“How do we classify angles?
(6th grade)
by Miranda Spang 2008
Required Materials:
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This print out of teacher instructions and student sheets
Internet and enough computers for students to work as pairs or individually access for last review/practice section only
Head phones for each student—for last review/practice section only
CA 6th Grade Math Content Standards:
2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
Time: approximately 3 class periods --Note that each lesson segment is listed in order
Objectives:
1. Students will be able to identify angles as vertical, adjacent, complementary, supplementary, and congruent
2. Students will practice oral language skills using sentence frames
Goals:
1. Students will build on their knowledge and application of academic vocabulary
2. Students will become more confident in reading a math text
Prior Knowledge: This is a beginning lesson using an excerpt from the first section of the geometry
chapter. However students should be familiar with 5th grade geometry standards, specifically they
should understand what an angle is.
Assessment:
Informal: Oral Language Practice—Think Pair Share (Worksheet 3)
Formal: Identifying Angles Individual Activity (Worksheet 6)
Contact information:
mirandaspang@gmail.com
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“How do we classify angles? (6th grade)
by Miranda Spang 2008
Table of Contents:
Cover page
Table of Content
Introduction and Connection to Fellowship
Page
1
2
3
Understanding the Need for Improved Math Curriculum and Technology Integration
4
More Connections to My Fellowship
Teacher notes for Extracting background Knowledge (Worksheet 1)
Student Worksheet 1: Extracting Background Knowledge
Teacher notes for Reading Elaboration Text (Worksheet 2)
Student Worksheet 2: Text on angle classification
Teacher notes for Elaboration Graphic Organizer (Worksheet 3)
Student Worksheet 3: Elaboration Graphic Organizer
Teacher notes for Oral Language Practice with Sentence Frames (Worksheet 4)
Student Worksheet 4: Oral Language Practice with Sentence
Teacher notes for Close Summary (Worksheet 5)
Student Worksheet 5: Close Summary
Teacher notes for Assessment (Worksheet 6)
Student Worksheet 6: Assessment
Teacher notes extension activity on integrating technology
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Educational Transfer Plan: “How do we classify angles?
Miranda Spang (2008)
mirandaspang@gmail.com
Introduction and Connection to Fellowship
University of California College Prep (UCCP) develops high quality online course content with the specific intent of
preparing underrepresented high school students for college. These interactive courses are freely available to students
and teachers, and are highly engaging using multimedia features such as simulations, videos, and podcasts. UCCP is housed
in Santa Cruz, and is part of the UC system, but not specifically connected with UC Santa Cruz, except for payroll. UCCP
courses are actually developed by teams of experts at various universities within the UC system and by external venders
when appropriate. A major goal of UCCP is to create greater equity and access by making AP courses readily available to
all students, as AP courses tend to be a gate keeper for many universities. Students at high schools with few or no
available AP courses are at a disadvantage to privileged communities where students have easy access to many AP
courses, for not only are AP courses college level, but many schools offer more credits for AP courses resulting in
elevated grade point averages which is a competitive advantage.
I have integrate what I learned this summer at UCCP into developing enhanced rigorous curriculum that prepares my
sixth grade students for the CST and for Algebra. UCCP is just in the beginning process of developing a pre-algebra
course and one of my responsibilities this summer has been researching already existing pre-algebra tools and courses.
For the most part, this search has been unfruitful. This is because there are very few educational resources freely
available at the middle school level. AP course material is becoming increasingly abundant as more universities buy into
the new idea of Open Educational Resources (OERs) or freely available education materials. Students around the world
can freely access courses online from top universities like MIT and Yale. After evaluating prestigious AP courses with all
sorts of wonderful bells and whistles, searching for middle school level materials quickly became a daunting task. There
are in fact some complete courses available, but such courses are typically designed for the home-school population and
come with a hefty price tag. The few freely available resources I came across are incomplete and lacking in quality.
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Understanding the Need for Improved Math Curriculum and Technology Integration
As a middle school teacher, I believe that in order to make any substantial progress in closing the achievement gap, more
effort needs to be placed at the middle and elementary levels. How well a student does in middle school is a major
indicator if that student will attend college or not. Unfortunately, many intelligent students in districts such as Oakland
Unified School district fall through the cracks in middle school and never make it the point where they even have an
option of taking an AP course. These students falling behind tend to be second language learners who appear to be
verbally fluent in English, but who are actually lacking in a full command of the English Language. These are the students
who reach a 3 or 4 on the CELT but don’t progress after reaching these advanced intermediate levels. Most middle
school curriculum does not fully address these specific needs of California Students. Thus, I have been a strong
advocate for this population in my fellowship, encouraging UCCP to target this high needs group. Below are points that
emphasize some of the major reasons there is a need at my specific school for the curriculum I have developed in my
ETP.
