**Table of Contents:**

**1. The Length of Thanksgiving Break**

**2. The Need for Thanksgiving Break**

**3. Intro to Green Team**

**4. More Thoughts on Pacing**

**5. Only Fifteen Standards -- You Wish!**

**6. Upcoming Plans for Sixth Grade**

**7. Upcoming Plans for Seventh Grade**

**8. Upcoming Plans for Eighth Grade**

**9. Today's "Day in the Life" Poster**

**10. Presidential Consistency**

**The Length of Thanksgiving Break**

This is what I wrote last year on my blog about the length of Thanksgiving break:

*Of course, since I was born, air travel has become more common, and families often live in different states on opposite coasts. Some news reports began to identify Wednesday, the day before Thanksgiving, as the biggest travel day of the year. Families that travel on Wednesday obviously can't send their children to school that day. So in the 1990's, some districts began to observe a five-day weekend from Wednesday to Sunday, including the largest district in the area, LAUSD, for a few years around this time. (Such schools still exist. This year, the eighth-grade daughter of our English teacher attends a school that has a five-day weekend for Thanksgiving.)*

*The schools I attended as a student always held school the day before Thanksgiving, but for a few years, when I was in the sixth through ninth grades, a staff development day was held on the Monday after Thanksgiving (the day now called Cyber Monday, but this was back when the Internet was still in its infancy).*

*In a way, the entire week off is the next logical step after a five-day weekend. Wednesday may be the biggest travel day of the year -- and so in order to get the jump on the crowds, flyers may leave on Tuesday instead. And once we take Tuesday off from school, we might as well take Monday off as well, since no one wants a lone day, a one-day week. And so the entire week is taken off.*

And as I wrote before, my current charter school had another day off for staff development on top of that, so students are home for a week and a day, starting the Friday before Thanksgiving!

**The Need for Thanksgiving Break**

As a teacher, I can say that we certainly need Thanksgiving break! The last week before the break was tough because it also marked the start of a new trimester, with grades to be completed and parent conferences to be held.

So what exactly did I do today, my first true weekday of Thanksgiving break? Well, I worked of course -- I met with the leader of the Green Team program that I want to implement for science. Not only that, but our English teacher will be going to our school on Wednesday. You see, she hasn't had time to work on the bulletin boards lately, so she decided to ask her daughter to come and help her -- since the girl's school, as I wrote earlier, has a five-day weekend starting Wednesday. The fifth grade teacher has also agreed to come in to decorate her own classroom.

This reminds me of something that Tina Cardone, leader of "Day in the Life," writes:

*A day you work during the summer (what do you mean teachers don’t take the entire summer off?)*

Clearly we teachers don't even take the entire Thanksgiving break off, much less summer. Now Cardone writes this in response to anti-teacher critics who say that not only don't teachers work during our holiday breaks, but we aren't satisfied with them and need to take more days off!

One such critic goes by the username "Floyd Thursby." He often writes that teachers like to take an extra day off before Thanksgiving:

https://edsource.org/2014/deal-announced-on-teacher-dismissal-bill-that-governor-would-support/63504

[

*If due process worked -- dw]**We wouldn’t have 12% call in sick the Tuesday before Thanksgiving with no fear of being fired.*
Here Thursby is referring to a district that observes a five-day weekend from Wednesday to Sunday, so "the Tuesday before Thanksgiving" refers to the last day of school before the holiday.

**Intro to Green Team**

So what exactly is this Green Team, anyway? Here is a quote from the brochure:

*"Let's Move Nation & Beyond's" Green Team Program is designed to engage students and their families; school faculty, administration and leadership; and the broader community on the importance of energy conservation topics. It will focus on campus-wide awareness, direct education to children, and Green Team leader development."*

As I wrote earlier, I met with the leader of the Green Team this afternoon. She tells me a little more about how this program will work:

-- There will be a monthly newsletter for all students K-8 informing them about ways they can help their families save energy and water. We're hoping that the first newsletter will be December 1st.

-- The next step is to introduce this unit in science with a Pre-Assessment. This Pre-Assessment should be given just before winter break.

-- In January, the science unit will begin in earnest. Students can bring in copies of their energy and water bills. By the end of the unit, we're hoping that students have implemented enough saving tips to see a noticeable reduction in their bills. The grade with the largest reduction can win prizes, which could be anything from a classroom pizza party to even some sort of field trip.

-- There will also be a science project or fair associated with this unit. If everything goes right, the projects will be completed by Earth Day, which is Saturday, April 22nd.

In order for this to work out, as the Green Team leader explains, there should be at least ten schools participating in the program. So far, five schools have signed on, counting my own. All of these schools are either charters, like my own, or small private schools. Unfortunately, our sister charter can't be included, because it's not actually within the Los Angeles city limits and thus isn't served by the LA Department of Water and Power (one of the sponsors of the program).

