It's also the last day before the week of Thanksgiving break -- therefore it's a minimum day. That's right -- I subbed for four consecutive days at this school and had four different bell schedules (extended homeroom, Wednesday common planning, regular, and minimum). And that's not even taking into account the period rotation. On Fridays the rotation is 0-1-6-2-3-4-5. (Well, at least you readers get to see this school's full range of schedules.)
In my old district, this is just about the end of the third quaver. In my new district, it's Day 56, near the end of the trimester.
For today's "Day in the Life," our focus resolution is:
4. Begin the lesson quickly instead of having lengthy warm-ups.
7:15 -- For zero period Algebra I, a guidance counselor comes in to give all the eighth grade students a presentation. It's all about academic plans for the rest of this year -- and to get the students to start thinking about high school next year.
Actually, last night I found my dry-erase packets for solving systems by elimination, but the regular teacher had already informed me about the presenter. I decided to bring the packets anyway just in case she doesn't show up and I'm left without a lesson.
7:50 -- The counselor dismisses zero period. Officially, this class is the same length everyday, but she decides that since it's a minimum day, there's no harm in letting these students leave early.
8:15 -- Homeroom/first period arrives. This is the second Algebra I class presentation.
9:00 -- First period leaves and sixth period arrives. This is the third Algebra I class presentation. A second presenter arrives -- apparently the second lady is a guidance counselor in training.
9:40 -- Sixth period leaves and second period arrives. This is the last Algebra I class presentation.
10:20 -- Second period leaves -- but now the schedule is a little tricky. On regular days there are two breaks, snack (nutrition) and lunch. But on minimum days students get only one break, "brunch." But there are two different brunches, Brunch A and Brunch B -- even though on regular days all students have the same lunch. (Notice that the only other time there are split breaks at this school is on rainy days -- please refer to my May 31st post.)
Today, Brunch A is before third period, while Brunch B is after third. Thus whether a student is on Brunch A or B hinges on what the third period class is. It isn't as simple as having all seventh graders on Brunch A and all eighth graders on Brunch B -- which is good, since my third period ASB class has both seventh and eighth graders. Instead, the rule is that all students who have third period math, science, or P.E. have Brunch A, while those with English, history, or elective have Brunch B. Since ASB is an elective, I have Brunch B today.
(Notice that on minimum days other than Friday, different periods rotate into the brunch position. In other words, this math teacher has Brunch A on all minimum days other than Fridays.)
The students' task today is to take down the pumpkin pie contest posters that are spread out around the school, since that contest was yesterday (as I wrote in yesterday's post). These are to be replaced with "Operation Santa," a toy donation drive that takes place between Thanksgiving and Christmas.
But there's another problem -- the administrators decide to hold a tardy sweep after Brunch A. In other words, the ASB students (who have Brunch B) can't be out removing posters lest they be caught in the tardy sweep. This means that the students don't finish switching the posters.
Clearly, the regular teacher didn't take the minimum day into consideration -- and there's no way he could have anticipated the sweep (which occurs unannounced).
11:00 -- Third period leaves, and I finally make it to Brunch B.
11:25 -- Fourth period arrives. This is the math support class. For these students, this is actually their second math class -- and they've already had a presentation in their main math class. So instead, the counselor and her assistant monitor the students as they work on ALEKS.
12:00 -- Fourth period leaves. The last period of the day is fifth period conference. This means that I'm done teaching students for the day -- much to the counselor's chagrin. She was planning to have her trainee give the presentation for the last class, only to find out that it was conference period. (If she'd known this, she probably would've had the trainee present in second period.)
The only classroom management issue is in fourth period. Indeed, the only name I write on the bad list all week is a guy in this class who was absent all week except today. Thus when he hears me say that we're working on ALEKS, he thinks I won't check to see whether he's doing it (whereas the other kids know from earlier this week that I'll indeed check on them). Even with three adults in the class, he refuses to work. The counselor informs me that he's failing almost all his classes.
