• Elementary Mathematics Grade 3 Unit 2

    Subject: Mathematics
    Grade: 3 
    Timeline: 15 days
    Unit 2 Title: Introduction to Properties of Multiplication and Division (0-5)

    Unit Overview: 
    This unit will give the opportunity for students to build a conceptual understanding of multiplication and its relationship to Division.  There is an emphasis on equal groups, building arrays, and using multiplication diagrams to solve and create problems.  Students will also be introduced to properties in the context of multiplication.

    Unit Objectives:
    At the end of this unit, all students must understand that multiplication is based on repeated addition of equal groups. Their understanding will be demonstrated through repeated addition, number models, building arrays, using multiplication diagrams, and using this understanding of multiplication to understand equal sharing and equal groups related to division. They also need to solve and create number stories using multiplication and division.  Students will also be expected to solve two step problems.  

    Focus Standards:
    PA.CCSS.Math.Content.CC.2.2.3.A.1 Represent and solve problems involving multiplication and division. (3.OA.1, 3.OA.2, 3.OA.3)
    PA.CCSS.Math.Content.CC.2.2.3.A.2  Understand properties of multiplication and the relationship between multiplication and division. (3.OA.5, 3.OA.6)
    PA.CCSS.Math.Content.CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic. (3.OA.9)

    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:
    • Multiplication is the same as repeated addition
    • Division is equal sharing
    • Multiplication and division are inversely related
    Competencies -Students will be able to:
    • Build arrays with equal groups
    • Solve division problems by equally sharing
    • Solve and model division and multiplication number story word problems with equal sharing and equal grouping
    • Solve multiplication and division related fact problems 

    • Unit 2 Progress Check
    • Daily RSA

    Elements of Instruction:
    Students leaving a second grade Common Core Classroom should have an understanding of equal groups and be able to build arrays. They also should be able to understand and demonstrate the concept of repeated subtraction.

    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:

    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:
    • Name That Number
    • Beat the Calculator
    • Array Bingo
    • Division Top-It
    • Division Arrays