Teacher: Todd Bingham
Date: 7/6/05
Grade: 6th grade
Subject: math
Topic: Geometry/Angles
Angles are everywhere
Time Allotment: 45 minutes
OVERVIEW:
This lesson is meant to introduce students to angles, the parts of angles, angle types,
measurement and degrees. Students will be learning about angles for the first time; therefore
the Direct Instruction strategy is the most useful for delivering this new material. This sixth
grade math lesson will take 40 minutes of the class period.
GOALS
The student will understand how to measure angles.
The student will understand the important terms related to angles.
The student will define the terms related to angles.
The student will list and describe angles found in the classroom and home.
The student will present angles found to the class.
OBJECTIVES
Given ten angles to measure with a protractor the student will measure 4 of 5 correctly.
Given a list of 7 geometric terms related to angles the students will correctly define 5 terms.
Given 10 separate degrees the students will draw and label (right, acute, or obtuse angles) 4
of 5 correctly.
NATIONAL STANDARDS
NCTM Mathematical StandardGeometry Standard- Instructional programs from pre-kindergarten through grade 12 should
enable all students toAnalyze characteristics and properties of two- and three-dimensional geometric shapes and
develop mathematical arguments about geometric relationships
Grades 6–8 Expectations:
In grades 6–8 all students should–
 precisely describe, classify, and understand relationships among types of two- and
three-dimensional objects using their defining properties;
 understand relationships among the angles, side lengths, perimeters, areas, and
volumes of similar objects
ELA Standard
1. Students conduct research on issues and interests by generating ideas and questions, and
by posing problems. They gather, evaluate, and synthesize data from a variety of sources
(e.g., print and non-print texts, artifacts, people) to communicate their discoveries in ways
that suit their purpose and audience.
NEW YORK STANDARDS
New York Standard 3-Mathematics
Students will understand mathematics and become mathematically confident by
communicating and reasoning mathematically, by applying mathematics in real-world
settings, and by solving problems through the integrated study of number systems,
geometry, algebra, data analysis, probability, and trigonometry.
Key Idea #5-Students use measurement in both metric and English measure to provide a
major link between the abstractions of mathematics and the real world in order to describe
and compare objects and data.
Performance Indicator-understand the attributes of area, length, capacity, weight, volume,
time, temperature, and angle.
Performance Indicator-estimate and find measures such as length, perimeter, area, and
volume using both nonstandard and standard units.
English Language Arts
Students will read, write, listen and speak for information and understanding.
Key Idea #1
Listening and reading to acquire information and understanding involves collecting data,
facts and ideas; discovering relationships, concepts and generalizations; and using
knowledge from oral, written and electronic sources.
Performance Indicator 1-gather and interpret information from children’s reference books,
magazines, textbooks, electronic bulletin boards, audio and media presentations, oral
interviews, and from such forms as charts, graphs, maps, and diagrams
Performance Indicator 2- select information appropriate to the purpose of their
investigation and relate ideas from one text to another
Performance Indicator 3-ask specific questions to clarify and extend meaning
MATERIALS
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Protractors for students and one larger class protractor
“Angles are Everywhere” graphic organizer for anticipatory set and copies for
students
“What’s the Angle?” worksheet for independent practice on angles
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“Angles” teachers guide for guided practice
Overhead projector for blank transparency
Computer use for modifications and independent practice website
“What’s The Angle?” worksheet made available on computer if needed
“What my angle?” website at
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html
ANTICIPATORY SET
I will begin class by standing at an angle and say that angles are everywhere, even the way
am standing is an angle. I will say that today’s lesson is about angles. I will then present the
graphic organizer to the students and project it on the LCD screen. I will tell the students
that angles are everywhere. There will be several simple angles on the “Angles Are
Everywhere” graphic organizer illustrating that angles are all around us.
I will wrap up the set by explaining that we will study angles, and then learn to measure and
draw angles. I will tell the students that they will all be angle experts. I will tell the students
that they need to understand that angles are part of their everyday life and that it is necessary
to study angles in order to understand many other concepts in geometry.
DEVELOPMENT
Now that I have the students’ interest I will ask the whole class to respond: “What are we
studying today?”, answer angles, followed by the question “Where are angles?”, answer
everywhere. I will commend the class, ask them to get out their math folder for taking notes,
and then define an angle as the figure formed by two rays (never ending lines) diverging
from a common point (vertex). I will draw on a blank transparency, or board an angle, rays
and vertex.
Next, I will explain that angles are measured in unit called degrees. I will then explain that
the angles we will study today can only go up to 180 degrees. I will then ask students if they
have ever heard or seen a protractor. After student response I will show the students a
protractor and define a protractor as the tool used to measure angles. Using the angle already
illustrated, I will draw one on the board, and use the protractor to measure the angle to
determine the degrees. I will place the bottom center of the protractor on the angle at the
vertex and along the bottom ray and measure where the top ray meets the arc of the
protractor. On that mark will be a degree (number) and that will give me the degree of the
angle. I will demonstrate this two- or three more times with new angles (67, 99, 35, 90, 162
degrees) for clarity and questions.
Finally, I will explain that there are three types of angles we will study today, right, acute,
and obtuse. I will define the right angle as 90 degrees, and that acute and obtuse angles are
measured by their relationship with right angles. I will define acute angles as all angles less
than 90 degrees and obtuse angles as all angles larger than 90 degrees. I will go back to the
illustrated drawing of angles and degrees and name them as right, acute, or obtuse (acute,
obtuse, acute, right, obtuse). I will demonstrate this two- or three more times with new
angles (46 acute, 111 obtuse, 90 right) for clarity.