Perhaps I could have prevented this problem. Back on Tuesday, the students want to change seats, and I reply that I'd let them do so the next day if they worked hard on ALEKS that day. (At the time, I thought that this was a two-day assignment, so that the seat privilege would be for just one day.) So there ends up being a large group (about 4-5) of boys and another large group of girls, with some other individuals and pairs scattered across the room. Yesterday I had trouble getting these students, especially in the large groups, to work (and fourth period was named the best class of the day almost by default after the Algebra I classes were too talkative). Today the absent student joins the large group (so now it's a group of 5-6 boys) and assumes that it's non-academic free time.
I could have prevented this by forcing the students to sit in assigned seats (that is, by denying their Tuesday suggestion). Another idea is, since the desks are naturally clustered in groups of three, that no more than three students can sit together. If a larger group can't decide which three of them get to sit together, then they must return to assigned seats.
The focus resolution only comes into play today when it's time to collect homework -- the teacher never specified to collect the HW, but I don't want them to lose the assignments over vacation. It takes a few minutes to collect assignments in zero period, but this takes too much time away from the counselor's presentation. In subsequent periods, I make three piles (Tuesday's textbook assignment, yesterday's worksheet, and an extra credit page) and students place their papers there. So I'm on my way to fulfilling the fourth resolution to save time at the start of class, but it still takes some time for the students to write their names and staple the assignments together.
In my old district, today marks the end of the third quaver. In my new district, today is Day 56, near the end of the first trimester. In fact, the counselor mentions this in her presentation. She tells the students that second trimester is the most important tri of eighth grade. This is because high schools will program them into classes before the end of this school year when third tri grades are available, and so placement is based mostly on second tri grades. (This is the same reason that junior year grades are the most important for college admissions.)
I've never thought of that before. It makes me wish that I'd known this two years ago at the old charter school -- my eighth graders needed to know how important second trimester is.
The counselor also discusses several math pathways for our students. Since our students are currently in Algebra I, they should make it to Geometry next year if they pass this class. Most students will be on a pathway to Calculus AB if they pass all their class. But there is also an honors pathway that leads to IB Math Studies as juniors and Calculus BC as seniors -- which leads some students to ask what the difference between Calc AB and Calc BC is. I jump in and explain the AP to them. I tell them that my alma mater, only grants course equivalency for scores of 5 (for AB or BC, but a BC score of 4 counts as an AB score of 5).
As we know, both AP and IB are traditionalist-approved. It's the students not in Algebra I (including all the math support classes) who are in trouble according to the traditionalists.
Next, the counselor informs the students about the PSAT 8/9 coming up on December 8th. Some students in each class have already signed up for the test.
Oh, and before I leave the counselor's presentation, I'll tell you that she shows the students this video on "Famous Failures" in order to motivate the students. (They have fun trying to guess the identity of the famous failure.)
Lesson 6-5 of the U of Chicago text is called "Congruent Figures." In the modern Third Edition, we must backtrack to Lesson 5-1 to learn about congruent figures.
This is what I wrote last have about today's lesson:
Lesson 6-5 of the U of Chicago text is on congruent figures. Congruence is one of the most important concepts in all of geometry, especially Common Core Geometry.
As I mentioned many times on this blog, the word congruent is defined very differently in Common Core Geometry than under previous standards. We all know what it means for two segments to be congruent -- that is, that they have equal length -- or for two angles to be congruent -- that is, that they have equal measure. The new definition of congruent appears to be original to the Common Core, and yet, it isn't. Years before the Core, the U of Chicago text used the following definition of congruent -- indeed, it is mainly because of this definition that I chose the U of Chicago as the textbook on which this blog is based:
Definition:
Two figures, F and G, are congruent figures [...] if and only if G is the image of F under a translation, a reflection, a rotation, or any composite of these.
