assessment plan final
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e b r a n 0 0 1 @ g m a i l . p l a t t s b u r g h . e d u
2012
Assessment Plan
Introduction to GeometryWindows User
Eric R. Bran
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TABLE OF CONTENTS
Introduction 2
Unit Plan Overview . 5
Weekly Assessment Plan . 6
Connections to Instructional Goals 18
Grading Policy .. 21
Assessment Samples . 23
Pretest Sample . 24
Formative Assessment Samples . 29
Sample 1 ... 29
Sample 2 ... 33
Sample 3 ... 37
Sample 4 ... 40
Summative Assessment Sample . 41
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INTRODUCTION
DESCRIPTION
This assessment plan is designed for the introductory unit of High School Geometry. In this unit,
the students will be exposed to various definitions, postulates, and theorems. These new
concepts will serve as the building blocks and the foundation of geometric logic. The unit will
begin with a review of basic algebraic topics and will gradually progress to new more complex
concepts. These concepts will be used alongside mathematical logic to prove postulates and
theorems later in the course. The students enrolled in this course will vary in grade, ability, and
experience. Depending on the school, the students may range from sophomores to seniors, and
sometimes even freshmen.
This course is intended to prepare students for the New York Geometry Regents examination.
The course includes basic geometric concepts and theory, and is focused heavily on practice
and reflection. Students will work with geometric models, postulates, and theorems, to develop
critical thinking skills necessary to solve geometric proofs.
INSTRUCTIONAL GOALS
The instructional goals of this unit are to cover the basics of high school geometry using
selected chapters from the text book, have students reflect on their learning preferences, and
promote respect, integrity, and patience in the classroom.
At the end of the unit, students will be able to:
Solve basic algebraic equations; Define the basic terms of geometry; Solve problems using different geometric definitions; Define complex terms of geometry; Deduce whether a claim is true by using different geometric definitions; Define the degree measures of special kids of pair of angles; Find the degree measure of special kinds of pair of angles.
CONTENT KNOWLEDGE
This unit plan is based on Mount Vernon City School Districts curriculum map for the High
School Regents Geometry course. A big resource for the unit is the online textbook which offers
detailed knowledge information and a variety of examples.
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The unit will contain the following lesson plans/chapters:
Solving Equations 1-1 Undefined Terms and Set Theory 1-3 Definitions, Lines, and Line Segments 1-4 Midpoints and Bisectors 1-5 Rays and Angles 1-6 More Angle Definitions 5-6 Perpendicular Bisector of a Line Segment 3-4 Direct and Indirect Proofs 3-5 Postulates, Theorems, and Proofs 4-3 Proving Theorems about Angles 14-1 Parallel Lines: Properties and Constructions
Knowledge:
At the end of the unit, students will be able to:
Work with integers; Apply properties of equality from algebra; Solve multi-step problems; Solve simple proportions by cross product; Simplify ratios; Find the square of a number; Find the square root of a number; Use the Pythagorean Theorem. Define points on a line and line segment; Define midpoint and bisector of a line segment; Find the midpoint and bisectors of a line segment; Define a ray and an angle; Define the bisector of an angle; Identify an angle bisector. Define perpendicular bisector Identify a perpendicular bisector Deduce whether a claim is true or false Identify the basic tools for doing proofs. Define Adjacent angles, Complementary angles, & Supplementary angles; Define parallel lines; Use properties of parallel lines; Construct a parallel to a given line at a given point; Identify linear pair of angles and vertical angles.
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Text
Gantert, A. X. (2008).AMSCO Geometry. New York, NY: AMSCO School Publications, INC. (ISBN:
978-1-56765-596-4)
ASSESSMENT GOALS
(1) Gather Ample Evidence
One of the hardest parts of teaching is trying to figure out how much the students are actually
learning. The main goal of this assessment plan is to gather as much evidence as possible to
gauge student learning. The hope is that by gathering as much information as possible, the
teacher can generate a unit grade which is reflective of the students learning and
achievements.
(2) Diversify Assessments for Accuracy
This assessment plan provides multiple methods of assessing student achievement in order to
provide the students with multiple outlets to demonstrate their proficiency. By providing
different opportunities for students to demonstrate what they know, the assessment data can
be more accurate at reflecting the reality. Sometimes students may struggle at taking test, but
excel at doing a presentation. The diversity in assessments allows for students to succeed even
if they struggle with certain assessments.
(3) Student Proficiency
A more ambiguous goal of this assessment plan is to provide the teacher with fast and reliable
information regarding his/her students. By including formative assessment methods, the
teacher can be better prepared to adjust instruction to be more effective. The diagnostics test,
for example, is intended for the teacher to create a lesson plan based on the needs of the
students.
