## Tuesday, December 15, 2015

### Day 71: Participation Quiz Systems of Equations Kobayashi Hot Dog Task & Differences between two functions: f(x) and t(n) (sneak log in too)

Today's estimation was how many times will Mr. Stadel wrap his lights around his tree. Most students estimated in the teens and some thought about the spool he unwrapped and related it to decorating their own trees.

Here's Dominic's two tables along with his graph from 2nd period! Great work.

I reported out students whose blog URL's I didn't know and whose parents signatures on Trimester 1 finals I didn't have. Then I discussed how I had used direction instruction yesterday when reviewing multiplying a fraction equation by 2 different numbers and choosing a 3rd best number, the LCD. I related that to research that says you learn more in cooperative learning groups following the study team norms, such as: not talking to other groups, explaining and justifying, asking good questions giving hints and not answers, not working ahead, etc.

I then said I was going to record positive and negative conversations and actions reflecting the study team norms on the board, and reviewed it with all students before a student presented and we had our closure.

2nd period Participation quiz:

3rd period participation quiz

5th period:

Students solved a system of equations by using a table, a graph, and using two rules to confirm the correct answer. One student Connor in 2nd period decided to try the Equal Values method before it had even been introduced to him.
He also showed the point of intersection on his neat graph.

In accelerated students decided if sequences were functions. I liked how students reminded themselves by using the glossary and being resourceful. A few students remembered the vertical line test. We also used it after looking at the graph of y=2*3^x. Students reasoned f(x) is a continous graph while a sequence is a function but a discrete graph of whole numbers, as Nuri put it.

I promised my students I would show them a topic from Algebra 2. I asked them in the top right how to solve 700 = 3^x after Gabriel proved that is was not a possible term number because 3 to the 5th power is 243 and 3 to the 6th power is 729. So, 700 is clearly between those. Harrison knew that you had to use the logarithm, which I said was like the inverse of an exponential function, it undoes it. Then the Law of Logarithms allows you to use the exponent, x, as the coefficient of log 3. Then divide by log 3 on both sides for the answer.

in the last 15 minutes we watched the following video and students chose to answer different questions that Robert Kaplinsky posed. Students answered the first few questions.

What questions do you have after watching:

Michael made a table and Sarah explained why there were 36 hot dogs by adding the rounds between the competitors 1 through 8, 8+7+6+5+4+3+2+1. Students also found the 20th round scores for each person by writing arithmetic sequence explicit equations.

K is Kobayashi and B is for Blackwidow. He proved the 20th round using his explicit equations. I didn't get a picture of Alex D's paper where he showed the total hot dogs they had eaten after that round. He came up with those equations also.