Work Sample Final

PACIFIC UNIVERSITY
Perimeter, Area, and Volume
8th Grade Pre-algebra
Jaclyn Fitzgerald
February 2011
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Contents
A. Critical Question and Rationale...........................................................................................................3
B. Oregon State Standards……………………………………………………………………………………………………………………….5
C. Learning Goals ...................................................................................................................................6
D. Key Points..........................................................................................................................................6
E. Content Relationships .........................................................................................................................7
F1. Assessment Plan.............................................................................................................................. 10
F2. Pre/Post-Assessments and Scoring Guide.....................................................................................12
F3. Authentic Performance Task and Scoring Guide ..........................................................................17
G. Unit Sequence ..................................................................................................................................24
H. Lesson Plans.....................................................................................................................................28
I. Accommodating Individual Differences ............................................................................................. 33
J. Promoting Cultural Competence.........................................................................................................36
K. Cross-curricular Integration ..............................................................................................................37
L. Applications of Technology and Multimedia .....................................................................................37
M. Communication and Feedback..........................................................................................................37
Q. Resources .........................................................................................................................................38

3
A. Critical Question and Rationale
Geometry comes from a Greek word meaning “to measure the earth”. As one of the
oldest math sciences, Geometry allowed ancient philosophers, astronomers, and mathematicians
to learn about our world far before there were satellites, Google Earth, and many of the other
luxuries we now enjoy. We can credit these great minds and hard workers with a great deal of
the knowledge that is still shared and learned today. Although our world is now only a computer
click away, learning about geometry can help students to take in and process their lives by
expanding their spatial understanding and abstract visualization.
As students progress through a perimeter, area, and volume geometry unit they will
quickly move from the two-dimensional objects that they are very familiar with to examining
three-dimensional objects and their properties. Along the way they will consider and extend their
understandings of perimeter, area, circumference, surface area, and volume. Students will also
begin to inspect and realize perfect squares and square roots. Aside from studying geometry,
students will be responsible for evaluating their effort in mathematics daily, so as to hopefully
encourage more on-task behavior toward their achievement in mathematics.
Instruction of this unit will take place in an eighth grade classroom at Ogden Middle
School, located in Oregon City, Oregon. While Oregon City is quite a large town Ogden is
located on the outskirts and is made up of four, generally rural, feeder elementary schools. Most
students at Ogden are Caucasian and approximately 37% of them receive free or reduced lunch.
For the past few years Ogden has successfully held high marks among national standards in
every subject and for every population except for Special Education. This middle school looks
eerily the same since I was in attendance a little over eight years ago; with the same lockers,
many of the same teachers, and even the same math books and curriculum. Although dated, the

4
present textbooks thoroughly cover geometry and will serve as a great resource throughout this
unit.
Mathematics has commonly been referred to by many as a subject that is difficult and
daunting. This loathing and anxiety for math happens for a variety of reasons and to a variety of
people, astonishingly even many students, teachers, and parents. This attitude about math is
distressing when students are at a time in their lives to make leaps and bounds in their learning
and toward their future success. This is a sentiment that many Ogden mathematic students hold
and show in the little amount of effort that they put forth in class and on their homework
assignments. Throughout this geometry unit goal-setting, progress charting, and reflection will
expectantly serve to end these poor math habits and set students on a stronger path to success and
math proficiency.
At the conclusion of this unit students will complete two assessment pieces- an authentic
performance task and a final exam. While the final exam will only provide a limited sketch of the
students’ understanding and recall of geometry concepts the authentic performance task will
offer a much more in depth and collective learning experience and evaluation. The authentic
performance task gives students the opportunity to teach others what they know, strengthen their
understandings, and reflect on their learning and effort in their mathematics class. With the
completion of the unit and these two assessment components students will have satisfied Oregon
and National Standards in regards to eighth grade geometry and be prepared for their high school
mathematics courses.

5
B. Oregon State Standards
Geometry and Measurement: Analyze two- and three-dimensional spaces and figures by using
distance and angle.
5.3.2 Find and justify relationships among the formulas for the areas of triangles and
parallelograms.
5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular-
and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or
vertices as well as types of faces.
5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and
rectangular prisms.
7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of
circles.
7.3.3 Solve problems involving areas and circumferences of circles.
7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and
cylinders, and volume of pyramids, cylinders, and cones.
7.3.5 Find and justify relationships among the formulas for the areas of different polygons when
determining surface area.
7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of
pyramids, cylinders, and cones.
7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing
them into basic shapes.
8.3.3 Use models and logical arguments to show that the sum of the angles of any quadrilateral is
360 degrees, and apply this fact to find unknown angles.
8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing
lengths.
8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional
contexts, including distances on coordinate graphs.
8.3.6 Use models and referents to explore and estimate square roots.
EL.08.WR.01 Use a variety of strategies to prepare for writing, such as brainstorming, making
lists, mapping, outlining, grouping related ideas, using graphic organizers, and taking notes.
EL.08.WR.31 Use effective note-taking techniques to ensure appropriate documentation of
quoted as well as paraphrased material.
EL.08.SL.04 Use feedback, including both verbal and non-verbal cues to reconsider and modify
the organizational structure and to rearrange words and sentences to clarify the meaning.
EL.08.SL.05 Use precise language, action verbs, sensory details, appropriate and colorful
modifiers, and the active rather than the passive voice in ways that enliven oral presentations.