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UNIT PLAN OVERVIEW
WEEK 1 Monday Tuesday Wednesday Thursday Friday
Lesson Title Solving
Equations
Solving
Equations
Solving
Equations
Class Activity Diagnostics
Test
Guided Notes Practice Lab Activity 1 Quiz
Homework Worksheet 1 Worksheet 2 Worksheet 3 Journal Entry 1 Geometry
Essay
WEEK 2 Monday Tuesday Wednesday Thursday Friday
Lesson Title Undefined
terms & setTheory
Definitions,
Lines, & LinesSegments
Midpoint &
Bisector
Rays & Angles More Angle
Definitions
Class Activity Lecture Guided Notes Practice Lab Activity 2 Quiz
Homework Worksheet 4 Worksheet 5 Worksheet 6 Journal Entry 2 Blueprint
Project Part I
Monday Tuesday Wednesday Thursday Friday
Lesson Title Perpendicular
Bisector of a
Line Segment
Direct and
Indirect
Proofs
Postulates,
Theorems,
and Proof
Class Activity Guided Notes Review Q&A Lab Activity 3 Test
Homework Worksheet 7 Journal Entry
3
Worksheet 8 Study for Test Blueprint
Project Part II
Monday Tuesday Wednesday Thursday Friday
Lesson Title Proving
Theorems
About Angles
Proving
Theorems
About Angles
Parallel Lines:
Properties &
Construction
Review
Class Activity Review Guided Notes Practice Presentations Presentations
Homework Worksheet 9 Worksheet 10 Finalize
Blueprint
Project
Journal Entry 4 Take Home
Quiz
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WEEKLY ASSESSMENT PLAN
WEEK 1
Monday Tuesday Wednesday Thursday Friday
Lesson Title Solving
Equations
Solving
Equations
Solving
Equations
Class Activity Diagnostics
Test
Guided Notes Practice Lab Activity 1 Quiz
Homework Worksheet 1 Worksheet 2 Worksheet 3 Journal Entry 1 Geometry
Essay
Common Core Standards
Week one is a review of knowledge that students will be expected to know before exploring the
complex concepts of geometry. There are no standards in the geometric strand for this kind ofreview.
Instructional Goals
At the end of the week, students will be able to:
Solve basic algebraic equations.Knowledge
At the end of the week, students will be able to: Work with integers; Apply properties of equality from algebra; Solve multi-step problems; Solve simple proportions by cross product; Simplify ratios; Find the square of a number; Find the square root of a number; Use the Pythagorean Theorem.
Informal Formative Assessments
White Board Warm up:
Students will be given a personal whiteboard in which they will write the answer to the warm-
up question. The warm-up questions will come straight out of the worksheet that was assigned
for homework the previous night. The teacher will instruct the students to display their answers
by raising their whiteboards. By doing this, the teacher can quickly gauge how many students
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got the question right. This also allows for the teacher to decide whether or not to move on to
the next set of warm-up questions.
Red, Yellow, Light:
At the end of each class, students will be given a post-it note. In this post-it note, they will write
a question they still have about the material learned and their name. Before exiting the
classroom they will place the post-it note in a traffic light poster by the classroom door. If the
students feel comfortable with the material learned, they will put the post-it on the green
section of the poster. If the students are still struggling with the material, the students will put
the post-it on the red section. If the students understand some of the material but still need
some clarity, the students will place their post-it in the yellow section. This assessment tool will
be used for the teacher to plan for the next lesson.
Thumbs up, Thumbs Down:
During the class, the teacher will check for understanding using the thumbs up, thumbs down
technique. If students feel good about the material they will put their thumbs up. If thestudents are confused they will put their thumb down. If the majority of the class is confused,
the teacher can spend more time explaining the material. If there are only a few students who
are confused, the teacher can take a mental note and help those students out when they work
individually.
Formal Formative Assessments
Diagnostics Test (Pass/Fail):
At the beginning of the unit, students will take a diagnostic test. This test is intended to gauge
what prior information the students know prior to the unit. It is essential for students to know
how to solve basic algebraic equations. By taking this diagnostics test, the teacher as well as the
students, can see where they need to work on to achieve success. A basic foundation on
algebra is important for the success in geometry. The diagnostic test will be 20 questions and
will take roughly 30 minutes. The students will swap papers and grade each other (NOTE: In
order to promote integrity in the classroom, students will be exposed to situations in which
they need to provide honest feedback to their peers). After the tests have been graded, the
teacher will collect them for evidence. This will serve as a guide to structure the algebra review
lesson of the following day.
Worksheet 1, 2, & 3 (30 points):
These three worksheets will focus on basic algebra review. Questions in this worksheet will besimilar to the diagnostics test in order to provide plenty of practice for content mastery. The
worksheets will be used at the beginning of the class to begin the warm-ups. During the warm-
up, the teacher will be able to work any problems that the students are confused about.
Worksheets will be collected, the teacher will make a copy of them, and finally the students will
receive the copies. Originals will be kept in student folders in the classroom for evidence of
student achievement.
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Journal Entry 1 (10 points):
Students will be asked to keep a journal throughout the course. They are welcomed to write as
often as possible, but there will only four of these journal entries will be answering a question.
These four will be graded. Students will answer the following questions: (1) What do you like
about the material weve covered? (2) What material are you currently struggling with? (3)
What would make your learning easier? (4) What motivates you to do well in a math class? The
journals will be collected every Friday.
Lab Activity 1 (20 points):
Every Thursday, students will work in groups to complete a task that relates their knowledge to
real-world application. On the first week, the students will get a choice between three
different topics: (1) Baseball, (2) Population, and (3) Space. The students will be instructed to
choose the topic that they are most interested in and form groups based on these preferences.
Each group will work on a specific algebraic worksheet that relates to their topic. Towards the
end of the class the group will select 2-3 representatives to share their findings to the class.Each student must hand-in their own worksheet with a sentence or two describing how they
contributed to the activity.
Quiz (20 points):
Students will be quizzed on all the material they have learned in week one. This quiz will take
the majority of the period and will cover material on simplifying equations, solving multi-step
problems, solving algebraic equations, defining terms, and solve problems using the
Pythagorean Theorem. Quizzes will be graded; the teacher will make a copy, and finally hand in
the copy to the students. The originals will be kept in a folder for evidence of student
achievement.
