Lesson 1-2 of the U of Chicago text is called "Locations as Points." (It appears as Lesson 1-1 in the modern edition of the text.) The main focus of the lesson is graphing points on a number line. Indeed, we have another description of a point:
Second Description of a Point:
A point is an exact location.
Yesterday I made a big deal about the first description of a point -- the dot -- since many of our students are interested in pixel-based technology. Locations as points aren't as exciting -- but still, the second description is something we think about every time we find a distance. The definition of distance is highlighted in the text:
Definition:
The distance between two points on a coordinatized line is the absolute value of the difference of their coordinates.
Other than this, the lesson is straightforward. Students learn about zero- through three-dimensional figures, but of course the emphasis is on one dimension. One of the two "exploration questions," which I included as a bonus, is:
-- Physicists sometimes speak of space-time. How many dimensions does space-time have?
The answer, of course, is four -- even though there might be as many as ten dimensions in string theory. We ordinarily only include Einstein's four dimensions and don't consider the extra six dimensions of string theory as part of "space-time."
Here's the other bonus question:
-- To the nearest 100 miles, how far do you live from each of the following cities?
a. New York
b. Los Angeles
c. Honolulu
d. Moscow
Well, part b is easy -- I worked in L.A. last year and my daily commute obviously wasn't anywhere near 100 miles, so my distance to L.A. is 0 miles to the nearest 100 miles. The U of Chicago text gives the distance from L.A. to New York as 2451 miles as the crow flies, but 2786 miles by car. I choose to give the air distance in part a, in order to be consistent with parts c and d (for which only air distance is available). We round it up to 2500 miles. My answers are:
a. 2500 miles
b. 0 miles
c. 2600 miles
d. 6100 miles
Hmmm, that's interesting -- I'm only slightly closer to New York than to Honolulu.
Here is the Blaugust prompt for today:
A Day in the LIfe (#DITL)
After yesterday's "An Hour (or 75-80 minutes) in the Life" and "A Week in the Life," we've finally see a format very familiar to us, "A Day in the Life." During my year of teaching, I wrote several "Day in the Life" posts for another challenge led by Tina Cardone. And I'll be continuing to write "Day in the Life" posts once again once subbing starts up again, which should be next week.
For today's Blaugust post I'll reblog one of the "Day of the Life" posts from the Cardone year. I want to choose an ordinary day, not one of Cardone's special days (first day of something, last day of something, and so on). And too many of my Cardone posts landed on weekends, holidays, or field trip days. Therefore I choose to quote the "Day in the Life" from October 18th, 2016:
7:45 -- I arrive at my school.
8:00 -- I report to the playground, where many students are beginning to arrive. The students are told to gather in a circle for the flag salute.
8:25 -- My first class, a sixth grade class, begins.
8:45 -- The dean comes in and announces the start of the CELDT test -- the California English Language Development Test. All students classified as English Learners -- which about a third of the class -- go downstairs to take the test.
9:45 -- My sixth graders leave and my seventh graders arrive. Many of these students are still out taking the CELDT test.
11:05 -- My seventh graders leave for nutrition.
11:25 -- My eighth grade class arrives. I begin the class the same way I start all my classes, with a Warm-Up question:
Question: (x^3)^6 = x^?
The answer is 18 -- and of course today is the 18th.
11:35 -- Today is the second day of the project we've been working on. It is called "Learning to Communicate," and it is the fourth project of the Illinois State text. (I explained how the Illinois State text is project-based back in my August PD post.) The first four projects are the same for all three grades, and so this is the third time today that I'm giving this project. It was tricky, though, since many of the students are out for the CELDT. There are no eighth graders taking the test -- this class is just a smaller class anyway.
The project requires students to draw various 3D figures on two types of graph paper. The first part, given last Friday, was on oblique graph paper. Today we use isometric paper. I found the isometric paper using Google -- here is the first link:
https://www.printablepaper.net/category/isometric_graph
Notice that the words "isometric" and "isometry" -- as in Common Core Geometry transformation -- are definitely related. Both mean "equal length" -- an isometry maps segments to segments of equal length, and on isometric paper, the sides of the cube are all the same length on the paper.
But some students struggled to draw a cube on the oblique paper on Friday, and so today I've already drawn some cubes and other figures on the isometric paper so students can just copy it. Yet many of the students still have trouble with it. They either try to draw an oblique cube on the isometric paper or merely draw a square.
I think back to the activity I gave back on the third day of school (which I mentioned back in my monthly post for August). I found the activity in another textbook, in a lesson called "Drawing in Perspective," even though the blocks were drawn obliquely or isometrically, not in perspective. In that lesson, the students drew "buildings," with most of them drawing flat rectangles. I've been hoping that they would improve after this lesson, but so far most of them haven't.