6
C. Learning Goals
After this unit, students will be able to:
1. Develop and use formulas to determine the perimeter and area of parallelograms,
triangles, and trapezoids and develop strategies to find the area of more complex shapes.
2. Analyze and use the Pythagorean Theorem and its converse to solve problems.
3. Diagram and identify parts of three dimensional figures.
4. Develop and use formulas to determine the circumference and area of circles.
5. Determine the surface area and volume of prisms, cylinders, pyramids, cones and
spheres.
6. Explore and estimate square roots.
7. Self-evaluate effort and attitude in math to take a role in increasing them by way of
improved on-task behavior and valuing mathematics in their daily lives.
D. Key Points
1. Find perimeter of rectangles, parallelograms, triangles, and trapezoids
2. Find area of rectangles, parallelograms, triangles, and trapezoids
3. Find the circumferences of a circle
4. Find the area of a circle
5. Graph polygons and circles on a coordinate plane
6. Use the Pythagorean Theorem
7. Classify three-dimensional figures
8. Construct three-dimensional figures
9. Develop formulas to determine the area of complex shapes
10. Use formulas to find the area of complex shapes
11. Take notes on a graphic organizer
12. Do daily homework math practice
13. Use graphic organizer to arrange and study math concepts
14. Teach a 7th
grade student
15. Set a goal to increase effort in math and improve on-task behavior
16. Track effort on homework and in class
17. Reflect on progress toward goals

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E. Content Relationships
Learning Goals Supporting Benchmarks
Supporting Lesson
Objectives
Supporting
Activities
Develop and use
formulas to
determine the
perimeter and area
of parallelograms,
triangles, and
trapezoids and
develop strategies to
find the area of
more complex
shapes
5.3.2 Find and justify
relationships among the
formulas for the areas of
triangles and
parallelograms.
different polygons when
7.3.7 Estimate and compute
the area and volume of
complex irregular shapes by
dividing them into basic
shapes.
-Students will
demonstrate prior
knowledge of perimeter
and area.
-Students will be able
to calculate the
perimeter and area of
rectangles and
parallelograms by
drawing them on graph
paper and discovering
the number of units the
figures occupy.
to calculate the
perimeter and area of
triangles and trapezoids
by comparing them to
rectangles and
parallelograms and
then drawing them onto
graph paper and
discovering the number
of units the figures
occupy.
-Exploring
rectangles (L1)
-Exploring
parallelograms (L1)
-Ticket out the door
(L1)
-Exploring triangles
(L2)
-Exploring
trapezoids (L2)
(L2)
Analyze and use the
Pythagorean
Theorem and its
converse to solve
problems.
8.3.4 Use models to explore
the validity of the
Pythagorean Theorem, and
use it to find missing
lengths.
8.3.5 Apply the Pythagorean
Theorem to find distances in
a variety of 2- and 3-
dimensional contexts,
including distances on
coordinate graphs.
to demonstrated their
understanding of the
Pythagorean Theorem
by diagramming the
relationship of the sides
of a triangle and the
equation: + =
(L3)
Diagram and
identify parts of
three dimensional
figures.
5.3.3 Describe three-
dimensional shapes
(triangular and- rectangular
prisms, cube, triangular- and
square-based pyramids,
cylinder, cone, and sphere)

8
by the number of edges,
faces, and/or vertices as
well as types of faces.
Develop and use
formulas to
determine the
circumference and
area of circles and
develop strategies to
find the area of
more complex
shapes.
7.3.1 Use models to explain
the reasonableness of
formulas for the
circumference and area of
circles.
7.3.3 Solve problems
involving areas and
circumferences of circles.
7.3.7 Estimate and compute
the area and volume of
complex or irregular shapes
by dividing them into basic
shapes.
Determine the
surface area and
volume of prisms,
cylinders, pyramids,
cones and spheres.
5.3.8 Decompose three-
dimensional shapes and find
surface areas and volumes
of triangular and rectangular
prisms.
7.3.4 Use models to explain
the reasonableness of
formulas for the surface
area of pyramids and
cylinders, and volume of
pyramids, cylinders, and
cones.
different polygons when
7.3.6 Solve problems
involving surface areas of
pyramids and cylinders and
volumes of pyramids,
cylinders, and cones.
Explore and
estimate square
roots.
8.3.6 Use models and
referents to explore and
estimate square roots.
-Exploring Squares
(L1)
Self-evaluate effort
and attitude in math
to take a role in
increasing them by
way of improved on-
EL.08.WR.01 Use a variety
of strategies to prepare for
writing, such as
brainstorming, making lists,
mapping, outlining,

9
task behavior and
valuing mathematics
in their daily lives.
grouping related ideas,
using graphic organizers,
and taking notes.
EL.08.WR.31 Use effective
note-taking techniques to
ensure appropriate
documentation of quoted as
well as paraphrased
material.
EL.08.SL.04 Use feedback,
including both verbal and
non-verbal cues to
reconsider and modify the
organizational structure and
to rearrange words and
sentences to clarify the
meaning.
EL.08.SL.05 Use precise
language, action verbs,
sensory details, appropriate
and colorful modifiers, and
the active rather than the
passive voice in ways that
enliven oral presentations.

10
F1. Assessment Plan
Goal 1: Develop and use formulas to determine the perimeter and area of parallelograms, triangles,
and trapezoids and develop strategies to find the area of more complex shapes
Formative:
 Pre-assessment
 Rectangle Drawing (L1)
 Parallelogram Drawing (L1)
 Triangle Graphing (L2)
 Trapezoid Graphing (L2)
 Group Discussions (ALL)
 Ticket out the door (ALL)
 Daily homework (ALL)
Summative:
 Authentic Performance Task
 Post-assessment
Goal 2: Analyze and use the Pythagorean Theorem and its converse to solve problems.
Formative:
 Pre-assessment
Summative:
 Post-assessment
Goal 3: Diagram and identify parts of three dimensional figures.
Formative:
 Pre-assessment
Summative:
 Post-assessment
Goal 4: Develop and use formulas to determine the circumference and area of circles and develop
strategies to find the area of more complex shapes.
Formative:
 Pre-assessment
Summative:
 Post-assessment
Goal 5: Determine the service area and volume of prisms, cylinders, pyramids, cones, and spheres.
Formative:
 Pre-assessment
Summative:
 Post-assessment
Goal 6: Explore and estimate square roots.
Formative:
 Pre-assessment
 Rectangle Drawing (L1)
Summative:
 Post-assessment