And there we have it -- this definition of congruent predates Common Core. But many opponents of Common Core do not like this new definition. One such opponent is Ze'ev Wurman, a member of the commission here in California that reviewed the Common Core standards. Although his views are posted at several websites, one of the best Wurman articles I found is at this link:
http://www.libertylawsite.org/2014/03/27/the-common-cores-pedagogical-tomfoolery/
Skipping down to the discussion of the math standards -- since, as Wurman himself points out, math is his area of expertise -- the author begins with some elementary school standards. For example, Wurman gives this standard:
1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Wurman states that this standard should have stopped after the first sentence. Instead, it goes on to prescribe some nonstandard algorithms for addition. I already discussed much of this in many previous posts. Since much of what Wurman writes about grades 1-3 echo what I wrote about the lower grades, I am in full agreement with Wurman for the lower grades.
But then Wurman moves on to Common Core Geometry. Here's what he writes about it:
A true content standard would simply say “Students prove triangle congruence” or, perhaps, “Students understand triangle congruence,” leaving the method of instruction to the teacher. Instead, Common Core not only dictates how to teach congruence, it insists on a specific experimental method of instruction that has an established a track record of failure where it was invented [...]
[emphasis Wurman's]
He then gives a link to a PDF file about the Russian mathematician and scientist A.N. Kolmogorov, whom the PDF credits as the creator of geometry based on transformations. Wurman implies that this geometry was tried out in Russia (i.e., the Soviet Union) and was a big failure.
As I mentioned many times on this blog, the word congruent is defined very differently in Common Core Geometry than under previous standards. We all know what it means for two segments to be congruent -- that is, that they have equal length -- or for two angles to be congruent -- that is, that they have equal measure. The new definition of congruent appears to be original to the Common Core, and yet, it isn't. Years before the Core, the U of Chicago text used the following definition of congruent -- indeed, it is mainly because of this definition that I chose the U of Chicago as the textbook on which this blog is based:
Definition:
Two figures, F and G, are congruent figures [...] if and only if G is the image of F under a translation, a reflection, a rotation, or any composite of these.
And there we have it -- this definition of congruent predates Common Core. But many opponents of Common Core do not like this new definition. One such opponent is Ze'ev Wurman, a member of the commission here in California that reviewed the Common Core standards. Although his views are posted at several websites, one of the best Wurman articles I found is at this link:
http://www.libertylawsite.org/2014/03/27/the-common-cores-pedagogical-tomfoolery/
Skipping down to the discussion of the math standards -- since, as Wurman himself points out, math is his area of expertise -- the author begins with some elementary school standards. For example, Wurman gives this standard:
1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Wurman states that this standard should have stopped after the first sentence. Instead, it goes on to prescribe some nonstandard algorithms for addition. I already discussed much of this in many previous posts. Since much of what Wurman writes about grades 1-3 echo what I wrote about the lower grades, I am in full agreement with Wurman for the lower grades.
But then Wurman moves on to Common Core Geometry. Here's what he writes about it:
A true content standard would simply say “Students prove triangle congruence” or, perhaps, “Students understand triangle congruence,” leaving the method of instruction to the teacher. Instead, Common Core not only dictates how to teach congruence, it insists on a specific experimental method of instruction that has an established a track record of failure where it was invented [...]
[emphasis Wurman's]
He then gives a link to a PDF file about the Russian mathematician and scientist A.N. Kolmogorov, whom the PDF credits as the creator of geometry based on transformations. Wurman implies that this geometry was tried out in Russia (i.e., the Soviet Union) and was a big failure.
Why should we use the transformation approach? In pre-Core Geometry, we must define the word congruent three times -- first for segments, then for angles, and finally for figures. But in some ways, this is an ad hoc approach. In the Common Core, we only define congruent once, and it applies to segments, angles, and figures all at once.
In the Common Core, congruent means "identical up to isometry" (and later on, we see that similar is defined as "identical up to a similarity transformation"). There are many concepts in college-level mathematics that are defined similarly -- such as topologically equivalent ("identical up to homeomorphism"), equinumerous ("identical up to bijection"), and so on. Furthermore, the Lebesgue measure of a set is defined so that two sets such that there is an isometry mapping one to the other have the same measure.