I'm a bit surprised that they're having trouble drawing cubes. I believe that I could draw an oblique cube in my early elementary years. But then again, I could never draw a person -- my figures weren't exactly stick figures, but they weren't much better. I reckon that there are several students who can draw lifelike human beings yet can't draw a cube. It is the difference between the "left brain" (the more analytic, mathematical side) and the "right brain" (the more artistic side).
12:05 -- Because I know how tough the 80-minute block schedule can be on middle school students, I provide a music break. My student support aide arrives during the music break. I get out my guitar and I play the following inspirational song:
LEARNING TO COMMUNICATE
1st Verse:
Communication
Involves many tools.
There's teaming, journaling,
And sketching in school.
When you draw the shapes,
To look 3D, like a cube.
Just compare it, then
Choose the best from your group.
Refrain:
Learning to communicate
Is what we all must do.
Communication
It's the meaning of life, too!
2nd Verse:
Communication
Not just with your friends.
If you're with someone else
The world won't come to an end.
It will be much better
If you talk to everyone.
Get along with others
Yeah, that's so much fun!
(Repeat Refrain)
12:15 -- At this point, a terrible incident occurs. I choose not to post the full details of the incident here on the blog due to its sensitive nature. To make a long story short, some students start writing a letter in hopes of getting another teacher at the school fired! My only involvement with the incident is that the letter is written during my math class. (My support aide is not sitting in a location where she can tell what the students were writing -- only I see and hear them.)
12:35 -- This is a good time to end the period with an Exit Pass. Students copy the following line:
Today, we drew 3D figures on isometric graph paper.
12:45 -- My eighth grade class goes out to lunch.
1:25 -- My sixth grade class returns for a special "Math Intervention" class. There is special software for this class. I spend much of the period making sure that the students all have the correct password.The online lesson is on unit rates. This lesson is challenging, since students have to divide to find the unit rates, and many of the numbers they need to divide are multi-digit. No one makes it to the top score of 100, but many students make it to the 90's -- the software starts asking challenge questions once a student reaches 90.
As for the questions involving single-digit numbers, I continue my campaign to stop students from becoming "drens," or reverse-nerds who can't do simple arithmetic. Here's how it works -- this Thursday, the students are scheduled to take a "Dren Quiz" on their 3's times tables. So I draw a multiplication table on the board that goes from 3's to 9's. When the Dren Quiz begins, I'll erase the 3's from the table, so that only the 4's through 9's remain. The table will remain on the board until it's time for them to take their 4's Dren Quiz (probably in December). This way students can have help with the higher times tables but will have to learn them before they're erased.
2:25 -- My sixth graders go out to P.E. class.
3:20 -- All of the middle school teachers plus the fifth grade teacher (at our K-8 school) gather in the classroom of the teacher victimized by the smear letter. We all try to comfort the poor teacher, who is visibly upset.
4:00 -- I go home for the day and head for my computer to type up this blog entry.
Returning to the present, today I just noticed that the website for my old charter school has been updated, and quite a few changes have been made to the teaching staff this year. The most important change is that this year, there is finally a separate science teacher. This means that if I had remained at the school, I'd have had to put up with teaching science for two years before being allowed to teach only math in my third year.
Actually, middle school students still have three main teachers, but with two of the three teachers being math and science, the third teacher is a "Humanities" teacher who apparently covers both English and history. This is more in line with the "Core" classes that my own middle school had back when I was a young student. Since there are only three middle school teachers, there can still be no conference period -- each teacher has one of the three grades at a time.
It makes sense that there would be an actual science teacher this year. After all, this is the year that the California Science Test counts for real. Back then, my main mistake with science was to assume that the projects in the Illinois State "STEM" text (such as "Learning to Communicate" mentioned in the "Day in the Life" above) counted as true science projects. Instead, I probably should have followed my counterpart at the sister charter and only gave projects from the science text. But if I could have made it to my third year and teach only math, only then should I have used the math STEM projects (like "Learning to Communicate" above).
Indeed, an argument could be made that if I was to teach science to only one of the three grades, that grade should have been sixth grade, not eighth grade. After all, the California Science Test given to the eighth graders that year didn't count, while the sixth graders are now currently eighth graders about to take the CAST for real.
My problem was that I was still thinking in terms of the old (pre-NGSS) version of CAST. With the old test, a student could have no science at all in sixth or seventh grades and still earn a perfect score on the CAST since it only tested eighth grade physical science. But the new test covers material from all three years of science. Thus I needed to teach science to all three grades -- but especially sixth grade, since CAST will eventually count for their cohort.