Originally, the Green Team program was intended for Grades 5-7. But it's awkward to include sixth and seventh grade at a middle school but not eighth, so now it's extended to eighth grade as well.

On the other hand, fifth grade usually isn't included at most middle schools. But we're a K-8 school, and so we can include fifth grade all we want. I've spoken with our fifth grade teacher on our PD day, and she's enthusiastic about the program as well. After all, even the fifth grade class has only the Illinois State text and thus the science is limited to only the STEM projects. Both of us know that both fifth and eighth grades have NGSS tests in May, so let's include both grades as this could be the only science they'll see. I might even drop by our school on Wednesday and let the fifth grade teacher know what I learned today -- since, if you recall, she'll be at the school that day to decorate!

As I said earlier, I definitely look forward to working with the Green Team in my room. I hope that it will help my students out with science -- and even save them a little money.

**More Thoughts on Pacing**

A week and a half ago, I wrote about my worries regarding the pacing. The Benchmark Tests threw me for a loop -- there were so many standards appearing on the tests that we hadn't covered yet. So I wrote how I'll make sure that every standard is covered before the next Benchmark Tests.

But here's the problem -- there are so many standards that don't appear on

*any*of the Benchmarks throughout the year, yet will appear on the actual SBAC! For example, let's take a look at the standards that appear on Benchmarks:
1st Trimester Benchmark: RP3a, NS2, EE2c, G4, SP3

2nd Trimester Benchmark: RP2, NS1, EE2b, G2, SP1

3rd Trimester Benchmark: RP3b, NS4, EE4, G2, SP5a

Notice how some standards appear to be missing -- for example, under the NS (Number Sense) thread, we see NS1, 2, and 4 included, but not NS3. Oh well, maybe NS3 isn't that important then -- or is it? Let's see what this missing standard actually is:

CCSS.MATH.CONTENT.6.NS.B.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

And now I'm thinking, what the...! This is

*clearly*a*very*important standard -- indeed, it might be the most important standard in all of sixth grade! I think all the way back to my old math texts back in elementary school. The first grade text had a picture of addition on the front cover -- and to me, this meant that first grade is the "year of addition." The second grade text had a subtraction picture on the cover, as second grade is the "year of subtraction." The third grade text had a multiplication picture on the cover, and so on. And the sixth grade text had a picture of*decimals*. So to me, this meant that sixth grade is the "year of decimals." So the idea that decimals would be omitted is strange indeed.
Furthermore, I think back to Parent Conferences, and I was telling one parent about how well his daughter was doing with long division. His reply was that this is good, because his daughter will be well-prepared to compute with -- you guessed it, decimals. So the idea of having a sixth grade math class without decimals is

*unthinkable*.**Only Fifteen Standards -- You Wish!**

Some people may argue that there are just too many standards in the Common Core. I remember in years back when I was trying to come up with alternatives to the Core here on the blog -- as I often did during holiday periods such as Thanksgiving break. I like the idea of there being only 15 standards, with five on each Benchmark. This gives us about two weeks on each standard -- enough time to do a STEM project followed by the lesson (but at the time I came up with this, I wasn't thinking about STEM projects or anything like that).

I actually tried to come up with such a simple plan for a sixth grade class -- until I realized that I'd left out some of the key standards, such as decimals! I was so embarrassed that I didn't even bother to post my sixth grade plan -- until unwittingly, I posted a sixth grade pacing plan two weeks ago based on the Benchmark Tests. Since decimals didn't appear on the Benchmarks, they didn't appear on my proposed pacing plan.

Again, it's so annoying that the so-called "pacing plan" (provided by Illinois State) doesn't correspond exactly to the Benchmarks (provided by Illinois State), and respects the order of neither the STEM text (provided by Illinois State) nor the traditional Student Journals (provided by Illinois State).

At this point, those familiar with my blog may say -- hey, I'm one to talk! My first year on the blog, I presented a Geometry text by doing Chapter 1, 2, 3, 4, back to 3 again, one lesson from 6, then to 5, 6, 7, and then skip all the way to 12. And the following year, I doubled down on chapter jumping by covering Chapter 7 before 5, and so on.

Of course, there's a difference here. Even though that text was the closest I've seen a pre-Core text get to Common Core Geometry, there were some differences, and so I jumped chapters in order to cover all of the tested material. On the other hand, the "pacing plan," Benchmarks, and texts all come from the same source, namely Illinois State. One would think that at the very least, the pacing plan and Benchmarks should correspond.

I'm thinking about a seventh-grader at my school. She'd struggled throughout elementary school math, yet managed to score "proficient" on last year's SBAC. She continues to succeed this year, as she earned the top score on the 7th grade Benchmark. But now I'm worried that her scores will go down, because there'll be so much material on the SBAC that I won't have covered. That will surely happen if I base my pacing plan solely on the Benchmarks!

