpret data in terms of describing quantity (similarity or differences)

2.N.2Count back from 100 by 1's, 10's using a number chart

2.N.6Develop an understanding of the base ten system:

10 ones = 1 ten10 tens = 1 hundred 10 hundreds = 1 thousand

2.N.7Use a variety of strategies to compose and decompose two-digit numbers

NB:Decompose is a process to break a number into smaller units to simplify computation.

For example, 36 = 30 + 6.

Compose is part of a process of grouping decomposed numbers that are easier to compute.

For example. 36 = 30 + 6

+ 23 = 20 + 3

50 + 9

59

2.N.11 Read written ordinal terms (first through ninth) and use them to represent ordinal relations

2.N.13 Recognize the meaning of zero in the place value system (0-100)

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)

2.N.16 Use a variety of strategies to solve addition and subtraction problems using one- and two-digit numbers with and without regrouping (partial - introduction)

2.N.19 Use compensation to add 2-digit numbers

NB: Compensation is a strategy that can be used for addition which usually involves increasing one addend while decreasing the other by the same amount. For example, when adding 46 + 38, add 2 to 38 to make 40 and take two away from 46, resulting in 44; then add 40 +44 to get 84.

2.A.1Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100

2.A.2Describe and extend increasing or decreasing (+,-) sequences and patterns (numbers or objects up to 100)

2.G.2Identify and appropriately name two-dimensional shapes: circle, square, rectangle, and triangle (both regular and irregular)

2.G.3Compose (put together) and decompose (break apart) two-dimensional shapes

2.M.9 Tell time to the half hour using both digital and analog clocks

2.S.2Collect and record data (using tallies) related to the question

2.S.3Display data in pictographs and bar graphs/pie charts using concrete objects or a representation of the object

NB:A pictograph is a graph that uses pictures or symbols to represent data. An accompanying key indicates the value associated with each picture or symbol. A bar graph is a graph that uses horizontal or vertical bars to display data.

example of pictograph - 1 car picture = 5 cars

A Pie (circle) graph is a graph in which the data is represented by sectors of a circle. The total of all the sectors should be 100% of the data.

2.N.6Develop an understanding of the base ten system:

10 ones = 1 ten10 tens = 1 hundred 10 hundreds = 1 thousand

2.N.14 Use concrete materials to justify a number as odd or even

2.N.16 Use a variety of strategies to solve addition and subtraction problems using one- and two-digit numbers with and without regrouping

2.N.18 Use doubling to add 2-digit numbers

2.N.19 Use compensation to add 2-digit numbers (described in 2nd quarter)

2.A.1Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100

2.A.2Describe and extend increasing or decreasing (+,-) sequences and patterns

(numbers or objects up to 100)

2.G.1Experiment with slides, flips, and turns to compare two-dimensional shapes

NB:A slide is a transformation where every point moves the same distance in one or two directions within the plane. A flip (reflection) is the figure formed by flipping a geometric figure over a line to obtain a mirror image. A turn (rotation) is a transformation that results when a geometric figure is rotated around a point.

2.G.5Explore and predict the outcome of slides, flips, and turns of two- dimensional shapes

2.M.1Use non-standard and standard units to measure both vertical and horizontal lengths

NB:Examples of non-standard units might include the length of an arm, a paper clip, footprints

2.M.2 Use a ruler to measure standard units (including whole inches and whole feet)

2.M.3 Compare and order objects according to the attribute of length

2.M.6 Know and recognize coins (penny, nickel, dime, quarter) and bills ($1, $5, $10, and $20)

2.M.7Recognize the whole dollar notation as $1, etc.

2.M.8Identify equivalent combinations to make one dollar

2.M.9 Tell time to the half hour and five minutes using both digital and analog clocks

2.S.2Collect and record data (using tallies) related to the question

2.S.3Display data in pictographs and bar graphs/pie charts using concrete objects or a representation of the object

2.S.5Discuss conclusions and make predictions from graphs

2.N.3Skip count by 3's to 36 for multiplication readiness

2.N.4Skip count by 4's to 48 for multiplication readiness

2.N.6Develop an understanding of the base ten system:

10 ones = 1 ten10 tens = 1 hundred 10 hundreds = 1 thousand

2.N.16 Use a variety of strategies to solve addition and subtraction problems using one- and two-digit numbers with and without regrouping

2.N.19 Use compensation to add 2-digit numbers

2.N.20 Develop readiness for multiplication by using repeated addition

2.N.21 Develop readiness for division by using repeated subtraction, dividing objects into groups (fair share)

2.A.1Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100

2.A.2Describe and extend increasing or decreasing (+,-) sequences and patterns (numbers or objects up to 100)

2.G.6Explore line symmetry

2.M.4 Recognize mass as a qualitative measure (e.g., Which is heavier? Which is lighter?)

