Monday, February 8, 2016

Day 98: Slope, Rounding Decimals & Factoring

Today's estimation was the amount of juju hearts in an 11 ounce package. Some students used the visual clues of the ones they could see through the bag, and I really liked when a student said that each one is about 4 grams, they rounded 311 grams to 320, then divided by 4 and got 80. That was really sound reasoning.

I was ambitious and wanted my students to finish most of the 7.2.2 slope lesson in one period. We reviewed everything except the last problem about hiccups with 3 different representations.

I started students by making a table to organize their ranks, fractions, and decimals for easy reference. Students first ranked lines based on their appearance, 1 being the fastest and 4 being the slowest. Students saw that A and C were parallel lines so they were the same speed so could be 2nd or 3rd place for a tie.

Then students discussed how the slope triangle for A was labeled and where the 4 and 6 came from. A few students quickly say it meant 4 kilometers per 6 seconds. I asked them how they knew and they said they looked at the axes. The rise was the y axis and the run or base of the triangle was the x axis or seconds.

Then when they were prompted for unit rate, I said if you're going down the highway you don't say I'm going 4/6. What's missing? They reasoned it was 4/6 kilometers per second.

When I saw walking around the room how many different answers students got for writing 4/6 as a repeating decimal, I definitely made it a point of discussion in all classes. Some even switched the numerator and denominator and said it was 1.5. I said is 4/6 less than or greater than 1? Is 1.5 less than or greater than 1? Then they figured out their issue.

For rounding 2/3, students reasoned it was 0.6 with a repeating bar. Some students wrote 0.66. Some 0.7. And finally some had 0.67. Students who got the right answer had a hard time articulating. Students eventually said you look at the place you're rounding to, the hundredths, and look at the 6 to the right of it. That number is 5 or greater, so the 6 in the hundredths place rounds up. I asked them what 0.7 was rounded to and they said to the tenths place.

Here is how I wanted their tables to start.

Here you can see all the work of rounding to the nearest hundredth.

I also liked this students reasoning. He said there was about 24 candies in the see through section. About 3 of those sections, so 24 times 3 is 72. You also see another student who thought 311 divided by 2.
Here I wrote the students different answers for rounding to analyze.
In accelerated I was concerned about half the class being confused about fractional exponents. So, I wanted to review the vocabulary in detail with students.

First I discussed the names of a radical. The symbol is the radical symbol. The number inside the radical is the "radicand." The index number is which root it is. I didn't print out the foldables from Math Equals Love but I used it as a reference. I love that she puts the asterisk to mention of there's no index number then the index is automatically a 2. I discussed how that is read, and the cube root if the index was 3.

As you can see, I tried color coding 16 to the 5/2 power. The 5 represented the exponent and the denominator 2 represented the index of the radical symbol. We even discussed the commutative property in that 16^5/2 is the same as (16^1/2)^5 and (16^5)^1/2 meaning the exponent of 5 can be on the radicand or it can be outside the radical's parentheses. They told me how to solve 27^3/2 power as well.

Then with 10 minutes to go we reviewed how to start, and complete the generic rectangle with the aid of a diamond. Then 4 example problems were on the board and 4 different student volunteers completed them. We only had time for them to present 2 of them.

Radical vocabulary, literally.
Sample student work: I'm going to put this one up for error analysis because there's a mistake in 4x^2+17x-15. 

After school I did most of a homework center supervision then jetted up to Skyline to see Alan Schoenfeld of Berkeley discuss Formative assessment lessons and his TRU math suite.

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