The 6th and 7th grade STEM texts each contain 27 projects. There's no way that I'll be able to cover all 27 projects throughout the year. But at least the Illinois State pacing plan matches each project with standards. By covering all of the projects, I'd cover all of the standards. But since I can't cover all of the projects, I'll be omitting standards that might occur on the SBAC.

Oh, and by the way, the idea that I should give a project once every two weeks also comes from Illinois State -- this is how often we must submit project forms to the developers. This means that I can comfortably fit 15 projects in the year -- five each trimester, plus a little cushion time for the Benchmark Tests themselves.

Illinois State brags that its curriculum prepares students for the SBAC. If I could improve the Illinois State text, here's how I'd do it:

-- There should be only 15 STEM projects. All standards that are likely to be tested on the SBAC should match up with one of these projects.

-- The first Benchmark should match up with Projects 1-5. The second Benchmark should match up with Projects 6-10. The third Benchmark should match up with Projects 11-15.

-- Some of the projects currently in the Illinois State sixth and seventh grade texts are listed with above grade-level standards. If such projects are to remain, they should be numbered Project 16 (or 17) and given after the SBAC, so as not to distract from on grade-level SBAC questions.

-- With so many standards to cover and fewer projects, we can't waste the first four projects on "Tools for Learning" that correspond only to Mathematical Practices rather than actual math standards.

Actually, as a teacher of all three grade levels, I like how the first few projects are for all three grade levels, so I don't have to prepare for three different projects at once. But it took nearly the entire first trimester just to get through "Tools for Learning" (that is, Unit 0). Perhaps there should be only one or two projects in Unit 0 -- or if we're to keep Unit 0 intact, they should at least correspond to the standards that appear on the first Benchmark. We can then keep the first Benchmark as it is, provided the second and third Benchmarks span the rest of the SBAC.

All of this is what I'd do if I could fix the Illinois State text -- but of course, I can't do that. But since I definitely don't want to skip decimals in sixth grade, I must already change the pacing plan that I gave in my November 10th post. I will continue to follow the projects in order, with a goal of reaching Project 15 around the time of the third Benchmark and the SBAC. Then I'll just teach the standards that correspond to each project, as these more nearly span the SBAC. This means that once again there will be missing standards at the second Benchmark, but to me it's more important that students feel ready for the SBAC, not the Benchmarks.

Let's look at each grade level in turn to see what the pacing plan will look like for the next few Learning Modules (that is, the next few projects):

6th grade

-- Module 6: RP1, RP2

-- Module 7: NS4

-- Module 8: RP3d

For Module 6, Standards RP1 and RP2 have already been covered. The big point of departure is Module 7, where we will jump to NS4, which is on greatest common factor. In Module 8, RP3d is on measurement -- recall that this is the standard my counterpart was teaching at our sister charter.

Module 8 is the last module in Unit 1: Mathematics in Motion. Recall that the goal is to reach Module 15 for the SBAC (with Module 16 squeezed in during or after SBAC). This marks the end of Unit 3, meaning that I won't be able to cover Units 4, 5, or 6. Yet there is a compelling reason to cover at least Unit 6 this year. Let's look at Unit 6 to find out why:

24. Go With the Flow

25. What Did You Do With All That Water?

26. The Air That I Breathe

27. What Can We Expect?

And the first part of Project 25 is:

Exploring I: What is the importance of conserving water?

In other words -- Project 25 is

This does mean that I might end up pairing Module 6 with Standard SP3. There are several reasons to do so -- SP3 was covered on the first Benchmark but not in any STEM project, while some of the other stats standards are covered in Unit 6.

Most likely I'll do Module 7 before winter break, then jump directly to Modules 24 and 25 on water right after winter break, when the Green Team begins in earnest. Sure, they'll miss Module 8 on measurement, but there's measurement in Module 24 as well.

The only problem with tying STEM projects to Green Team is that these projects only appear in the sixth grade text. Unfortunately, 7th and 8th (and 5th) graders won't have access to these projects.

7th grade

-- Module 6: none (MP only)

-- Module 7: G2, G5

-- Module 8: G3

-- Module 9: EE6, G4

-- Module 10: G6, G7

For some reason, Module 6 in the seventh grade text is just like Modules 1-4, with "Mathematical Practices" as the only standards listed. But Module 5 lists G1, on map scales, as a standard. Both Modules 5 and 6 involve maps, so G1 is a good standard to cover here. As we can see, this leads into more geometry standards for the remainder of Unit 1.