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Goal 7: Self-evaluate effort and attitude in math to take a role in increasing them by way of improved
on-task behavior and valuing mathematics in their daily lives.
Formative:
 Effort charts
 On-task records
 Group Discussion (L1)
Summative:

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F2. Pre/Post-Assessments and Scoring Guide
Directions: Please complete the following problems using all that you know or have
learned. Show as much of your work as possible so that I can at least give you partial credit
on problems that you have given the incorrect answer, but also know that if you do not
show any work then you cannot receive full credit. BREATHE! You are going to do great
=)
(1) Find the perimeter and area of the following figures: (Goal 1 and 4)
Perimeter: _______________
Area: ____________________
Perimeter: _______________
Area: ____________________
Perimeter: _______________
Area: ____________________
Perimeter: _______________
Area: ____________________
5 cm
10 cm
7 in
9 in
8 in
8 cm
7 cm
5 cm
9 cm
8 ft
9 ft9 ft
7 ft
Circumference: ______________
Area: ____________________
10 mm

13
(2) Find the perimeter/circumference and area of the following figures: (Goal 1 and 4)
12
10
12 12
13

14
(3) Use the Pythagorean Theorem to find the missing side lengths in the figures below: (Goal 2)
(4) Explain the Pythagorean Theorem using the figure below and drawing in whatever else you
need: (Goal 2)
(5) Label an edge, face, and vertex on the figure below: (Goal 3)
5
13
8
15

15
(6) Find the perimeter and area of the figure below: (Goal 1)
(7)Find the surface area and volume of the figures below: (Goal 5)
(8) Draw a diagram below to help you answer- what is the square root of 36? (Goal 7)
10 cm
5 cm
8 cm
4 cm
3 cm
4 cm
17 m
10 m
4 cm
6 cm3 cm
5 cm

16
Pre-/Post Assessment Scoring Guide:
Descriptors 5 4 3 2.5 1
(1) Find the
perimeter and
area of the
following figures.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(2) Find the
perimeter/circum
ference and area
of the following
figures.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(3) Use the
Pythagorean
Theorem to find
the missing side
lengths in the
figures below.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(4) Explain the
Pythagorean
Theorem using
the figure below
and drawing in
whatever else you
need.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(5) Label an edge,
face, and vertex
on the figure
below.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(6) Find the
perimeter and
area of the figure
below.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(7) Find the
surface area and
volume of the
figures below.
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.
(8) Draw a
diagram to help
you answer- what
is the square root
of 36?
The correct
answer with
all necessary
work shown.
The correct
answer with
work I
cannot
follow.
The correct
answer with
no work.
The incorrect
answer with
all work
shown
The incorrect
answer with
insufficient or
no work
shown.

17
F3. Authentic Performance Task and Scoring Guide
Name: Jaclyn Fitzgerald
Grade Level: 8
Work Sample Title: Perimeter, Area, and Volume
Benchmarks:
5.3.2 Find and justify relationships among the formulas for the areas of triangles and
parallelograms.
5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular-
and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or
vertices as well as types of faces.
5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and
rectangular prisms.
7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of
circles.
7.3.3 Solve problems involving areas and circumferences of circles.
7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and
cylinders, and volume of pyramids, cylinders, and cones.
7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of
pyramids, cylinders, and cones.
7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing
them into basic shapes.
8.3.3 Use models and logical arguments to show that the sum of the angles of any quadrilateral is
360 degrees, and apply this fact to find unknown angles.
8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing
lengths.
8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional
contexts, including distances on coordinate graphs.
8.3.6 Use models and referents to explore and estimate square roots.
EL.08.WR.01 Use a variety of strategies to prepare for writing, such as brainstorming, making
lists, mapping, outlining, grouping related ideas, using graphic organizers, and taking notes.
EL.08.WR.31 Use effective note-taking techniques to ensure appropriate documentation of
quoted as well as paraphrased material.
EL.08.SL.04 Use feedback, including both verbal and non-verbal cues to reconsider and modify
the organizational structure and to rearrange words and sentences to clarify the meaning.
EL.08.SL.05 Use precise language, action verbs, sensory details, appropriate and colorful
modifiers, and the active rather than the passive voice in ways that enliven oral presentations.

18
Unit Goals:
After this unit, students will be able to:
1. Develop and use formulas to determine the perimeter and area of parallelograms,
triangles, and trapezoids and develop strategies to find the area of more complex shapes.
2. Analyze and use the Pythagorean Theorem and its converse to solve problems.
3. Diagram and identify parts of three dimensional figures.
4. Develop and use formulas to determine the circumference and area of circles.
5. Determine the surface area and volume of prisms, cylinders, pyramids, cones and
spheres.
6. Explore and estimate square roots.
7. Self-evaluate effort and attitude in math to take a role in increasing them by way of
improved on-task behavior and valuing mathematics in their daily lives.
TASK DESCRIPTION:
Ogden 7th
graders need our help! Another round of OAKS testing is coming up and they need to
know more geometry so that they can do well on their tests too. Luckily, over the next two weeks
you will become a Geometry master and the perfect person to help them! I know we can all learn
a lot and exceed on this test!!!
You are going to help a seventh grader in two ways:
-Meet with a 7th
grader and teach them a geometry topic
-Create a visual of your geometry topic for them to review and hang up in their math class.
You are going to help yourself by:
-Reflecting on your teaching of your geometry topic, your learning during this chapter, your
likes and dislikes, and your effort goals.
COMPONENT 1: Teaching the 7th
Graders
Goals Addressed: 1, 2, 3, 4, 5, and/or 6
COMPONENT DESCRIPTION:
All students will teach a 5-10 minute lesson on a geometry topic to a seventh grader. You may
do something with them similar to one of our activities in class or you can come up with your
own ideas. You are so creative and smart so I am really excited to see how you would teach
someone what you know. (Note: a great place to start could be your own math book- look
through the example problems!)
CRITERIA:
-Pick a geometry concept you feel you know a lot about from the available list or have a different
one approved by the teacher.