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Math CST scores need to improve especially within our Hispanic population to meet our API goals
Given that current district curriculum does not support the needs of English Language Learners ( ELL make up 80%
of the student body) and we currently do not offer any English Language Development (ELD) classes, supplemental
materials should promote English Language Development within the content area
Because the district curriculum and textbook lack sufficient examples guidance in problem solving and conceptual
understanding students need access to supplemental materials
Students have little practice in reading math texts, yet this is a skill that will bring them success in highschool and
college
Students struggle with mathmatical texts and many teachers don’t explicitly teach this skill
The majority of students in my school come from economically disadvantaged homes and have limited access and
knowledge of internet tools, therefore in working towards closing the achievement gap schools need to provide
multiple opportunities for underprivileged to develop technological proficiency
More Connections to My Fellowship
One of my tasks at UCCP this summer is to take and evaluate Moodle 100, an online introduction course to Moodle, a free
learning management system. Originally the hope was that I would be able to take Moodle 101 for course development so
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I could begin to develop my own rudimentary course to use in my classroom, but unfortunately Moodle 100 is a mandatory
perquisite. As a result my current goal has been downsized to simply enhancing current district math curriculum by
making it more accessible to my second language learners and more engaging by incorporating the use of internet
technology.
Besides connecting my ETP to my fellowship through quality content that addresses the needs of underserved populations
and technology integration as discussed above, my lesson is designed using the lesson design strategies I learned this
summer during my fellowship to specifically to meet the needs of my English language learners at intermediate and
advanced CELT levels. I just finished a week long training to become certified in conducting trainings on: A Focused
Approach to Constructing Meaning: Explicit Language for Content Instruction (CM), which provides a detailed framework
for teachers to infuse academic language into the classrooms. CM is an approach to lesson planning which guides the
teacher through a process of analyzing the text the student will be using to determine not only key content vocabulary,
but also the language frame work that supports the content at the level of the text, paragraph, and sentence.
Content teachers typically do teach content vocabulary well, but leave all supporting language, sentence and text
structures to the Language Arts teachers. Yet, students need a deep understanding of this content supporting language
to access the content and fluently communicate their understanding and related thoughts at an academic level. For
students to have a command of the content at both a written and oral level, we must explicitly teach students the
expected academic language to support our content.
This approach in math enables students to read math texts with understanding, follow standardized test directions, and
to eloquently communicate about math in both written and oral contexts using appropriate academic language. As you
well see the following lesson uses this approach to address the academic language needs of my students. In this lesson I
have repeated certain sentence frames that I want my students to use and understand such as:
_________________are recognized easily because they_______________ and refer to figure _____. Academic
language like this used in texts and on standardized exams, but many content teachers neglect to explicitly teach this
language and neglect o provide opportunities for oral and written practice. Note that the lesson that follows is a
beginning of the year lesson and offers more scaffolded support of simple academic language than would be given later in
the year.
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“How do we classify angles?
(6th grade)
Procedure 1:
Time: 10 minutes
Laying the Groundwork: Background knowledge about the content and language
What explicit instruction is required to teach the function and the language to express it (I Do it)? What structured
cooperative activities will provide students with practice (We Do It)?
Students need to be familiar with angles from previous courses. Students should know what that an angle is composed of
two rays and a vertex, they should also be familiar with: plane, parallel lines, and intersect. Additionally, it is important
that they know how to describe an angle both verbally and in letter format.
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Display images of angles and ask students to write down what they already know about angles on worksheet 1 (step
1)
Have students share with the table group to practice oral communication skills
Have students write down at least one thing they learned from their table mates (step 2)
Choose a student to label parts of an angle on large diagram you have already place in the front of the room—check
ahead of time to make sure this student has correct understanding
Have students redraw and label parts correctly in step 3, even if they already got it.
Space to add modification notes and or reflection:
Teacher Notes for worksheet 1
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Extracting background information
for “How do we classify angles?”
Step 1: Write down everything you
know about angles. Be sure to draw
and label the parts of an angle and
tell how to reference an angle.
Step 2: Share with your group.
Make sure you are actively listening
and sharing. Once your group is done
write down at least one thing you
learned from sharing or that you
didn’t include in part 1.
Step 3: Copy Angle diagram from the
board and label correctly in space below.
Make sure that the angle is appropriately
referenced.
Worksheet 1
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Reading elaboration text for
“How do we classify angles?”
