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Differentiated Instruction &
Understanding By Design
Lesson Plan Format
Title: Geometry of Polygons
Subject Matter Emphasis and Level: Math-6th grade
Author: Kristie Vanden Hoek
School District: Mt. Vernon Middle School
Email: [email protected]
Brief Description of the Lesson/Unit:
In this unit, students learn to describe different kinds of lines and angles. They also learn
to measure the size of angles using a protractor. They learn to classify triangles by the
measure of their angles and by the lengths of their sides. They also learn to classify
polygons and quadrilaterals. Students investigate polygons whose shapes consist of
repeated patterns. They examine figures that are flipped over a line, rotated around a
point, and slide to a new position.
SD Content Standards:
Students are able to identify and describe the characteristics of triangles and
quadrilaterals.
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Identify and describe similarities and differences of triangles:
Scalene
Isosceles
Equilateral
Right
Acute
Obtuse
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Identify and describe similarities and differences of quadrilaterals:
Trapezoid
Parallelogram
Rectangle
Rhombus
Square
Students are able to identify and describe angles.
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Identify and describe differences of angles:
Acute
Obtuse
Right
Students are able to use basic shapes to demonstrate geometric concepts.
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Demonstrate lines of symmetry.
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Use basic shapes to demonstrate congruency (triangle, rectangle, square,
parallelogram).
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Use basic shapes to demonstrate perpendicular lines (triangle, rectangle, square,
trapezoid).
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Use basic shapes to demonstrate parallel lines (rectangles, squares,
parallelograms).
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Identify a reflection.
Stage 1: Identify Desired Results
1. What enduring understandings are desired?
Students will know how to classify polygons by their geometric name, angles, and
lines. They will also be able to tell the different transformations a polygon can do
from one location to another.
2. What essential questions will guide this unit and focus
teaching/learning?
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Name as many kinds of lines in daily life as you can. Would any of the lines you
names extend forever? Explain.
Which is longer, a segment or a line? How much longer?
If two segments do not intersect, does that mean that they are parallel? Explain.
Why would mathematicians sometimes use three letters to name an angle instead
of just using the vertex?
How do you know that an angle measures 45° when there are two sets of numbers
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on a protractor?
If someone tells you the measure of an angle, how can you tell if the angle is an
acute angle, a right angle, or an obtuse angle?
Describe the pattern of the angle measures in a triangle.
Without actually putting them together, how can you tell whether 3 lines form a
triangle?
Name something that is the shape of a quadrilateral, a pentagon, a hexagon, and
an octagon.
A geometry book said that a square is a “rectangular rhombus.” Do you agree?
Explain your reasoning.
How are trapezoids and parallelograms similar? How are they different?
Quadrilaterals can be classified based on whether or not their opposite sides are
parallel. Can triangles also be classified in this way? Explain.
How do the halves of a figure compare to each other when you divide a figure?
How can you prove that two shapes are the same?
Without using tracing paper, what patterns do you see that could help you
determine if a polygon would cover a sheet of paper without any overlaps or
spaces in between?
3. What key knowledge and skills will students acquire as a result of
this unit?
Students will learn to describe different kinds of lines and angles. They also learn to
measure the size of angles using a protractor. They learn to classify triangles by the
measure of their angles and by the lengths of their sides. They also learn to classify
polygons and quadrilaterals. Students investigate polygons whose shapes consist of
repeated patterns. They examine figures that are flipped over a line, rotated around a
point, and slide to a new position.
4. What prior learning, interests, misconceptions, and conceptual
difficulties might be brought to this unit?
Prior knowledge-Students will come with the understanding of what a line is, what an
angle is, and the different polygons.
Interests-Students will be able to work on activities that interest them while formatting an
understanding of their geometric polygons and terms.
Difficulties-Students may struggle with the relationship of the angles and lines in a
polygon.
Stage 2: Determine Acceptable Evidence
1. What evidence will show that students understand?
The evidence will be determined by-observing, paper work, answers to essential
questions, projects, assignments
Performance Tasks:
Complete a tic-tac-toe design by choosing their assignments.
Other Evidence:
Quizzes, Tests, Prompts, Work Samples (summarized):
Each day the students will be prompted with an essential question to make sure their
understanding is correct. They will have quizzes over their prior knowledge so I know if
I need to work with some students more on their understanding. They will fill in their
Tic-Tac-Toe design which contains their assigned projects.
Unprompted Evidence: (observations, dialogues, etc.)
observations on their projects, conversation with the students to see if they are
understanding the correct terminology, students' questions during their work time.
Student Self-Assessment
Students will color in each box as they complete their assignment. As soon as they
have at least three activities done in a tic-tac-toe design, they know they are done.
Stage 3: Plan Learning Experiences and Instruction
1. What sequence of teaching and learning experiences will equip
students to develop and demonstrate the desired understandings?
Major Learning Activities:
Describe different kinds of lines and angles.
Measure the size of angles using a protractor.
Classify triangles by the measure of their angles and the lengths of their sides.
Classify polygons and quadrilaterals.
Investigate polygons whose shapes consist of repeated patterns.
Examine figures that are flipped over a line, rotated around a point, and slid to a new
position.
Materials & Resources (technology & print):
Paper and pencil
Geometric shapes
Protractor
Journal
Books
Magazines
Newspapers
Management:
Working independently on their chosen assignment
Music used for calmly transitions and volume level of the kids
A tic-tac-toe board in the classroom between two students. Each class period if each
student behaves they can put their name in a box. Once they get a tic-tac-toe, they get a
prize.
Support Services and Special Teacher Notes:
Make sure students have a complete understanding of essential questions before they
begin their tic-tac-toe.
Extensions and Adaptation:
Extensions and Adaptation:
Gifted-Students may choose to do alternative activities, but need to be discussed with
teacher first. Tic-tac-toe design will be more advanced.
Adaptations-Activities in the tic-tac-toe will be at their level of understanding.
Stage 4: Plan Differentiation
2. What differentiated instruction strategies are being used in this
lesson/unit?
Differentiated activities that meet all the intelligences
Differentiated Process:
Tiered activities for each intelligence
Interest levels to all students
Manipulative and hand-on work
Varying length of time required
Encouraging students to create their own helpful product to understand the geometry unit
Differentiated Content:
Students will be able to choose their activities that meet their intelligence and their
needs.
Differentiated Product:
Verbal Linguistic - write a poem including the terms you learned about geometric
polygons, lines, angles, sides, symmetry, and transformations
Naturalist - go outside and record as many geometric drawings in a journal
Musical - write own lyrics to familiar tunes describing the different polygons, lines,
angles, sides, symmetry, and transformations
Logical Mathematical - illustrate and identify the different polygons, lines, angles,
sides, symmetry, and transformations
Visual Spatial Interpersonal - given toothpicks, create the different polygons, lines,
angles, sides, symmetry, and transformations
Visual Spatial - identify various examples of polygons, lines, angles, sides, symmetry,
and transformations in books, magazines, and/or newspapers
Intrapersonal(group) - record observations of polygons, lines, angles, sides,
symmetry, and transformations throughout the school
Visual Logical - cut out various types of polygons, lines, angles, sides, symmetry, and
transformations and explain the similarties and differences
Bodily Kinesthetic - create different polygons, lines, angles, sides, symmetry, and
transformations