## Saturday, March 26, 2016

### Day 129: WODB Terms, Exponents & System of Exponentials

My colleague Mrs. Alibhai didn't have a substitute during my 1st period prep and I took the chance to do Mr. Stadel's File Cabinet task followed up with a very quick Graham Fletcher's Sugar Cubes volume task.

Two students shared the two most popular solving methods. Some students got the surface area of each face and divided it by the area of a post it. Others divided all the dimension by 3 to see how many post it notes wide and tall each face of the file cabinet was.

For the volume task, students estimated how many sugar cubes were in a box. Then they were given the answer. The Act 2 video showed the dimensions of the base. They figured out the height, the final missing dimension. I asked students how their work related to a formula. So, I stressed the connection between the division and substituting, multiplying, and then dividing.

The WODB I used all day long was from a Google slides I got from La Cucina Matematica and I can't give the author credit, let me know if you made it because I like it. It was a challenging one for some students.

The basic format of class was share out, review an power of a power problem with a coefficient to reinforce order of operations, as well as a problem where students were dividing power numbers with negative exponents.

It truly uncovered gaps in students understanding of adding and subtracting integers. Then students took their assessment with exponents, identifying functions, and the angle relationship vocabulary skill.
 After the first go round 2nd period each class I singled out 27x^2 and asked what's the 2 called? (exponent) What's the x called? (base). Is 27 part of the base? There were mixed answers in every class. In one class I discussed it is the base of the exponent if there were parentheses around the 27 and the x.

 The first class, like most classes, had trouble with the top left. I like how they said instead of only one with an exponent of 3, they said it's the only odd exponent, the rest are even. I liked seeing students use the words divisible, factor, and coefficient.
 A common misconception was 45 was not divisible by 3. Many students were quick to say 15 times 3 is 45. So, I asked how we could build off that fact. So, they realized it was the only that had a factor of 5.
 I modeled for students how to simplify 2y(4x^3)^2. On last week's assessment students mistakenly multiplied the coefficient by the coefficient in parentheses first. I said that this was not the order of operations because the exponents operation hadn't been used first.
 Here is the dividing power numbers example problem. It uncovered a lot of weaknesses in integer operations. A majority of students are still not fluent with power numbers with negative exponents and how to write them as a power number with a positive exponent.

 In 5th period I loved Moreen saying that the top left had the only coefficient that could be cube rooted and get a whole number as a result. They also noticed the coefficient of 45 could not be written as 3 to a power of a whole number.
I didn't take a picture of the board in accelerated, but I reviewed how to write an exponential equation from 2 coordinates. I modeled how we substituted the ordered pair into y=a*b^x for each coordinate, and then divide them by each other to make the a values become 1. Then they solved for b, and then substituted that into one of the equations to solve for a. Then substitute a and b into the standard exponential equation.
 Here is a ratio problem I want to use in the future.
 I want to use this visual pattern I found on Twitter. It looks interesting, especially question 3.