Procedure 2:
Time: 20 minutes
A. Learning the Material: Skills and language needed to express understanding of the content
What explicit instruction is required to teach the function and the language to express it (I Do it)? What structured
cooperative activities will provide students with practice (We Do It)? What independent activities will provide students
with additional practice (You do it Together)?
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Write essential question on the board: “How do we identify special angles in geometry?”
Read text as Think Aloud reference the diagrams in the think aloud ( I DO) pointing out vocabulary definitions such
as: diagram, plane, surface, etc.
Have students help you identify the function—elaboration
Have students read text to each other in pairs—each student should have a turn (You do it Together)
As they are reading have them underline words that they are unsure of—at the end of the less on they should go
back and put a star next to words they feel they now understand well. Note that there may be words they still
don’t fully understand—this is OK. You will want to point out that even though there might be some words we are
unsure of, we can still understand the main ideas.
Write essential question on the board: “How do we identify special angles in geometry?”
Space to add modification notes and or reflection:
Teacher Notes for worksheet 2
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Name _________________________ Class: ____
Text: Mathematics Concepts and Skills Course 1
McDougal Littell (2001)
A plane is a flat surface that extends indefinitely
in all directions. Two lines that lie in the sample plane intersect if they meet at a point.
If two lines in the same plane do not intersect, they are parallel. Parallel lines are indicated using arrowheads on the
lines as shown in the diagram.
In a plane, two, different lines are either parallel or they intersect. In the diagram line A and line C are parallel, while
line A and line Z intersect. Label line Z.
Adjacent angles share a common vertex and a common ray. One pair of adjacent angels are h and g.
Consider the four angles formed by the intersecting lines shown in the diagram at the right. The angles opposite each
other are called vertical angles. Notice that e and h are vertical angles. Two angles are congruent if they have the
same measure. The symbol  means “is congruent to.”
In the above diagram, f and g are examples of congruent angles. In this example f and g are also vertical angles.
Congruent angles do not have to be across from each other nor do they have to be next two each other. Notice that the
angles below are congruent angles.
Congruent Angles
Goal 2: Special Pairs of Angels
Worksheet 2
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Two angles are
supplementary if the
sum of their
measures is 180.˚ Ang
Two angles are
complementary if the sum
of their measures is 90.˚
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Elaboration T-Chart for
“How do we classify angles?”
Time: 10 minutes
Procedure 2:
B. Learning the Material: Skills and language needed to express understanding of the content
What explicit instruction is required to teach the function and the language to express it (I Do it)? What structured
cooperative activities will provide students with practice (We Do It)? What independent activities will provide students
with additional practice (You do it Together)?
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As a whole group read and complete the elaboration graphic organizer (worksheet 3)
Completion of the sheet requires that an example be drawn for each angle type to be referenced in the next
activity (worksheet 4)
Space to add modification notes and or reflection:
Teacher Notes for worksheet 3
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Elaboration Graphic Organizer
for of key content geometry
vocabulary
Classification of
Angle Pairs
“How do we
classify angles?
Complementary
Supplementary
Vertical
Congruent
Figure 1
Figure 2
Figure 3
Figure 4
Adjacent
Figure 5
add up to 90˚
add up to 180˚
are opposite
and equal in
degrees
have the same
measurement
in degrees
side by side
angles that
share a
common vertex
and a ray
Worksheet 3
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Oral language practice with
sentence frames for—
How do we classify angles?
Procedure 2:
Time: 15 minutes
C. Learning the Material: Skills and language needed to express understanding of the content
What explicit instruction is required to teach the function and the language to express it (I Do it)? What structured
cooperative activities will provide students with practice (We Do It)? What independent activities will provide students
with additional practice (You do it Together)?
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This is an oral language practice. Students should first read the sentence frames and decide what word should go
where—but not write anything down, yet. Before writing students should read their section to their partner.
Make sure you remind students of what it means to be an active listener
Review as a whole class—this is the now the time for students to write.
Space to add modification notes and or reflection:
Teacher Notes for worksheet 4 (Spang 2008)
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Oral Language Practice—Think Pair Share
How do we classify angles?
Read over the sentence frames below. Take one minute to think about what we learned about angles and determine
what will best complete each sentence. Do not write anything down yet. Partner 1 shares what he or she got for 13. Partner 2 listens. Switch role for 4 – 6. Remember that answers may vary especially for 2 – 6. Use the
knowledge gained by listening to your partner to improve your chances of getting a correct more response.
1. There are five basic classifications of _____________that we must learn.
2. __________________angles are defined as _________________________. Refer to figure___________.