19
-Prepare a 5-10 minute lesson to teach to a 7th
grade student
-Plan a lesson that makes sense, includes an activity, and meets your goal of teaching a 7th
grader
about your topic.
-Provide at least two examples of test questions that they can use your geometry topic to
solve/answer.
-Learning should be fun! Make your lesson fun for you and your 7th
grade student!
-Turn-in a short description of your geometry topic, learning goals and related vocabulary you
are going to use, your teaching plans (maybe your script or activity ideas?), and a list of needed
materials for the teacher to review at least a week before.
-Have a classmate review your lesson the class period before.
-Fill out a self-assessment after completing your lesson
-Collect lesson reviews from two different classmates
COMPONENT 2: Geometry Topic Visual
Goals Addressed: 1, 2, 3, 4, 5, and/or 6
To best help our 7th
graders we need to give them something that they can take with them.
Remember, it takes over 20 times of looking at something before we are really going to be able
to remember it and use it for something. By giving them a visual of the geometry topic that you
taught them then they can hang it up in their math class and review it whenever they need to.
CRITERIA:
-Must include the title or name of your geometry topic.
-Must include diagrams, pictures, or procedures necessary to understand the topic and answer
test questions about the topic
-Must include all necessary vocabulary related to your topic
-Include at least two different examples of test questions that they may use your geometry topic
to answer and show the step-by-step solution process (should have two different solution
processes) and answers so anyone can follow them. (Note: again look at your text book! There
are a ton of great example questions available!)
COMPONENT 3: Reflection
Goals Addressed: 7
You have learned so much these past few weeks and I want to know all about it! First of all I
want to know how teaching your geometry topic went. Do you think they understood and could
use it on their test? Then I want to tell me about your learning this chapter and your likes and
dislikes about how your math class is set up now. Lastly, I want you to tell me all about your
effort goals. Write about why it is your goal, what changes you had to make to accomplish it, and
if you did actually met your goals. Be completely honest, you will not be graded down; I just

20
want to know what you are truly thinking and feeling! You can do this in a paper or individual
poster for you to present to me privately. The criteria below are mostly for the paper, but if you
choose to do a poster you still must find a way to creatively present these criteria on your poster.
CRITERIA:
-Typed, double-spaced, 12 pt font, Times New Roman, and 1 inch margins (if you need access to
a computer contact me)
-At least one page in length
-At least one paragraph about your geometry topic teaching, one paragraph about how you are
learning in math class, and one paragraph about your effort goal(s).
-Attach completed lesson self-assessment
-Attach completed effort chart
Component 1:
Teaching
5 3 1
Pick a geometry
concept you feel you
know a lot about
from the available list
or have a different
one approved by the
teacher.
Picked a geometry topic
from the list or an
appropriate geometry
topic that was approved
by the teacher.
Picked an appropriate
geometry topic that was
not on the list and did
not get approval from
the teacher.
Picked a geometry
topic that was not on
the list and did not
get approval from
the teacher. Topic is
inappropriate: not in
math text book or
other class resources.
Turn-in a short
description of your
geometry topic,
learning goals and
related vocabulary
you are going to use,
your teaching plans
(maybe your script or
activity ideas?), and
list of needed
materials for the
teacher to review a
week before.
Turned in plan on-time
with thorough
descriptions showing
strong understanding of
the geometry topic, 2 or
more learning goals, all
possible vocabulary that
is relevant in teaching
and learning this topic,
includes well thought
out teaching plans and
describes activities, and
provides a list of all
materials needed.
Turned in plan on-time
with minimum
description that limits
showing their
understanding of the
topic, provides only one
learning goal they have
for the 7th
grade student,
lists most vocabulary
that is important to
teach the topic, lists
teaching plan ideas
Turned in plan on-
time but provides
little to no details or
information about
their understanding
of the topic, the
learning goals they
have for their 7th
grade students, the
vocabulary the
lesson will include,
their teaching plan,
and/or the list of
needed materials.
Prepare a 5-10
minute lesson to
teach to a 7th
grade
student
Plan a lesson that
Lesson length is
appropriate for teaching
the topic in a fun way.
Activity includes the
student. The learning
Lesson length is over 5
minutes and under 10
minutes but more/less
information could have
been used for the lesson
to make the most sense.
Lesson length is
under 5 minutes or
over 10 minutes.
Includes a very short
activity that does not
involve the 7th
grade

