•  Second Graders will have math homework Monday-Thursday.  Please check the green homework folder for the math and the homework helper guide.

                       

    Second Grade Math Modules 1-8

    Module 1

    Sums and Differences to 100

    Module 1 sets the foundation for students to master sums and differences to 20. Students then apply these skills to fluently add one-digit to two-digit numbers through 100 using place value understanding, properties of operations, and the relationship between addition and subtraction.

    Strategies/Concepts in Module 1

    • Add and subtract like units.
    • Make a ten to add within 20 and within 100.
    • Subtract single-digit numbers from multiples of 10 within 100.
    • Take from ten within 20 and within 100.
    • Module 2
    • In Module 2, students engage in activities designed to deepen their conceptual understanding of measurement and to relate addition and subtraction to length.
    • Strategies/Concepts in Module 2
    • Addition and Subtraction of Length Units
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    • Understand concepts about the ruler.
    • Measure and estimate length using different measurement tools.
    • Measure and compare lengths using different length units.
    • Relate addition and subtraction to length.

    Module 3

    Place Value, Counting, and Comparison of Numbers to 1,000

    In Module 3, students will expand their skills with and understanding of units by bundling ones, tens and hundreds up to a thousand using counting sticks and disks.  Instruction includes a great deal of counting; by ones, tens, and hundreds.

    Strategies/Concepts include:

    • Forming Base Ten units of ten, a hundred, and a thousand.
    • Understanding Place Value Units of one, ten and a hundred.
    • Three-digit numbers in unit, standard, expanded, and word forms.
    • Modeling Base Ten numbers within 1,000 with money.
    • Modeling numbers within 1,000 with place value disks.
    • Comparing two, and three digit numbers.
    • Finding 1, 10, and 100 more or less than a number.

     

    Module 4

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      Module 4 is devoted to three major areas of work. The first two are building fluency in two-digit addi-tion and subtraction within 100 and applying that fluency to one- and two-step word problems of vary-ing types within 100. Students’ increasing fluency with calculations within 100, begun in Grade 1, allows word problems to transition from being mere contexts for calculation into opportunities for students to see and analyze the relationships between quantities. Daily application problems and specific lessons in Topics A, C, and F provide students with guided and independent practice as they negotiate a variety of problem types, including the more complex comparison problems. Note that most two-step problems involve single-digit addends, and do not involve the most difficult comparison problem types.

      The third major area of work is developing students’ conceptual understanding of addition and subtrac-tion of multi-digit numbers within 200 as a foundation for work with addition and subtraction within 1000 in Module 5.

      Module 5
                   

    In Module 5, students build upon their mastery of renaming place value units and extend their work with conceptual understanding of the addition and sub-traction algorithms to numbers within 1,000, always with the option of modeling with materials or drawings. Throughout the module, students continue to focus on strengthening and deepening conceptual understanding and fluency.

    Topic A focuses on place value strategies to add and subtract within 1,000. Students relate 100 more and 100 less to addition and subtraction of 100. They add and subtract multiples of 100, including counting on to subtract (e.g., for 650 – 300, they start at 300 and think, "300 more gets me to 600, and 50 more gets me to 650, so… 350"). Students also use simplifying strategies for addition and subtraction: they extend the make a ten strategy to make a hundred, mentally decomposing one addend to make a hundred with the other (e.g., 299 + 6 becomes 299 + 1 + 5, or 300 + 5, which equals 305) and use compensation to subtract from three-digit numbers (e.g., for 376 – 59, add 1 to each, 377 – 60 = 317). The topic ends with students sharing and critiquing solution strategies for addition and subtraction problems. Throughout the topic, students use place value language and properties of operations to explain why their strategies work.

    In Topics B and C, students continue to build on Module 4’s work, now composing and decomposing tens and hundreds within 1,000. As each of these topics begins, students relate manipulative representations to the algorithm, then transition to making math drawings in place of the manipulatives. As always, students use place value reasoning and properties of operations to explain their work.

     

    Module 6

      

    Grade 2 Module 6 lays the conceptual foundation for multiplication and division in Grade 3 and for the idea that numbers other than 1, 10, and 100 can serve as units.

    In Topic A, students begin by making equal groups using concrete materials, learning to manipulate a given num-ber of objects to create equal groups (e.g., given 15 objects, they create 3 groups of 5 or 5 groups of 3), and pro-gress to pictorial representations, where they may begin by circling a group of 5 stars, adding 5 more, then add-ing 5 more. They determine the total and relate their drawings to the corresponding repeated addition number sentence (pictured below). Students calculate the repeated addition sums by adding on to the previous addends, step by step, or by grouping the addends into pairs and adding. By the end of Topic A, students are drawing ab-stract tape diagrams to represent the total and to show the number in each group as a new unit (pictured be-low). Hence, they begin their experience towards understanding that any unit may be counted, e.g., 3 dogs, 3 tens, or even 3 fives. This is the bridge between Grades 2 and 3: Grade 2 focuses on the manipulation of place value units, whereas Grade 3 focuses on the manipulation of numbers 1 through 10 as units.

