The Triangle Sum Setup
Lesson 14 of 16
Objective: SWBAT develop and use the property that the sum of the measures of the angles of any triangle is 180°
When students enter the class I form pairs at random and hand each pair a copy of the Moon Mullins cartoon and a piece of construction paper. Once they are settled I address the class and ask that they carefully read the cartoon together. I direct everyone to draw a triangle of any kind, just like Kayo's grandfather indicated. I walk around assessing and asking groups to draw a "weird" triangle if they wanted. (Too many students draw an equilateral triangle or some kind of right triangle). At this point, and after everyone's triangles are drawn, I like to ask students to hold up their triangle so that other groups can see the variety of triangles drawn. Then I ask that students cut their triangles corners and try to form a straight line, just like in the cartoon.
I ask the class:
- Did you get the same result as Kayo’s grandfather?
- What have we demonstrated about the angles of a triangle?
This launch activity usually runs successfully and is always interesting to many students. Many of my students may have never actually demonstrated the Triangle Sum Property with a hands on activity like this one. I’ve had many “ah” moments, despite students previously knowing that the sum of the angles is 180 degrees. But I tell the class that this is really not a proof of this property and that the following activity proves what we just demonstrated.
Materials used in this lesson: Scissors, construction paper, ruler, Moon Mullins Cartoon
I hand each student the resource Triangle sum property. This resource gives students an opportunity to use their knowledge of supplementary and alternate interior angles to prove the triangle sum property. I let students answer the questions in their groups and walk around checking their answers to the guided questions. In order for students to confirm their responses I ask that they use both of the links below and manipulate the triangles, observing the angle measures and their sums. I make sure that students use both links and that they watch the video in link 2. (Java is required to be able to use the interactive applet)
Once the sum of the measures of a triangle has been established, then it becomes easier, and makes better sense, to apply the property. For example, to find the measure of a third angle of a triangle if the other two measures are known. The Triangle sum property can by applied to different circumstances involving the finding of unknown angles. The Application Resource Worksheet is intended for this objective.
Due to the level of challenge involved, many students enjoy problems when results from one step are used to get results from another. It is important to make sure, however, that students know the reasons for the results they obtain at each step in the process. When I call on students to share their answers, I make sure to question inquiringly throughout their response to make sure they fully understood each step toward the answer.
Question 2: With students who have difficulty with this question I tell them to use the strategy of testing a special case. picking easy values for x and y, for example, 30 and 70 degrees. Then calculate the measure of the third angle using these values. It will measure 80. Then I tell these students to look for the choice that will give a value of 80 when 30 and 70 are substituted for x and y.
Question 3: Most students will be led to draw conclusions of angle measures based on how they look in the images. I warn students to read the given information in a problem and search for symbols in the images that state facts about the diagram. Angle RPS in this image looks like a right angle when in fact it is 105 degrees. I let students know that sometimes they may see the statement, "image not drawn to scale". Yet, sometimes this statement may not show up.
I ask students to hand in their resource worksheet making sure all answers are completed. I make sure I read and assess these, and go over the questions together the following day. This is where I question students asking that they justify steps that led toward the answer they obtained.
A good strategy to use to end this lesson is a Summary Statement made by a volunteer students. I plan to ask several students to summarize what they learned today with specific examples. I try to keep it down to one idea per student to give more students a chance. I allow the use of the whiteboard if needed, and I write the summary statements on one side of the board for students to copy. Whenever there is an idea or concept not mentioned, that I feel is important, I hint to the class to see if someone comes up with it. It always works.
Once I assess student work on the Application Resource Worksheet, and discuss the questions as a whole in class, I then give this homework assignment for my students to complete:
I assign it when I feel right about the level of mastery of the lesson goals. This may mean that the homework is assigned at a later date.