Saturday, February 27, 2016

Day 109: Scientific Notation FAL Day 2 & Solving for A in Quadratics

Todays estimation was a Steve Jobs biography. It also gave us a chance to remember how influential of a person he was. Students knew he founded Apple and was also behind the iPhone.

Most of the class finished their posters yesterday, so I started today with analyzing the posters. I asked students what they matched the thickness of a dollar with. They said 1 x 10^-4 and 0.0001. We had a discussion how to properly say a number in scientific notation. I asked students to confirm why the decimal was equal to the scientific notation expression. Students told me the exponent of -4 means to move the decimal point 4 space to the left on the 1.

A common mistake yesterday was writing 0.012 in scientific notation, since it was a blank card. Some groups wrote 12 x 10^-3 and others wrote 1.2 x 10^-2. I asked them to confirm whether these were equivalent to the decimal. They said both were. I asked if both were in scientific notation then. They said that 1.2 was the correct one because it was less than 10 and greater than or equal to 1.

Finally I asked students what they matched the height of a door with, which was 2 x 10^0. It was matched to a blank card. Some students wrote 20, and some wrote 2 meters. I asked students to convince myself and the class which was right and why. Some students explained that the exponent of 0 means not to move it left or right, just leave the decimal where it is. 

Matthew in 2nd period and Andrew in 4th period, had the same amazing alternative explanation: they said that since 10^3 is a 1 with 3 zeros, then 10^0 is a 10 with zero zeroes. My mind was blown and I verbalized how impressed I was to the class. I have NEVER thought of it that way and it is SO intuitive.
Analyzing the matches on their poster.

The thought that blew my mind.
Then students were given arrows that had multipliers on them. They had to find relationships between two objects to see how much bigger one object was than another. I think that some students used our prior work with scale factor for this, used calculators, and mental math to reason about it. As students worked I wrote down matches they made that we would analyze before the Friday assessment.

Two of the relationships found.
As a class I asked students how to say the number 80,000,000. I was happy that many quickly shouted out 80 million. So, I asked raise your hand and tell me how to write it in scientific notation. Students said it was 8 x 10^7. I noticed students counting by pointing so I asked how they were figuring it out. They said they were counting the number of zeroes after 8 because the number of zeroes would be the exponent of the 10.

Now here's where the magic happened. I asked students what they noticed about how the 2 factors multiplied to get the product. At least five students noticed that all you do is multiply 1 times 8, and then when you multiply the powers of 10 you add the exponents. So they said -4 plus 7 was 3, so the answer has an exponent of 3. I asked volunteers to rephrase what the volunteer had said.
When I asked students to tell me 4,000 in scientific notation, more hands raised when I said, guys, we have a clue on the board here of how 8,000 is written in scientific notation.
Students verbalizing what the exponent did to the number being multiplied.
Another interpretation of an exponent of 0.
A relationship students found using mental math.
Here students reasoned you multiply 4 by 2 to get 8, and add the exponents 1 and 2 to get 10 to the third power.
In this class I threw in the challenge of saying 0.0001 properly instead of "zero point zero zero zero 1." There were at least 5 different ways students thought you said it. This reminds me that I should review place value at the beginning of the year, and try to spiral it in more often.
Here's an example of what the MARS FAL posters looked like. I took a picture of this one because they used some creativity to make the arrow rise off the poster so another arrow could go under it.
In accelerated we started with reviewing what could be on the trimester 2 final. It's pretty much most of the skills from the Friday weekly assessments. Some students wanted to review it in class. I may do this next week, and if so I'll have to find a fun way to do it with stations to get students out of their seats.
Trimester 2 final topics
Today students saw how an equation in factored form could be written when you see the 2 x intercepts. A graph was given so they could clearly see where the vertex was. They solved for a, by substituting the coordinates of the vertex (4,32), and then substituting the a value back into the equation to properly write the equation. Then students wrote it in standard form by multiplying it out.

Zoe told us the answer for part d of the problem, but we didn't have time to hear an explanation so we will pick up with that on Monday.

Solving for a
Then I had some private tutoring with a 7th grader. We went over the 5 important numbers needed to make a box plot. I took the idea of tracing his hand from Sarah over at Math Equals Love. We also discussed that the whisker in a box and whisker plot is the length of the range, because range is maximum minus minimum. This wasn't the best example because the minimum was the same as the lower quartile so it looked a tad strange.

Working on box plots.
Then at dinner I got a text from a student I tutor in Algebra 2 that he nailed his quiz. Pleasant surprise.
And to end the night, I met up with some teachers I met at CPM's academy of best practice math camp this past summer in seattle. They were in town for the CPM conference and we ate some delicious dinner at Kincaids in Burlingame.

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