This has several implications for the blog:
- First of all, for those who worry that the summer class might be cancelled, there will be no Post Purge of 2018. Last year, I'd written about a teaching job that never materialized and deleted all posts that referred to that job. This year, it's semi-expected that a summer class would be cancelled, and so with the warning in today's post, there's no need to delete any mentions of it.
- Two years ago, when I was first hired to work at my old charter school, I wrote many posts in May, June, and July about plans for my upcoming class. But many of these plans were based on misconceptions about my class, especially regarding the Illinois State text and the lack of a separate science teacher (the cause of my sixth resolution). In order to avoid making this mistake again, I don't want to write too much about my upcoming summer class until at least the first teacher training day relating to the summer position -- Wednesday, May 23rd.
- This course covers the first three weeks of summer (June 18th-July 6th). It's actually the first semester of Algebra I. The second semester will be covered the following three weeks of summer by another teacher. The class will meet four days a week (Monday through Thursday) for a half-day, which will leave me time to blog all four days of class each week. This will mark the first time that I'll ever blog four times in a week during summer vacation.
- My original summer plans were to return to blogging about Mocha computer music. But with the summer class, I'll return to Mocha music this week. Keep in mind that with this class meeting for a half-day, that makes for a very long class. I wish to return to having "Music Break" each day to give the students a brain break. The hope is that I can actually use Mocha to help me compose music -- the songs that I will sing in class. (Of course, if the class is cancelled then I'll stop the music posts and wait until the summer to post them.)
I'm glad for the opportunity to return to teaching math, but still, I'm slightly sad that the class I was chosen to teach was Algebra I and not Geometry. This is, after all, a Geometry blog -- and I chose to blog about Geometry because it's my favorite math class.
But then again, I must admit that the class I have the most experience teaching is Algebra I -- in particular, the first semester of Algebra I. My semester of student teaching was indeed the first semester of Algebra I. And as I've written in the past, the first semester of Algebra I actually overlaps Common Core 8 -- so I essentially taught this class last year at my old charter as well. (Of course, Common Core 8 also contains some Geometry as well.) So perhaps my resume is strongest in Algebra I, which explains my being selected for the job.
Teaching this summer Algebra I course won't be easy, not by a long shot. After all, students are presumably taking Algebra I in the summer because they failed it during the year. Thus Algebra already turns these students off -- and now this class is costing them lots of summer fun. I've referred to this in past posts -- I don't like the idea of beginning the Geometry course with so much algebra, since for students who struggled throughout the year (including the summer) trying to pass Algebra I, the last thing they want to see at the start of their next course is more algebra. (I recommend no algebra in Geometry until Chapter 3, around the time of the PSAT.)
But as I said earlier, let's worry about the summer when the summer comes. Today I subbed in a middle school math class -- the same class I covered a few weeks ago, on April 24th. As it turns out, this teacher will be out tomorrow as well, so this qualifies as a multi-day assignment. And as on all multi-day assignments, we revert to the first focus resolution in today's "Day in the Life":
1. Implement classroom management based on how students actually think.
7:15 -- As I wrote back on April 24th, this teacher has a zero period class. This is the first of four eighth grade Algebra I classes.
The teacher is jumping around in the latter chapters of the Big Ideas text. Back on April 24th, the students were in Lesson 10-3 on the Pythagorean Theorem. Since then, the teacher moved on to Chapter 12 on statistics before returning to today's Lesson 10-1, on square root functions. The emphasis is to make sure that lessons that will appear on the SBAC are covered -- and this is rather tricky in an eighth grade Algebra I class where they'll be tested on Common Core 8 Standards.
Students are to graph the basic function y = sqrt(x), as well as related functions obtained from the parent function via translations or reflections over a coordinate axis. There are many places for students to be confused -- such as distinguishing y = sqrt(x - 1) from y = sqrt(x) - 1. They learn that these two functions indeed have different domains and ranges.
8:15 -- Zero period leaves and first period arrives. I begin the homeroom announcements. Unlike the first few times I subbed here when the school was on a special schedule, this time the school is actually on the regular schedule. Homeroom leads directly into first period (as is intended), and the Monday period rotation (the natural order 1-2-3-4-5-6) is followed. Recall that on other days of the week, the classes are followed in a different order, but first period (and zero, of course) is always in the morning. First period is the best class of the day in terms of behavior -- at least with the class quiet, I'm able to get through the entire lesson, with five examples from the text covered.
