• Elementary Mathematics Grade 3 Unit 6


    Subject: Mathematics
    Grade: 3
    Timeline: 14 days
    Unit 6 Title: Comparing Fractions and Equivalent Fractions

    Unit Overview: 
     
    This unit will give the opportunity for students to expand on their learning of fractions from Unit 5.  There is focus on comparing fractions with like denominators OR like numerators, and identifying and creating equivalent fractions with denominators 2, 3, 4, 6, and 8. Fractions will be created with fraction bars, number lines, and visual models to conceptualize learning.  Students will apply their knowledge of fractions by working with word problems throughout the unit.

    Unit Objectives:
     
    At the end of this unit, all students must be able to identify equivalent fractions using pictures, number lines, fraction bars or other tools, and compare fractions with the same denominator or the same numerator.  

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.1.3.C.1  Explore and develop an understanding of fractions as numbers. (3.NF.1, 3.NF.2, 3.NF.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, 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:
    • Fractions show equal parts of a whole or a collection.
    • Equivalent fractions are the same size, though not necessarily the same shape.
    • Fractions can be easily compared when they have the same numerator OR the same denominator.
    Competencies -Students will be able to:
    • Identify fractions of a whole and fractions of a collection
    • Place fractions on a number line
    • Compare fractions with the same numerator OR the same denominator using > or <.
    • Identify and generate simple equivalent fractions using the denominators 2, 3, 4, 6, and 8.
    • Solve number stories involving fractions.

    Assessments:
    • Unit 8 Assessment
    • Daily RSA

    Elements of Instruction:
     
    Students leaving a second grade Common Core Classroom have knowledge of measuring and estimating lengths using inches, feet, centimeters and meters.

    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.

    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.
    Games for unit eight include: 
    • Equivalent Fractions Game
    • Fraction Top-It