Developing Right and Straight Angle Intuition

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Objective

SWBAT apply the idea of angle measure in a context involving algebraic modeling.

Big Idea

Introduce and explore the connections between supplementary and complementary angles using algebra.

Lesson Beginning

15 minutes

This is a quick, simple and manageable lesson full of challenge and multiple access points. The goals of this lesson are covered in the developing right and straight angle intuition video. 

I start off with my normal class routine and incorporate a few minutes for students to measure the angles on the Complementary and Supplementary Angles Handout. I will circulate as the students work and look for a student who is working efficiently (i.e., Harry"). When the students have had a chance to work through the sheet, I will ask them, “How was "Harry" able to finish all the angle measurements by only measuring half the angles given?” 

If students have another technique to efficiently get all of the angles, I will point this out as well. If not, I will ask the students to try to figure out how Harry was able to find all of the angles by only measuring half of them. This should lead to a discussion around the definition of complementary and supplementary angles. I plan to push the students' thinking into algebraic terms during this discussion. For example, I will ask students to define one angle in terms of another:

If two angles are complementary and one angle is 30 degrees, the measure of the other angle is 90 minus 30. Can we describe this using an equation?

Undoubtedly some will state “something plus 30 is 90.” Here, I help the student reverse his/her statement to solve for the “something.” Then, I encourage him/her to extend this to algebra. If two angles are complementary and one is x. How can we define the other angle? I will support this reasoning with a sketch. I might need to try a talk move here and give the students a moment to work it out and agree what the answer is and why it makes sense. I really want the students to understand the answer as 90 – x. If they get stuck on this, I will leave the question as unsolved and move forward within the lesson. Then, I will return to the discussion at the end of class.

Lesson Middle

30 minutes

Again, several ideas are covered in the developing_right_and_straight_angle_intuition video.

The idea in this section is to have partners choose appropriate challenges and go accordingly. I give my usual spice rack choices, but today I suggest that students start at mild and work towards spicy. My job is to circulate and find great examples that could lead to interesting questions or discussions. I often like to capture great quotes from student conversations and write them on the board as talking points for later. I find that it helps me to collect good examples if I circulate with a particular goal in mind. 

Extensions and Scaffolds:

The idea is to set up angles that can be easily measured, and, to offer problems that can be solved more efficiently if students use algebraic reasoning. This means that if students are struggling with algebra they can work through most of the problems by simply measuring the angle diagrams printed on their hand out. When students have supplemental angle pairs, they will be dealing with algebraic expressions. For example, if angle A = 2x + 10 and B = 2x – 10. Since A + B = 180, students need to simplify (2x + 10) + (2x – 10) = 180.

I have prepared in advance of this lesson to talk about these equations. I expect some students to struggle with the parenthesis. My students often get stuck with parenthesis and wonder if they need to do anything. I am also ready to talk about combining like terms and balancing equations.

 

Lesson End

20 minutes

The close of this lesson attempts to wrap up conversations that arose during class (see the developing_right_and_straight_angle_intuition to hear me talk about the closing). 

If I did not get a chance to cover the concept of x and 90 –x and x and 180 – x,  I will do it now. I will ask students to make a sketch as we discuss these expressions.  Otherwise, I will discuss student questions and issues from the problems the students chose. If students managed today's work easily, I may have create a problem of their own and demo it on the board.