• Elementary Mathematics Grade 2 Unit 2


    Subject: Mathematics
    Grade: 2 
    Timeline: 11 days
    Unit 2 Title: Place Value

    Unit Overview: 
     
    This unit will give the opportunity for students to explore place value. Students will be exposed to place value within 1000. Students will compare 2 and 3 digit numbers using <, >, and =. Students will make exchanges; ones for tens and tens for hundreds.

    Unit Objectives:
     
    At the end of this unit, all students must understand that ten is a bundle of ones and one hundred is ten bundles of ten.  Students must demonstrate knowledge of how numbers increase within 1,000 and make exchanges within 1,000.  Students will be able to use 0 as a place holder.  Students will be able to use <, >, and = to compare numbers. 

    Focus Standards:
              
    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, 2.NBT.4)
    PA.CCSS.Math.Content.CC.2.1.2.B.2 Use place value concepts to read, write and skip count to 1000. (2.NBT.2, 2.NBT.3)

    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 look for an entry point to its solution.  They then plan a solution pathway rather than jumping into a solution attempt.  They monitor and evaluate their progress and change course, if needed.  Students might rely on using concrete objects or pictures to help conceptualize and solve a problem.  They then check their answers to problems using a different method, and continually ask themselves, “Does this make sense?”  These students can also 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.   
     
    #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 symbols they choose, are careful about specifying units of measure, calculate accurately and efficiently, and express numerical answers with a degrees of precision appropriate for the problem context.
     
    #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:
    • What the value of a digit in the ones place is equal to
    • What the value of a digit in the tens place is equal to
    • What the symbols <, >, and = mean
    Competencies -Students will be able to:
    • State the values of each digit in a two digit number
    • Use symbols to compare two 2-digit numbers

    Assessments:
    • Unit 2 Progress Check
    • Exit Slips (Quizzes)
    • Daily RSA

    Elements of Instruction:
     
    First grade common core state standards for numbers and operations in base-10; students will demonstrate that a bundle of ten ones is a group called a ten.  Students will understand the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens and zero ones.  Expect to use differentiation options for students who may not have mastery of these skills from first grade.  Students will compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols <, >, and =.

    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 to Games. 

    Interdisciplinary Connections:
    • Daily Routines
    • Related Literature Books

    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 two include: 
    • Number Grid Game
    • Base-10 Exchange
    • Addition Top-It