So in some ways, the Common Core definition is more rigorous than the pre-Core definitions. Also, in some ways, the Common Core definition predates Kolmogorov by a wide margin -- Euclid himself used it as the Principle of Superposition in his proof of SAS (Proposition I.4).
In Hilbert's formulation of Euclid's axioms, congruence is a primitive notion -- that is, it is undefined just as point, line, and plane are. Actually, it's two undefined terms, since Hilbert considers segment and angle congruence separately. As I mentioned before, we can't define an undefined term, but instead we know what it means through the use of axioms or postulates. Hilbert provides six axioms of congruence -- these cover the Equivalence Properties and Segment and Angle Congruence Theorems as given in this section, some of the Point-Line-Plane and Angle Measure Postulates, and SAS. We notice that Hilbert's congruence is completely nonmetric -- there is no notion of distance or angle measure anywhere.
So which formulation should we use? This is a Common Core site and so I use the Common Core definition of congruence, but in the long run, which is best for the students? The usual guiding principles is that if a concept is easy for the students to understand and leads to a higher concept, then the students should learn how to prove it. But if the lower concept is difficult for the students, it should be made into a postulate and not proved in class.
So we can see a full continuum, from more proofs to more postulates:
- Common Core: SAS, ASA, SSS all proved (using transformations)
- Hilbert (supported by David Joyce): SAS postulated, ASA, SSS proved (using SAS)
- Status quo: SAS, ASA, SSS all postulated (most texts)
- Minimalist: SAS, ASA, SSS not mentioned (isosceles/parallelogram properties postulated)
The argument from Wurman and other Common Core opponents is that proving SAS, ASA, SSS from transformations only confused students (which would be the reason why this would have been a big failure in the Soviet Union) and that they should be assumed as postulates. But then, we wonder, why not go one step further and state that all proofs confuse students, so that all proofs involving SAS, ASA, SSS should be dropped, and the properties of triangles and parallelograms assumed? Why is the status quo, where SAS, ASA, SSS are assumed and used in proofs, exactly the right level of complexity for the students?
Well, this is what I hope to find out through this blog. It could be that these Core opponents are correct, and that the status quo level of complexity is exactly appropriate for high school students taking geometry. To me, this is not as clear-cut as elementary math, where the standard algorithms for addition and subtraction are clearly superior to the nonstandard algorithms. This is the reason that I agree with the traditionalists for K-3 math, but not high school math yet.
As for the other theorems proved in this chapter, the Equivalence Properties of Congruence is proved in a way that is standard for many types of transformations -- by using the identity, inverse, and composite functions. The Segment and Angle Congruence Theorems are proved using reflections only, since the text states (in the "Shorter Form" of the definition of congruence) that only reflections, or a composite thereof, are needed to establish congruence. But sometimes it's easier for students to visualize other transformations -- for example, in the Segment Congruence Theorem, one can simply translate X to Z, so that X' and Z coincide. Then one can rotate W' to Y, so that W" andY coincide. In the text, both of these are reflections instead.
Notice that this lesson, 6-5, is the first lesson in which the word congruent appears. The U of Chicago text is careful to use phrases such as "of equal length (measure)" instead of congruent.
I've mentioned before that many people -- both teachers and subjects -- use the words equal and congruent interchangeably. There are two distinctions to make -- one is that numbers (including lengths and angle measures) are equal, while segments and angles are congruent. The other is that we don't know that any figures are congruent until we know of an isometry mapping one to the other, which the Segment and Angle Congruence Theorems provide.
In this course, the latter distinction has priority. I admit that I myself have called angles "equal" (when it's their measures that are equal) on this blog -- because I don't want to call them "congruent" until reaching the Segment and Angle Congruence Theorems. I am especially guilty of this when I write phrases such as "Angle A = Angle B" because it's so much easier than trying to write an angle symbol in ASCII. Occasionally, I would underline a slash: m / A = m / B is the best I can do. Of course, I can't really draw a congruent sign at all, unless I write ~= and you just imagine that the tilde is directly above the equal sign.
