Here is today's Pappas question of the day:
A = {perfect cubes < 32}, B = {multiples of 3}, A intersect B = ?
See that A is the finite set {1, 8, 27} and B is the infinite set {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...} -- there's no point in listing elements of B greater than 32 since they can't possibly be in A. So the intersection of these sets is {27} -- and of course, today's date is the 27th.
Even though the intersection of two arbitrary sets can be very large (even infinite), the intersection of two sets in a Pappas question is always a singleton (a one-element set) -- since that lone element must be the date. Thus Pappas questions almost never ask for the union of two sets, only the intersection.
Some readers might point out that the intersection isn't actually {27} but {27, 0, -27, -216, -729, ...}, since both cubes (but not squares) and multiples of three can be zero or negative. Usually, in a Pappas problem, it's assumed that we're talking about natural numbers, since only these can be the date.
It might be possible to give this problem in a middle school classroom. Set theory isn't usually taught in most schools these days, except for special situations (such as N(S) from the U of Chicago Geometry text from last year). It might be possible to ask a middle school student this question:
Name a natural number less than 32 that is both a perfect cube and a multiple of 3.
But I won't ask my students anything of the sort this week -- the second week of the Big March. In many ways, even though I consider the Big March to begin the Tuesday after President's Day, at least that's a four-day week. We truly feel the grind of the Big March today, the Monday after Prez Day, since it's the first of several five-day weeks.
The idea that the Big March doesn't really start until today is definitely true in school districts that have something called a "February break." I've already mentioned how some districts combine Lincoln's Birthday with President's Day to form a four-day weekend. Well, some other districts end up taking the entire week of President's Day off instead.
This idea of a "February break" or "President's Day vacation" isn't common in California. The only time I've seen it here back when there were furlough days due to budget cuts. Recall that when furlough days were common a few years ago, they were immediately inserted on the Monday, Tuesday, and Wednesday before Thanksgiving. (These days proved to be so popular that now we regularly have Thanksgiving week off even after we stopped needing furlough days.) Anyway, in the old year-round schools at LAUSD (see my June 19th post for more info), some tracks were already off all of November. So these tracks inserted the furlough days after President's Day instead. Other than that, I've never heard of a California school observing a week off in February.
As it turns out, one of the districts with a full week off just happens to be New York. There are so many New York teachers writing for "Day in the Life," and so I keep reading about the February break in their posts. Since New York schools have such a short winter break, President's Day vacation is greeted with open arms. For them, today marks the start of the Big March, with no more days off until spring break. (Wow, from "Regents" to "February break," I'm learning more about Big Apple schools than ever I wanted to this year!)
Okay, back to what I was saying about this week in my classroom. I'm not going to give any math questions like the Pappas question this because I'm not teaching much math this week. I warned you about this in my last post, and near the start of eighth grade block, I received the email message that makes it official -- I must indeed establish separate math and science grades this trimester. And so I declare this week to be Science Week, and I'll have to teach mostly science this week. Notice that the announcement about science doesn't affect today's lesson, as it's just coding Monday anyway.
Moreover, near the end of eighth grade block I received another tough message -- this one about the visit from Illinois State coming up on Wednesday. I was wondering whether I'd have a hour-long observation of one of my classes that day. Well, actually I'll be giving an hour-long presentation on how I plan to teach the Illinois State curriculum the rest of the year. That's going to be hard -- of course I'd rather have the hour-long observation, since it's not as if I wouldn't have to teach during that hour anyway. Now I have to come up with things to say for a full hour -- mostly likely a detailed lesson plan of what I'll be doing, week by week, until the SBAC. Yes, from the sudden need to plan science lessons to the presentation, I'm definitely feeling the pain of the Big March this week!
First things first -- since this is a two-day post, I might as well write about Science Week. Notice that this actually isn't my first Science Week of the year. The week between Rosh Hashanah and Yom Kippur, back in October, was my first Science Week. I used the High Holidays as an excuse to tell the students about lunar calendars and hence the motions of the earth, moon, and sun. But this time, I want to make sure that the students are learning the correct material for their respective grade levels.
Exactly one month ago, I wrote about how I should have taught science this year:
Of course, I now know what I should have done about science. I already mentioned how I'm fond of three-week cycles -- well, I should have used the original Study Island period by cycling among Foldable notes, a project, and a quiz on Study Island. The science period should occur every week, even after music tinkered with the schedule. This would have led quite nicely to the current test prep block for science, where I could continue the same three-week cycle. Avoid all pre-tests until the students are confident that I'll actually teach the material.