So who is this mysterious new science teacher? It's none other than the history teacher from the year that I taught. Most likely, he added Foundational-Level Science to his history credential, thus allowing him to teach only science this year. I recall that his classroom management was strong, which allows him to teach a new subject with minimal behavior problems. And he's the one who will have to answer the students' complaints of "We never learned this!" when reviewing for the CAST and stumbling upon something they should have learned back in sixth grade with me.
The English teacher -- the victim of the smear campaign from "Day in the Life" above -- is no longer listed as a teacher. Fortunately, she did survive the smears to finish that year and teach one more year at the school before leaving this year. Right around the time I left, she took on a student teacher -- her own student support aide. Both the master and student teachers were listed on the website as English teachers last year, suggesting that he, the student teacher, taught English at the sister charter. Now his name is still listed as a Humanities teacher along with a new name, so I can't be sure whether he's at my old charter or the sister charter.
Who's teaching my subject, math? Well, my successor teacher -- the former kindergarten teacher who just happened to have a math credential -- finished my year and started the next. But a few months ago, her name was dropped from the list and a new teacher took her place -- and it was none other than my old student support aide (also mentioned in "Day in the Life"). I recall that she told our students that math wasn't her strongest subject -- which is why the students should respect and listen to me, not to her. But apparently she became the math and science teacher anyway -- again, her classroom management was very strong (which is why the kids obeyed her, not me), and that more than makes up for her just okay math skills. But now my former aide is no longer listed there -- instead, there is a new math teacher.
Today we return to the blog of Blaugust participant Megan Dubee:
https://www.megandubee.com/single-post/2018/08/30/Writing-Summaries
She writes:
That disappointment aside, we did do our first Desmos AB in class today, and I particularly loved the moment pictured above.
Now I know what "Desmos" is, but not what "AB" is. No, it's not Calculus AB -- a quick search of the Desmos website reveals that it stands for "Activity Builder."
Anyway, recall that for a previous MTBoS challenge (possibly Cardone's), almost every post mentioned Desmos. I've never worked at a school -- either as a teacher or as a sub -- with Desmos software, but note that the calculator for the California version of SBAC is powered by Desmos.
So far, Desmos hasn't appeared in many Blaugust posts -- but, as Dubee points out above, most teachers don't give Desmos lessons too close to the first day of school (setting up accounts). That's why she waited until today to give finally her first Desmos AB.
She continues:
So many of my students are freshmen who haven't used Desmos before, so they were really surprised to find out that I could pace them and anonymize them.
But based on the photo that Dubee posted, the class appears to be Algebra II -- a class in which we don't expect to see many freshmen. (Under Courses near the top of the page, she does mention BC -- and this time I do mean Calculus BC -- so there could indeed be freshmen in Algebra II who are on pace to take Calc BC as seniors.) Even then, I expect rational functions, the topic of this lesson, to be covered in the second semester of Algebra II -- not at the start of the year.
Anyway, the students are supposed to graph a rational function in Desmos, and then write a summary about what they find. I assume that they type this summary directly into Desmos, and then:
I pulled four different statements using Snapshots (love this feature!) for comparison and analysis.
Earlier this week I compared Sarah Giek's manipulatives to Illinois State DIDAX manipulatives since DIDAX was available in my classroom. Similarly, as I reflect on my old class, I couldn't have used Desmos because that wasn't supported in my classroom. Instead, or class used IXL.
So let's compare Megan Dubee's Desmos lesson to my own IXL lesson -- the one that I mentioned at 1:25 in the "Day in the Life" above. The first difference we notice is that I spent much of the time answering my sixth graders' repeated question "What's my IXL password?" -- and recall that this was as late as October. On the other hand, Desmos passwords don't appear to be an issue, not even for Dubee's freshmen at the start of the year.
Sometimes I wonder whether it would have helped to post IXL passwords on the wall. Then students could check their passwords without having to ask me. For some students this might have helped, but I recall there was one boy who didn't know how to type. Sadly, I didn't realize this until just before I left the school -- and so I'd yelled at him so many times about not entering his password correctly.
There was an additional issue with IXL -- my classroom actually didn't have enough laptops for all of the sixth graders. And I never really came up with a good activity for the other students to do.
On this blog, I posted what I should have done about this. Each day during IXL time, I pass out a worksheet for all of the students. The students who have computers can use this worksheet as scratch paper and record only their 0-100 IXL score on the paper. But for those without laptops, I assign them eleven questions (the minimum number of questions needed to earn a 70 on IXL) for them to copy and answer on the worksheet. All eleven questions must be answered correctly -- otherwise they continue to redo them until they are correct.
Which students get the laptops? It could be the best-behaved students, or it could rotate. Those who have trouble typing, such as the boy I mentioned above, might always get the paper assignment.
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