9:20 -- First period leaves and second period arrives. Although this isn't the quietest class of the day, they get through the examples quickly. It helps that the smartest student in the class by far is enrolled in this class. When I warn the class that -1 isn't in the domain of sqrt(x) because no real number squared gives -1, he proudly proclaims that sqrt(-1) is i. And I believe that having such a smart kid in the class motivates the others to learn more -- for example, the girl sitting next to him is able to avoid falling for the y = sqrt(x + 1) vs. y = sqrt(x) + 1 trick.
10:15 -- Second period leaves and it's time for snack. On the way out, I speak to the smart kid. He tells me that he independently studies higher math, which is how he knows about i. Last year, he took the SAT (as part of the Johns Hopkins CTY contest) and earned a score of 750 in math. I tell him that I myself, as a young student at the same age, took the SAT and earned a math score of 700, so he definitely has me beat!
10:30 -- Third period arrives. This is not a math class, but ASB Leadership. The students create posters -- Wonder Woman and the Hulk encourage students to do well on the SBAC, while seventh graders are informed about the upcoming election for class president.
11:25 -- Third period leaves. Fourth period is the teacher's conference period, thus giving me a break that lasts through lunch.
1:05 -- Fifth period arrives. This is the last Algebra I class of the day -- and unfortunately, it's the most talkative. I wonder whether the reason for doing well with first and second period and struggling with fifth is that back on April 24th, fifth period was the class that was supposed to take the online placement test when the Chromebooks stopped working. In other words, the last time I subbed for them, the class didn't go so well -- and so they act up when they see me again.
I don't want to make too many assumptions about my upcoming summer school class, but I do make the basic assumption that I must be able to keep the class quiet, or they won't learn anything during the entire summer. And so this is the class I must watch out for when I return tomorrow -- I must show strong enough management to keep fifth period quiet, or my summer class won't be a success.
2:00 -- Fifth period leaves and sixth period arrives. This is a Math Support class for students who need extra help. Just as on April 24th, students work on ALEKS and Prodigy on Chromebooks. It is the second best behaved class of the day, after first period.
2:55 -- Sixth period ends, and thus ends a long day of subbing.
By the way, now that I'll be teaching Algebra I soon, here is the Table of Contents for the Big Ideas Algebra I text:
1. Solving Linear Equations
2. Graphing and Writing Linear Equations
3. Solving Linear Inequalities
4. Solving Systems of Linear Equations
5. Linear Functions
6. Exponential Functions and Equations
7. Polynomial Equations and Factoring
8. Graphing Quadratic Functions
9. Solving Quadratic Equations
10. Square Root Functions and Geometry
11. Rational Equations and Functions
12. Data Analysis and Displays
Let's compare this to the Table of Contents for the Glencoe Algebra I text -- which is the text I'm more likely to teach out this summer:
1. Expressions, Equations, and Functions
2. Linear Equations
3. Linear Functions
4. Equations of Linear Functions
5. Linear Inequalities
6. Systems of Linear Equations and Inequalities
7. Exponents and Exponential Functions
8. Quadratic Expressions and Equations
9. Quadratic Functions and Equations
10. Radical Functions and Geometry
11. Rational Functions and Equations
12. Statistics and Probability
The main difference is that Glencoe spends Chapter 1 reviewing the order of operations, while Big Ideas jumps directly into solving equations in Chapter 1 (Chapter 2 in Glencoe). Since the two texts have the same number of chapters, the difference is that Glencoe combines graphing and solving quadratics (Chapters 8-9 in Big Ideas) into a single chapter (Chapter 9 in Glencoe). The other key difference is that the whole idea of a function appears much earlier in Glencoe (Chapter 3) than in Big Ideas (Chapter 5).
This is what I wrote last year about today's lesson:
Lesson 15-9 of the U of Chicago text is on "The Isoperimetric Theorems in Space." These are the 3D analogs of the theorems we discussed on Friday.
Isoperimetric Theorem (space version):
Of all solids with the same surface area, the sphere has the most volume.
Of all solids with the same volume, the sphere has the least surface area.
We don't even bother trying to prove these theorems. As we've seen, the 2D proofs are very difficult, so imagine how much more so the 3D proofs would be.
This is the final lesson in the U of Chicago text. Here is how the U of Chicago closes the text:
"The Isoperimetric Theorems involve square and cube roots, pi, polygons, circles, polyhedra, and spheres. They explain properties of fences, soap bubbles, and sponges. They demonstrate the broad applicability of geometry and the unity of mathematics. Many people enjoy mathematics due to the way it connects diverse topics. Others like mathematics for its uses. Still others like the logical way mathematics fits together and grows. We have tried to provide all these kinds of experiences in this book and hope that you have enjoyed it."
Well I for one have certainly enjoyed this text, and I hope you, the readers of this blog, have as well.
