Download Solve equations and inequalities in one variable.

Seton Hall University
College of Education & Human Services
Graduate Studies and Special Programs
GSSP Lesson Plan
8.1 – Quadrilaterals – Finding Angle Measurements in Polygons
Name: Rudy Valentino
Date: 2/8/2012
School: Linden High School
Setting/Grade Level: Classroom / 9th & 10th
Subject(s) (List any interdisciplinary (cross-curricular) connections): Geometry CP – Algebra I
Lesson Theme or Topic: Finding Angle Measurements in Polygons
Composition of Class:
Male
Inclusion Class:
No
Yes
Female
ESL
IEP
AUDIENCE DESCRIPTION General Characteristics:
Four Classes of 98 students – Sizes are 24, 23, 24, and 25
Classes have two students with an IEP (Both classified as ADHD)
Classes has ten ESL or ELL students at different WiDA levels
Linden High School Students by Grade:
9th – 426 (24.2%)
10th – 442 (25.1 %)
11th – 449 (25.5%)
12th – 443 (25.2%)
My Classes by Grade:
9th – 31(32.3%)
10th – 62 (64.6%)
11th – 2 (2.1%)
12th – 1 (1.0%)
Linden High School Students by Gender:
Male - 886 (50.3%)
Female - 877 (49.7%)
My Classes by Gender
Male – 55 (57.3%)
Female – 41 (42.7%)
Linden High School Students by Ethnicity:
Asian - 38 (2.2%)
Black - 637 (36.1%)
Hispanic - 621 (35.2%)
White - 437 (24.8%)
Other – 30 (1.7%)
My Classes by best two Learning Styles
Body – 38 (39.6%)
Logical – 46 (47.9%)
Music – 24 (25%)
Nature – 16 (16.7%)
Verbal – 34 (35.4%)
Visual – 34 (35.4%)
Linden High School Students by Lunch Assistance:
Free Lunch Eligible - 686 (38.9%)
Reduced-Price Lunch Eligible - 217 (12.3%)
Combined Free or Reduced - 903 (51.2%)
My Classes Personality
Interpersonal – 52 (54.2%)
Intrapersonal – 27 (28.1%)
Both – 19 (19.8%)
Linden High School has 16.4% students with disabilities
504
1. Entry Competencies:
The students have already learned algebraic equation solving based on one variable. They also are
familiar with the properties that make up a polygon, and how to classify them based on the number of
sides, angle orientation and congruent sides. All the vocabulary for this lesson has also been
previously covered in past lessons and mastered by the students. The students have the skills needed
for the lesson and should be able to excel once the pieces are placed together for them. We will be
taking the information they already know and use it to form theorems on polygons and solve problems
based on new information. Some students in the class do have a dislike for geometry as a whole or any
of the lessons involved in teaching it.
2. What Accommodations and Modifications are needed for your audience:
Student with ADHD
I will have the student sit in the front of my classroom close to the projector screen and away from the
window and door. This will insure that I have them in an area where I can focus their attention on
what I am doing and not outside distractions. I plan on giving this student an outline of the notes I
will be using in class to make sure they are able to stay on task and if they stray they are able to pick
up with the class easier. The student will also be able to come to the board to place answers on it after
examples are given to the class. Since the students have the tendency not to want to stay seated, they
will be allowed to get up for a drink of lavatory break each day if I notice them getting restless. They
are also allotted more time on tests if needed, however have never needed or requested the extra time.
ESL/ELL Learner
This student will also receive assisted notes that we will be using for the lesson where they only have
to fill out part of the notes instead of taking them from scratch. This will help them focus on the lesson
as opposed to trying to understand what I am saying. I will also use visuals and show step by step on
my document reader how problems are solved to go along with telling the class. By writing down each
step, they could follow me even if they do not understand me. I also have each student who really
struggles with the English language sit in a group with a bilingual student to help translate any tough
word to that student for understanding. On tests I will give them extra help explaining a word problem
if they are having trouble understanding what a word is. I will also let them use books to help them
translate certain words, and soon let them use their phones when that technology becomes more readily
available.
GOALS, OBJECTIVE(S), STANDARDS
1. Established Goals
Students will be able to have the full understanding of all the concepts involving finding different
angle measurements in or outside polygons depending on the number of sides and configurations they
have derived from a sketch or statement.
