• Elementary Mathematics Grade 3 Unit 4


    Subject: Mathematics
    Grade: 3 
    Timeline: 18 days
    Unit 4 Title: Geometric Measurement with Area and Perimeter

    Unit Overview: 
     
    This unit will begin by giving students the opportunity to reason with shapes and their attributes. There is focus to understand shapes in different categories (rhombuses, rectangles, and others) may share attributes (have four sides), and that the shared attributes can define a larger category (quadrilaterals).  Next, the students will cover measurement using standard and metric measurements to the ¼ inch and 1 centimeter.   The students will finally move to apply their knowledge of addition and multiplication as they find the area and perimeter of various polygons. They will calculate the perimeter of polygons and will determine unknown sides of a polygon when given the perimeter.  Students will use the knowledge of perimeter and area to solve real world problems.

    Unit Objectives:
     
    At the end of this unit, all students must be able to identify polygons and their attributes.   They will be able to categorize them according to their attributes.   The students will be able to measure using centimeter to the nearest whole and inches to the nearest ¼ inch.  Finally, all students must be able to find the perimeter of a polygon, calculate the unknown side of a polygon when given the perimeter, find the area of a polygon by counting square units, find the area of a rectangle by using multiplication and solve real world problems by using knowledge of perimeter and area.

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.3.3.A.1 Identify, compare, and classify shapes and their attributes. (3.G.1)
    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.4) 
    PA.CCSS.Math.Content.CC.2.4.3.A.5 Determine the area of a rectangle and apply the concept to multiplication and to addition. (3.MD.6, 3.MD.7)
    PA.CCSS.Math.Content.CC.2.4.3.A.6 Solve problems involving perimeters of polygons and distinguish between linear and area measures. (3.MD.5, 3.MD.8)
     

    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:
    • Perimeter is the distance around, or boundary of a figure.
    • Area is the space that is inside a polygon.
    • Area is measured in square units.
    • Multiplication is a strategy that is used to determine the area of a figure.
    • Length can be measured in standard or metric measurements.
    • Understand shapes belong to different categories.
    • How to recognize examples of polygons.
    Competencies -Students will be able to:
    • Calculate the perimeter of a polygon
    • Determine the area of a shape by decomposing units
    • Calculate the area by counting unit squares
    • Calculate the area by using multiplication
    • Find missing side lengths when given the area or perimeter and one of the sides.
    • Solve real world problems with perimeter and area
    • Measure lengths to the nearest whole centimeter and nearest quarter inch
    • Draw polygons
    • Explain the shared attributes for each polygon
    • Categorize shapes with shared attributes
    • Solve real world problems with perimeter and area

    Assessments:
    • Unit 4 Assessment
    • Daily RSA

    Elements of Instruction:
     
    Students leaving a second grade Common Core classroom have learned to tell time within 5 minutes using am and pm. They have no experience with weight and volume.

    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:
     
    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 four include:
    • Centimeter Ruler in Resources
    • Polygon Cards
    • Centimeter Grid Paper
    • Geometry Detective