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					                           Mathematics Alignment Lesson
                            Grade 5 Quarter 2 Day 46

       Common Core State Standard(s)                                     Alignment Lesson
                                                                 Understanding Hierarchy Diagrams
   5.G.3 Understand that attributes belonging to
   a category of two-dimensional figures can        1. Display and distribute Transparency/Blackline Master,
   also belong to all subcategories of that             “Hierarchy Tree,” and follow the instructions on Teacher
   category. For example, all rectangles have           Guide, “Hierarchy Tree.”
   four right angles and squares are rectangles,
   so all squares have four right angles.           2. Ask students if there are any circumstances where a specific
                                                        type of rhombus could also be classified as a rectangle. The
   5.G.4 Classify two-dimensional figures in a          answer is yes because a square is a specific type of rhombus
   hierarchy based on properties.                       that is also a rectangle. Explain that the hierarchy tree
                                                        doesn’t always accurately show the relationship between
                                                        shapes, because in the hierarchy tree, the rectangle and
    Standards for Mathematical Practice                 rhombus have two independent branches. Sometimes the
                                                        relationships between shapes can be shown in a better way.
   Standard 1 – Make sense of problems and
                persevere in solving them.          3. Display and distribute Transparency/Blackline Master,
   Standard 3 - Construct viable arguments and          “Hierarchy Diagram.” Have students work in pairs to place
                critique the reasoning of others.       the names of all the figures listed in the hierarchy tree into the
   Standard 6 - Attend to precision.                    hierarchy diagram. Remind students to think carefully about
                                                        the definitions as they classify and place the name of each
                                                        figure.
               Materials Needed:
                                                    4. Engage students in Math Talk about their thinking and
      Transparencies/Blackline Masters,                reasoning for placing the shapes into the hierarchy diagram.
          “Hierarchy Tree,” “Hierarchy
             Diagram”                               5. Instruct pairs of students to create a different hierarchy tree
                                                        with at least 10 different polygons. The diagram they create
                                                        can include some of the same figures as the hierarchy tree
                                                        discussed earlier today, but it must include some different
                   Assessment                           ones as well. Encourage students to think about classifying
                                                        figures based on different sets of attributes (i.e. symmetry, sets
   Informal:                                            of parallel sides, types of angles). Each student will need a
    Hierarchy diagrams completed by pairs              copy of his/her hierarchy tree to complete the homework.
    Hierarchy trees created by pairs
    Assess student reasoning through
                                                    6. Invite pairs of students to share their hierarchy trees and
                                                        discuss similarities and differences between the different trees
       explanations given during math talk.
                                                        created.

                                                    7. For homework, students should create a hierarchy diagram
                                                        using the hierarchy tree they created with their partners. At
                   Homework                             the beginning of class tomorrow, students will compare their
      Using the hierarchy tree you created             diagrams with their partners’ diagrams, so instruct students not
       with your partner, create a hierarchy            to share their thinking with their partners until then.
       diagram that shows the relationships
       among shapes. Remember not to
       compare diagrams or share your thinking
       with your partner until you are instructed
       to do so during class tomorrow.                    Source: Teacher Created from NC DPI
                                                          Unpacking Document


Wake County Public School System, 2012
                       Teacher Guide     Grade 5   Day 46   Standards 5.G.3, 5.G.4



                                            Vocabulary


 Acute Triangle: a triangle with three acute angles


 Obtuse Triangle: a triangle with one obtuse angle


 Pentagon: a polygon with five sides


 Polygon: a closed plane figure made up of three or more straight line segments for its
          sides


 Quadrilateral: a polygon with four sides


 Rectangle: a parallelogram with four right angles


 Rhombus: a parallelogram with all equal sides


 Right Triangle: a triangle with one right angle


 Square: a parallelogram with four equal sides and four right angles


 Triangle: a polygon with three sides




Wake County Public School System, 2012
                       Teacher Guide     Grade 5     Day 46    Standards 5.G.3, 5.G.4

                                         Hierarchy Tree
1. Ask students to study the arrangement of the geometric figures in the diagram. Ask the
    following questions:
         What do you notice about the shapes as you move down the tree?
            The definitions become narrower the lower you move; the definitions of the shapes at the top
            are broader.
         Why is there an arrow pointing from quadrilateral to rectangle?
            A rectangle is a more specific quadrilateral.
         Why is there an arrow pointing from quadrilateral to rhombus?
            A rhombus is a more specific quadrilateral.
         Where on the tree would you add acute triangle?
            under triangle
         What attributes of these figures have been used to create this hierarchy diagram?
            number of sides, lengths of sides, number and types of angles
2. Ask students to independently add the following figures to the hierarchy tree: acute triangle,
    pentagon, square, obtuse triangle, right triangle. Circulate and make observations and
    conjectures about students’ thought processes in order to guide your questioning during Math
    Talk.
3. Once all students have had opportunity to complete their diagrams, engage students in Math
    Talk about their placements. Use the key below and the definitions of the figures to guide
    students toward appropriate placements. The placement of the square should promote a
    lengthy discussion. Since a rectangle is a quadrilateral with four right angles and a rhombus is
    a quadrilateral with four equal sides, a square is both a rectangle and a rhombus and arrows
    should lead from both rhombus and rectangle to square. This discussion surrounding the
    square also leads to the creation of the next hierarchy diagram.
                                                   Polygon




                             Quadrilateral                             Triangle          Pentagon




                   Rectangle              Rhombus            Acute                Obtuse
                                                            Triangle              Triangle
                                                                     Right
                                                                    Triangle

                                Square
Wake County Public School System, 2012
              Transparency/Blackline Master   Grade 5   Day 46    Standards 5.G.3, 5.G.4

                                                                 Name: ________________________
                                                                  Date: ________________________


                                         Hierarchy Tree


                                              Polygon




               Quadrilateral                                          Triangle




   Rectangle                     Rhombus




Wake County Public School System, 2012
                                   Transparency/Blackline Master   Grade 5   Day 46   Standards 5.G.3, 5.G.4

                                                                                                       Name: ________________________
                                                                                                        Date: ________________________

                                                       Hierarchy Diagram




Wake County Public School System, 2012
                                         Answer Key    Grade 5   Day 46   Standards 5.G.3, 5.G.4

                                                      Hierarchy Diagram
                                                         Answer Key




Wake County Public School System, 2012
                                          Answer Key   Grade 5   Day 46   Standards 5.G.3, 5.G.4



                                                       Polygon

                                                                            Triangle
                             Quadrilateral                                                          Right
                                                                                                   Triangle
                       Rectangle                                               Acute
                                                                              Triangle              Obtuse
                                   Square                                                           Triangle



                                         Rhombus
                                                                                            Pentagon




Wake County Public School System, 2012

				
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