    In Topic B, students organize the equal groups created in Topic A into arrays, wherein either a row or column is seen as the new unit being counted. They use manipulatives to compose up to 5 by 5 arrays one row or one col-umn at a time, and express the total via repeated addition number sentences. For example, students might ar-range one column of 5 counters, then another, and another to compose an array of 3 columns of 5, or 15 coun-ters. As they compose and decompose arrays, students create different number sentences yielding the same to-tal (e.g., 5 + 5 + 5 = 15 and 3 + 3 + 3 + 3 + 3 = 15). They find the total number of objects in each array by counting on from left to right. "Three plus 3 is 6. Six plus 3 is 9. Nine plus 3 is 12." As Topic B progresses, students move to the pictorial level to represent arrays and to distinguish rows from columns by separating equal groups horizon-tally and vertically (e.g., 3 columns of 5 or 5 rows of 3). Then they use tiles, moving them closer together in prep-aration for composing rectangles in Topic C. Topic B concludes with students using tape diagrams to represent array situations and the RDW process to solve word problems.

    In Topic C, students build upon their work with arrays to develop the spatial reasoning skills they will need in preparation for Grade 3’s area content. They use same-size squares to tile a rectangle with no gaps or overlaps and then count to find the total number of squares. After composing rectangles, students partition, or decom-pose, rectangles: first with tiles, then with scissors, and finally, by drawing and iterating a square unit. In doing so, they begin to see the row or the column as a composite of multiple squares or as a single entity, or unit, which is, in turn, part of the larger rectangle. Students further develop spatial structuring skills by copying and creating drawings on grid paper. Note that the concept of a square unit begins in Grade 3 and is not assessed in Grade 2. Throughout the topic, students relate repeated addition to the model. They are encouraged to think flexibly and to consider the many ways to construct or partition a given array. Students are not multiplying or dividing in Grade 2; rather, this topic lays the foundation for the relationship between the two operations: As equal parts can be composed to form a whole, likewise, a whole can be decomposed into equal parts.

    Topic D focuses on doubles and even numbers , thus setting the stage for the multiplication table of two in Grade 3. As students progress through the lessons, they learn the following interpretations of even numbers:

    1. . A number that occurs as we skip-count by twos, starting with the number two, is even. If we start with 3 and skip count by twos we will generate odd numbers.

    2. When objects are paired up with none left unpaired, the number is even.

    3. A number that is twice a whole number (doubles) is even.

    4. A number whose last digit is 0, 2, 4, 6, or 8 is even.

    Armed with an understanding of the term even, students learn that any whole number that is not even is called odd, and that when 1 is added to or subtracted from an even number, the resulting number is odd.

    Initially, students arrange pairs into two rows, and realize that an even number is the sum of two equal addends or a repeated sum of twos. They then write number sentences to express the even number (e.g., 2 rows of 7 can be expressed as 7 + 7 or as 2 + 2 + 2 + 2 + 2 + 2 + 2). Next, students pair objects to make groups of two with none left over, thus discovering one means of determining whether a group of objects (up to 20) has an even or odd number of members. Finally, they learn that any number up to 20 whose last digit is 0, 2, 4, 6, or 8 is even. After gaining a firm understanding of even numbers, students learn that all other whole numbers are odd. They use the previously learned rules and patterns to identify larger numbers as even or odd and to defend their reason-ing. The module concludes with an investigation of what happens when we add two even numbers, two odd numbers, or an odd number with an even number, and their relationship to repeated addition (e.g., 3 + 3 is even, but 3 + 3 + 3 is odd).

    Terminology

     

    New or Recently Introduced Terms

    Array (arrangement of objects in rows and columns)

    Columns (the vertical groups in a rectangular array)

    Even number (a whole number whose last digit is 0, 2, 4, 6, or 8)

    Odd number (a number that is not even)

    Repeated addition (e.g., 2 + 2 + 2)

    Rows (the horizontal groups in a rectangular array)

    Tessellation (tiling of a plane using one or more geometric shapes with no overlaps and no gaps)

    Whole number (e.g., 0, 1, 2, 3,…

    Familiar Terms and Symbols

    Addends

    Doubles

    Equation

    Number path

    Number sentence

    Pair

    Rectangle

    Skip-counting

    Square

    Sum

    Tape diagram

    Total

    Unit

    Suggested Tools and Representations

    Counters

    Number path

    Rectangular array

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