3. _____________________angles are recognized easily because they _______________________________.
Refer to figure__________.
4. ______________________angles are identified by _______________________.
Refer to figure__________.
5. ______________________angles are recognizable because they_______________________________>
Refer to figure ______________.
6. The last type of angle pairs are ________________________angles and can be recognized easily because
they _________________________. Refer to figure _________________.
7. I am great at identifying different types of_________________________ and will do well on the
__________, because I will _____________________and I will _______________________.
Worksheet 4 (Spang 2008)
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Close Summary for—How do we classify angels?
Procedure 2:
Time: 15 minutes
D. Learning the Material: Skills and language needed to express understanding of the content
What explicit instruction is required to teach the function and the language to express it (I Do it)? What structured
cooperative activities will provide students with practice (We Do It)? What independent activities will provide students
with additional practice (You do it Together)?
 Make sure you have intersecting lines posted on the board that look similar to the diagram below
Review the concept of sentence frames if needed and the vocabulary/ description & elaboration T chart if needed
Read the answer choices in the T chart together as a whole class
Have students work in table groups to complete the sentence frames
Read through correcting any errors as a whole class
At this point have students go back to original text to star words they are no longer uncertain of—take note of
words they still have issues with, teach if necessary—but build confidence by congratulating them on how much
they now understand
Space to add modification notes and or reflection:
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Teacher Notes for worksheet 5 (Spang 2008)
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Consider the ______________ formed by the ____________________ in the diagrams on the board. These
angles are generally divided into five classifications:.___________________________, ________________,
___________________, _________________, & ______________________,
Complementary angles can be recognized by the fact that together they_____________________________.
Supplementary angles are composed of __________________________________________. Vertical angles
are formed when a line intersects two parallel lines. Vertical angles are the angles that ______________
______________________. Congruent angles are_______________________________________.
These classifications may overlap, for example all vertical angles _________________________. In only
one specific instance ___________________________________________________________. This
occurs if and only if____________________________________________.
Likewise, in only one specific
case can angles be _________________________________. This occurs if and only if both angles are 45˚.
Vocabulary
Description and Elaboration (Facts and Details)
Congruent
add up to 90˚ forming a right angle
are also always congruent
Adjacent
classified as being both complementary and
congruent.
Supplementar angles that add up to 180˚, forming a straight
can angles be classified as being both supplementary
y
line
and congruent
Vertical
simply defined as being equal in degree
intersecting lines
Angles
are opposite each other and equal in degrees
both angles are 90˚
Worksheet 5
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Assessment for—How do we
classify angles?
Procedure 3
Time: 15 minutes
Applying the Knowledge: Producing the Final Outcome
What independent activities will provide students with additional practice (You do it Independently)?
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Have students independently work through the last worksheet. Remind them that they may refer back to the
graphic organizer and text
As students are working walk around the room and observe students. Are they referring back to the text? Graphic
organizer? Are they meeting the objectives and goals? Are students ready to move on to finding the missing
angle?
Once students are done correct as a whole class to reinforce concepts
Space to add modification notes and or reflection:
Teacher Notes for worksheet 6 (Spang 2008)
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Classification of angles
Name ___________________
Describe the relationship between the angle pairs in the diagrams below.
Independent Assessment
1.
These angles are _________________________angles.
This is evident because__________________________________.
2.
These angles are _________________________angles.
This is evident because__________________________________.
3.
These angles are _________________________angles.
This is evident because__________________________________.
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4.
These angles are _________________________angles.
This is evident because__________________________________.
5. Refer to DEA and CEB in the diagram below
These angles are _________________________angles.
This is evident because__________________________________.
.
6. Refer the diagram below
Two angles that are adjacent are: __________and _____________.
This is evident because__________________________________.
Worksheet 6 (Spang 2008)
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Integrating Internet technology
“How do we classify angles?
Procedure 3
Time: 1 period
Review/Practice/Extention: Integrating Internet Technology
What independent or paired activities will provide students with additional content practice and internet skill building?
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Have students participate in review in pairs or individually at: http://uk.youtube.com/watch?v=aAX1k_DP8Ec
and http://uk.youtube.com/watch?v=H5je8J9GPPI
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Have students go to the following sight and complete the interactive lesson: 16 Working with angles
http://www.learnalberta.ca/Launch.aspx?content=%2fcontent%2fmesg%2fhtml%2fmath6web%2fmath6shell.html
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Have students play games related to the content at the following sites:
http://www.oswego.org/ocsd-web/games/bananahunt/bhunt.html
http://www.toonuniversity.com/6m_angle_d.html
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