• Elementary Mathematics Grade 4 Unit 6


    Subject: Mathematics
    Grade: 4 
    Timeline: 13 days
    Unit 6 Title: Geometry II

    Unit Overview: 
     
    This unit will give students the opportunity to take another look at Geometry; with an emphasis on identifying angles, drawing angles, and measuring angles.  Students will be using full-circle protractors to measure and draw angles. Students will revisit acute, obtuse, straight, right, and reflex angles. Students will be introduced for the first time to complementary and supplementary angles.  Students will review various concepts of graphs that were fully developed in third grade. 

    Unit Objectives:
     
    At the end of this unit, students must be able to use a full-circle and half-circle protractor to measure and draw angles.  They must be able to classify angles – acute, obtuse, right, straight, and reflex.  Students will also incorporate their developed knowledge of computation and angles to identify angle measures of complementary and supplementary angles. Finally, students will briefly review bar graphs, line graphs, and pictographs—concepts that were studied in third grade.   

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.4.4.A.6 Measure angles and use properties of adjacent angles to solve problems. (4.MD.6, 4.MD.7)

    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 looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” 
     
    #4 Model with mathematics.  
     
    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.  
     
    #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, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course 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 the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. 

    Concepts - Students will know:
    • Angles have properties
    • Angles can be measured
    • Angles are named for their measurements 
    Competencies -Students will be able to:
    • Name the properties of angles
    • Use a protractor to measure angles
    • Name the type of angles based upon measurements

    Assessments:
    • Unit 6 Assessment
    • Daily RSA
    • Optional Quizzes (3)

    Elements of Instruction:
     
    Learners in 4th grade will extend their understanding of angles from third grade by learning how to use and measure with a protractor.        

    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:
    • Mental Math and Math message routines

    Additional Resources / Games:
    Student will play various games to enhance their abilities to construct and measure angles.  These games include:
    • Angle Tangle
    • Angle Race