2. Student Knowledge, Skills and Enduring Understandings
The student will be able to:
1. Find the sum of the interior angles of a polygon based on its number of sides.
2. Find the number of sides of a polygon based on the sum of its interior angles
3. Find a missing angle measurement inside a polygon based on the number of sides and other angle
measurements inside that polygon.
4. Find the measure of the exterior angles of a polygon based on other exterior angle measurements
5. Find the measure of each angle of a regular polygon based on the number of sides it has
3. Common Core State Standards initiative:
Mathematics
High School: Algebra
Creating Equations
Create Equations that describe numbers or relationships.
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential functions.
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation has a solution.
Construct a viable argument to justify a solution method.
Solve equations and inequalities in one variable.
A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
High School: Functions
Building Functions
Build a function that models a relationship between two quantities
F-BF.1. Write a function that describes a relationship between two quantities.
 Determine an explicit expression, a recursive process, or steps for calculation from a context.
 Combine standard function types using arithmetic operations. For example, build a function that
models the temperature of a cooling body by adding a constant function to a decaying
exponential, and relate these functions to the model
High School: Geometry
Congruence
Prove geometric theorems
G-CO.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
segment’s endpoints.
G-CO.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.
Make geometric constructions
G-CO.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.
NJCCC Technology Standards
8.1 Educational Technology
A. Technology Operations and Concepts
B. Creativity and Innovation
C. Communication and Collaboration
METHODOLOGY
Collaborative Learning – Students will go over the lesson as a class so the students will remain focused
on task.
Problem Solving – Students will solve problems based on angles of polygon measurements to ensure
understanding.
Drill/Practice – Students will practice multiple problems on their own to reinforce the lesson
View/Listen/Answer – At the end of the period I will put problems on a PowerPoint slide for the class to
answer.
Group Discussion – We will discuss the rules as a class, describing why it is rational.
Discovery/Inquiry – They will use rulers at start of period to discover as the sides of a polygon increase
you can draw another triangle inside of it. From this they will infer that as the sides of polygons increase
by 1 the interior angles increase by 180˚. This enforces the definition of the rule much better than having
them copy down the formula.
Technology/Delivery – I will use projector to enforce my lesson for the visual and ESL.ELL learners. I
will also utilize assisted notes to keep the students on track and focused at the pertinent information
involved. This will involve using a document reader to project classwork as well as students work on the
board to save time (they don’t have to come up and rewrite their answers). I will also be projecting a
PowerPoint slide show with examples of problems to close the lesson.
Reflection/Response – The class will answer problems and give their reasoning. This is important to
make sure that the class understands the lesson. It also helps me pace the lesson appropriately, not going
too fast for the lower level students.
Lecture – It will be very short, and used to get the theorem across to the students who could not discover
it on their own. It will also be used to describe the problems, along with how to solve them, which we
complete in class.
Other: Use of hands on manipulative – We will use rulers to draw diagonals inside polygons at the start
of class in an effort to have the students create the interior angle theorem. These types of activities are
very good for the kinesthetic and visual learners.
MATERIALS AND RESOURCES:
Rulers
Assisted Note Packet – Chapter 8
Document Reader
Worksheet handouts (8.1B)
Calculator
Geometry Sketchpad
TECHNOLOGY UTILIZED
X
X
X
Audio CD’s/Cassette Tapes
X
Overhead Transparencies
X
Tape Record/CD Player/MP3
VCR/TV/DVD
Assistive Technology Devices (Type)
Calculator
Smart Board
X
Computers/Printers – What PowerPoint slides are on
Basic software tools (Excel, Word, Access)
My class rosters are in Excel, and the worksheets and
Assistive notes are in Adobe format.
X
PowerPoint Slides – Great for the student with a
language barrier and visual learners. They are used
as an exit activity where class answers questions
orally. That helps ensure that they have grasped an
understanding of the lesson.
Commercial Software (e.g. Inspiration)
Geometer’s Sketchpad
Blog, Wiki, other Web-based communication
Digital Storytelling
Podcast
Other not listed – Document Reader – Good because
I am able to write my lesson on it using the 8.1
handout as an outline. Makes the pictures much
larger and brighter on the board and well as allows
me to face the class while giving my lesson instead
of being at the board. Also allows me to put students
work up on the projector for the whole class to see.
Internet/Websites (type in URLs)
www.mybigcampus.com
A “Facebook” like website where I post notes from
the day along with homework problems for the night.