I've mentioned before that many people -- both teachers and subjects -- use the words equal and congruent interchangeably. There are two distinctions to make -- one is that numbers (including lengths and angle measures) are equal, while segments and angles are congruent. The other is that we don't know that any figures are congruent until we know of an isometry mapping one to the other, which the Segment and Angle Congruence Theorems provide.
In this course, the latter distinction has priority. I admit that I myself have called angles "equal" (when it's their measures that are equal) on this blog -- because I don't want to call them "congruent" until reaching the Segment and Angle Congruence Theorems. I am especially guilty of this when I write phrases such as "Angle A = Angle B" because it's so much easier than trying to write an angle symbol in ASCII. Occasionally, I would underline a slash: m / A = m / B is the best I can do. Of course, I can't really draw a congruent sign at all, unless I write ~= and you just imagine that the tilde is directly above the equal sign.
Now all of this was three years ago. So what does Wurman have to say this year?
https://edsource.org/2018/renewed-push-to-offer-sat-and-act-as-californias-11th-grade-test/601564
Building on Doug’s point, one should recall that while the grade 3-8 achievement scores are barely visible to the general public, the 11th grade results serve as a prominent measure of “college-readiness” and get much larger exposure in state and national press. Consequently, the political interest of SBAC leadership to “pad” those results is understandable, even if not welcome.
The results can be seen by the fact that SBAC’s “college readiness” differs *widely* from the previous measures of college-readiness as defined by CSU. This is also the driving force behind forcing CSU and CCC to eliminate their entry-level examinations and remediation courses, so the fake SBAC “college-readiness” will not be exposed for the fraud it is for as long as possible.
For example, the 2015 ETS report comparing the previous STAR-based college-readiness (embodied by the EAP program) found that only 76% of those who scored “college ready” in ELA by SBAC would score as college-ready by the CSU measure, and over 40% of SBAC’s “conditionally-ready” would be scored as not-ready by CSU. In math, less that 40% of those found “college ready” by SBAC are found college-ready by CSU’s own measure. (See tables 3.6-3.8 here: http://www.cde.ca.gov/ta/tg/ca/documents/eapstudy.pdf)
One can find more information on issues with SBAC test in California here: https://www.hoover.org/research/troubling-saga-smarter-balanced-test
(This debate is actually all about replacing the junior SBAC test with SAT. Wurman doesn't comment on this -- instead, he criticizes colleges replacing their placement test with SBAC. I assume he accepts SAT scores more than SBAC scores. And if SBAC were the junior state test, then maybe PSAT 8/9 fits as the state test for those respective years.)
Today is the last day before the week-long Thanksgiving break. (It's also approximately the end of the third quaver.) It's also an activity day -- after all, it would be awkward for yesterday's lesson to be basically an activity (and even Wednesday's lesson contained a semi-activity) and then not give an activity today. And so I'm only repeating one of the worksheets from last year and then adding an activity page.
Last year at my old school, I gave the students an activity on graphing turkeys. The idea is that I want to give an activity that is somewhat fun on the last day before the holiday -- and perhaps when they are done graphing, they can color the turkeys. The problem is that the turkeys take much too long to graph, and the activity ends up not being much fun at all.
This is what I wrote about the turkey activity -- again, it was two years ago:
10:15 -- My eighth graders leave and my sixth graders arrive. Just like the seventh graders, this class works on the turkey graphing activity. During this time, I hand out four licorice sticks to all students who earned an A on yesterday's quiz.
11:05 -- My sixth graders leave for nutrition, except for one girl who has incurred a short detention for going to the restroom yesterday when our school has a no-pass policy.
11:25 -- My sixth grade class returns from nutrition. Ordinarily we don't have the same class before and after the break, but our schedule is awkward this week due to Parent Conferences. The three middle school teachers decided that we would see all three grades before the break, and then rotate so that we see one grade each day after the break. Today happens to be sixth grade for me.
Ordinarily when I see sixth grade for the second time in a day, it's considered Math Intervention and the students use our other software program, IXL. (Again I don't give the link here.) I wrote about Math Intervention in my "Day in the Life" post for October.
