Lesson Plan: Angle Sum of a Triangle

Author:Judith , Hubert Pöchtrager, Carolin Kern

Lesson Information

Subject:	Mathematics, Geometry
Grade Level:	6th grade
Duration:	about 50 min
Technology:	Computer for teacher and a projector OR digital devices (notebooks, tablets, phones) for students

Topic

Exploring the angle sum of a triangle.

Learning Outcomes

By the end of this lesson, students should...
... know that the sum of a triangle's interior angles is 180°.
... be able to account for rounding errors in the calculation.

Lesson Objectives and Assessment

Lesson objectives
Students are able to calculate the sum of the interior angles of a given triangle.
Students are able to calculate the third interior angle of a triangle if the other two interior angles are known.
Students are able to indicate the values of the interior angles with one decimal place, so that rounding to whole numbers leads to an angle sum of 179° or 181°.
Students are able to explain how rounding errors can affect the final result of calculating the sum of interior angles of a triangle.
Assessment

Discussion about the sum of interior angles of a triangle, as well as about how rounding errors can affect the final result
Written revision of calculating the angle sum, as well as of finding the missing angle in a triangle
Written summary of the discussion about how rounding errors can affect the angle sum of a triangle

Teaching Strategies

Question 1: What is the sum of all interior angles of a triangle? First, students should come up with their own hypotheses about the sum of the interior angles of a triangle. The following two activities could support them in this:

Each student draws a random triangle on a plain sheet of paper, measures the interior angles and calculates their sum. Afterwards, the students form small groups and compare their results. In this way, they can come up with a hypothesis, stating that the sum of interior angles of a triangle is 180° and independent of the shape of the triangle.

Each student draws a random triangle on a plain sheet of paper and marks each of the vertices in a different color. Then, students cut out their triangles and cut them into three pieces, each containing one of the vertices. In this way, the triangle pieces can be repositioned, so that all the marked vertices meet at the same point. Does the result of this experiment help to strenghten or refute the hypothesis?

Subsequently, the digital worksheet is used to verify the students' hypothesis. Depending on the technology in your classroom, you may select one of the following options: Option 1: Teacher computer and projector The interactive worksheet is presented using a projector. Students should solve the following tasks:

Task 1: Calculate the sum of the triangle's interior angles.
Then, the teacher changes the shape of the triangle.
Task 2: Calculate the sum of the new triangle's interior angles.
Repeat this procedure of changing the triangle and calculating the sum of the interior angles several times.
Note: When changing the shape of the triangle, make sure that the sum of the angles sometimes adds up to either 179,9° or 180,1°!

Option 2: Student computers (or tablets or mobile phones) Your students work on the same tasks mentioned above. However, they work individually or in pairs using their own digital devices. Which knowledge did the students gain while working on these tasks?

Discussion 1

What is the sum of the interior angles of a triangle?
Why is the sum of the interior angles of the triangle in the worksheet not always exactly 180°?
Find values for the interior angles (with two decimals) which yield a sum of 179.9° or 180.1° after rounding to one decimal place.

Question 2: How can we calculate the size of a missing angle in a triangle? Again, student should come up with their own strategy of calculating the size of the missing angle in a triangle.

Each student draws a random triangle on a plain sheet of paper and measures two of the interior angles. Using the known value of the angle sum, students should now calculate the third angle and verify their solution by measuring the angle.
Discussing in pairs, students should compare their strategy and check each other's solution for the size of the missing angle.

After students came up with a working strategy to calculate the size of the missing angle, they may use the second interactive worksheet in order to practice the calculation process. Depending on the technology setting in your classroom, you may again pick one of the following options: Option 1: Teacher computer and projector

Display a triangle with one missing angle and let all students calculate the size of the missing angle.
Display the value of the missing angle to let students check their results.
Discuss the calculation strategies or address mistakes.
Modify the triangle and repeat the calculations.
Note: In the beginning, you might want to make sure that no rounding errors affect the calculation. In later examples, you might want to choose the given angles so that the angle sum is not exactly 180° in order to encourage discussion about rounding errors again.

Option 2: Student computers (or tablets or mobile phones)

Let the students work on individually or in pairs on the same tasks using their own digital devices.
Ask them to take notes about the triangles they are using and summarize discussion questions that might arise.

Discussion 2 Encourage a class discussion to summarize strategies of calculating the size of missing angles in a triangle and address the issue of rounding errors possibly influencing the calculations.

Technology Integration

Your students do not need any technical prior knowledge in order to work with the interactive worksheet during the lesson. If you are using a teacher computer and projector for your lesson, you need to check whether they are fully functional. Additionally, you will need a working Internet connection for your computer. If your students should work with their own devices (e.g. notebooks, tablets, smartphones), you need to make sure to have a sufficient number of devices available which are connected to the Internet. It is recommended to test the network connection prior to the lesson. If you do not have access to a reliable Internet connection during your lesson, you may download the interactive worksheet prior to the lesson and save copies of the file on all student devices.