• Elementary Mathematics Grade 2 Unit 2

    Subject: Mathematics
    Grade: 2 
    Timeline: 15 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:
    • Ten “ones” bundled together creates a “ten”
    • Ten “tens” bundled together created a “hundred”
    • Zero is used as a place holder in numbers that have a 0 in one or more digits
    • Numbers with more hundreds, tens, or ones means that the number is larger than the one being compared
    Competencies -Students will be able to:
    • Read and write numbers to 1,000 using  number names 
    • Read and write numbers using base-10 numerals
    • Read and write numbers to 1,000 using expanded form
    • Use zero as a place holder in numbers that include 1 or more zeros
    • Compare two or more numbers within 1,000 using <, >, or =

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

    Elements of Instruction:
    Students leaving a grade one Common Core classroom understand that two digits of a two digit number represent amounts of tens and one. They understand special cases such as:  10 can be thought of as a bundle of ten ones-called a “ten”, the numbers from 11-19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones, the numbers 10, 20, 30, 40, 50, 60, 70, 80, or 90 refer to one, two, three, four, five, six, seven, eight, or nine tens.  They can also compare two digit numbers based on meanings of tens and ones digits, recording the results of comparisons using <, >, or =.

    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.  These games are foundational for this unit and should be used with students who are struggling with these foundations.
    • Monster Squeeze(Reading and comparing numbers)
    • High Low (Reading numbers; counting; comparing numbers)
    • More or Less (Counting; Comparing numbers using more and  less
    • Number Grid Game (Counting by 1s and 10s; navigating a number grid
    • Teen Frame (Counting, representing, and comparing numbers to 20)
    • Top It (Reading and comparing number 1-20)

    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: 
    • Digit Game
    • Base-10 Exchange
    • Top-It (with relation symbols)
    • Money Exchange Game.