One of the bonus Exploration questions mentions the ancient Carthaginian queen Dido. I wrote about her last year as well:
"According to one of the legends of history, Dido, of the Phoenician city of Tyre, ran away from her family to settle on the Mediterranean coast of North Africa. There she bargained for some land and agreed to pay a fixed sum for as much land as could be encompassed by a bull's hide."
"Her second bright idea was to use this length to bound an area along the sea. Because no hide would be needed along the seashore she could thereby enclose more area."
We know that the solution to the Isometric Problem is the circle -- the curve that encloses the most area for its length. We've also seen questions in which we are to maximize area by building a fence along a river to enclose a rectangular area -- the answer is a rectangle whose width is exactly half of its length. Combining these two ideas, we can solve the Dido problem:
"According to the legend, Dido thought about the problem and discovered that the length of hide should form a semicircle."
So we see that without water, the largest area is a circle -- with water, it's a semicircle. If we restrict to rectangles, without water the largest area is a square -- with water, it's a semi-square (that is, half of a square, or a rectangle whose width is half of its length).
"[Dido's new lover] Aeneas was a man on a mission, and he soon departed to found a new civilization in Rome. Dejected and distraught, Dido could do no more for Aeneas than to throw herself on a blazing pyre so as to help light his way to Italy...Rome made no contributions to mathematics whereas Dido might have."
By the way, let's tie this back to Pappas and ask, what numerals would Dido have used? Carthage is actually derived from the Phoenician culture. Notice that the Square One TV video "The Mathematics of Love" seems to imply that the Phoenicians used our (current) numerals (in contrast with the Roman), even though Phoenician has nothing to do with Hindu-Arabic. So in the end, I don't know what numerals Carthaginians might have used.
The teacher is jumping around in the latter chapters of the Big Ideas text. Back on April 24th, the students were in Lesson 10-3 on the Pythagorean Theorem. Since then, the teacher moved on to Chapter 12 on statistics before returning to today's Lesson 10-1, on square root functions. The emphasis is to make sure that lessons that will appear on the SBAC are covered -- and this is rather tricky in an eighth grade Algebra I class where they'll be tested on Common Core 8 Standards.
Students are to graph the basic function y = sqrt(x), as well as related functions obtained from the parent function via translations or reflections over a coordinate axis. There are many places for students to be confused -- such as distinguishing y = sqrt(x - 1) from y = sqrt(x) - 1. They learn that these two functions indeed have different domains and ranges.
8:15 -- Zero period leaves and first period arrives. I begin the homeroom announcements. Unlike the first few times I subbed here when the school was on a special schedule, this time the school is actually on the regular schedule. Homeroom leads directly into first period (as is intended), and the Monday period rotation (the natural order 1-2-3-4-5-6) is followed. Recall that on other days of the week, the classes are followed in a different order, but first period (and zero, of course) is always in the morning. First period is the best class of the day in terms of behavior -- at least with the class quiet, I'm able to get through the entire lesson, with five examples from the text covered.
9:20 -- First period leaves and second period arrives. Although this isn't the quietest class of the day, they get through the examples quickly. It helps that the smartest student in the class by far is enrolled in this class. When I warn the class that -1 isn't in the domain of sqrt(x) because no real number squared gives -1, he proudly proclaims that sqrt(-1) is i. And I believe that having such a smart kid in the class motivates the others to learn more -- for example, the girl sitting next to him is able to avoid falling for the y = sqrt(x + 1) vs. y = sqrt(x) + 1 trick.
10:15 -- Second period leaves and it's time for snack. On the way out, I speak to the smart kid. He tells me that he independently studies higher math, which is how he knows about i. Last year, he took the SAT (as part of the Johns Hopkins CTY contest) and earned a score of 750 in math. I tell him that I myself, as a young student at the same age, took the SAT and earned a math score of 700, so he definitely has me beat!
10:30 -- Third period arrives. This is not a math class, but ASB Leadership. The students create posters -- Wonder Woman and the Hulk encourage students to do well on the SBAC, while seventh graders are informed about the upcoming election for class president.
11:25 -- Third period leaves. Fourth period is the teacher's conference period, thus giving me a break that lasts through lunch.
1:05 -- Fifth period arrives. This is the last Algebra I class of the day -- and unfortunately, it's the most talkative. I wonder whether the reason for doing well with first and second period and struggling with fifth is that back on April 24th, fifth period was the class that was supposed to take the online placement test when the Chromebooks stopped working. In other words, the last time I subbed for them, the class didn't go so well -- and so they act up when they see me again.
I don't want to make too many assumptions about my upcoming summer school class, but I do make the basic assumption that I must be able to keep the class quiet, or they won't learn anything during the entire summer. And so this is the class I must watch out for when I return tomorrow -- I must show strong enough management to keep fifth period quiet, or my summer class won't be a success.