8th grade

-- Module 6: NS1, NS2, EE2, G9

-- Module 7: G1a thru G2

-- Module 8: G3 thru G5

-- Module 9: G6 thru G8

For Module 6, the only standard we haven't covered yet is G9, on volume -- and notice that this is followed by more geometry standards. These include G1 and G2 -- which mark the gateway to the transformation geometry with which we associate Common Core.

As you know from my first two years on the blog, geometry is my favorite topic, and I spent so much time writing about transformations and geometry. So of course I have lots to say about how I plan on teaching the eighth grade geometry units.

As it turns out, only G2 and G4 appear on the Benchmarks. Again, blindly following the Benchmarks leaves out many important topics, such as G5 (parallel lines and angles) and G6 thru G8 (on the Pythagorean Theorem), that definitely appear on the SBAC.

I've said before that in many ways, Common Core 8 is like Integrated Math I. Ironically, even though this is a geometry blog, that statement is more applicable to algebra than to geometry. The algebra content of Integrated Math I should match both the algebra content of Common Core 8 and the first half of Algebra I. Therefore, if we take the first half of the a pre-Core Algebra I text, this provides us with enough algebra to cover both Common Core 8 and Integrated Math I.

But the analogous statement for geometry is impossible. We

Let's look at one Common Core 8 standard in particular:

CCSS.MATH.CONTENT.8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

This standard clearly mentions

So instead, let's come up with an informal argument for the Parallel Consequences. Recall that the Corresponding Angles Consequence ultimately goes back to translations. So if two parallel lines are cut by a transversal and angles 1 and 2 are corresponding angles. then they are congruent. In this case, I'll tell the eighth graders to imagine the translation mapping angle 1 to 2 -- this translation is clearly in the direction of the transversal itself. Likewise, for alternate interior angles, the students can imagine rotating one of the angles 180 degrees to coincide with the other.

One advantage of this trick is that I don't even need to use the terms "corresponding angles" or "alternate interior angles" at all. Instead of focusing on these terms, students think only about the transformations mapping one to the other. And by doing so, they learn to appreciate the relationship between transformations and congruence.

https://hermathness.wordpress.com/

Here is a link to Menard's November 21st post:

https://hermathness.wordpress.com/2016/11/21/%EF%BB%BFms-menard-and-the-very-blustery-day-ditl-november-21-2016/

Menard begins:

So obviously Menard's school doesn't take the entire week off, or even a five-day weekend.

Most of Menard's school day revolves around her Algebra II classes. Tomorrow she'll give her students a test, so today she has her students work on a "practice exam" in groups. The thing is, her "practice exam" is the actual test! She writes:

Backing up a little, I notice that Menard's Parent Conferences day is also November 17th! (Her post is dated the 18th because she wanted to include a second day of conferences.) As I wrote earlier, most schools in New York City have a Labor Day start, so the conferences mark the end of the first quarter, not the first trimester.

Menard writes:

Unfortunately, Menard's analogy falls flat here. The longest day of the year is the

As it turns out, my own Summer Education Solstice was the 16th, as that was my long day where I had to arrive early and stay late (though not as late as Menard). For both of us, our respective "solstices" were quite busy, but the day after the solstice for both of us was quite light, since most of the parents had talked to us the previous day.

You might recall when I wrote about the "Classical Curriculum." In this curriculum, Grades 5-8 are basically a repeat of Grades 1-4 for history and science. I wrote about the idea of extending this concept to math. I've already written about how first grade is the "year of addition" of whole numbers, second grade the "year of subtraction," third grade the "year of multiplication," and fourth grade the "year of division."

So under the "Classical Curriculum," we can make fifth grade another "year of addition," but for rational numbers (including fractions and integers). Sixth grade becomes a "year of subtraction," seventh grade a "year of multiplication," and eighth grade a "year of division." This is very different from the Common Core or most pre-Core standards. Fifth grade is a bit early for addition of integers, while eighth grade is a bit late for division of fractions and decimals.

But now I've seen actual middle school students, and now I'm starting to like the idea of this math "Classical Curriculum" a bit more. I've noticed that more often than not, it's the

So delaying division of rationals into eighth grade forces these students to continue thinking about the algorithms of arithmetic as opposed to reaching for a calculator. This bridges the gap between Grades 4-6, when they first learn and practice long division, and Algebra II/Pre-Calc, when they learn about long division of polynomials.

But there's one more proposal that I want to discuss in this post -- Presidential Consistency. This is the idea that presidents hypocritically propose various education reforms for the public schools, then shield their own children from it by sending them to private schools that don't implement these education reforms. Presidential Consistency Core is automatically

We have a newly elected president, Donald Trump. I feel that I can safely mention politics at the bottom of a long holiday post -- and besides, notice that Wendy Menard openly discusses politics right at the top of her November 21st post, and even more so in her November 9th post (that is, the day after the election). But this post isn't about the president-elect but about his young son Barron, especially since his education plans have been announced over the weekend.

http://blogs.edweek.org/edweek/campaign-k-12/2016/11/education_of_barron_trump_and_other_first_kids.html

Barron is ten years old, with his 11th birthday in March. So I assume that he's a fifth grader. The announcement is that Barron will at least remain at his New York City private school until the end of the current school year, so that he won't have to switch schools mid-year. I assume that even though he attends a private school, his calendar follows other Big Apple schools, with no school until after Labor Day and the last day of school just barely before June 30th.

