Last year, I did "A Day in the Life" because this regular teacher had mostly math classes. This year, most of her classes are science. With two of the classes being co-teaching and the rest having aides, there's no need for "A Day in the Life" today. But I will describe the classes in more detail.
The only math class of the day rotates into the last position today. It is co-teaching seventh grade. As it turns out, this lesson is the same as the one I co-taught in my April 23rd post -- surface area. It turns out that at this school, surface area is taught after volume whereas at the school I subbed in two weeks ago, surface area comes first. (This explains why the lessons are two weeks apart.)
It goes without saying that I sing "All About That Base" again today. This time I sing both verses of the prism version, since these kids have already studied volume.
Now let me describe the science classes, but before I start, let me give you a warning. We're done with Hofstadter's book, and so my "ixnay" rules are over. Thus I will be making a full comparison to the science I "taught" -- or, more accurately, failed to teach -- at the old charter school two years ago.
The regular teacher has two science classes of her own -- one seventh grade and one eighth. The eighth graders are currently learning about DNA and genetics. They are to create a DNA key chain and then begin a genetics worksheet, but only one student completes the key chain today.
Notice that Hofstadter actually writes about DNA in the book that we just finished. In Chapter 6, he writes the following:
"Take the case of the genetic information commonly said to reside in the double helix of deoxyribonucleic acid (DNA). A molecule of DNA -- a genotype -- is converted to a physical organism -- a phenotype -- by a very complex process, involving the manufacture of proteins, the replication of the DNA, the replication of cells, the gradual differentiation of cell types, and so on."
But Hofstadter mainly describes the four bases. These are A, T, C, and G, which stand for Achilles, Tortoise, Crab, and -- oops, I mean adenine, thymine, cytosine, and guanine. In fact, most science classes in school focus on the four bases, and not the sugar and phosphate groups to which the bases are attached. When I was a young high school student, I created a DNA model where I used four different rolls of coins (pennies, nickels, dimes, and quarters) for the four bases and modeling clay to join them together. I twisted it to show that the double helix is twisted.
On the other hand, for today's DNA key chain process, it's not necessary to twist the chain. Instead, different colored beads are used to represent the phosphates and sugars. Four colors of smaller beads represent the four bases. The bases are to be joined only to the sugars, not to the phosphates, just as in real DNA molecules.
Meanwhile, the seventh graders are learning about functions of a flower. The students are to label the flower parts and identify their jobs on a worksheet. Those who finish this start making a puzzle out of pictures of flower parts. This time, about a third of the class completes the first worksheet.
The only real classroom management issue involves the last of the regular teacher's own classes -- a sort of study hall. The aide notices that two boys in this class have several missing assignments in both math and history, but they choose to work on a coloring worksheet instead -- and they complain when she doesn't give them color pencils. She points out that both she and I are good at math -- if they work on an actual math assignment instead, both students could improve their math skills and maybe even earn an "A" on their next text.
These two boys are also in the last of the co-teaching classes -- another seventh grade science. This class is learning about bee decline instead. The students are to draw a picture of a bee and answer some questions about why bees are disappearing. Of course, these two boys focus only on the bee picture, not the questions.
Notice that when I co-taught this class in my May 31st post, there was also a bee lesson -- so I assume that this class always covers the bee unit in May. (That day, the bee unit had just completed, and so the students got to watch The Bee Movie instead.) The regular teacher's own seventh grade science actually covered bees before the current flower unit -- that is, the special ed class is actually ahead of the gen ed class.
OK, so let's compare this to the charter science class. Recall that I had a Bruin Corps member -- a UCLA student who happened to be a molecular biology member. Thus we discussed DNA a little for my eighth graders -- though I don't think my Bruin Corps student mentioned sugar or phosphates. Of course, I was wrong to make my science lessons be dependent on Bruin Corps -- I should have developed a science course on my own. My seventh graders learned about neither bees nor flowers, just because I had neither an apiarologist nor a botanist as a student volunteer.
Both Foldables and Interactive Notebooks make an appearance today in seventh grade science. The bee assignment is completed in "Sketchnotes," a type of Foldable. The other seventh graders glue their flower worksheet into notebooks. Once again, I did use Foldables for seventh grade science a few times, but Interactive Notebooks might have helped my students learn more.
The regular teacher also tells me to make sure that I'm teaching the class, not the aide. This was definitely a problem back at the old charter, when my support staff member often took over the classroom management. Something similar happens today -- the aide is the one who deals with the obsessed artist boys. In the past, when I try to intervene, I end up arguing instead. There's nothing I could have added that would have convinced them to work on solid academics.
For example, I could have told them that drawing pictures might impress a few friends, but knowing math and science -- and why the decline of bees hurts the food supply and how to stop it -- might impress billions. But there's no way to say this without arguing. The aide is already threatening to write down their names and punish them, and so there's nothing else for me to say or do.
Yesterday, the eighth graders completed their state science test. (That's right -- our SBAC review actually aligns with the middle school SBAC test, even though our review is based on the high school Geometry standards.) This is the first cohort for which the California Science Test actually counts.
I ask some of the eighth graders to describe the test. Once again, science standards going all the way back to sixth grade are on the test, and so some of them struggled to remember. They inform me that there are both multiple choice questions and essay questions to answer.
