Create Problems with Right and Straight angles
Lesson 2 of 16
Objective: SWBAT demonstrate their understanding of supplementary and complementary angles.
I begin today's lesson with my normal class routine. I build in a few minutes for students to try to solve various angle problems. These problems should have algebraic expressions as angle measurements. I will choose some problems from one of the sites from my list of essential digital tools. Or, I may revisit some of the problems from the previous lesson.
After they have worked a few problems, I will ask, "How do you think these problems were created." I might need to give students a moment to work it or come up with a strategy.
After the students take a crack at it, I will present two main strategies (see shaun's_video). My goal is for students to understand how to create a medium problem where a variable value is also an angle value (or a spicy problem where a variable value is not also an angle value, but needs to be substituted into an expression to find the angle value).
To launch today's mini-project, I have students work in partners or groups to create a problem to share with the class. This can be done on chart paper or in a notebook and then shared via document camera. Depending on the resources available (and the group) I will make my expectations for today's lesson clear so students have a concrete vision of the goal. For example, if my students are working on chart paper, I will discuss the layout of their work and request that the diagram is clear and that their algebra is hidden until the class has had a chance to solve their problem.
As the students work, I will periodically stop the class to highlight examples. When I find a great example, I will save the student work to share with other classes. As this part of class unfolds, I go into facilitation mode. My primary efforts will be spent helping groups create a problem that they find interesting enough to share. I will help groups play with line layouts to find a diagram that peaks their interest.
Extensions and Scaffolds: The idea is to encourage divergent thinking and have students create their own algebraic supplementary and complementary angle problem. Be ready for students to wrestle with the idea of decomposition, substitution and combining like terms. For example, if a student creates a pair of supplementary angles and one angle is 30. They have to be comfortable with the idea of representing this angle as x. If x = 30 then we can decompose x into 100x – 99x (or any other combination) and then rewrite this as 3000 – 99x by substituting 30 into the term 100x. Then the other angle would be 180 – x and could be decomposed in a similar fashion into 180 -2x + x and then rewritten as 180 – 2x + 30 = 210 – 2x. As you can see this is complex and requires strong algebraic intuition. Fortunately students love to control the parameters of their problem. They love to take ownership of their problem.
As I circulate during this lesson, I generally come across several interesting problems and students who are doing well enough with the topic to share with the class. As we prepare for the end of class, I provide 15-20 minutes for groups to share and discuss their work in front of the class.
When a group shares, I like to have the group present their problem and then ask the class to try and solve problem. The presenters then walk around the room and see how the class is doing. When the class has had enough time working on the problem, I give the presenters a chance to show their solution. I have a planned set of questions that I will ask to assess group knowledge:
- What are complementary and supplementary angles?
- What is decomposition?
- Could you have decomposed the variable in another way?
- How did you know those two angles would add up to 180/90?
- Why did you add those two expressions like that?
- Did you need to solve for x by doing that?
- If one angle is equal to x, when is the other angle 180 – x?
I expect to get some nice questions around decomposing 180 or 90 – x and the distributive property. I always remind myself that students tend to mix this up. For example, if they decompose x into 3x – 2x, then 90 – x becomes 90 – 3x + 2x. I think this issue is common enough that I may ask some specific questions around this to make sure that everyone has a chance to think about it.