## Sunday, April 24, 2016

### Day 144: Pythagorean Theorem Practice & Exponential Equations

Today was a difficult estimation. I was pleasantly surprised at the amazing thinking some of my students produced. I admit that I am not the greatest with geography, and the estimation was the flight distance from Los Angeles, CA to Dulles, VA. Many of my students and I had taken a similar trip when flying to Virginia for the Sojourn to the Past trip so some had more background knowledge than others.

I was impressed with one student who watched the monitor on the back of the seat in front of him during a flight and saw that the cruising speed of the airplane was 300 miles per hour. The flight took 7 hours to the east coast, so he estimated 300*7 or 2100 miles. Wow.

Another great line of thinking was a student who knew that to drive from SF to LA it's about 400 miles. So, that's about 1/7 the trip to the east coast, so he did 400 times 7 and got 2800. Both great lines of thinking.

Today was the followup to Dan Meyer's taco cart. I had different students start off class by summarizing the question we were attempting to answer yesterday, and to briefly describe how we figured out the time it took each person to arrive at the taco cart. It was great to hear them summarize it.

I started by having students draw a right triangle. I asked them what the longest side of the right triangle is called. Some remembered it was called the "hypotenuse." I had them chorally repeat it after me, because they can have difficulty pronouncing it sometimes. They remembered the shorter sides were called the "legs." I reiterated the hypotenuse is always directly across from the 90 degree right angle.

I asked them what the relationship was between the side lengths, and they stated a squared plus b squared equals c squared. I asked if it mattered what order we add numbers in. They said no, so I said therefore it doesn't matter which leg is a or b, they could be either. Then students found the hypotenuse if the legs were 24 and 32. They also found a leg when given one leg and a hypotenuse. Students told me what to write on the board and unfortunately I didn't snap any photos of their work.

I stressed that when solving you start with writing the equation, showing your substitution, simplifying, and showing all steps. While they are still new to the concept, I want them to know the 8th and 9th grade expectation. I reminded them that you can get partial credit if you make a simple calculation error and if it can be easily found in your organized work.

 Establishing the vocabulary associated with the theorem.
 Modeling showing all your work. Students can get confused at the last step to undo the squaring by square rooting.
 Establishing more background knowledge.
 In a students mathography I was bummed to see that 4 years ago his 4th grade teacher was still doing timed tests. Bummer.
In accelerated I assigned each group a different classwork problem for them to show their solving steps on a white board. One group had a cube root problem and a couple students pointed out that you don't do plus or minus when cube rooting 8, because -2 cubed is not equal to positive 8. That was a great little discussion. The classwork was a mixture of absolute value, exponential equations, square root equations, and more.
 This group showed how to rewrite 36 as 6^2 so that each expression had the same base of 6.
 Nicholas showed what he had learned in Kumon to use logs. It looks mathematically correct to me!
 Myself and some of my colleagues celebrated a double baby shower for myself and Mrs. Bronson. You can see the firepit in full effect here.
 And some rain came, along with a nice rainbow. The canopy worked fairly well.