The sixth graders are often very loud during IXL time, and today is no exception. As I implied back in October, some students still have trouble with their passwords. Since then, I came up with the idea of handing out computers to only some of the students and putting the rest on a waiting list. All students who fail to login to IXL within five minutes must forfeit their computers and give them to someone on the waiting list.
I intend for the students who lose their computers to go back to the turkey activity. Instead, these students interpret this time to be free time -- they talk very loud and run around the classroom, and even some of the students who have laptops join them. In short, IXL time for sixth graders has become a big mess! Today, it might have been better just to have all of the students continue to graph the turkey, since none of them have actually finished it. I should have either foregone IXL entirely or reserved it for those few students who actually complete the turkey.
And so now, I want to post an activity that the students will enjoy more. We see how the sixth graders started playing around because they got tired of graphing.
The middle school students at my old school did a different activity last year. They were to draw pictures (not necessarily turkeys) on graph paper by coloring in the boxes (rather than graphing coordinates).
This activity reminds me of Lesson 1-1 of the U of Chicago text. The first description of a point is "A point is a dot," and the squares on the graph paper represent dots that form the image. And the very first word defined in our Geometry text is pixels -- and we notice that this is exactly what the students created, pixelated art.
I've spent so much of this post writing about science, but art is the other part of the curriculum that I failed to teach last year. Art is the "A" of STEAM, and the Illinois State text encourages that art be taught in conjunction with math and science.
Anyway, I notice that the middle school students worked on this project the entire week before Thanksgiving break -- not just one day. This allows the students to take pride in their work -- and if they don't finish the first day, they can continue the next day.
Indeed, perhaps I could have kept the turkey coordinate graphing project intact last year by simply spreading it out over the entire week. Monday of course was for coding, but then I could have let them graph on Tuesday, Wednesday, and Thursday. Then perhaps the sixth grade scene I posted earlier doesn't occur -- students would be eager to finish the graph, since there would be plenty of time left to color the turkeys.
I also mentioned that there was some leeway to take a week off from Common Core Math, especially during short three-days weeks (due to PD days). The week before Thanksgiving was a four-day week since there was only one PD day, but the weeks leading up to winter break, Presidents Day, and Chavez Day were all three-day weeks, hence suitable for similar arts projects.
This is one arts project that doesn't require the die cut machine, which I didn't know how to use. In the end, whether I would have given last year's turkey graph or this year's pixel graph depends on Illinois State. It's possible that my successor teacher found this assignment in the Illinois State text (even though it was difficult to find arts projects above Grade 5) -- and of course, priority always goes to Illinois State projects. (Ironically, the only middle school arts projects that I could easily find in the Illinois State text were in conjunction with science, not math.)
But for this year, I will post the pixel version of this assignment -- the one that the middle school students enjoyed this week. (Yes, I know I'm posting it as a one-day activity since I usually don't post multi-day projects on the blog.)
You may ask, what does this have to do with today's Lesson 6-5? Well, suppose the students choose to draw a human face, or even a turkey viewed head-on. Humans, turkeys, and other animals exhibit bilateral symmetry. So the two eyes will be congruent.
And so let me announce my holiday posting schedule. As usual, there will be two holiday posts during Thanksgiving break. The first post is planned for Tuesday, with the second post the following Saturday.
Enjoy your Thanksgiving break. The district whose calendar I'm observing will resume school on Monday, November 26th.
Last year at my old school, I gave the students an activity on graphing turkeys. The idea is that I want to give an activity that is somewhat fun on the last day before the holiday -- and perhaps when they are done graphing, they can color the turkeys. The problem is that the turkeys take much too long to graph, and the activity ends up not being much fun at all.
This is what I wrote about the turkey activity -- again, it was two years ago:
10:15 -- My eighth graders leave and my sixth graders arrive. Just like the seventh graders, this class works on the turkey graphing activity. During this time, I hand out four licorice sticks to all students who earned an A on yesterday's quiz.