But what should have I done about the whole state standards/NGSS mess? (Right now, I try to explain NGSS to the students, but they don't listen. Based on my bad lessons, they think that I know nothing about science, so why should I know what NGSS is?) Perhaps I could have taught eighth grade physical science and seventh grade life science, but NGSS for sixth grade, as the transition to NGSS will be complete by the time they reach eighth grade. For life science, I don't feel comfortable with an animal dissection lab, but there are some microscopes in the room, so I could have used these in a lesson.
So this is exactly what I want to do this week. I want to give a physical science lesson to eighth grade, a life science lesson to seventh, and an NGSS wild card lesson (which could be on any of the three strands -- earth, life, or physical) to sixth grade. To determine which lesson to teach, I look at the list of standards under Study Island. I use Study Island as a guide because this is the website that purports to give the California version of the Next Generation Science Standards.
Let's start with sixth grade first. The first topic (well, the second topic -- the first topic is called "Pretest," which I'm skipping as per above) is "Structure, Function, and Information Processing." It consists of two subtopics -- "Cells" and "Living Systems." So it's clearly a life science lesson.
Now I can't actually use the three-week cycle that I mentioned last month, but I can make it into a three-day plan, as follows:
Tuesday: Foldable notes
Thursday: Science project
Friday: Quiz
On Wednesday, I'll teach the math topic that I originally scheduled for this week. After all, this is my Student Journal day.
So what sort of project should I give my sixth graders on Thursday? Well, we know that the only way to see cells is with a microscope, and I mentioned last month that we indeed have microscopes.
But where exactly am I going to get a cell to show the students? Well, cells are easy to find, as every single organism is made up of cells, but that doesn't tell me how to get a cell slide that my students can put under the microscope. This is the problem I have with teaching science -- I don't know where exactly science teachers get things. All I remember from my own days as a science students is that the teacher gave us the slides and we put them under the microscope. Of course I made no thought as to where the slides come from.
If I can't get the slides, the project could be to made a model of a cell. This doesn't necessarily mean that it will be the Edible Cell Model that I mentioned in that same post from a month ago.
In seventh grade, the second topic (after the first topic pretest) is "Matter and Energy in Otganisms and Ecosystems," with "Energy in Ecosystems" as its first subtopic. I want to focus on life science with my seventh graders, and it's clearly a seventh grade topic.
Here is the plan for seventh grade:
Tuesday: Foldable notes
Friday: Quiz
Recall that seventh graders don't meet on Wednesdays, so Thursday is the day that I must reserve for the math Student Journal. There's no time for a science project this week, but Energy in Ecosystems isn't a topic that naturally lends itself to a project anyway, except for something like cutting out pictures of different organisms and use them to create a food web. But this is more easily drawn in the Foldable rather than cut out.
Notice that so far, I have yet to mention either Green Team or Bruin Corps. Remember what I wrote in my post from a month ago -- one reason I've dug such a hole with science is that I was too dependent on Green Team and Bruin Corps to provide science lessons.
In particular, there's no sign of the Green Team project starting soon. And it might be possible for me to ask the Bruin Corps member who comes on Thursdays -- a biology major -- to provide me with some cell slides. But I won't, because I wish to avoid being dependent on a college student to provide me with science lessons.
We now move on to the eighth grade lesson. The second topic is "Genetics & Biotechnology" -- but I actually covered this back in November and December, back when I was still asking my Bruin Corps member to help me with the lessons. The third topic is "Natural Selection and Adaptations" -- but this is a life science topic, and I prefer sticking with physical science in eighth grade. (Of course, genetics is also life science, but at the time I was still milking lessons from my Bruin Corps member.)
There's a good reason to teach the fourth topic this week, "Space Systems." Not only is it a physical science lesson, but in a way I've already started this topic. First of all, the "Earth, Sun, and Moon" lesson from October is the second subtopic. The first is "The Universe" -- and I begin this subtopic today, some of the Monday Five questions I give today are on the solar system! The workbook from which I get the Monday Five often gives themed questions during the week, and the theme this week happens to be outer space. There are questions on the length of Jupiter's and Saturn's year, the distance of Earth and Neptune from the sun, and shooting starts.
By the way, the seventh grade Monday Five is also themed. This week's theme is spiders -- and hey, I can fit spiders into this week's lesson. Here's an example of a food chain that contains spiders:
Producer: Pea Plant
Primary Consumer: Aphid
Secondary Consumer: Beetle
Tertiary Consumer: Spider
Quaternary Consumer: Bird
On Friday in all classes will be a quiz. I've already scheduled a 50-point quiz for this Friday, and I might as well keep it, but make it into a science quiz. After all, the whole point of Science Week is to establish a science grade. So let's take a look at how my grading should work.
