Thursday, October 6, 2016

Student Journal: Exponents (Days 35-36)

I didn't purchase only math books at the library book sale -- I also got a science book. It is Concepts in Science, the so-called "Newton edition," dated 1975. I can't tell what grade level it's for, especially considering how science standards have changed in the past 40 years. It very well could be a text for elementary school.

Here is the table of contents -- unit titles only, not chapter titles:

1. The Bounce of Sound
2. The Bounce of Light
3. The Travels of a Drop of Water
4. The Travels of a Breath of Air
5. The Travels of a Handful of Soil
6. The Fall of a Tree
7. The Journeys of a Salmon and a Duck
8. Free -- Within a System

Of course, as a math teacher, I'm having trouble teaching science -- and even the elementary school teachers like our fifth grade teacher may need to teach science beyond the Illinois State text. Our school is working on perhaps having a group of students participate in a science competition.

In math, we're returning to traditional lessons in the "Student Journal." The eighth graders are now starting to work with exponents, in accordance with the following standard:

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

Theoretically, each Learning Module in the Illinois State STEM text is associated with a particular standard and lesson in the Student Journal. But this isn't true of the first four modules -- these appear in all three grade levels, but they don't correspond to traditional lessons for all three grades.

So I decided to go through the Student Journal in order. The journal is arranged so that all the standards are followed in the naive order given by the Common Core. We already finished all of the Number System standards, and so we move on to Expressions and Equations. As it turns out, it's logical to cover standards 8.EE.A.1 and 8.EE.A.2 on exponents now, since Learning Module 5 in the STEM text corresponds readily to standards 8.EE.A.3 and 8.EE.A.4 on scientific notation.

Today's lesson is mostly on negative exponents. Of course, I give my students the classic example:

2^3 = 8
2^2 = 8/2 = 4
2^1 = 4/2 = 2
2^0 = 2/2 = 1
2^-1 = 1/2
2^-2 = (1/2)/2 = 1/4
2^-3 = (1/4)/2 = 1/8

and so on. Negative (and zero) exponents are notoriously confusing for students to remember -- as are the Laws of Exponents, which I'll be teaching tomorrow. After all, think about it -- anything to the zero power is one? Negative exponents are reciprocals. To multiply powers, we add something?

Sixth graders are beginning unit rates, and seventh graders learn about constants of proportionality. I sing the following song, which incorporates lessons from all three grades. The opening lines about a girl making jewelry comes from the sixth grade Student Journal:


A girl makes jewelry,
Four red for every white bead.
If there are ten white,
How many red beads will she need?
The proportionality constant is four,
It is no less and no more.
It is what you multiply,
The number of white beads by
To get forty red beads.

A girl writes a big two,
The four next to it is small.
What is this equal to,
Hey what does it mean at all?
The number exponent is four,
It is no less and no more.
It's how many times you multiply,
The number base itself by
To get the answer 16.

Today is the sixth, and so we look at Dawneen Zabinske, whose posting day is the sixth:

It took a while for me to find Ms. Z's blog as the link provided to me was incorrect. I'm glad I found the link, because Ms. Z is a South Carolina middle school teacher.

Ms. Z hasn't written her October 6th post yet. But there are some interesting things in some of her older posts, including her September 6th post:

Ms. Z teaches both sixth and seventh grade math this year. Her school is sort of like military school, and so her classes are divided into all-male and all-female "cadets."

She writes about some of the behavior problems she is having:

The intervention centers around a achieving a goal for the week. The class started with zero points and points are added every 5 minutes they are compliant with the rules: 40 minutes of class = 8 points. They can also earn additional points for asking a relevant question or answering another student's question or coming to the board to work a problem. However, if they begin to break from the rules, they can lose a point for each 5 minutes they are off task. This worked for about a week and they got close to their goal but didn't quite make it. I have tried rearranging seat assignment. I have tried having students write a discipline essay about their behavior and ways to correct it. I have called or texted parents; I have submitted teacher-managed incident referrals to the office. It's only a few that are causing the disruptions every day; and it's not just my class - it's every class. Usually this point system has worked at least for a few months and a few rewards. I'm seeing with this group - I'm probably going to have to go with individual points/rewards or split the group into two and offer a competition between groups. I might eliminate the taking away of points so to focus more on the positive and less on the negative.

In earlier posts, I mentioned a similar point/minute system, and I must admit that so far I'm not having much more luck than Ms. Z is. Right now my plan is to schedule a computer day right after two key days when I'm hoping that the behavior will improve -- more on this when I reach my own monthly posting day.

By the way, when I was looking for the correct link for the 6th, I actually found something written by the poster for the 30th, Kevin Cormier. But it's not a blog post or a "Day in the Life" entry -- it's actually an article written for Huffington Post:

The article is dated October 3rd, three days after Cormier's scheduled posting day. He writes about using data to guide instruction. My own school is big on data-driven instruction -- indeed, we are to have a "data wall" where students can easily access their data.

Oh, and speaking of middle school, I have no plans to watch James Patterson's Middle School movie that comes out this weekend.

This is a two-day post, so I don't post tomorrow. It means that I'm only posting twice this week, when my goal is to post thrice a week -- this actually happens a few times this year when there's a Monday holiday and both Tuesday and Friday are multiples of three. But each time this happens, it means that the previous week was a four-post week, with entries on Monday, Tuesday, Thursday, and Friday. So in the end, it works out to average about three posts per week.

My next post will be on Monday.

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