Wednesday, November 4, 2015

Day 45: Participation Quiz & Proving Pythagorean Theorem

Today we estimated Mr. Meyer's height. Student's were surprised to see a teacher taller than Mr. Stadel I think. Haha. Students usually estimated around 6'6" or 6'8". I love the reactions when the answer is revealed.

I handed back assessments and reviewed answers, common mistakes, and how it was graded. A lot of students wrote down four points from their line of y=x-1, instead of just the x and y intercept. I had a volunteer read the Math Notes box on page 136 about a Complete Graph so that the requirements were reinforced after learning the Goofy Graphing lesson last week.

Lesson 3.2.3 is a perfect opportunity to have a participation quiz because it basically reviews the Big C's pattern and they must use the rule to figure out the number of tiles in Figure 50. I recorded their quotes, cooperative actions, and some of their uncooperative actions on the board. With 10 minutes left in the period, students reported out their answers and how they got them, and the last 4 minutes I reviewed the Participation Quiz. There were plenty of 3 second claps for individual students and for the whole class.

Students substituted 50 for x showing their work and explaining their process in words for the rule y=6x+3. They also described reversing the process and substituting 45 tiles for y to find out what figure number had 45 tiles.

In accelerated, I asked students if they had any ideas how to remember the rule for when 3 side lengths formed an acute triangle. They correctly told me the square of the small and medium sides had to be greater than the longest side squared. I asked how we could remember this. No one had an idea. So I asked the class, "What is the most popular and commonly known acute triangle in the world?" Hands shot up and they said equilateral. I asked why, and students said that that it has the same side lengths and each angle is 60 degrees. I asked what is it called when they have all the same angles. One student knew that it was called "equiangular." We said that word chorally because lots of students seemed to not believe it was a real world.

I drew a picture of an equilateral triangle with sides of 3 and angles of 30 degrees. I asked them why do you think this helps us remember the rule for acute triangles? Students volunteered that the sum of  3 squared plus 3 squared is greater than 3 squared, so that's how you could remember. I told them that's the only way I remember.

Then students were given my card stock copies of 4 congruent right triangles that when arranged form an empty space that has an area of c squared. Then they drew that. Next they rearranged it and were asked why the empty space was also equal to a squared plus b squared. They showed that the sides of the right triangles formed those smaller squares.

Then I handed out the copy of the 2 squares next to each other that had an area of a squared and b squared. I then asked them to measure the side of length b. It was 1 1/2 inches. I then modeled measuring it on the bottom left side and making a dashed line to the top left corner to form a side of c. Then the side next to b is labeled a. Students asked how do we know that was a? I should have asked the class why, but I told them that look at the top. Isn't the top a + b? So the bottom is b + a, which is the same.

Then they cut along the dashed lines, and I asked them to see if they could rearrange it. They realized that the area of the original 2 squares hadn't changed, but they now formed a large square of sides c, forming c squared.

I then showed them this YouTube video. I asked them what this proved. They were able to explain it, and they liked the visual.