Recall that our online grading program automatically weights the assignments by categories:
40% Formal Assessment and Projects
20% Quizzes
15% Participation
15% Homework
10% Classwork
First of all, the points are weighted so that they fit these categories. So if I were to give 100 points in each category, they are weighted so that each Formal Assessment point is worth four times as much as a Classwork point. I think this is deceptive to the students, and so I circumvent this weighting by giving 400 Formal Assessment points, 200 Quiz points, 150 each for Participation and Homework, and finally 100 Classwork points, for a total of 1000 points in math.
Second, even with the points weighted properly, many students still think that 1% is one point -- so students with a grade of 79% say that they are "one point away from a B." In reality, 79% can represent a score anywhere from 790 to 799 out of 1000, so they may be anywhere from one to ten points away from a B.
Third, notice that I won't have time to give all five components during science week. Notice that if I were to give that one quiz and no other grade, that quiz would comprise 100% of the grade, not 20%, since four categories are missing. If I were to give only that quiz and Classwork, the quiz would make up 2/3 of the grade and the classwork 1/3, since 20% is double 10%. On the other hand, if I gave only that quiz and a project, then the quiz would be only 1/3 of the grade and the project 2/3, since 40% is double 20%.
All of this seems to present an appealing solution. Since there's only one week of science, it's reasonable to let the total number of points be 100 -- then one point really is 1%. There's already going to be a 50-point quiz, and Quizzes are 20%. So all we have to do is find another component that's also worth 20% and assign 50 points to that category. Then each of the 50-point assignments is half the grade, as desired. The problem, of course, is that there is no other category worth exactly 20%, nor are there two categories that add up to 20%.
The easiest way to make the math work out is to include Quizzes, Participation, and Homework. We see that these categories add up to 20% + 15% + 15% = 50%, so the percents end up doubling to 40, 30, and 30 respectively. So I could make the quiz worth 40 points instead of 50, and let the participation and homework be worth 30 points each.
But this is also problematic. With only one week available, there would most likely be only time for one homework assignment worth 30 points. If a student fails to turn it in, that student must be perfect on everything else just to get the lowest possible C -- so if that student then gets just one problem wrong on the quiz, the grade earned is F (since there are no D grades). Notice that there will be parent conferences at the end of the the trimester, where the report cards are given. And this isn't going to play well at parent conferences -- a student gets one question wrong on the quiz (which is still an A on the quiz) and a perfect score in participation (another A), yet due to not turning in one homework assignment, the grade that appears on the report card is F.
This is why I'm suddenly so obsessed with science grades -- I'm thinking about the parents. Any parent in that situation would cuss me out over giving an F for missing one homework assignment, then cuss me out for not teaching science until just before grades are due and then basing the grade on just one week of work. And this is with some parents already upset with me over the math homework that I'm required by Illinois State to give online, even though not everyone has Internet access!
So I'm still trying to figure things out. Perhaps I should use the 40-30-30 grading, but counting the Foldable as "homework." That way the points are weighted properly, yet since the Foldable is done in class, students who don't do the homework aren't severely penalized. (Or I could give the homework but use the controversial 0=50% grading system for that assignment only, so the student who misses the assignment but excels on everything else earns a B rather than an F. Or I could give three homework assignments worth 10 points each, but that means I have to come up with three different assignments on the fly.)
Well, let's see how my science lessons go tomorrow. This is actually an exciting time to teach science, as scientists have made two major discoveries in recent weeks:
-- Astronomers have discovered seven new exoplanets -- that is, planets outside our solar system. It's possible that at least one of these planets is Earthlike, or habitable.
-- Here on Earth, geologists have discovered two new continents.
One of these new continents is Zealandia -- named after the only part of it that's above sea level -- New Zealand. But I'm actually more interested in the other new continent -- Mauritia.
Recall from some of my 2014 and 2015 spherical geometry posts that the antipodes -- or point directly opposite -- of California is in the Indian Ocean. I think it would be fun if the antipodes of California turned out to be a continent after all -- and it's Mauritia that's nearer the antipodes rather than Zealandia.
But since my coordinates are approximately Latitude 34N, 118W, the antipodes would have to be near Latitude 34S. Mauritius, for which Mauritia is named, lies at around Latitude 20S, and all maps of Mauritia I've seen so far have the new continent extend northward from Mauritius towards the Equator, and not southward towards 34S. So unfortunately, there appears to be no new continent at my antipodes after all -- oh well.
This is a two-day post. My next post will be Wednesday, March 1st -- and I'm glad that tomorrow's a no-post day, since I need the extra time to create that one-hour presentation for Illinois State!
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