Geometry Essay (30 points):
Students will be asked to research a working definition for geometry and explain it in their own
words. They will be asked to research how professionals use geometry in their careers and how
it can be useful in the students life. Furthermore, the students will be asked to research a
profession of their choice and find out if the profession uses any kind of geometry and explain
how. The paper will be graded using a rubric.
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WEEK 2
Monday Tuesday Wednesday Thursday Friday
Lesson Title Undefined
terms & set
Theory
Definitions,
Lines, & Lines
Segments
Midpoint &
Bisector
Rays & Angles More Angle
Definitions
Class Activity Lecture Guided Notes Practice Lab Activity 2 Quiz
Homework Worksheet 4 Worksheet 5 Worksheet 6 Journal Entry 2 Blueprint
Project Part I
Common Core Standards
CCSS.Math.Content.HSG-CO.A.1 Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
CCSS.Math.Content.HSG-GPE.B.6 Find the point on a directed line segment between two given
points that partitions the segment in a given ratio.
Instructional Goals
At the end of the week, students will be able to:
Define the basic terms of geometry; Solve problems using different geometric definitions.
Knowledge
At the end of the week, students will be able to:
Define points on a line and line segment; Define midpoint and bisector of a line segment; Find the midpoint and bisectors of a line segment; Define a ray and an angle; Define the bisector of an angle; Identify an angle bisector.
Informal Formative Assessments
White Board Warm up:
Students will be given a personal whiteboard in which they will write the answer to the warm-
up question. The warm-up questions will come straight out of the worksheet that was assigned
for homework the previous night. The teacher will instruct the students to display their answers
by raising their whiteboards. By doing this, the teacher can quickly gauge how many students
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got the question right. This also allows for the teacher to decide whether or not to move on to
the next set of warm-up questions.
Red, Yellow, Light:
At the end of each class, students will be given a post-it note. In this post-it note, they will write
a question they still have about the material learned and their name. Before exiting the
classroom they will place the post-it note in a traffic light poster by the classroom door. If the
students feel comfortable with the material learned, they will put the post-it on the green
section of the poster. If the students are still struggling with the material, the students will put
the post-it on the red section. If the students understand some of the material but still need
some clarity, the students will place their post-it in the yellow section. This assessment tool will
be used for the teacher to plan for the next lesson.
Thumbs up, Thumbs Down:
During the class, the teacher will check for understanding using the thumbs up, thumbs down
technique. If students feel good about the material they will put their thumbs up. If thestudents are confused they will put their thumb down. If the majority of the class is confused,
the teacher can spend more time explaining the material. If there are only a few students who
are confused, the teacher can take a mental note and help those students out when they work
individually.
Line of Understanding:
Students will be asked to line up based on how comfortable they feel with the material
provided in the lessons. Those who are really comfortable with the material will line up on one
side of the line. Those who are not as comfortable will line up towards the other side of the
line. The teacher will instruct the students to find the midpoint of the line and fold it based on
that point. At this point students should be facing another student. This will become the
partners for the lab activity on Thursday. By doing this grouping method, the teacher is able to
gauge how students feel about the material. At the same time, the grouping is intentionally to
have one student who isnt as comfortable with the material to be with someone who is (NOTE:
students will be exposed to different opportunities in which they will practice patience and
respect towards their classmates and the material).
Formal Formative Assessments
Worksheet 4, 5, & 6 (30 points):
These three worksheets will focus on basic geometric definitions. Questions in theseworksheets will gather information on how well the students are able to identify geometric
definitions using a variety of diagrams, models, and representations. Students will be asked to
find the midpoint of segments, and bisectors of angles. The worksheets will be used at the
beginning of the class to begin the warm-ups. During the warm-up, the teacher will be able to
work any problems that the students are confused about. Worksheets will be collected, the
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teacher will make a copy of them, and finally the students will receive the copies. Originals will
be kept in student folders in the classroom for evidence of student achievement.
Journal Entry 2 (10 points):
Students will be asked to keep a journal throughout the course. They are welcomed to write as
often as possible, but there will only four of these journal entries will be answering a question.
These four will be graded. Students will answer the following questions: (1) Do you think
definitions are important? Why or why not? (2) How can knowing the definitions of geometric
terms be useful in the future of the course? (3) What is an effective method for you to really
learn the definitions provided in this course? The journals will be collected every Friday.
Lab Activity 2 (20 points):
The teacher will provide a set of images. Students will choose their top 3 images and bring them
back to their desk. Students will work in groups to complete a lab activity. Each student will
share why they chose their images to the group. Together they will work to try and find angles,angle bisectors, lines, lines segments, midpoints, and rays. They will use markers to draw on the
images. On the back of the image, the students will write all the terms that they discovered.
Students will submit all their work to the teacher, who will make student copies. Originals will
be kept for evidence of student achievement.
Quiz (15 points):
Students will be quizzed on all the material they have learned in week two. This quiz will take
the only half of the period. The quiz will cover of the period and will cover material on basic
geometric definitions. Quizzes will be graded; the teacher will make a copy, and finally hand in
the copy to the students. The originals will be kept in a folder for evidence of student
achievement.
Part I Blueprint Project (60 points):
Students will be asked to complete the first part of the Blueprint Project. The students will think
about their dream home. They are to think about how many levels, windows, doors, and what
kind of furniture will be in their dream home. They will be instructed to draw a blueprint of one
of the floors. Architects use basic geometric concepts to build scale models before building
homes. The students will receive instructions to use as many geometric concepts as possible in
their Blueprint. Students who incorporate all the different geometric concepts will receive 3
extra points added to their upcoming test. Students will also write an essay describing how
their blueprint encompasses the different geometric concepts theyve learned in week two.