21
makes sense, includes
an activity, and meets
your goal of teaching
a 7th
grader about
your topic.
goals match the lesson
and topic and are met
after the lesson.
Includes a basic
activity. Learning goals
seem to connect to the
topic but not the lesson
plan.
student. Learning
goals do not seem to
match the topic or
lesson.
Provide at least two
examples of test
questions that they
can use your
geometry topic to
solve/answer.
Creates two or more test
questions. Uses these
questions to show how
to solve a test problem
with their geometry
topic.
Creates two test
questions, but does not
use them to teach the
process of using the
geometry topic on a test.
Creates less than two
test questions. Does
not use the test
questions at all in
teaching the student.
Learning should be
fun! Make your
lesson fun for you
and your 7th
grade
student!
Lesson appeared very
fun! Included hands on
or moving around
activities that kept
student interested.
Creative and original
activity ideas.
Lesson seemed
interesting. Student was
involved in more than
just listening and
watching. May have
used in-class learning
stations
Did not seem at all
fun. May have only
talked to the student
about math and did
not involve them.
Fill out a self-
assessment after
completing your
lesson
Grades self accurately
and provides comments
explaining reasoning.
Grades self accurately
but provides no
comments or reasoning.
Does not grade self
accurately and adds
no comments.
Collect lesson reviews
from two different
classmates
Attaches 2 or more
lesson reviews.
Attaches less than 2
lesson reviews.
Attaches no lesson
reviews.
Component 2: Visual 5 3 1
Include Title/Name of
Geometry topic.
Visual includes a
creative title that makes
viewers aware of the
Geometry topic without
just stating it. The title
is big enough and easy
to read.
Visual includes
Geometry topic as the
title. The title is big
enough and easy to
read.
Visual includes
Geometry topic as
the title. The title is
small and hard or
impossible to read.
Include diagrams,
illustrations, pictures,
and solution process
to understand and
use the Geometry
topic.
(This can be part of
your 2 test questions
below)
Included several
diagrams/illustrations/
pictures. The process of
using the Geometry
topic is shown step-by-
step with very clear
labels and explanations.
Included few diagrams/
illustrations/pictures.
The process of the
Geometry topic is
shown but is unclear or
difficult to follow.
Included little or no
diagrams/illustration
s/ pictures. The
process of using the
Geometry topic is
shown but so limited
it is not helpful.
Include all necessary
Visual includes
vocabulary that is
necessary to understand
Visual includes
vocabulary that is
necessary to understand
Visual includes
limited or no
vocabulary that is

22
and related
vocabulary.
the Geometry topic.
Related vocabulary is
also included to extend
the topic and connect it
with other math topics.
the Geometry topic. No
other related vocabulary
is used to connect with
other math topics.
helpful in
understanding the
Geometry topic. No
related vocabulary is
included.
Include two different
test questions.
Visual provides two
different test questions.
Two different types of
solving processes or
steps using the
Geometry topic are
shown and labeled.
Visual provides two
different test questions
but solves them both the
same way.
Visual provides less
than two test
questions or two
questions that are too
similar.
Component 3:
Reflection
5 3 1
Format: Typed,
double-spaced, 12 pt
font, Times New
Roman, 1 inch
margins
Paper follows format
guidelines exactly.
Paper has some
incorrect formatting.
Paper has mostly or
all incorrect
formatting.
At least one pate in
length including at
least on paragraph on
each prompt: your
teaching, your
learning in math
class, and your effort
goal(s).
Paper is one page in
length or longer and
includes at least one
paragraph about each
prompt.
Paper is less than one
page in length but still
includes a paragraph
covering each prompt.
Paper is less than
one page in length
and is missing one
or more prompt
paragraphs.
Attach completed
effort chart and goals
Goals are written in the
correct location and
everyday effort
honestly evaluated and
graphed on the chart.
Goals are written in the
correct location and
effort is evaluated and
graphed on the chart for
most days.
Goals are written in
the correct location
but effort is not
evaluated and
graphed on the chart
for most days or
student is dishonest
about their actual
effort.

23
Possible Lesson Topics:
-Angles (pg 223)
-Transversals (pg 228)
-Triangle Sum Theorem (pg 234)
-Angle measures of polygons (pg 239)
-Finding the slope of a line (pg 244)
-Congruence (pg 250)
-Transformations (pg 254)
-Symmetry (pg 259)
-Tessellations (pg 263)
-Area and Perimeter of Rectangles and Parallelograms (pg 280)
-Area and Perimeter of Triangles and Trapezoids (pg 285)
-Pythagorean Theorem (pg 290)
-Circles (pg 294)
-Volume of prisms and cylinders (pg 307)
-Volume of pyramids and cones (pg 312)
-Surface Area of prisms and cylinders (pg 317)
-Surface Area of pyramids and cones (pg 321)
-Spheres (pg 324)
Reflection Prompts: Here are some ideas to get you started, but do not feel like you have to
answer all of these or just stick to these questions and ideas. I want to hear your honest opinions.
Your teaching-
-Were you comfortable enough with your topic to teach it?
-What did you like? What did you not like?
-Did it seem that your student understood your topic?
-Could your student complete your test problems?
-How much did you include your student?
-If there is anything you could change what would it be and why?
Your feelings about class and my teaching-
-How is math going for you?
-What do you like? What do you wish could be different?
-Is my teaching help you? Is there anything more I could do to help you?
-Do you feel like you are learning just as much as when you are learning from your normal
classroom teacher?
Your effort chart and goal(s)-
-What were your goals and why?
-Did you have to make any changes to reach your goals?
-Did you reach your goals or make some progress?
-Do you feel that goal setting has helped you at all? If so, how?

24
G. Unit Sequence
Lesson # Lesson Title Lesson Highlights
Lesson 1
Perimeter and Area of Rectangles
and Parallelograms
-Homework Question and Answer
-Correct homework
-Introduce effort chart and set goals.
-Transition Music: record score, turn in, write
down assignment, and record effort score.
-Mini-lesson:
-Students score their in-class effort and plot
their in-class and homework scores on their
chart.
-Ticket out the door: complex, irregular figure
Lesson 2
Perimeter and Area of Triangles and
Trapezoids
-Correct homework
-Mini-lesson:
chart.
-Ticket out the door: triangles and trapezoids
Lesson 3 Perimeter and Area Review
-Correct homework
-Perimeter and area practice problems, review
stations
chart.
Lesson 4 Circles
-Correct homework
-Mini-lesson:
chart.
Lesson 5 The Pythagorean Theorem
-Correct homework
-Mini-lesson:

25
chart.
Lesson 6 More Pythagorean Practice Problems
-Correct homework
-Students complete further practice problems
and visit review stations to gain a better
understanding of Pythagorean Theorem.
chart.
Lesson 7 Coordinate Pythagorean
-Correct homework
-Mini-lesson:
chart.
Lesson 8 Mid-chapter quiz and review day
-Correct homework
-Take the mid-chapter quiz
-If time allows, visit review stations.
chart.
Lesson 9 Volume of prisms and cylinders
-Correct homework
-Mini-lesson:
chart.
Lesson 10 Volume of pyramids and cones
-Correct homework

