• Elementary Mathematics Grade 3 Unit 7


    Subject: Mathematics
    Grade: 3
    Timeline: 18 days
    Unit 7 Title: Representing and Interpreting Data

    Unit Overview: 
     
    The unit focuses on data and money.  Tally charts, bar graphs, pictographs and line plots will be analyzed and constructed.  The students will conduct surveys and complete a bar graph project. Students will write and solve problems about data representation.  Students will count, compare, and make change for amounts of money, and estimate money amounts.

    Unit Objectives:
     
    At the end of this unit, all students will be able to conduct a survey and create a tally chart, bar graph, and pictograph based on the results of the survey.  They will be able to interpret and create line plots.  Lastly, they will need to ask questions about their graphs and be able to answer those questions.  The Common Core Standards require students to the students to solve one- and two-step “how many more” and “how many less” problems using information presented in a scaled bar graph.  Students must be able to count and compare coins and bills through $5.00, make change using a collection of coins and bills, with no more than $2.00 change given, and round amounts of money to the nearest dollar.

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.4.3.A.4  Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs.  (3.MD.3)
    PA.CCSS.Math.Content.CC.2.4.3.A.3  Solve problems and make change using a combination of coins and bills. 

    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, the ability to decontextualize-to abstract the 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 contextualize-to pause as needed to during the manipulation process in order to probe into the referents for the symbols involved.
     
    #3 Construct viable arguments and critique the reasoning of others.  
     
    Mathematically proficient students understand and use states assumptions, definitions, and previously established results in constructing arguments.  They make a statement that they believe to be true but not yet proved and then build a progression of statements to explore its truth.  They justify their conclusions, communicate them to others and respond to the arguments of others.  Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.  
     
    #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 use clear definitions in discussions with others and in their own reasoning.  They state the meaning of the symbols they choose, including the equals sign, consistently and appropriately.  They calculate accurately and efficiently and give carefully formulated explanations to each other.
     
    #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. 
     
    # 8 Look for and express regularity in repeated reasoning.
     
    Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. They continually evaluate the reasonableness of their intermediate results.

    Concepts - Students will know:
    • Tally charts, pictographs, bar graphs, and line plots are used to represent data
    • Information can be transferred from one type of representation to another
    • Different coins have different values
    Competencies -Students will be able to:
    • Describe and compare information from various data representation
    • Collect, organize, and display data
    • Ask and answer questions about data
    • Compare amounts of money
    • Solve number stories about money
    • Make change for a given amount of money

    Assessments:
    • Unit 7 Assessment
    • Daily RSA
    • Graphing Project

    Elements of Instruction:
     
    Students leaving a second grade Common Core classroom have drawn picture graphs and bar graphs with a single-unit scale. They have done simple put-together, take-apart, and compare problems using information from a bar graph.  Second graders have represented equivalent forms of the same number up to 500, using pictures and concrete objects including coins.

    Differentiation:
     
    Each lesson has differentiation options for each portion of the lesson.  

    Interdisciplinary Connections:
     
    None

    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.  
    Resources for unit seven include: 
    • Bar Graph Project with Rubric
    • Spinning for Money Directions and Spinner
    • Coin Top-it Directions and Cards