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WEEK 3
Monday Tuesday Wednesday Thursday Friday
Lesson Title Perpendicular
Bisector of a
Line Segment
Direct and
Indirect
Proofs
Postulates,
Theorems,
and Proof
Class Activity Guided Notes Review Q&A Lab Activity 3 Test
Homework Worksheet 7 Journal Entry
3
Worksheet 8 Study for Test Blueprint
Project Part II
Common Core Standards
CCSS.Math.Content.HSG-CO.A.1 Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and
SSS) follow from the definition of congruence in terms of rigid motions.
Instructional Goals
At the end of the week, students will be able to:
Define the complex terms of geometry; Deduce whether a claim is true by using different geometric definitions.
Knowledge
At the end of the week, students will be able to:
Define perpendicular bisector Identify a perpendicular bisector Deduce whether a claim is true or false Identify the basic tools for doing proofs.
Informal Formative Assessments
White Board Warm up:
Students will be given a personal whiteboard in which they will write the answer to the warm-
up question. The warm-up questions will come straight out of the worksheet that was assigned
for homework the previous night. The teacher will instruct the students to display their answers
by raising their whiteboards. By doing this, the teacher can quickly gauge how many students
got the question right. This also allows for the teacher to decide whether or not to move on to
the next set of warm-up questions.
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Red, Yellow, Light:
At the end of each class, students will be given a post-it note. In this post-it note, they will write
a question they still have about the material learned and their name. Before exiting the
classroom they will place the post-it note in a traffic light poster by the classroom door. If the
students feel comfortable with the material learned, they will put the post-it on the green
section of the poster. If the students are still struggling with the material, the students will put
the post-it on the red section. If the students understand some of the material but still need
some clarity, the students will place their post-it in the yellow section. This assessment tool will
be used for the teacher to plan for the next lesson.
Thumbs up, Thumbs Down:
During the class, the teacher will check for understanding using the thumbs up, thumbs down
technique. If students feel good about the material they will put their thumbs up. If the
students are confused they will put their thumb down. If the majority of the class is confused,
the teacher can spend more time explaining the material. If there are only a few students whoare confused, the teacher can take a mental note and help those students out when they work
individually.
Formal Formative Assessments
Worksheet 7 & 8 (20 points):
These two worksheets will focus on more complex geometric definitions. Questions in these
worksheets will gather information on how well the students are able to identify geometric
definitions using a variety of diagrams, models, and representations. Students will be asked to
find perpendicular bisectors of a line segment, identify midpoint of segments, and find
bisectors of angles. The worksheets will be used at the beginning of the class to begin the
warm-ups. During the warm-up, the teacher will be able to work any problems that the
students are confused about. Worksheets will be collected, the teacher will make a copy of
them, and finally the students will receive the copies. Originals will be kept in student folders in
the classroom for evidence of student achievement.
Journal Entry 3 (10 points):
Students will be asked to keep a journal throughout the course. They are welcomed to write as
often as possible, but there will only four of these journal entries will be answering a question.
These four will be graded. Students will answer the following questions: (1) How can you check
to see if information you find in the internet is true? (2) List 2-3 questions that you would ask inorder to find out if a claim is true or false. (3) How would you determine a claim to be true in all
situations? (4) Conversely, how would you prove a claim to not be true in all situations?
Lab Activity 3 (20 points):
The teacher will hand out index cards. The students will be instructed to write a fact about
themselves that others in the classroom may not know. The teacher will collect the facts and
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read them out loud. Students will record their facts in a piece of paper. The students will be
asked to go around the room asking their peers yes or no questions. The objective is to try to
figure out who wrote each fact. Students will be asked to answer the following questions: (1)
how did you eliminate possible solutions? (2) What process did you use to complete the task?
(3) How did you use inductive reasoning to complete the task?
Formal Summative Assessments
Test (100 points):
This is a summative assessment which contains content from the first week all the way to the
second week. This test incorporates algebraic equations and geometric definitions. There are
some short answer questions and some multiple choice questions, but no partial credit will be
awarded. This is a way to keep this assessment as objective as possible.
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WEEK 4
Monday Tuesday Wednesday Thursday Friday
Lesson Title Proving
Theorems
About Angles
Proving
Theorems
About Angles
Parallel Lines:
Properties &
Construction
Review
Class Activity Review Guided Notes Practice Presentations Presentations
Homework Worksheet 9 Worksheet 10 Finalize
Blueprint
Project
Journal Entry 4 Take Home
Quiz
Common Core Standards
CCSS.Math.Content.HSG-CO.C.9 Prove theorems about lines and angles. Theorems include:vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent; points on a perpendicular bisector of a
line segment are exactly those equidistant from the segments endpoints.
CCSS.Math.Content.HSG-CO.C.10 Prove theorems about triangles. Theorems include: measures
of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the
length; the medians of a triangle meet at a point.
CCSS.Math.Content.HSG-CO.C.11 Prove theorems about parallelograms. Theorems include:opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram
bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
CCSS.Math.Content.HSG-CO.D.12 Make formal geometric constructions with a variety of tools
and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting
an angle; constructing perpendicular lines, including the perpendicular bisector of a line
segment; and constructing a line parallel to a given line through a point not on the line.