26
-Mini-lesson:
chart.
Lesson 11 More volume practice
-Correct homework
-Introduce effort chart and set goals.
-Volume practice problems and review stations
chart.
Lesson 12 Surface area of prisms and cylinders
-Correct homework
-Mini-lesson:
chart.
Lesson 13 Surface area of pyramids and cones
-Correct homework
-Mini-lesson:
chart.
Lesson 14 Review surface area
-Correct homework
-Surface area practice problems, review stations
chart.
Lesson 15 Spheres
-Correct homework

27
-Mini-lesson:
chart.
Lesson 16
Review Day and Authentic
Performance Task practice and work
-Correct homework
-Students visit review stations to prepare for
post-assessment
-Practice their 5-10 min teaching with a
classmate.
chart.
-Ticket out the door: Classmate lesson review
Lesson 17 Authentic Performance Task
- Discuss rules for the day
-Gather all materials
-Teach 7th
grade students
-Return to class and discuss
-Computer lab: Authentic Performance Task
reflection work.
Lesson 18 Post-assessment
-Turn in Authentic Performance Task
Reflection with effort charts.
-Take post-assessment test
-Start on homework for the following night.

28
H. Lesson Plans
Name: Jaclyn Fitzgerald Date: February
2011
Lesson 1 Title: Perimeter and Area of Rectangles and Parallelograms
Grade Level/Subject: 8th
/Mathematics
Benchmark(s):
7.3.7 Estimate and compute the area and volume of complex irregular shapes by dividing them into
basic shapes.
Objectives(s):
- Students will demonstrate prior knowledge of perimeter and area.
-Students will be able to calculate the perimeter and area of rectangles and parallelograms by
drawing them on graph paper and discovering the number of units the figures occupy.
Lesson Assessment: Ticket out the door-complex, irregular figure.
Materials: Graph paper, document camera, pencils, effort charts Length of Lesson: 50 min
Pacing Procedures/Activities
(Teacher & Student)
Teacher
Actions/Notes
8 min
5 min
4 min
2 min
26 min
Homework Questions?
Correct Homework
Further Questions?
Introducing effort charts-
Each student explores effort chart and sets goals for
mathematics. If you are trying to improve your effort on
homework what are some things you could do? Students list
changes they need to make.
What would putting more effort in to class look like?
Transition music- Students record their HW scores, their new
assignment, and effort chart data.
Set:
So today we are going to be talking about area and perimeter
and learn how to calculate them for rectangles and
parallelograms.
Information/Input:
So I am going to give everyone a piece of graph paper and I
Check understanding
from previous lesson
Introduce my critical
question and effort
chart
Motivation-degree of
concern
Group Discussion
Theme: Disco
Estimated homework
length- 40 min
Stating Objective
Hand out graph paper

29
want you to first draw as many different rectangles as possible
in the next 30 seconds. How many were you able to make?!
Exploring Rectangles:
Okay, so for example if I made a rectangle on my graph paper
that was 6 units on the base and 2 units for the height my
perimeter would be a sum of all the side lengths so
6+6+2+2=16 and what would my area be and how do you
know? I want you to talk with your table partner and decide
how calculating the perimeter could be done with
multiplication.
Remind of in-class effort goals.
What did you come up with?
What if I made a rectangle that was 4 units for the base and 4
units for the height? It is a square of course because all of the
sides are the same length! Is a square a rectangle? YES, so go
ahead and draw this onto your graph paper and now we must
add together all the sides for the perimeter which would be:
4+4+4+4=16 units. Pencil in the air if you know how could this
be represented as a multiplication problem?
Okay, so go ahead and finish this problem by finding the area
and take the next two minutes to make as many more rectangles
(and squares) as you can, but you must calculate the perimeter
and area for each before drawing your next rectangle.
Remind of in-class effort goals.
Exploring Squares:
Okay now try and make as many different rectangles as
possible that have an area of 24 units squared.
Exploring Parallelograms:
What about the perimeter of parallelograms? Well the perimeter
is calculated the same as we have been doing using the side
lengths, but area is a little different. Well this is where graph
paper can really come in handy because the height of a
parallelogram is the height from the bottom base to the top
base; it is NOT the side length. So by using a parallelogram on
a coordinate graph then we can count the height between the
bottom base and the top base. So I am going to provide you
with a couple of coordinates and we are going to practice
finding the perimeter and area of parallelograms.
Parallelogram practice
Model
TPS
Guided Practice
Check for
understanding
Independent Practice
Parallelogram practice
coordinates and
problems.

30
5 min Closure: Ticket out the door-
Okay so I want you to practice with one last figure on a new
half-sheet of graph paper. By yourself or with your table partner
I want you to copy down the figure here and show you work in
figuring out the perimeter. This may require you moving or
seperating things a little bit. This finished problem is you ticket
out the door today.
When you are finished I would like you to complete your effort
chart for in-class today and then it should be time to pack up
your things.
Pre-drawn figure, TPS
Check for
understanding
Extensions: Provide more of the “Ticket out the door”
complex, irregular figure problems as soon as it is clear that
they have mastered area during the lesson. Ask them to take
daily notes on my lesson to distribute to other students that need
more assistance.
Accommodations: Post advanced organizer on the board.
Classmate made notes to take home with them.
Name: Jaclyn Fitzgerald Date: February 2011
Lesson 2 Title: Perimeter and Area of Triangles and Trapezoids
Grade Level/Subject: 8th
/Mathematics
Benchmark(s):
7.3.7 Estimate and compute the area and volume of complex irregular shapes by dividing them into
basic shapes.
Objectives(s):
- Students will demonstrate prior knowledge of perimeter and area.
-Students will be able to calculate the perimeter and area of triangles and trapezoids by comparing
them to rectangles and parallelograms and then drawing them onto graph paper and discovering the
number of units the figures occupy.
Lesson Assessment: Ticket out the door-finding the perimeter and area of a triangle and trapezoid on
a figure
Materials: Graph paper, document camera, pencils Length of Lesson: 50 min
Pacing
Procedures/Activities
(Teacher & Student)
Teacher
Actions/Notes

