Thursday, March 24, 2016

Day 128: Triangle Sum Theorem & System of Inequalities

In anticipation of a discussion on triangles and the triangle sum theorem, I used this shapes WODB from Mary Bourassa:

In a majority of classes students pointed out the bottom right being a right triangle as well as the isosceles triangle in the top left. When students mentioned the obtuse triangle, I asked if there were any other shapes with obtuse angles? They realized the hexagon did so bottom left was the only shape with exactly 1 obtuse angle.
I asked students what we call the "pointy side" of a triangle. Some wanted to say vertices, which I told them was the plural for vertex.
One class said the top right was the only one with an even amount of sides.
More observations.
In the classwork, I gave students a few minutes to solve for the missing angle of a triangle. In 5th period I made the connection between showing an addition problem followed by a subtraction problem as showing work, and the 8th grade level of work of writing an equation, simplifying, and solving for x. It was a great comparison.

After 4 different volunteers shared the equations and the solving process, I explained that they had just proven the triangle sum theorem, and demonstrated the desmos feature where if you drag any of the three vertices the angles sum does not change.

Then students applied this skill to triangles with algebraic expressions as their angle measurements, where they had to solve for x and substitute it later to find the other angles. This will be on the assessment the week we get back from spring break.
Students rearranged 4 sets of 3 color coded duplicated triangles. They arranged them so that the 2 marked angles and the unknown angle lined up to form a straight line, or straight angle.

Kyle came in at lunch about yesterday's 100^1/2 problem. He rewrote it this way. I also asked him what 10 squared was and substituted it for 100 in parentheses. He saw how that was one of the methods to solve. He also noticed the patterns of 100 squared, 100 to the 1st, and 100 to the 0, with 100 to the 1/2 snuck in between.
In accelerated students did WODB with the linear equations in y=mx+b form. It had y=4x, y=-2x+4, y=3x-1, and y=x+7. Unfortunately I didn't take a picture. I like that Markos said y=x+7 didn't belong because if you add up the VISIBLE m and b values you get an odd number.

I did not photocopy the separate graphs of 2 inequalities to show how they overlapped unfortunately, but students graphed it in their composition books independently to start class and compared notes on how they shaded it. Then they practiced it with another graph. I showed them mine halfway through. Then they looked at how many regions there were when an inequality intersected a parabola. There were 5. Students had to test to see which region to shade. I think some started to see the pattern that greater than was above the line and less than was below the line.

Tomorrows assessment will have solving linear inequalities, interpreting and graphing their solutions.

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