CCSS.Math.Content.HSG-CO.D.13 Construct an equilateral triangle, a square, and a regular
hexagon inscribed in a circle.
Instructional Goals
At the end of the week, students will be able to:
Define the degree measures of special kinds of pairs of angles; Find the degree measures of special kinds of pair of angles.
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Knowledge
At the end of the week, students will be able to:
Define Adjacent angles, Complementary angles, & Supplementary angles; Define parallel lines; Use properties of parallel lines; Construct a parallel to a given line at a given point; Identify linear pair of angles and vertical angles.
Informal Formative Assessments
White Board Warm up:
Students will be given a personal whiteboard in which they will write the answer to the warm-
up question. The warm-up questions will come straight out of the worksheet that was assigned
for homework the previous night. The teacher will instruct the students to display their answersby raising their whiteboards. By doing this, the teacher can quickly gauge how many students
got the question right. This also allows for the teacher to decide whether or not to move on to
the next set of warm-up questions.
Red, Yellow, Light:
At the end of each class, students will be given a post-it note. In this post-it note, they will write
a question they still have about the material learned and their name. Before exiting the
classroom they will place the post-it note in a traffic light poster by the classroom door. If the
students feel comfortable with the material learned, they will put the post-it on the green
section of the poster. If the students are still struggling with the material, the students will putthe post-it on the red section. If the students understand some of the material but still need
some clarity, the students will place their post-it in the yellow section. This assessment tool will
be used for the teacher to plan for the next lesson.
Thumbs up, Thumbs Down:
During the class, the teacher will check for understanding using the thumbs up, thumbs down
technique. If students feel good about the material they will put their thumbs up. If the
students are confused they will put their thumb down. If the majority of the class is confused,
the teacher can spend more time explaining the material. If there are only a few students who
are confused, the teacher can take a mental note and help those students out when they work
individually.
Formal Formative Assessments
Worksheet 9 & 10 (20 points):
These two worksheets will focus on word problems using all the geometric definitions taught in
the unit. The worksheets will be used at the beginning of the class to begin the warm-ups.
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During the warm-up, the teacher will be able to work any problems that the students are
confused about. Worksheets will be collected, the teacher will make a copy of them, and finally
the students will receive the copies. Originals will be kept in student folders in the classroom for
evidence of student achievement.
Journal Entry (10 points):
Students will be asked to summarize what theyve learned about themselves throughout this
unit as well as what they learned about geometry.
Take-Home Quiz (15 points):
Students will do a take-home quiz. This quiz will be covering all the information covered in the
past few weeks. It will involve word problems, basic constructions, and using definitions. The
purpose of this assessment is to give students practice as they move on to the next unit. These
quizzes will be graded by their peers on the following day. The teacher will collect them, double
check the grade, and hand back a photocopy of the quiz. The original will be kept for evidence
of student achievement.
Formal Summative Assessment
Part II - Blueprint Project (60 points):
The students will complete the second part of the blueprint project. They will be asked to scale
their blueprint up to triple its size. The students are not required to redraw the blueprint but all
measurements should be reflected on the scale. The students will also be asked to find the area
of their blueprint and how much carpeting they should purchase to cover the whole floor.
Students will be asked to write a final reflection paper describing anything theyve learned in
the unit and how they used the information to complete the project. The students will give a 5
minute presentation showcasing their finalized product. The presentation and essay will be
graded on a scale. The blueprint will be graded on how accurate their computations and how
much geometry they applied to their project.
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CONNECTIONS TO INSTRUCTIONAL GOALS
WEEK 1
Instructional Goals
Students will be able to solve basic algebraic equations
Students will be expected to know basic algebra to succeed in this geometry course.
Throughout the week, the students will be reviewing topics from their prior algebra class. The
students will have the opportunity to ask questions and practice the concepts being reviewed
during the lessons. The teacher will use informal formative assessments to check for
understanding throughout the lessons.
At the beginning of the week, the teacher will administer a diagnostics pre-test. The results of
this test will serve as a guide for the lesson planning of the week. The test is on a pass/fail basis,
because it is not meant to hurt the students grades. The test has the purpose to gauge howmuch prior knowledge the students are bringing to the unit. The first week is all about gearing
the lessons to meet the needs of that specific class so they can review information that they
should already know.
Students will demonstrate their progress by submitting worksheets that provide practice of the
lesson taught. At the end of the week, the students will have to take a full-period quiz in which
they will be asked to demonstrate how much algebra they are able to understand before
beginning on geometric concepts. Along with these objective assessments, the students will be
required to keep a journal for the course. They will be asked to reflect on the concepts and on
their own learning preference. This subjective tool will be used to assess students aptitude inthe classroom.
On Thursday, the students will work in a lab activity that will test their knowledge of algebraic
equations. During this assessment, the students will work together to solve-multi step
problems. They will be asked to write a paragraph or two explaining how they contributed to
the group work. The reason for this written portion is for the teacher to have evidence of
student engagement in the classroom. The teacher can also compare their observations of the
students with what they write to see if they are writing honestly.
The final homework for the week is meant to prep the students with a basic definition of
geometry. Starting on Monday, the students will be starting to learn more complex definitionsof geometry and therefore need a basic understanding of what geometry is and what it is used
for.
Assessments: Diagnostics Test, Worksheets, Lab Activity, Research Paper, Journal, & Quiz.