11:05 -- My sixth graders leave for nutrition, except for one girl who has incurred a short detention for going to the restroom yesterday when our school has a no-pass policy.
11:25 -- My sixth grade class returns from nutrition. Ordinarily we don't have the same class before and after the break, but our schedule is awkward this week due to Parent Conferences. The three middle school teachers decided that we would see all three grades before the break, and then rotate so that we see one grade each day after the break. Today happens to be sixth grade for me.
Ordinarily when I see sixth grade for the second time in a day, it's considered Math Intervention and the students use our other software program, IXL. (Again I don't give the link here.) I wrote about Math Intervention in my "Day in the Life" post for October.
The sixth graders are often very loud during IXL time, and today is no exception. As I implied back in October, some students still have trouble with their passwords. Since then, I came up with the idea of handing out computers to only some of the students and putting the rest on a waiting list. All students who fail to login to IXL within five minutes must forfeit their computers and give them to someone on the waiting list.
I intend for the students who lose their computers to go back to the turkey activity. Instead, these students interpret this time to be free time -- they talk very loud and run around the classroom, and even some of the students who have laptops join them. In short, IXL time for sixth graders has become a big mess! Today, it might have been better just to have all of the students continue to graph the turkey, since none of them have actually finished it. I should have either foregone IXL entirely or reserved it for those few students who actually complete the turkey.
And so now, I want to post an activity that the students will enjoy more. We see how the sixth graders started playing around because they got tired of graphing.
The middle school students at my old school did a different activity last year. They were to draw pictures (not necessarily turkeys) on graph paper by coloring in the boxes (rather than graphing coordinates).
This activity reminds me of Lesson 1-1 of the U of Chicago text. The first description of a point is "A point is a dot," and the squares on the graph paper represent dots that form the image. And the very first word defined in our Geometry text is pixels -- and we notice that this is exactly what the students created, pixelated art.
I've spent so much of this post writing about science, but art is the other part of the curriculum that I failed to teach last year. Art is the "A" of STEAM, and the Illinois State text encourages that art be taught in conjunction with math and science.
Anyway, I notice that the middle school students worked on this project the entire week before Thanksgiving break -- not just one day. This allows the students to take pride in their work -- and if they don't finish the first day, they can continue the next day.
Indeed, perhaps I could have kept the turkey coordinate graphing project intact last year by simply spreading it out over the entire week. Monday of course was for coding, but then I could have let them graph on Tuesday, Wednesday, and Thursday. Then perhaps the sixth grade scene I posted earlier doesn't occur -- students would be eager to finish the graph, since there would be plenty of time left to color the turkeys.
I also mentioned that there was some leeway to take a week off from Common Core Math, especially during short three-days weeks (due to PD days). The week before Thanksgiving was a four-day week since there was only one PD day, but the weeks leading up to winter break, Presidents Day, and Chavez Day were all three-day weeks, hence suitable for similar arts projects.
This is one arts project that doesn't require the die cut machine, which I didn't know how to use. In the end, whether I would have given last year's turkey graph or this year's pixel graph depends on Illinois State. It's possible that my successor teacher found this assignment in the Illinois State text (even though it was difficult to find arts projects above Grade 5) -- and of course, priority always goes to Illinois State projects. (Ironically, the only middle school arts projects that I could easily find in the Illinois State text were in conjunction with science, not math.)
But for this year, I will post the pixel version of this assignment -- the one that the middle school students enjoyed this week. (Yes, I know I'm posting it as a one-day activity since I usually don't post multi-day projects on the blog.)
You may ask, what does this have to do with today's Lesson 6-5? Well, suppose the students choose to draw a human face, or even a turkey viewed head-on. Humans, turkeys, and other animals exhibit bilateral symmetry. So the two eyes will be congruent.
And so let me announce my holiday posting schedule. As usual, there will be two holiday posts during Thanksgiving break. The first post is planned for Tuesday, with the second post the following Saturday.
Enjoy your Thanksgiving break. The district whose calendar I'm observing will resume school on Monday, November 26th.
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