In fact, I notice that the science teacher I co-taught today is actually a sub. I suspect that all of the science teachers are out today -- perhaps to help grade the science tests? I know that teachers are the graders for the district assessments for English and math, but I don't know who must grade the paragraphs for the state science test. If I hadn't left the old charter school, I might have found myself grading state tests at the end of the year.
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
The altitude to side BC is 5 units. What's the altitude to side
(Here's the given info from the diagram: In Triangle ABC, BC = 16, AC = 5.)
This is another question where we must find the area of the triangle in two different ways:
A = (1/2)bh
(1/2)(10)h = (1/2)(16)(5)
5h = (1/2)(1/6)(5)
h = (1/2)(16)
h = 8
Therefore the desired altitude is eight units -- and of course, today's date is the eighth.
Question 3 of the SBAC Practice Exam is on solution sets:
Click the table to indicate whether each equation has no real solution, one real solution, or infinitely many real solutions.
- 5/(20x) = 1/(4x)
- 3x = 4 + 5x
- sqrt(2x + 3) + 6 = 0
Of these three equations, only one is undoubtedly a first semester Algebra I problem. It's easy to solve this linear equation:
3x = 4 + 5x
-2x = 4
x = -2 (one real solution)
The first equation could be taught in first semester Algebra I. Even though it's not linear, it's easily transformable into a linear equation using cross multiplying, which may be studied in first semester:
5/(20x) = 1/(4x)
20x = 20x (infinitely many solutions)
Notice that the solution isn't "all real numbers" -- x = 0 can't be a solution, since x appears in the denominators in the original equation. But the SBAC question indicates "infinitely many solutions," which is not the same as saying that all real numbers are solutions.
The last equation is definitely not a first semester Algebra I problem. Notice that just last week, I subbed in an eighth grade Algebra I class that was studying radical equations -- and last week was clearly in the second semester:
sqrt(2x + 3) + 6 = 0
sqrt(2x + 3) = -6
2x + 3 = 36
2x = 33
x = 16.5
But let's check this answer:
sqrt(2 * 16.5 + 3) + 6 = 0
sqrt(36) + 6 = 0
6 + 6 = 0
12 = 0 (no real solution)
This is an extraneous root. In fact, it should have been obvious at the step sqrt(2x + 3) - 6 that the principal square root of (2x + 3) can never be -6.
Let me write out how exactly I'd teach solving the second equation to my students:
3x = 4 + 5x
Let's get all the x's on the left side and all the numbers on the right side. We want to get rid of the 5x on the right side, so instead of adding 5x, let's subtract 5x:
3x - 5x = 4 + 5x - 5x
-2x = 4
So this is -2 times x. But I don't want -2 times x -- I want just x. So instead of multiplying by -2, let's divide by -2:
-2x/-2 = 4/-2
x = -2
Both the girl and the guy from the Pre-Calc class correctly answer "infinitely many solutions" and "one real solution" for the first two parts. But both answer "one real solution" for the third, which as we see is incorrect. The girl shows her work -- she clearly falls for the extraneous root trick. Thus our students need more work checking for extraneous roots.
Question 4 of the SBAC Practice Exam is on adding and subtracting polynomials:
Enter an expression equivalent to (3x^2 + 2y^2 - 3x) + (2x^2 + y^2 - 2x) - (x^2 + 3y^2 + x) using the fewest number of possible terms.
This is definitely a second semester Algebra I problem. Let's take care of the subtraction first:
(3x^2 + 2y^2 - 3x) + (2x^2 + y^2 - 2x) - (x^2 + 3y^2 + x)
= 3x^2 + 2y^2 - 3x + 2x^2 + y^2 - 2x - x^2 - 3y^2 - x
= 3x^2 + 2x^2 - x^2 + 2y^2 + y^2 - 3y^2 - 3x - 2x - x
= 4x^2 - 6x
This is a straightforward combining like terms problem, except that all y^2 terms are eliminated.
Both the girl and the guy from the Pre-Calc class correctly answer 4x^2 - 6x for this question, although the boy also factors it to x(4x - 6).
SBAC Practice Exam Question 3
Common Core Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
SBAC Practice Exam Question 4
Common Core Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Commentary: Equations with variables on both sides appear in Lesson 6-6 of the U of Chicago Algebra I text, while proportions appear in Lesson 5-7. For the square root equation, my Pre-Calc students last week pointed out that -6 is also a square root of 36, yet they fail to notice x = 16.5 isn't a solution because the sqrt() symbols indicate the principal square root only. It's also possible for two wrongs to make a right here -- some students claim that 2x = 33 has no solution because it's impossible to divide an odd number by 2!
This is a straightforward combining like terms problem, except that all y^2 terms are eliminated.
Both the girl and the guy from the Pre-Calc class correctly answer 4x^2 - 6x for this question, although the boy also factors it to x(4x - 6).
SBAC Practice Exam Question 3
Common Core Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
SBAC Practice Exam Question 4
Common Core Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Commentary: Equations with variables on both sides appear in Lesson 6-6 of the U of Chicago Algebra I text, while proportions appear in Lesson 5-7. For the square root equation, my Pre-Calc students last week pointed out that -6 is also a square root of 36, yet they fail to notice x = 16.5 isn't a solution because the sqrt() symbols indicate the principal square root only. It's also possible for two wrongs to make a right here -- some students claim that 2x = 33 has no solution because it's impossible to divide an odd number by 2!
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