PROCEDURE
Time allocated for lesson: 54 minutes
Day 1
Step 1: Introduction – We will start with a short exercise on drawing different polygons based on the
number of sides they have (From Triangle to decagon), to ensure that they remember their names. We
will then draw diagonals from the top left vertex to all the other vertexes of the polygon. They will then
label the number of triangles that each polygon is composed of next to the number of sides that it has. As
the class uses their notes, I will show on Geometer’s Sketchpad with the use of colored triangles.
Step 2: Essential Questions – The class will figure out the relationship between the number of sides and
number of triangles in a polygon. Based on this information and the number of degrees inside a triangle
they will come up with the formula for the sum of interior angles inside a convex polygon.
Step 3 Exploration – The learners will complete one beginner problem with my guidance then two on
their own. Then I will have 2 students come and place their problems under my document reader and
explain their answers to the class. Next we will cover a more complicated problem as a class and I will
once again assign two for them to do on their own. Once again two students will come up and explain
their answers to the class on the document reader. We will repeat this with all four concepts covered in the
lesson.
Step 4: Application – They will practice their skills on more example problems on their own, and as a
class.
Step 5: Closure and Assessment – To close out the lesson we will complete 8 short problems relating to
the lesson on a PowerPoint slide show. One problem at a time pops up and I will give the students
approximately one minute to solve it before I will call on someone to explain the answer and the process
they followed to arrive at it. Lesson notes as well as homework will be posted on MyBigCampus for
absent students or students who could not keep up with the note taking in class.
Day 2
Step 1: Introduction – We will start with a series of “Do Now” problems from the material we covered
the day before. They will consist of
a) Finding an interior angle based on sides of a polygon and other angles
b) Finding an exterior angle based on other exterior measurements
c) Finding the measure of each angle in a regular polygon
d) Finding the name of a polygon based on the sum of its interior angles
We will then go over homework from the previous night on the document reader, with me showing step
by step how each problem is solved.
Step 2: Essential Questions – The students will then have a chance to ask any questions they had form
the homework or “Do Now” problems. After this is complete we will practice more problems as a class.
Step 3 Exploration – The learners will complete a series of questions based on a worksheet I will hand
out to them. The problems will be based on each of the concepts that were covered on Day 1; however
they will increase with difficulty. Each problem will get more difficult, with algebraic equations being
added into the mix and representing angle measurements. The students will then have to solve for a
variable as opposed to an n angle. Some word problems to relate these concepts to real life activities will
be used to close out the problems in class. Then I will have students place answers on the board in an
assigned space along with their work and go over with the class.
Step 4: Application – They will practice their skills on the example problems on their own, utilizing their
group’s members if necessary and having trouble with a problem.
Step 5: Closure and Assessment – To close out the lesson we will complete four problems based on the
concepts covered the last two days. We will do this one at a time, with the students comparing their
answers with their groups when they are complete. They will then discuss the problems and their
methodology if they received different answers to see who was correct and what they did differently.
Lesson notes as well as homework will be posted on MyBigCampus for absent students or students who
could not keep up with the note taking in class.
ASSESSMENT, PERFORMANCE TASKS, PROJECTS
A test will be given in on Day 12 of our unit. For today’s lesson I will assess the students by walking
around and checking their work as they complete the problems assigned after each part of the lesson. I
will also be able to observe their understanding by how well they do during our closing exercise. I do not
allow the same student to answer more than one question and will be walking around to assist any
students that are still having trouble. This allows multiple students (eight) to participate and show us
what they have mastered. I also try and call on students form different groups (I have 6 sets of 5 set up in
the class at all times). Their final assessment will be their homework assignment which is to complete a
worksheet for me (8.1A) involving 10 problems similar to the ones we will learn how to solve in class.
These will be checked and reviewed the following day of class on the document reader.
DIFFERENTIATION STRATEGIES AND TECHNIQUES
Student with ADHD
A) Students sit in the front of my classroom close to the projector screen and away from the window
and door.
B) Students will be handed an outline of the notes that I will be using in class.
C) Students will be able to come to the board to place answers on it
D) Students will be allowed to get up for a drink of lavatory break each
E) Students are also allotted more time on tests if needed
ESL/ELL Learner
A) Students will be handed an outline of the notes that I will be using in class.
B) I will use visuals and show step by step on my document reader how problems are solved.
C) Each student who struggles with the English language will sit in a group with a bilingual student to
help translate any tough word to that student for understanding.
D) On tests I will give them extra help explaining a word.
E) Students will be able to use books to help them translate certain words.
F) As technology evolves they will be able to use their phones/iPads, iPods as digital translators.