It's possible that for sixth grade, Barron will attend a DC school -- maybe even Sidwell Friends, the same school as Sasha and Malia Obama. Under my Presidential Consistency plan, the curriculum would follow the outgoing president's children's school under the end of the year, so that just like Barron, no one would have to switch curricula mid-year either. If Barron were to attend Sidwell then Presidential Consistency Core wouldn't change -- it would be defined as Sidwell's standards.

For the remainder of this post, let's assume that Barron continues to attend his current school for sixth grade and beyond -- this is Columbia Grammar and Preparatory School:

https://www.cgps.org/

Let's focus on the middle school math standards -- one because I'm a middle school math teacher, and two because this is what Barron is learning now:

https://www.cgps.org/middle-school-grades-5-7/mathematics

Notice that at Columbia, "middle school" is defined as Grades 5-7 (similar to how the Green Team defines "middle school"), so Barron is already a middle school student. As I compare Columbia's math curriculum to Common Core, most of Columbia's standards are either the same as Common Core's or are possibly one year earlier (for example, I notice that "systems of linear equations" is listed as a seventh grade topic at Columbia). Therefore Consistency Core could move some of Common Core's standards down one grade.

I thought this part is fascinating:

[6th graders] also use tables, graphs, written language, and symbolic rules to examine patterns. To bring these concepts to life, students invest imaginary funds in the stock market and use formulas to figure out their gains and losses over time, as well as research a future career and determine a budget to support themselves in NYC.

Interestingly enough, my old sixth grade math teacher had us play a stock market game as well.

One might expect that with a tougher seventh grade curriculum, all eighth graders might be pushed into Algebra I. The following link shows that this is not the case:

https://www.cgps.org/prepschool/mathematics

We see "an introductory Pre-Algebra course" mentioned as one of the classes, so this class is available for eighth graders. Meanwhile, of the Geometry course, it's stated that students follow a "traditional study of Euclidean plane geometry." I interpret this as indicating that transformations will not appear in this course, so opponents of transformation geometry would appreciate that.

I'm also a middle school

https://www.cgps.org/middle-school-grades-5-7/science

I notice that STEM is mentioned, so I assume that the Barron is doing STEM projects similar to what I'm doing in my own classes. The sixth and seventh grade courses appear to be one year ahead of the old pre-NGSS standards here in California -- the fifth grade course doesn't correspond to any class that I can easily recognize.

This concludes the post -- my last post of the Thanksgiving break. My next post won't be until Tuesday, November 29th -- the second day back from break, since the November 17th post was actually a two-day post covering both Days 63 and 64. Enjoy your Floyd Thursby day (that is, the Tuesday before Thanksgiving) and the rest of your holiday!

Of course, there's a difference here. Even though that text was the closest I've seen a pre-Core text get to Common Core Geometry, there were some differences, and so I jumped chapters in order to cover all of the tested material. On the other hand, the "pacing plan," Benchmarks, and texts all come from the same source, namely Illinois State. One would think that at the very least, the pacing plan and Benchmarks should correspond.

I'm thinking about a seventh-grader at my school. She'd struggled throughout elementary school math, yet managed to score "proficient" on last year's SBAC. She continues to succeed this year, as she earned the top score on the 7th grade Benchmark. But now I'm worried that her scores will go down, because there'll be so much material on the SBAC that I won't have covered. That will surely happen if I base my pacing plan solely on the Benchmarks!

The 6th and 7th grade STEM texts each contain 27 projects. There's no way that I'll be able to cover all 27 projects throughout the year. But at least the Illinois State pacing plan matches each project with standards. By covering all of the projects, I'd cover all of the standards. But since I can't cover all of the projects, I'll be omitting standards that might occur on the SBAC.

Oh, and by the way, the idea that I should give a project once every two weeks also comes from Illinois State -- this is how often we must submit project forms to the developers. This means that I can comfortably fit 15 projects in the year -- five each trimester, plus a little cushion time for the Benchmark Tests themselves.

Illinois State brags that its curriculum prepares students for the SBAC. If I could improve the Illinois State text, here's how I'd do it:

-- There should be only 15 STEM projects. All standards that are likely to be tested on the SBAC should match up with one of these projects.

-- The first Benchmark should match up with Projects 1-5. The second Benchmark should match up with Projects 6-10. The third Benchmark should match up with Projects 11-15.