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WEEK 2
Instructional Goals
The Students will be able to define the basic terms of geometry
After week one, the students should be able to solve basic algebraic equations. The students
will share with their peers what they found on the definition of geometry. This opening activity
will be used to kick-start the lesson on basic geometric terms. Students will be assessed on how
well they understand the definitions by demonstrating it on the worksheets. At the end of the
week, the students will take a quiz on the definitions they learned. Teacher will use informal
formative assessment techniques mentioned in the weekly assessment plan overview to check
for student understanding. The blueprint project will also test the students ability define the
different geometric terms by asking them to list what definitions they used in their blueprint.
The worksheets reflect whether the students are able to look at multiple problems and use
definitions correctly to come to an acceptable solution.
The student will be able to solve problems using different geometric definitions.
During the lab activity on Thursday, students will be given pictures and will be asked to find
geometric concepts within the images. They will share with each other their findings, and will
write how they contributed to the activity. They will also list all the geometric definitions they
used to complete the activity. This will directly assess how well students are able to use the
definitions and apply them to solve geometric problems. Students will also be asked to write a
journal entry so they can demonstrate if they see the importance of these definitions. The
blueprint project will also test the student s ability to construct the geometric terms learned
throughout the week as well as define them in their blueprint creation.
Assessments: Research Paper, Worksheets, Journal, Quiz, Project.
WEEK 3
Instructional Goals
The students will be able to define complex terms of geometry
Students will be exposed to new geometric definitions. These definitions will be more complex
than the ones from week two. The students will demonstrate their knowledge through the
different worksheets. During this week, they will also be tested on all the material they havelearned so far. They will be tested on the algebraic review, basic geometry definitions, complex
geometric definitions, and the applications of their definitions. This test will be multiple-choice
with some short answers. This is an objective cumulative assessment because the answers are
either right or wrong, not partial credit will be awarded. The worksheets reflect whether the
students are able to look at multiple problems and use definitions correctly to come to an
acceptable solution.
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The students will be able to deduce whether a claim is true by using different geometric
definitions
During the lab activity, the students will play a game that will test their ability to reason logically
and to deduce whether a claim is true or not. They will be asked to reflect on the process they
used to find the answers. This subjective assessment will be collected to show evidence of
student proficiency in the process behind direct and indirect proofs. The test will also challenge
students to solve problems by accurately selecting statements that are true.
Assessments: Worksheets, Journal, Lab Activity, Test.
WEEK 4
Instructional Goals
The students will be able to define the degree measures of special kinds of pairs of angles
Students will be assessed to see if they can define special kinds of pairs of angles by submitting
the worksheets. These worksheets will provide extra practice from the lesson learned in the
class. The teacher will review the answers of these worksheets in the warm-up. Students will be
assessed on how well they know the definitions in a take-home quiz at the end of the week.
The worksheets reflect whether the students are able to look at multiple problems and use
definitions correctly to come to an acceptable solution.
The students will be able to find the degree measures of special kinds of pair of angles
Students will submit worksheets to show that they can apply the definitions theyve learned to
word problems and other geometric problems. They will also be assessed on their proficiency in
the take-home quiz at the end of the week. The worksheets reflect whether the students are
able to look at multiple problems and use definitions correctly to come to an acceptable
solution.
Students will be assessed for the entire unit during this week. They will present their finalized
version of their blueprint project. The presentation will be graded on a rubric as well as the
other components of the project. The project is designed to be worked in steps throughout the
month. The assessment should provide accurate information on student progress and gauge
the student mastery of the subject. As usual the students will be asked to submit a journalentry, this time it will summarize their experience with geometry for the introductory unit. A
completed project should be reflective of all the definitions and applications of such that the
students were exposed to throughout the month.
Assessments: Worksheets, Journal, Quiz, Presentation, Project.
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GRADING POLICY
GRADING SCALE RATIONALE
To pass the unit, a student must earn at least 65% of the total possible points from the
assignments. In other words, the student must earn at least 325 points to pass the unit. The
student can look at the unit requirements and be able to determine their grade based on how
many points they score in each assignment.
GRADING SCALE
UNIT REQUIREMENTS RATIONALE
The goal of this assessment plan is to provide students with a variety of ways to demonstrate
what theyve learned. In order to compute a single score for this unit/month, the teacher mustbe mindful of the grading policy. Each assignment has a point value, some are worth more than
others, but essentially they are all weighed based on how useful the information gathered can
be, in order to determine what the students have learned.
At the top of the list, we have the Blueprint Project. In this summative project, students will be
assessed on how well they can apply what they have learned in the unit. They will have the
opportunity to demonstrate their learning, their struggles, and conscious reflection of what
theyve learned. This will be the final unit project and is worth the most amounts of points.
When we look at tests and quizzes in this particular grading policy, these are objective tools for
teachers to measure what the students know. The test is cumulative and therefore must beworth a large amount, 100 points in this case. The quiz on the other hand, only measures a
portion of the content and therefore is worth a little less than the test, 50 points in this case.
Some students may not be great test takers, and they may struggle earning these points.
Because of this, variety is important.
Percentage Score Letter Grade
95-100% A
90-94.9% A-
85-89.9% B+
80-84.9% B75-79.9% B-
70-74.9% C+
65-69.9% C
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The take-home worksheets are a way for students to practice what they learned in each
particular day. There are ten worksheets throughout the unit. Each worksheet will be graded
separately; the lowest two scores will be dropped to account for special circumstances that
occur in each students life. Each worksheet is worth 10 points and will have a total of 20
questions; each will be worth .5 points. Notice that these worksheets are also objective,
students either get the answer correct, or they dont. Keeping the majority of the assessments
objective increases the validity of the assessments.
