Download Grade 8 Activity 3.2: Angles of Triangles

Grade 8 Activity 3.2: Angles of Triangles
Essential Question: How can you describe the relationships among the angles of a triangle?
Activity Objective: Students will explore the sum of the angle measures of a triangle and the
vocabulary associated with triangles.
CC State Standards: 8.G.5
CC Mathematical Practice Focus: MP3, MP6, MP8
Pacing: 45 minutes
INTRODUCTION (5 minutes)
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Warm Up
o Make teams of three students. Give them 3 minutes to make a list of as many words
as they can that begin with the prefix tri-. Provide dictionaries if necessary. The
goal of this activity is to demonstrate that tri- is a common prefix.
ACTIVITY 1 (5 minutes)
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Exploring the Interior Angles of a Triangle
This activity physically places the three interior angles of a triangle on a line.
o
The sides of the triangle must be straight; otherwise the three angles will not lie
adjacent to one another when placed about a point on the line.
o It is okay to have multiple copies of the same triangle because different pairs of
students will get one copy of the triangle.
o The conclusion, or rule, that students should discover is that the angle measures of
any triangle will sum to 180°.
ACTIVITY 2 (5 minutes)
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Exploring the Interior Angles of a Triangle
This activity uses parallel lines and transversals to explore the interior angles of a triangle.
o If students are stuck, ask them to think about what they learned in the last lesson.
They should mark the diagram with what they know.
o Students should make the connection that angles B, D, and E are the same as the
three angles they placed about a point in Activity 1, where their conjecture was that
the sum of the three angle measures is 180°. What is different in this activity is that
students are asked to justify their answers.
In this activity, you want to hear students make statements based upon evidence they have.
Instead of, “Angles C and E are the same measure because they look it,” students should say,
“Angles C and E are the same measure because lines m and n are parallel and angles C and
E are alternate interior angles.”
ACTIVITY 3 (10 minutes)
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Exploring an Exterior Angle of a Triangle
This activity investigates the relationship between exterior angles and interior angles.
o Teaching Tip: When asked to draw a triangle, suggest to students that they draw a
scalene triangle. Draw the triangle large enough so that it is easy to see and
measure.
o Teaching Tip: If gaining access to sufficient pairs of scissors is a problem, have precut triangles available for students to use.
o If students are unclear about the direction “extend one side” in part (c), explain that
they should draw a ray and place the triangle against the ray, as shown. The
extended ray is one side of angle D and the second side of angle D is a side of the
triangle ABC.
Activity 4 (10 minutes)
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Measuring the Exterior Angles of a Triangle
This activity uses a protractor to investigate interior and exterior angles.
o “What are the interior angles of the triangle?”
o “What are the exterior angles of the triangle?”
o “What do you notice about the measure of an exterior angle of a triangle?”
o Extension: Students may also observe that the sum of the exterior angle measures
is 360°. Compare results with different groups of students. Is this true for the
triangles drawn by all the students?
Encourage students to be precise with their language. They may say that the exterior
angle is the sum of two interior angles. Which two? How do they describe the two
angles?
Check For Understanding (5 minutes)
What is your answer?
Students should understand that conjectures need to be verified. Repeating an investigation
on a different type of triangle gives additional evidence, or in some cases, it might become
a counter-example.
Reflection for Angles of Triangles
This lesson used discovery learning to find the exterior angle measurements of a triangle.
Students were able to build on prior knowledge, specifically by using the measurements of the
interior angles. Students were scaffolding their knowledge about parallel lines and transversals to
find both the interior and exterior angles of a triangle. There was more discovery based learning in
the second activity. Students carefully ripped the corners off angle a and angle b, together corners
a and b would form exterior angle d. Students could now calculate the exterior angles by adding
the two nonadjacent angles together, which then lead to the discovery that the exterior angles add
up to 360 degrees.
In this particular activity the proof of student learning would be more evident in the book
lesson that would take place the following day. The new math curriculum does a wonderful job of
connecting the concepts from the discovery based activity to the lesson. Giving students a day to
discover makes the following day’s lesson run much smoother. Students understand the concept
better and are more successful with the daily work. I believe that an extra day to process this new
information through and activity has been beneficial for my students. Prior to the activities, my
students struggled when they learned the concepts. The ones that do the talking are doing the
learning! If students had a difficult time with the activity, the lesson provides a time to re-teach
and answer questions that before they are given their daily. Normally there is not much reteaching the day following an activity, this allows for more work time in class. Students
appreciate this work time and they are very diligent to get that assignment done. Many of my
students go home to babysitting and other duties so if school work does not get done in class
chances are it will not get done.
All activities in this new book are done with a partner so there is cooperative learning that
is taking place constantly. Students help each other through the activity. There are many open
ended questions throughout the lesson, and higher level thinking skills are being used. In addition
to thinking about math students are also creating with math. The closure for the activity was to use
different types of triangles to find exterior angles this could also be used as a counter-example.
Students hand this exit ticket to me at the door, I check for understanding and also use this
information to help me prepare for the next day’s lesson.
Suggestions for next year I would have the students make triangles that take up half of a
sheet of paper. Some students made triangles that were not even an inch so they were hard to
manipulate. The directions for activity two were difficult to follow so I would do this part with
more guidance. I would also require students to use correct terminology when referring to the
angles and be more precise in measurements. I would make some accommodations by making
some pre-cut triangles for some of my students. This lesson and activity was new for me, exterior
angles were not part of the 8th grade standards prior to this year so I was learning right along with
the students.