-- Some of the projects currently in the Illinois State sixth and seventh grade texts are listed with above grade-level standards. If such projects are to remain, they should be numbered Project 16 (or 17) and given after the SBAC, so as not to distract from on grade-level SBAC questions.

-- With so many standards to cover and fewer projects, we can't waste the first four projects on "Tools for Learning" that correspond only to Mathematical Practices rather than actual math standards.

Actually, as a teacher of all three grade levels, I like how the first few projects are for all three grade levels, so I don't have to prepare for three different projects at once. But it took nearly the entire first trimester just to get through "Tools for Learning" (that is, Unit 0). Perhaps there should be only one or two projects in Unit 0 -- or if we're to keep Unit 0 intact, they should at least correspond to the standards that appear on the first Benchmark. We can then keep the first Benchmark as it is, provided the second and third Benchmarks span the rest of the SBAC.

All of this is what I'd do if I could fix the Illinois State text -- but of course, I can't do that. But since I definitely don't want to skip decimals in sixth grade, I must already change the pacing plan that I gave in my November 10th post. I will continue to follow the projects in order, with a goal of reaching Project 15 around the time of the third Benchmark and the SBAC. Then I'll just teach the standards that correspond to each project, as these more nearly span the SBAC. This means that once again there will be missing standards at the second Benchmark, but to me it's more important that students feel ready for the SBAC, not the Benchmarks.

Let's look at each grade level in turn to see what the pacing plan will look like for the next few Learning Modules (that is, the next few projects):

**Upcoming Plans for Sixth Grade**6th grade

-- Module 6: RP1, RP2

-- Module 7: NS4

-- Module 8: RP3d

For Module 6, Standards RP1 and RP2 have already been covered. The big point of departure is Module 7, where we will jump to NS4, which is on greatest common factor. In Module 8, RP3d is on measurement -- recall that this is the standard my counterpart was teaching at our sister charter.

Module 8 is the last module in Unit 1: Mathematics in Motion. Recall that the goal is to reach Module 15 for the SBAC (with Module 16 squeezed in during or after SBAC). This marks the end of Unit 3, meaning that I won't be able to cover Units 4, 5, or 6. Yet there is a compelling reason to cover at least Unit 6 this year. Let's look at Unit 6 to find out why:

24. Go With the Flow

25. What Did You Do With All That Water?

26. The Air That I Breathe

27. What Can We Expect?

And the first part of Project 25 is:

Exploring I: What is the importance of conserving water?

In other words -- Project 25 is

*directly related*to the goals of the Green Team! Our partnership with the Green Team is a strong incentive to cover this project during the year. After all this discussion about how I want to give the projects in order, suddenly now I want to jump to Unit 6. Keep in mind that I haven't really done a good job with the sixth grade projects -- I spent only one day on each of the first two projects of Unit 1, and this wasn't nearly enough for them to learn anything. Tying STEM projects to Green Team means that I'll definitely have time to cover the projects, as there will already be time reserved to Green Team.This does mean that I might end up pairing Module 6 with Standard SP3. There are several reasons to do so -- SP3 was covered on the first Benchmark but not in any STEM project, while some of the other stats standards are covered in Unit 6.

Most likely I'll do Module 7 before winter break, then jump directly to Modules 24 and 25 on water right after winter break, when the Green Team begins in earnest. Sure, they'll miss Module 8 on measurement, but there's measurement in Module 24 as well.

The only problem with tying STEM projects to Green Team is that these projects only appear in the sixth grade text. Unfortunately, 7th and 8th (and 5th) graders won't have access to these projects.

**Upcoming Plans for Seventh Grade**7th grade

-- Module 6: none (MP only)

-- Module 7: G2, G5

-- Module 8: G3

-- Module 9: EE6, G4

-- Module 10: G6, G7

For some reason, Module 6 in the seventh grade text is just like Modules 1-4, with "Mathematical Practices" as the only standards listed. But Module 5 lists G1, on map scales, as a standard. Both Modules 5 and 6 involve maps, so G1 is a good standard to cover here. As we can see, this leads into more geometry standards for the remainder of Unit 1.

**Upcoming Plans for Eighth Grade**8th grade

-- Module 6: NS1, NS2, EE2, G9

-- Module 7: G1a thru G2

-- Module 8: G3 thru G5

-- Module 9: G6 thru G8

For Module 6, the only standard we haven't covered yet is G9, on volume -- and notice that this is followed by more geometry standards. These include G1 and G2 -- which mark the gateway to the transformation geometry with which we associate Common Core.

As you know from my first two years on the blog, geometry is my favorite topic, and I spent so much time writing about transformations and geometry. So of course I have lots to say about how I plan on teaching the eighth grade geometry units.

