Download Common Core State Standard(s)

Mathematics Alignment Lesson
Grade 5 Quarter 2 Day 46
Common Core State Standard(s)
5.G.3 Understand that attributes belonging to
a category of two-dimensional figures can
also belong to all subcategories of that
category. For example, all rectangles have
four right angles and squares are rectangles,
so all squares have four right angles.
5.G.4 Classify two-dimensional figures in a
hierarchy based on properties.
Standards for Mathematical Practice
Standard 1 – Make sense of problems and
persevere in solving them.
Standard 3 - Construct viable arguments and
critique the reasoning of others.
Standard 6 - Attend to precision.
Materials Needed:

Transparencies/Blackline Masters,
“Hierarchy Tree,” “Hierarchy
Diagram”
Assessment
Informal:
 Hierarchy diagrams completed by pairs
 Hierarchy trees created by pairs
 Assess student reasoning through
explanations given during math talk.
Alignment Lesson
Understanding Hierarchy Diagrams
1. Display and distribute Transparency/Blackline Master,
“Hierarchy Tree,” and follow the instructions on Teacher
Guide, “Hierarchy Tree.”
2. Ask students if there are any circumstances where a specific
type of rhombus could also be classified as a rectangle. The
answer is yes because a square is a specific type of rhombus
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
rhombus have two independent branches. Sometimes the
relationships between shapes can be shown in a better way.
3. Display and distribute Transparency/Blackline Master,
“Hierarchy Diagram.” Have students work in pairs to place
the names of all the figures listed in the hierarchy tree into the
hierarchy diagram. Remind students to think carefully about
the definitions as they classify and place the name of each
figure.
4. Engage students in Math Talk about their thinking and
reasoning for placing the shapes into the 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
ones as well. Encourage students to think about classifying
figures based on different sets of attributes (i.e. symmetry, sets
of parallel sides, types of angles). Each student will need a
copy of his/her hierarchy tree to complete the homework.
6. Invite pairs of students to share their hierarchy trees and
discuss similarities and differences between the different trees
created.
7. For homework, students should create a hierarchy diagram
Homework

Using the hierarchy tree you created
with your partner, create a hierarchy
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.
Wake County Public School System, 2012
using the hierarchy tree they created with their partners. At
the beginning of class tomorrow, students will compare their
diagrams with their partners’ diagrams, so instruct students not
to share their thinking with their partners until then.
Source: Teacher Created from NC DPI
Unpacking Document
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
Rectangle
Rhombus
Triangle
Acute
Triangle
Right
Triangle
Square
Wake County Public School System, 2012
Pentagon
Obtuse
Triangle
Transparency/Blackline Master
Grade 5
Day 46
Standards 5.G.3, 5.G.4
Name: ________________________
Date: ________________________
Hierarchy Tree
Polygon
Quadrilateral
Rectangle
Rhombus
Wake County Public School System, 2012
Triangle
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
Quadrilateral
Rectangle
Right
Triangle
Acute
Triangle
Square
Rhombus
Wake County Public School System, 2012
Triangle
Obtuse
Triangle
Pentagon