GUIDED PRACTICE
I will begin the guided practice by asking students to take a look around the room and ask
for volunteers to point out any angles. Take a few volunteers depending on participation and
enthusiasm and ask them if they can point out any characteristics (vertex, ray, acute, obtuse,
right, acute) of the angle they have located. After an authentic discovery in the classroom, I
will reiterate that angles are everywhere.
Using the “Angles” teacher’s guide (see attached) : the class will begin measuring, labeling
and drawing angle as a group. I will begin by asking volunteers to define angles, rays,
vertex, and degree. I will ask for class agreement on the definitions and then write them on
the board.
Next, I will draw three angles, estimated from the angles in the teacher’s guide and have
three volunteers label the angle parts. I will ask for students to agree or disagree. If they are
correct I will leave them up, if they need to be corrected I will ask the students to help me
make corrections. Then I will ask for three separate volunteers to measure the angles using
the larger classroom protractor. Each volunteer in turn will need to explain to the class the
process of measuring angles and then give their estimate of the degree of the angle. I will
ask the class to identify whether the angle is right, acute, or obtuse. I will check for
agreement and ask for class assistance in making possible corrections.
Finally, I will ask for three new volunteers to draw angles. I will give them the degrees
(check teacher’s guide). Each volunteer in turn will need to draw the angle using the
classroom protractor and explain the process. I will ask the class to identify whether the
angle is right, acute, or obtuse. I will ask for classroom agreement and ask for assistance in
making the necessary corrections.
I will work along slowly with them for clarity, and make corrections when needed to instill
student mastery. Throughout the process I will repeat the questions below until I am
satisfied that all or most students have grasped the basic concepts of the lesson so far.
Finally, I will ask the students these questions:
Where are angles?
 everywhere
What is an angle?
 the figure formed by two rays (never ending lines) diverging from a common point
(vertex).
What components make up an angle?
 ray and vertex
What is the unit of measurement for an angle?
 degrees
What is the tool used to measure angles?
 protractor
What are three types of angles?
 right, acute, and obtuse
What makes these three angles different?
 a right angle is
ACCOMODATIONS
1. Vision Impairment-enlarged worksheets, larger angles demonstrated
2. Cerebral Palsy and Traumatic Brain Injury (TBI)-worksheet available to be completed on
the computer for those with fine motor deficiencies
3. Learning Disabled- LD students can have directions to worksheet reread and assistance
available for reading, spelling, and any questions during guided and independent practice. If
necessary I will create a modified with fewer questions and diagrams and examples of
questions to assist in mastery or best results.
4. Gifted Learner-In the independent practice I have proved some additional exercises for
students who are fast learners.
The website provided “What my angle?” website at
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html will work well
with all students, but may be most beneficial for all the above-mentioned students.
CLOSURE
Finally, I will ask the students these questions:
Where are angles?
What is an angle?
What components make up an angle?
What is the unit of measurement for an angle?
What is the tool used to measure angles?
What are three types of angles?
What makes these three angles different?
I will then tell the students they are on their way to becoming angle experts and with some
additional independent practice they should be there in no time. Finally I will tell the
students that with this new-found mastery, tomorrow they will be ready for triangles and
other polygons.
INDEPENDENT PRACTICE
1. The students will work on and complete or take home the “What’s The Angel” worksheet
that asks them to define the seven terms they learned in the lesson. I will provide each
students with a protractor It also has five angles to measure, given a protractor, and label
(right, acute, obtuse) and five angles to draw, given a protractor, and label (right, acute,
obtuse).
2. Students who finish the worksheet will find and list as many angles (at least 5-10) as they
see in the classroom on a sheet of loose leaf paper. If time permits, and the class volume is
low enough, they can attempt to estimate the angles they have found with their protractor.
This above exercise will be completed at home, using angles found in and around the home,
and the student will bring the list in and present their findings to class.
Students who complete the assignment may also go to “What my angle?” website at
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html and play anyone
of the educational games related to angles.
EVALUATION
Diagnostic- I will check the student responses to the “Angles Are Everywhere” graphic
organizer and student recognition of angles in graphic organizer. The question posed to the
student’ “Do you recognize angles in the presentation”, will help me pre-assess prior
knowledge. If students ask questions related to the presentation and recognize the angles
given; I will have a better understanding that they have some familiarity with angles.
Formative- The student responses through my checking for understanding (CFU) by asking
the questions:
 Where are angles?
 What is an angle?
 What components make up an angle?
 What is the unit of measurement for an angle?
 What is the tool used to measure angles?
 What are three types of angles?
 What makes these three angles different?
Will provide me with a better understanding of their comprehension.
The observation of the students and their verbal and non-verbal cues will allow me to gauge
their level of comprehension.
The individual and class participation during the guided practice will help me to address
areas of unclear parts of lesson.
Summative- The worksheet “What’s The Angle?” with blank spots for answers will provide
me with quantitative evidence that students understood the lesson. It also aligns with my
objectives and goals for the lesson. Students finding, describing, writing, and presenting to
class angles they have found in the classroom and at home.
REFLECTION
Did I “hook” the students in the anticipatory set by standing at an angle? What could have I
done differently?
Did I explain and demonstrate the angles topic effectively?
Did my demonstration engage my students during the lecture?
Did the guided practice engage the students’ interest in the lesson?
Should I break the lesson up over the course of two days?
Did I take the time to see that all the students were assisted and on the way toward mastery?
Did I meet the needs of my classified students?
Are all my students needs meet, not just my classified students?
 Did I answer all their questions?
 Call on most or all students?
 Make myself available during and after the lesson for any additional student
questions?
Was “Where’s the Angle?” worksheet appropriate for the lesson?
Did the worksheet, ”Where’s the Angle?” accurately gauge mastery?
What would I do differently a second time?
References
Robinson, M. (2000). What’s my angle?. Retrieved July 8, 2005 from
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html