31
10 min
4 min
3 min
25 min
Homework Questions?
Correct Homework
Further Questions?
Transition music- Students record their HW scores, their new
assignment, and effort chart data.
Set:
Show triangles and trapezoids as parts of a parallelogram. How
do we find the area of parallelograms? If these triangles and
trapezoids make up half of a parallelogram, then what do you
think that means for the area of the triangle or trapezoid?
Information/Input:
So today we are continuing to work with perimeter and area but
now we are learning how to calculate these for triangles and
trapezoids.
Exploring Triangles-
1. On your graph paper create your x- and y-axis and plot
these points.
2. We need to use this graph paper to find the height of the
triangle.
3. Now as we found out before a triangle is half of the area
of a parallelogram and that is important to keep in mind
when calculating the area of a triangle.
Okay now try this one on your own (Pg 287 #17). When you are
finished hold up the answer with your fingers
Exploring Trapezoids-
Now a trapezoid is a little different because unlike the
parallelogram, it has two different base lengths that we must take
into account when calculating its area- show on a trapezoid and
compare to a parallelogram.
Okay so draw this figure on your graph paper with these
coordinates
Just like the triangle, a trapezoid is only half of the area of a
parallelogram so we must use that when calculating the
trapezoid’s area.
So what is the height of our trapezoid?
When finding the area we must use both bases as I said before,
because they are different lengths, so in our calculations we add
them together (Note: make sure you show this sum in your
Check understanding
from previous lesson
This Week’s Theme:
Disco
Estimated homework
length: 40 min
Check for
understanding
Group discussion
Motivation: Success
Stating Objective
Modeling, Guided
Practice
Independent Practice,
Check for
understanding
Modeling
Provide figure
coordinates
Check for
understanding- choral
response

32
10 min
calculations, don’t just do this in your head!)
Model calculation for class.
Now how about a trapezoid that looks like this….
What is the height and our two bases?
Write down on your paper the equation to calculate the area of
this triangle and then share it with your table partner.
Closure:
Okay, now I know you can be successful on your homework
tonight. Remember though that for both the triangle and
trapezoid finding the perimeter is just the same as before because
it is always the sum of all the side lengths of any figure. Also,
that a triangle and trapezoid have half the area of the
parallelogram.
Ticket out the door-
In the time you have left please complete this problem as your
ticket out the door:
Okay draw this figure here and answer the questions.
When you are finished I would like you to complete your effort
chart for in-class today and then it should be time to pack up
your things.
Model
Provide practice
problem, guided
practice
TPS
Pre-drawn figure (pg
288), Check for
understanding
Extensions: Worksheet- Lesson 6-2 Practice B. Take notes for
other students in class. Ask them to take daily notes on my
lesson to distribute to other students that need more assistance.
Accommodations: Post advanced organizer on the board.
Classmate made notes to take home with them.

33
I. Accommodating Individual Differences
Individual Differences Attributes Activities
Multiple Intelligences
Logical/Mathematical
-Likes to count.
-Likes to be organized
-Is very precise.
-Good at problem solving.
-Recognizes patterns and relationships.
-Finding area (L1,2)
-Effort chart (ALL)
Verbal/Linguistic
-Good at remembering written and spoken
information.
-Enjoys reading and writing.
-Good at debating or giving persuasive
speeches.
-Able to explain things well.
-Often uses humor when telling stories.
-Authentic Performance
Task
-Think Pair Share (ALL)
Spatial
-Able to visualize in their head.
-Good depth perception.
-Good with directions and maps.
-Thinks of the big picture.
-May speak fast.
-Graphing to calculate
area (L1,2)
-Diagramming three-
dimensional figures (L9)
Musical
-Likely able to sing, play musical
instruments, and compose music.
-Appreciates musical expression.
-Sensitive to rhythm, pitch, meter, tone,
melody, or timbre.
-Transition music (ALL)
-Closing music (ALL)
Body/Kinesthetic
-Learns by doing.
-Uses the body to solve problems.
-Coordinates mind and body to think.
-May need to move to think.
-Handles objects skillfully.
-Review stations (L 3, 6,
8, 11, 14)
Interpersonal/Social
-Good at communicating verbally.
-See situations from different perspectives.
-Create positive relationships with others.
-Good at resolving conflict in groups.
-Enjoys team builders.
-Collecting homework
(ALL)
- Authentic Performance
Task
Intrapersonal/Introspe
ctive
-Introverted
-Intuitive
-Independent
-Perfectionist
-Self-aware
-Effort goals and chart
(ALL)
Naturalist
-Able to discriminate between living things.
-Sensitive to features of the natural world.
-Good at categorizing information about
nature.
-Prefers topics related to nature.

