Monday, March 21, 2016

Day 125: WODB Probability / Angles & Alg tiles inequalities

I titled today's WODB "Probability." I reminded students that they had prior experience in 7th grade with spinners and using a paperclip and a pencil to do experimental probability. Here is what students reasoned about, thanks to Chris Hunter coincidentally for both of them, this and the algebra tile one for Algebra I:
Plenty of conversations await.

I like that 2nd period noticed the bottom left was only one where the probability of green was greater than 0 and less than 1/4. It didn't work if it was just less than 1/4 because top right had no green.
I like top left that probability of orange is less than 25 percent.
This class mentioned how the bottom left was the only one that has the smallest and largest angles.
I like bottom left: only one where P(purple) is less than 25%. The standard bottom right of blue being only one without a 1/4 or 25% chance.
To start class I wanted to review and activate students background knowledge with 3 warmup problems:

  1. Review what a right angle looked like, and solve for a missing angle. I challenged students to write an equation if they could. Also complete the sentence <x and 18 degrees are complementary angles.
  2. Given 135 degrees and a straight angle, solve for missing angle y and complete the relationship sentence. They are supplementary angles.
  3. Given one angle degree, 93 degrees, and a missing angle, identify they are vertical angles and congruent.
I asked students if they knew a way to remember complementary and supplementary. I mentioned that complementary has 1 p, and if you reflect p over the y-axis you get 9, or 90 degrees. Supplementary has 2 p's, so write 2 p's, reflect it, and you get 99, or 90+90. I'm not sure if this falls into the #nixthetrix category or not, let me know. I also pointed out that complimenting someone's hair is spelled differently then a complementary angle (sums to 90).

Then students investigated tracing paper and different angles such as corresponding. Tomorrow we will introduce alternate interior, same side interior, and corresponding. I'm thinking of doing a color coding activity with it tomorrow, because the names can get confusing when they are brand new. Students come up with conjectures on when they are congruent or sum to 180 (same side interior).

In accelerated students chewed on this Which one doesn't belong? It was totally awesome.
Prepare for some vocabulary and factoring!
I love that the top left is the only one that was a perfect square trinomial. A student first said that it was only one that can be written as (x+2)^2. I asked students to add on and they identified the type of trinomial. Since students were completing the square on the assessment, I took the opportunity to reiterate that in x^2+4x+4 the c or third term, is the middle term divided by 2 and then squared. I should have made the connection that the b/2 is represented by the 2 inside the parentheses.

Also, I may have had the image zoomed in but a student claimed the top left tile was an xy tile. He wanted to measure it, so I invited him to and he was correct. It was 20 by 21 cm on the SMARTBoard. I don't know if this is true or just the way the image was zoomed in.

To confirm the a, b, and c values were all even for the bottom right, I asked N to tell us the equations for each corner because he must have written them down when he was analyzing them. They also found top left was the only one with less than 5 x tiles.

Is there only 1 for bottom left? Bottom left is only one with more than 4 unit tiles?

Oh I forgot, I absolutely love the statement for top right: it's the only one where (x+2) is not a factor. Someone also added that when add a b and c, you do not get a number divisible by 3. I don't know how that student found that!
The bottom right was only with more than 5 x tiles. Nicholas earned a 3 second clap when you said bottom right was "only one where a, b, and c in ax^2+bx+c are all even numbers.
During class students practiced solving linear inequalities and interpreting the solutions as well as graphing the solutions. One had no solution, infinite solution, so those were new. Also, the homework tonight has an inequality where you divide by a negative on both sides, so I want to have a student discuss that tomorrow and show a little experiment where you multiply both sides of an inequality, add, multiply by a negative, and then divide by a negative to stress how the direction of the inequality sign switches in those instances.

Students solved a system of equations, and then an inequality about a tree that had to be at least a certain height and no more than a height.

Davin explaining each of his solution methods.

Davin demonstrated how if you have 4 times as many Turks as Kurds, and a total of 66 million residents in the country of Turkey, how many of each? He showed a system of equations elimination as well as Kramer's rule that he had learned on his own. It was a great review for me!

We are going to read the problem and Jeffrey is going to introduce his solution method that we didn't have time to go over here.

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