• Elementary Mathematics Grade 2 Unit 10

    Subject: Mathematics
    Grade: 2 
    Timeline: 15 Days
    Unit 10 Title: Application of Addition Strategies

    Unit Overview: 
    In this unit, students apply knowledge of several strategies for solving word problems. Unit 9 has three main areas 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.2.4.2.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. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and 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 the 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. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

    #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, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

    #6 Attend to precision. 
    Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

    #7 Look for and make use of structure. 
    Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have.

    Concepts - Students will know:
    • How to add numbers using partial sums
    • To use addition to solve numbers stories
    Competencies -Students will be able to:
    • Solve multi-digit addition problems using partial sums addition
    • Use addition strategies to solve number stories

    • Unit 9 Progress Check and Exit Slips (Quizzes)
    • Daily RSA

    Elements of Instruction:
    Expect to use differentiation options for students who may not have mastery of these skills. First Grade Common Core Standards for Number and Operations in Base 10 states that when given a two-digit number, student can mentally find 10 more or 10 less than the number, without having to count; and explain the reasoning used. First Grade Common Core 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.

    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.

    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 nine include:  
    • Money Exchange
    • Addition Spin
    • Pick a Coin
    • Hit the Target