As it turns out, only G2 and G4 appear on the Benchmarks. Again, blindly following the Benchmarks leaves out many important topics, such as G5 (parallel lines and angles) and G6 thru G8 (on the Pythagorean Theorem), that definitely appear on the SBAC.

I've said before that in many ways, Common Core 8 is like Integrated Math I. Ironically, even though this is a geometry blog, that statement is more applicable to algebra than to geometry. The algebra content of Integrated Math I should match both the algebra content of Common Core 8 and the first half of Algebra I. Therefore, if we take the first half of the a pre-Core Algebra I text, this provides us with enough algebra to cover both Common Core 8 and Integrated Math I.

But the analogous statement for geometry is impossible. We

*cannot*say that the geometry content of Integrated Math I matches both the geometry content of Common Core 8 and the first half of high school Geometry. This is because there are some topics in the first half of Geometry that are inappropriate for Common Core 8 (such as two-column proofs), while there are some topics in Common Core 8 that don't appear until the second half of Geometry (such as similarity).Let's look at one Common Core 8 standard in particular:

CCSS.MATH.CONTENT.8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

*For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so*.This standard clearly mentions

*informal arguments*. So we obviously don't want to see any sort of two-column proofs. Also, we agonized for years on the blog over the proofs of the Parallel Consequences -- some of those proofs are barely appropriate for high school Geometry, thus certainly not appropriate for Common Core 8.So instead, let's come up with an informal argument for the Parallel Consequences. Recall that the Corresponding Angles Consequence ultimately goes back to translations. So if two parallel lines are cut by a transversal and angles 1 and 2 are corresponding angles. then they are congruent. In this case, I'll tell the eighth graders to imagine the translation mapping angle 1 to 2 -- this translation is clearly in the direction of the transversal itself. Likewise, for alternate interior angles, the students can imagine rotating one of the angles 180 degrees to coincide with the other.

One advantage of this trick is that I don't even need to use the terms "corresponding angles" or "alternate interior angles" at all. Instead of focusing on these terms, students think only about the transformations mapping one to the other. And by doing so, they learn to appreciate the relationship between transformations and congruence.

**Today's Day in the Life Poster****The "Day in the Life" poster whose monthly posting date is the 21st is Wendy Menard, a New York high school teacher:**

https://hermathness.wordpress.com/

Here is a link to Menard's November 21st post:

https://hermathness.wordpress.com/2016/11/21/%EF%BB%BFms-menard-and-the-very-blustery-day-ditl-november-21-2016/

Menard begins:

*This post comes to you at 6:22 AM on the first very cold and blustery day of the season. It’s the start of the short pre- Thanksgiving week, and I am looking forward to the 4 day weekend probably as much as my students.*So obviously Menard's school doesn't take the entire week off, or even a five-day weekend.

Most of Menard's school day revolves around her Algebra II classes. Tomorrow she'll give her students a test, so today she has her students work on a "practice exam" in groups. The thing is, her "practice exam" is the actual test! She writes:

*I think it may have dawned on some of the students that they were looking at the actual exam, and this will be the only time I can use this element of surprise. Hopefully, I will see better results and more work that evidences understanding tomorrow.*Backing up a little, I notice that Menard's Parent Conferences day is also November 17th! (Her post is dated the 18th because she wanted to include a second day of conferences.) As I wrote earlier, most schools in New York City have a Labor Day start, so the conferences mark the end of the first quarter, not the first trimester.

Menard writes:

*Today is the Autumnal Education Equinox – the longest day of the teacher’s year: Parent Teacher Conferences.*Unfortunately, Menard's analogy falls flat here. The longest day of the year is the

*summer solstice*, not the autumnal equinox. So I assume she means to say "Today is the Summer Education Solstice."As it turns out, my own Summer Education Solstice was the 16th, as that was my long day where I had to arrive early and stay late (though not as late as Menard). For both of us, our respective "solstices" were quite busy, but the day after the solstice for both of us was quite light, since most of the parents had talked to us the previous day.

**Presidential Consistency****This wouldn't be a Thanksgiving break post without more talk about the Common Core debate. As a matter of fact, I've been thinking more about some ideas that I've posted on the blog in the past.**

You might recall when I wrote about the "Classical Curriculum." In this curriculum, Grades 5-8 are basically a repeat of Grades 1-4 for history and science. I wrote about the idea of extending this concept to math. I've already written about how first grade is the "year of addition" of whole numbers, second grade the "year of subtraction," third grade the "year of multiplication," and fourth grade the "year of division."

So under the "Classical Curriculum," we can make fifth grade another "year of addition," but for rational numbers (including fractions and integers). Sixth grade becomes a "year of subtraction," seventh grade a "year of multiplication," and eighth grade a "year of division." This is very different from the Common Core or most pre-Core standards. Fifth grade is a bit early for addition of integers, while eighth grade is a bit late for division of fractions and decimals.

