# q2-day46geometry-understandinghierarchydiagram

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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
 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

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

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

Hierarchy Diagram

Wake County Public School System, 2012

Polygon

Triangle
Triangle
Rectangle                                               Acute
Triangle              Obtuse
Square                                                           Triangle

Rhombus
Pentagon

Wake County Public School System, 2012

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