Often in math, teachers neglect to use writing as an assessment tool. In this plan, there are a
few writing assignments that are intended for students to reflect on their own learning. These
are subjective forms of assessments and will be graded based on a rubric. These include the
journals, the geometry paper, and the blueprint project. There are also hands-on activities in
which students get to demonstrate their learning right in the classroom.
Participation is in this grading policy to encourage student engagement in the lessons. At the
end of the week each student will rank themselves on a participation scale. They will be askedto provide a rationale as to why they have ranked themselves where they have. By doing this,
the teacher can collect physical evidence of student participation. The teacher will need to
maintain notes on the students in order to compare what the teacher sees and what the
students see in terms of participation. Notice the point value for participation is fairly low, this
is to minimize the subjectivity in the final grading but still allow students to take some
ownership of their learning.
By increasing the variety of assessment tools, the teacher is giving the students the opportunity
to demonstrate what theyve learned in different ways. By keeping the majority of the
assessment tools objective, then the teacher can make easy and accurate analysis of the
assessments when creating that single grade at the end of the unit. The teacher has to simply
add all the points that a student has earned and find what percentage of the total points the
students have earned. It is important to note that the teacher will keep copies of all the work
that the students hand in, this will be used as evidence and can be used to parallel APPR
standards.
UNIT REQUIREMENTS
Blueprint Project .. 120pts
Test .. 100ptsWorksheets .. 80pts
Lab Activities .. 60pts
Quiz .. 50pts
Journal .. 40pts
Participation .. 20pts
Geometry Paper .. 30pts
500pts
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ASSESSMENT SAMPLES
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PRETEST ASSESSMENT SAMPLE
Name: ________________________________________________ Date: _________________
**NODA = None of the above
1. a
2. A
3.
4.
5.
6.
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7.
8.
9.
10.
11.
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12.
13.
14.
15.
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16.
17.
18.
19.
20.
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Geometry Diagnostics Pre-Test Answer Key
1 D 11 D
2 C 12 C
3 C 13 C
4 B 14 D
5 C 15 A
6 B 16 C
7 D 17 A
8 B 18 C
9 E 19 D
10 B 20 E
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FORMATIVE ASSESSMENT SAMPLES
LAB ACTIVITY 1
Name: ________________________________________ Date: __________________
Instructions: select one of the three topics below and wait for the teacher to give further
instructions.
(1)Baseball(2)Population(3)Space
Your selection: _______________________
Before you leave take a piece of loose-leaf and answer the following questions:
(1)How did you contribute to the activity?(2)Were you more interested in the other options more than yours?(3)What did you learn?
Students will receive the slip of paper above and submit it with their work
TEACHER INSTRUCTIONS
Every Thursday, students will work in groups to complete a task that relates their knowledge to
real-world application. On the first week, the students will get a choice between three
different topics: (1) Baseball, (2) Population, and (3) Space. The students will be instructed to
choose the topic that they are most interested in and form groups based on these preferences.
Each group will work on a specific algebraic worksheet that relates to their topic. Towards the
end of the class the group will select 2-3 representatives to share their findings to the class.
Each student must hand-in their own worksheet with a paragraph or two describing how they
contributed to the activity.
CHOICES SAMPLE BELOW
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CHOICE 1: BASEBALL (SAMPLE)
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CHOICE 2: POPULATION (SAMPLE)
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CHOICE 3: SPACE (SAMPLE)
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WORKSHEET 1 SOLVING ALGEBRAIC EQUATIONS
Name: _________________________________________ Date: ______________________
1.) 16 = x + 4 2.) - 3 = x + 7
3.) x / - 7 = 2 4.) x + 3 = 6
5.) 7 + x = 9 6.) 10 + 6x = 52
7.) 4x + 9 = 37 8.) 2x + 5 = - 3
9.) - 7x + 1 = 36 10.) 3x + 6 = 42
11.) 2 + 2x + 4x = 14 12.) 6x + 7 + 5x = 18
13.) 79 = 3x + 7x + 9 14.) - 6 + 3x - 4x = - 16
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15.) - 3x + 2 + 7x = - 2 16.) 5x - 10 = - 4x - 10
17.) 6x + 1 = 4x + 7 18.) - 3x + 2 = x - 46
19.) - 5 + 5x = - x + 55 20.) 7x + 4 = 6x + 8
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WORKSHEET 1 SOLVING ALGEBRAIC EQUATIONS (ANSWER KEY)
1) 16 = x + 4 answer: x = 12 2) - 3 = x + 7 answer: x = -10
3) x / - 7 = 2 answer: x = -14 4) x + 3 = 6 answer: x = 3
5) 7 + x = 9 answer: x = 2 6) 10 + 6x = 52 answer: x = 7
7) 4x + 9 = 37 answer: x = 7 8) 2x + 5 = - 3 answer: x = -4
9) - 7x + 1 = 36 answer: x = -5 10) 3x + 6 = 42 answer: x = 12
11) 2 + 2x + 4x = 14 answer: x = 2 12) 6x + 7 + 5x = 18 answer: x = 1
13) 79 = 3x + 7x + 9 answer: x = 7 14) - 6 + 3x - 4x = - 16 answer: x = 10
15) - 3x + 2 + 7x = - 2 answer: x = -1 16) 5x - 10 = - 4x - 10 answer: x = 0
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17) 6x + 1 = 4x + 7 answer: x = 3 18) - 3x + 2 = x - 46 answer: x = 12
19) - 5 + 5x = - x + 55 answer: x = 10 20) 7x + 4 = 6x + 8 answer: x = 4
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Worksheet 2 Graphing
Name: _______________________________________ Date: ____________________
1. Draw a representation of the following functions.y = x
2y = -x
2
2. Define the following terms.a. Maximum of a function:
b. Minimum of a function:
3. Determine whether the function has a minimum or a maximum.
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a) y = -3x2 2x + 7 b) y = 2x
2 5x + 1
c) y = -2x2 + 4x - 1 d) y = (1/2)x2 + 3x
4. Complete the following table of values for the formula y = -2x2 + 4x. (12 points)X -3 -2 -1 0 1 2 3 4
y
5. Graph the following functions. Dont forget to include the table of values for each function aswell as the list of ordered pairs. Also mark the max or the min along with the y-intercept.