But now I've seen actual middle school students, and now I'm starting to like the idea of this math "Classical Curriculum" a bit more. I've noticed that more often than not, it's the

*eighth*graders who are reaching for a calculator, not*sixth*graders. This is because sixth graders have been studying the standard algorithms of arithmetic for the past few years. But after sixth grade, the learning of the algorithms is complete. All of seventh grade is spent forgetting about the algorithms, so by the time they reach eighth grade, "do arithmetic" means reaching for a calculator.So delaying division of rationals into eighth grade forces these students to continue thinking about the algorithms of arithmetic as opposed to reaching for a calculator. This bridges the gap between Grades 4-6, when they first learn and practice long division, and Algebra II/Pre-Calc, when they learn about long division of polynomials.

But there's one more proposal that I want to discuss in this post -- Presidential Consistency. This is the idea that presidents hypocritically propose various education reforms for the public schools, then shield their own children from it by sending them to private schools that don't implement these education reforms. Presidential Consistency Core is automatically

*defined*to be the curriculum used at whatever school the First Children attend. This way, charges of hypocrisy don't come up, as the president's children would have the same curriculum as everyone else.We have a newly elected president, Donald Trump. I feel that I can safely mention politics at the bottom of a long holiday post -- and besides, notice that Wendy Menard openly discusses politics right at the top of her November 21st post, and even more so in her November 9th post (that is, the day after the election). But this post isn't about the president-elect but about his young son Barron, especially since his education plans have been announced over the weekend.

http://blogs.edweek.org/edweek/campaign-k-12/2016/11/education_of_barron_trump_and_other_first_kids.html

Barron is ten years old, with his 11th birthday in March. So I assume that he's a fifth grader. The announcement is that Barron will at least remain at his New York City private school until the end of the current school year, so that he won't have to switch schools mid-year. I assume that even though he attends a private school, his calendar follows other Big Apple schools, with no school until after Labor Day and the last day of school just barely before June 30th.

It's possible that for sixth grade, Barron will attend a DC school -- maybe even Sidwell Friends, the same school as Sasha and Malia Obama. Under my Presidential Consistency plan, the curriculum would follow the outgoing president's children's school under the end of the year, so that just like Barron, no one would have to switch curricula mid-year either. If Barron were to attend Sidwell then Presidential Consistency Core wouldn't change -- it would be defined as Sidwell's standards.

For the remainder of this post, let's assume that Barron continues to attend his current school for sixth grade and beyond -- this is Columbia Grammar and Preparatory School:

https://www.cgps.org/

Let's focus on the middle school math standards -- one because I'm a middle school math teacher, and two because this is what Barron is learning now:

https://www.cgps.org/middle-school-grades-5-7/mathematics

Notice that at Columbia, "middle school" is defined as Grades 5-7 (similar to how the Green Team defines "middle school"), so Barron is already a middle school student. As I compare Columbia's math curriculum to Common Core, most of Columbia's standards are either the same as Common Core's or are possibly one year earlier (for example, I notice that "systems of linear equations" is listed as a seventh grade topic at Columbia). Therefore Consistency Core could move some of Common Core's standards down one grade.

I thought this part is fascinating:

[6th graders] also use tables, graphs, written language, and symbolic rules to examine patterns. To bring these concepts to life, students invest imaginary funds in the stock market and use formulas to figure out their gains and losses over time, as well as research a future career and determine a budget to support themselves in NYC.

Interestingly enough, my old sixth grade math teacher had us play a stock market game as well.

One might expect that with a tougher seventh grade curriculum, all eighth graders might be pushed into Algebra I. The following link shows that this is not the case:

https://www.cgps.org/prepschool/mathematics

We see "an introductory Pre-Algebra course" mentioned as one of the classes, so this class is available for eighth graders. Meanwhile, of the Geometry course, it's stated that students follow a "traditional study of Euclidean plane geometry." I interpret this as indicating that transformations will not appear in this course, so opponents of transformation geometry would appreciate that.

I'm also a middle school

*science*teacher, so let's look at the science curriculum:https://www.cgps.org/middle-school-grades-5-7/science

I notice that STEM is mentioned, so I assume that the Barron is doing STEM projects similar to what I'm doing in my own classes. The sixth and seventh grade courses appear to be one year ahead of the old pre-NGSS standards here in California -- the fifth grade course doesn't correspond to any class that I can easily recognize.

This concludes the post -- my last post of the Thanksgiving break. My next post won't be until Tuesday, November 29th -- the second day back from break, since the November 17th post was actually a two-day post covering both Days 63 and 64. Enjoy your Floyd Thursby day (that is, the Tuesday before Thanksgiving) and the rest of your holiday!

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