• Elementary Mathematics Grade 2 Unit 8


    Subject: Mathematics
    Grade: 2 
    Timeline: 11 days
    Unit 8 Title: Addition, Algorithms, and Strategies

    Unit Overview: 
     
    In this unit, addition and subtraction number stories are used as a vehicle for developing mental arithmetic skills. The unit ends and with work on pencil-and-paper strategies. Unit 6 has three main area of focus:  to solve number stories, to develop strategies for adding 2- and 3- digit numbers, and to demonstrate, describe and apply change, comparison, and parts-and-total situations.

    Unit Objectives:
     
    At the end of this unit, all students must be able to use addition within 100 to solve one- and two- step word problems by developing strategies of counting up, combining groups (ones, tens, etc.) separately, and adjusting and compensating.

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.2.2.A.2 Use mental strategies to add and subtract within 20. (2.OA.1)
    PA.CCSS.Math.Content.CC.2.1.2.B.1 Use place value concepts to represent amounts of tens and ones and to compare three digit numbers. (2.NBT.1)
    PA.CCSS.Math.Content.CC.2.1.2.B.3 Use place value understanding and properties of operations to add and subtract within 1000. (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9)
    PA.CCSS.Math.Content.CC.2.4.2.A.3 Solve problems using coins and paper currency with appropriate symbols. (2.MD.8)

    Mathematical Practice Standards:  
     
    #1  Make sense of problems and persevere in solving them.  
     
    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution  They analyze givens, constraints, relationships, and goals.  They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.  Proficient students check their answers to problems using a different method.  They continually ask themselves, “Does this make sense?”  They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
     
    #2  Reason abstractly and quantitatively.  
     
    Mathematically proficient students make sense of quantities and their relationships in problem situations.  They bring two complementary abilities to bear on problems involving quantitative relationships; the ability to decontextualize – to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents – and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for symbols involved.  Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
     
    #4  Model with mathematics.  
     
    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation.   
     
    #5  Use appropriate tools strategically.
     
    Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, or a calculator. Proficient students are sufficiently familiar with tools appropriate for their grade to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.

    Concepts - Students will know:
    • Addition Algorithms and Strategies
    Competencies -Students will be able to:
    • Use addition within 100 to solve one- and two- step word problems.
    • Develop strategies of counting up, combining groups (ones, tens, etc.) separately, adjusting and compensating to solve one- and two- step word problems.

    Assessments:
    • Unit 6 Progress Check
    • Daily RSA

    Elements of Instruction:
     
    First Grade Common Core State Standards for Number and Operations in Base 10 states that when give a two-digit number, student can mentally find 10 more or less than the number, without having to count; and explain the reasoning used.  First Grade Common Core State Standards for Operations and Algebraic Thinking also states that the student can use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent a problem.

    Differentiation:
     
    Each lesson has differentiation options for each portion of the lesson. Additional differentiation options are listed with directions and student masters in the Teacher’s Guide. These games are foundational for this unit and should be used with students who are struggling with these foundations.  Games include:
    • Domino Top-It (Practice addition facts with comparing sums)
    • Addition Card Draw (Practice adding 3 numbers less than 20
    • Animal Weight Top-It (Practice adding and comparing numbers)
    • Basketball Addition (Practice adding 3 or more 1-digit and 2-digit numbers

    Interdisciplinary Connections:
    • Program related literature books and daily math routines.

    Additional Resources / Games:
     
    Students will play a variety of games that directly support the content of the lesson and the overall goals for the unit. Games for unit six include:
    • Hit the Target
    • Addition Top-It
    • Fact Extension Game
    • Three Addends
    • Name That Number