a. y = -x2 3 (15 points)
b. y = -2x2 + 4x (15 points)
c. y = -x2 + 6x + 1 (15 points)
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d. y = ()x2 + 1 (15 points)
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Journal Entry 1 (10 points):
In a journal entry answer the following questions:
(1) What do you like about the material weve covered?
(2) What material are you currently struggling with?
(3) What would make your learning easier?
(4) What motivates you to do well in a math class?
Note: Journals are collected every Friday.
Rubric
Excellent (10 pts) Good (8 pts) Okay (6 pts) U/N (5 pts)
Journal Entry Student answers allthe questions with
2-3 examples and
clear details. Entry
ranges from 200-400
words.
Student answers allthe questions with
1-2 examples but
lacks detail. Entry
ranges from 100-
300 words.
Student answerssome questions
with 1 example.
Entry is between
100-200 words.
Student ismissing some
answers. Entry is
under 100 words.
U/N = unsatisfactory
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SUMMATIVE ASSESSMENT SAMPLE
BLUEPRINT PROJECT
DESCRIPTION
Students will work on a summative project throughout the month. There are different parts to
this assignment and they will be graded on a rubric. Rubric is attached. All parts must bepresent at the due date to be considered for full credit.
BLUEPRINT
Think of your dream home. Think about how big it would be, what kind of furniture you would
have, how many doors you would have, how many rooms there would be, how many windows,
etc. create a blueprint of the main floor of your dream house using geometric concepts. You
must include doors, windows, and at least three rooms. Provide measurements and label the
parts of your blueprint.
SCALING, AREA, AND PERIMETER
Find the perimeter and area of your blueprint. You must then scale all the dimensions so that
the measurements are four times the size of the original. Develop and equation that would
scale any measurement to these specifications. Find the area and perimeter using the new
dimensions. Make a conjecture as to what happened to the area and perimeter when the
dimensions were scaled up.
REFLECTION
Write a reflection paper 250-400 words. Include what you have learned in this past unit, what
you struggled with, and any obstacles you overcame. Provide examples that demonstrate your
thinking. Be thoughtful and introspective but most importantly be honest with yourself.
PRESENTATION
Develop a 5-7 minute presentation showing your classmates what you have accomplished with
this project. The presentation will be on the last two days of the unit.
DEFINITIONS LIST
Look back at your finalized project and develop a list of concepts that you used in your project.
Briefly explain where youve used the concepts. For example, I used parallel lines when
constructing the walls of my living room.
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BLUEPRINT PROJECT RUBRIC
4 3 2 1
Blueprint Final blueprint is
submitted in a very
organized and neatmanner. Student
used tools such as
straightedge and
compass to create
blueprint. All the
requirements,
dimensions and
labels are included.
Final blueprint is
submitted in an
organized and neatmanner. Student
used some tools
such as straightedge
to create the
blueprint. Most
labels and
dimensions are
included.
Final blueprint is
submitted in an
organized andneat manner.
Student failed to
use geometric
tools to create
the
constructions.
Only some labels
and dimensions
are included
Final blueprint is
unorganized.
Student freehands the
blueprint.
Missing labels
and dimensions.
Scaling, Area,
Perimeter
All computations are
correct. Student
submits the scaling
key. Student shows
all the work.
Some computations
are missing. Student
submits the scaling
key. Student shows
all work.
Computations
are incorrect.
Student submits
scaling key.
Student shows
only some work.
Missing
computations,
only answers
given. Student is
missing work.
Reflection Student describes
with at least 3
examples how they
will utilize the
information theyve
learned in their
future.
Student describes
with 2-3 examples
how they will utilize
the information
theyve learned in
their future. No
more than 3
grammatical andspelling errors
Students
describes with 1-
2 examples how
they will utilize
the information
theyve learned
in their future.
More than 3grammatical and
spelling errors.
Student fails to
defend their
thought with
examples. More
than 6
grammatical and
spelling errors.
Presentation Student stays within
the time frame of
the presentation.
Student explains 3-5
things theyve
learned in the unit.
Student goes over
time frame by a
minute or two.
Student explains 2-4
things theyve
learned in the unit.
Student goes
over the time
frame by over 5
minutes. Student
explains 1-2
examples theyve
learned in their
unit.
Student fails to
meet time
requirement or
goes over by 5
minutes. Student
does not provide
examples as
evidence of their
learning.Definitions List Students
demonstrate the use
of all the geometric
definitions reviewed
in the unit.
Students
demonstrate the
use of the majority
of the geometric
definitions reviewed
in the unit
Student
demonstrates
only some of the
definitions
reviewed in the
unit
Student does not
demonstrate any
of the definitions
reviewed in the
unit.
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