34
Learning Styles
Sensing/Thinking
-Enjoys activities that include drills and the
recalling of facts.
-Needs clear expectations with feedback.
-Difficulty with change.
-Active but business like
-Provide feedback (ALL)
-Advanced Organizer
(ALL)
Sensing/Feeling
-Focus on personal values and interpersonal
relationships.
-Know how learning relates to getting along
with others.
-Needs and wants support and
encouragement.
-Functions best in verbal interactions.
-Learns best with content that has meaning.
-TPS/Partner work (ALL)
Task
Intuitive/Thinking
-Wants instruction that focuses on meaning
and relationships.
-Wants to understand the reasoning behind
things.
-Solves problems through logic and analysis.
-Enjoys experimentation
-Finding area and
perimeter (L1, 2)
Intuitive/Feeling
-Wants instruction that allows personal
exploration of a subject.
-Likes new challenges.
-Very creative and imaginative.
-Can see the beauty in things.
-Has difficulty organizing and planning time.
-Estimated Homework
Length (ALL)
Task
Special Needs
ADD/ADHD
-Needs large tasks broken down into smaller
parts.
-Possibly on medication
-Needs instant and positive feedback
-Needs simple and clear instructions and
scheduling.
-Possibly has difficulty completing or
turning in tasks.
-Likes teacher to model tasks.
-Advanced Organizer
(ALL)
Task
-Correcting homework
(ALL)
-Modeling (ALL)
-Effort goal setting and
analysis (ALL)
IEP/504
parts.
-Needs simple and explicit instructions.
-Likes cooperative group work and visual
materials.
-Advanced Organizer
(ALL)
Task
-Modeling (ALL)
-Exploring Rectangles
(L1)
-Exploring Parallelograms
(L1)
-Exploring Squares (L1)

35
Aspergers Syndrome
-Interest concentrated in particular areas.
-Has difficulty interacting with others.
-Is physically clumsy.
-May have a sophisticated vocabulary but
difficulties with figurative language.
-Advanced Organizer
(ALL)
-Independent Practice
(ALL)
Learning Disabilities
parts.
-Enjoys cooperative group work and visual
materials.
-Needs simple and explicit instructions.
-Advanced Organizer
(ALL)
Task
-Exploring Rectangles
(L1)
-Exploring Squares (L1)
-Exploring Parallelograms
(L1)
-Modeling (ALL)
TAG
-Curious but logical thinker.
-Focused, passionate, and creative.
-Exhibits an understanding and awareness of
problems.
-Is advanced intellectually.
-Demonstrates oral proficiency.
Task
-Lesson Extensions (ALL)
Low SES
-Needs school to be a safe and friendly place.
-Wants to be included in lessons.
-Needs teacher’s positive support.
-May have limited or no resources at home.
-Needs teacher to have open communication
lines with home.
-Enjoys cooperative group work.
-Safe and friendly
classroom (ALL)
ELL
-Wants teachers approval
-Enjoys hands on activities and cooperative
group work.
-Needs opportunities to listen, speak, read,
and write
-TPS/Partner Work (ALL)
-Guided Practice (ALL)
-Effort Chart (ALL)

36
J. Promoting Cultural Competence
Collaborating with parents and families to nurture and support competence in home and school
cultures:
 Written letter to family introducing myself and the unit of study.
 Communication with parents about achievement.
 Involving an interpreter when necessary.
 Inviting family volunteers and observers into the classroom.
 Inviting parents to meet with me at conferences.
Communicating high expectations:
 Student goal setting.
 Providing specific and explicit scoring rubric for tasks, assignments, and assessments.
 Communicating the value of improvement.
 Providing students with the opportunity to revise so that they may turn in their best work.
 Consistent and immediate feedback on work.
Including instructional strategies that correspond with the norms and values of culture(s):
 Providing students with consistent opportunities to self-regulate and self-reflect.
 Combining various guided practice, work group sizes, and independent work time.
 Fostering a welcoming and safe environment.
 Presenting a variety of different activities to accommodate all learners.
Engaging students in cooperatively developed and community-oriented learning:
 Using cooperative learning strategies.
 Offering group assignments and partner work.
 Sharing math learning with others.
 Working with an authentic audience.
Integrating diverse ways of knowing, understanding, and representing knowledge:
 Presenting a variety of different activities to accommodate all learners.
 Allowing for various ways of presenting information (oral, visual, written).
Connecting students’ cultural backgrounds and personal experiences to the acquisition of new
knowledge and skills:
 Using personal understanding and ideas to teach others.

37
K. Cross-curricular Integration
Cross-curricular Integration Activities
Literacy-Writing
-Authentic Performance Task Components 1, 2,
and 3
-Graphic Organizers
Literacy- Speaking
-Authentic Performance Task Component 1
-Class Discussions (ALL)
Literacy- Reading -The History of Pythagoras
Social Studies -The History of Pythagoras
L. Applications of Technology and Multimedia
Technology and Multimedia Activities
-Document Camera -ALL lessons
-Computer Lab -Authentic Performance Task Component 3
M. Communication and Feedback
Students:
 Consistent and immediate feedback on work
 Providing specific and explicit scoring rubric for tasks, assignments, and assessments.
 Consistently updating grades and attendance on ESIS.
Families:
 Written letter to family introducing myself and the unit of study in all necessary
languages.
 Inviting family volunteers and observers into the classroom.
 Responding promptly to emails from family members.
 Communicating with parents about achievement.
 Consistently updating grades and attendance on ESIS for family to track.
 Inviting parents to meet with me at conferences.
Colleagues:
 Attending Professional Learning Community weekly meetings and staff meetings.
 Communicating and collaborating with my mentor teacher and team members.
 Inviting administrators into the classroom often.
 Establishing an open line of communication with resource staff members.

38
Q. Resources
Debra Barrett
Ogden Middle School
Oregon City, Oregon
503-785-8300
Benntt, J., Burger, E.B. & Chard, D. J. Holt Mathematics: Course 3. Holt McDougal.
Benntt, J., Burger, E.B. & Chard, D. J. Holt Mathematics: Teacher Resources. Holt McDougal.
Benntt, J., Burger, E.B. & Chard, D. J. Holt Mathematics: Assessment. Holt McDougal.
National Council of Teachers of Mathematics: http://www.nctm.org/
Oregon Public Education Network (OPEN)-Practice Scoring:
http://www.openc.k12.or.us/scoring/
National Library of Virtual Manipulatives: http://nlvm.usu.edu/
Oregon Department of Education Math Scoring Guide

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