Wednesday, April 6, 2016

Day 130: exterior angle theorem & feasible region

Erick Lee provided the following WODB:

Students analyzed four equations. I had to prompt students to add on to other students thoughts to add academic language that they knew but weren't using. For example for y=3x-1 they said it's the only one with subtraction. I asked why that means when it's on a graph and they said it had a negative y intercept. Also for top right I made sure they understood X had no visible coefficient but what coefficient could it have without changing it (1). 
As I learned from last years students the first problem where they have to use three letters to name an angle instead of one is more difficult than I previously thought. They end up figuring out that the middle letter is the vertex of the angle you are trying to name. We also takes about how you could flip flop the first and last letters. 

Interestingly Yazan shared that his 3rd grade sister asked him for help on her homework and naming angles was the topic. So in another 5 years we will see if the kids growing up with common core remember how to name angles. 
Students were introduced to naming angles of a triangle using the three lettered vertices. Students reasoned that the vertex must be the middle letter of the angle. Some classes even described angle a as angle bac.

I was surprised that a student substituted y for 0 to see that x was 2. They said that it was the only equation with an x-intercept of 2. Above you can see how I reviewed drawing a straight line and students saying it was 180 degrees, or a straight angle. Then I made a a ray splitting the angle and asked for the missing angle. I also prompted students on finding the 3rd angle in a right triangle. All of these skills were necessary to discover the exterior angle conjecture.
More thoughts.
Then I reviewed a straight angle. They told me it was 180 degrees. Then I drew a ray to separate it to make supplementary angles. If one was 35 they subtracted 35 from 180 to get 145. They needed this skill as well as finding the missing angle of a triangle to successfully discover the exterior angle. 

They came up with the conjecture that leads to the theorem that the sum of the remote interior angles is equal to the exterior angle. Then they solved some problems with it. 

Equations wodb. And inequalities.

Chris Hunter provided this linear inequality starter. So awesome.
I like how students saw that the bottom right was the only one with shading or a solution in each of the 4 quadrants. The top left was the only solid boundary line with solutions on the line. The top right was the only parabola, the rest were inequalities. I liked how a student noticed that the bottom right was the only one where the origin was a solution.
It was a great WODB starter because it lead right into students using clues from a CPM lesson to find where people saw a crash while they were on plane flights from different locations. They wrote inequalities and shaded the region that could be a solution. It's also shaded above the line but the only island near it is Samoa. I like how it integrated geometry.
Students had to pay attention to the scale of the map of intervals being 1000 kilometers.

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