2.M.5Compare and order objects, using lighter than and heavier than

2.M.9 Tell time to the half hour and five minutes using both digital and analog clocks

2.S.2Collect and record data (using tallies) related to the question

2.S.3Display data in pictographs and bar graphs/pie charts

2.S.5Discuss conclusions and make predictions from graphs

Reinforce any topic requiring additional work

Problem Solving Strand - Taught throughout the year

Students will build new mathematical knowledge through problem solving

2.PS.1 Explore, examine, and make observations about a social problem or mathematical situation

2.PS.2 Interpret information correctly, identify the problem, and generate possible solutions

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

2.PS.3 Act out or model with manipulatives activities involving mathematical content from literature and/or story telling

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).

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

2P5.5Use informal counting strategies to find solutions

2.PS.6 Experience teacher-directed questioning process to understand problems

2.PS.7 Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking

2.PS.8Use manipulatives (e.g., tiles, block&) to model the action in problems

2.PS.9 Use drawings/pictures to model the action in problems

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

2.PS.10 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.

2.RP.1 Understand that mathematical statements can be true or false

2.RP.2 Recognize that mathematical ideas need to be supported by evidence

Students will make and investigate mathematical conjectures.

2.RP.3 Investigate the use of knowledgeable guessing as a mathematical tool

2.RP.4 Explore guesses, using a variety of objects and manipulatives Students will develop and evaluate mathematical arguments and proofs.

2.RP.5 Justify general claims, using manipulatives

2.RP.6 Develop and explain an argument verbally or with objects

2.RP.7 Listen to and discuss claims other students make

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

2.RP.8 Use trial and error strategies to verify claims

Communication Strand- Taught throughout the year

Students will organize and consolidate their mathematical thinking through communication.

2.CM.1 Understand how to organize their thought processes

2.CM.2 Verbally support their reasoning and answer

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

2.CM.3 Share mathematical ideas through the manipulation of objects, drawings, pictures, charts, and symbols in both written and verbal explanations

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

2.CM.4 Listen to solutions shared by other students

2.CM.5 Formulate mathematically relevant questions

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

2.CM.6 Use appropriate mathematical terms, vocabulary, and language

Connections Strand

Students will recognize and use connections among mathematical ideas.

2.CN.1Recognize the connections of patterns in their everyday experiences to mathematical ideas

2.CN.2 Understand and use the connections between ,lumbers and the quantities they represent to solve problems

2.CN.3Compare the similarities and differences of mathematical ideas

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

2.CN.4 Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas

2.CN.5 Understand meanings of operations and how they relate to one another

2.CN.6 Understand how mathematical models represent quantitative relationships

Students will recognize and apply mathematics in contexts outside of mathematics.

2.CN.7 Recognize the presence of mathematics in their daily lives

2.CN.8 Recognize and apply mathematics to solve problems

2.CN.9 Recognize and apply mathematics to objects, pictures and symbols

Representation Strand

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

2.R.1 Use multiple representations, including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations

2.R.2 Share mental images of mathematical ideas and understandings

2.R.3Use standard and nonstandard representations

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

2.R.4Connect mathematical representations with problem solving

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

2.R.5Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)

2.R.6Use mathematics to show and understand social phenomena (e,g, count and represent sharing cookies between friends)

2.R.7Use 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)

Suggested List of Mathematical Language for Grade 2

compare examine explain explore formulate

identify the problem interpretjustify

make observationsmodel using manipulatives

develop an argument explore guesses investigate

justify claims true/falseuse trial and error

formulate questions organizeshare ideas

use the language of mathematics

apply mathematics compare similarities and differences recognize patterns

understand meaning of operations understand relationships

multiple representations nonstandard representation

standard representation

collectioncommutative property of additioncompensation compose decompose division doublesdoubles minus one doubles plus one estimateeven numberfact family (related facts)

fair sharehundred chartidentity element for addition label

multiplication odd number place value regroup repeated addition repeated subtraction

two-digit numberzero as the identify element in addition

decreasing sequences equal togreater than > increasing sequences

less than <whole numbers

compose shapes decompose shapes flip (reflection) irregular shape

line symmetry properties rectangleregular shapes

slide (translation) squaretriangleturn (rotation)

dollar ($) equivalent estimate feethalf hour heavier lighter nonstandard units standard units

comparedata predict similarities/differences

talliestally mark