2:00 -- Fifth period leaves and sixth period arrives. This is a Math Support class for students who need extra help. Just as on April 24th, students work on ALEKS and Prodigy on Chromebooks. It is the second best behaved class of the day, after first period.
2:55 -- Sixth period ends, and thus ends a long day of subbing.
By the way, now that I'll be teaching Algebra I soon, here is the Table of Contents for the Big Ideas Algebra I text:
1. Solving Linear Equations
2. Graphing and Writing Linear Equations
3. Solving Linear Inequalities
4. Solving Systems of Linear Equations
5. Linear Functions
6. Exponential Functions and Equations
7. Polynomial Equations and Factoring
8. Graphing Quadratic Functions
9. Solving Quadratic Equations
10. Square Root Functions and Geometry
11. Rational Equations and Functions
12. Data Analysis and Displays
Let's compare this to the Table of Contents for the Glencoe Algebra I text -- which is the text I'm more likely to teach out this summer:
1. Expressions, Equations, and Functions
2. Linear Equations
3. Linear Functions
4. Equations of Linear Functions
5. Linear Inequalities
6. Systems of Linear Equations and Inequalities
7. Exponents and Exponential Functions
8. Quadratic Expressions and Equations
9. Quadratic Functions and Equations
10. Radical Functions and Geometry
11. Rational Functions and Equations
12. Statistics and Probability
The main difference is that Glencoe spends Chapter 1 reviewing the order of operations, while Big Ideas jumps directly into solving equations in Chapter 1 (Chapter 2 in Glencoe). Since the two texts have the same number of chapters, the difference is that Glencoe combines graphing and solving quadratics (Chapters 8-9 in Big Ideas) into a single chapter (Chapter 9 in Glencoe). The other key difference is that the whole idea of a function appears much earlier in Glencoe (Chapter 3) than in Big Ideas (Chapter 5).
This is what I wrote last year about today's lesson:
Lesson 15-9 of the U of Chicago text is on "The Isoperimetric Theorems in Space." These are the 3D analogs of the theorems we discussed on Friday.
Isoperimetric Theorem (space version):
Of all solids with the same surface area, the sphere has the most volume.
Of all solids with the same volume, the sphere has the least surface area.
We don't even bother trying to prove these theorems. As we've seen, the 2D proofs are very difficult, so imagine how much more so the 3D proofs would be.
This is the final lesson in the U of Chicago text. Here is how the U of Chicago closes the text:
"The Isoperimetric Theorems involve square and cube roots, pi, polygons, circles, polyhedra, and spheres. They explain properties of fences, soap bubbles, and sponges. They demonstrate the broad applicability of geometry and the unity of mathematics. Many people enjoy mathematics due to the way it connects diverse topics. Others like mathematics for its uses. Still others like the logical way mathematics fits together and grows. We have tried to provide all these kinds of experiences in this book and hope that you have enjoyed it."
Well I for one have certainly enjoyed this text, and I hope you, the readers of this blog, have as well.
One of the bonus Exploration questions mentions the ancient Carthaginian queen Dido. I wrote about her last year as well:
"According to one of the legends of history, Dido, of the Phoenician city of Tyre, ran away from her family to settle on the Mediterranean coast of North Africa. There she bargained for some land and agreed to pay a fixed sum for as much land as could be encompassed by a bull's hide."
"Her second bright idea was to use this length to bound an area along the sea. Because no hide would be needed along the seashore she could thereby enclose more area."
We know that the solution to the Isometric Problem is the circle -- the curve that encloses the most area for its length. We've also seen questions in which we are to maximize area by building a fence along a river to enclose a rectangular area -- the answer is a rectangle whose width is exactly half of its length. Combining these two ideas, we can solve the Dido problem:
"According to the legend, Dido thought about the problem and discovered that the length of hide should form a semicircle."
So we see that without water, the largest area is a circle -- with water, it's a semicircle. If we restrict to rectangles, without water the largest area is a square -- with water, it's a semi-square (that is, half of a square, or a rectangle whose width is half of its length).
"[Dido's new lover] Aeneas was a man on a mission, and he soon departed to found a new civilization in Rome. Dejected and distraught, Dido could do no more for Aeneas than to throw herself on a blazing pyre so as to help light his way to Italy...Rome made no contributions to mathematics whereas Dido might have."
By the way, let's tie this back to Pappas and ask, what numerals would Dido have used? Carthage is actually derived from the Phoenician culture. Notice that the Square One TV video "The Mathematics of Love" seems to imply that the Phoenicians used our (current) numerals (in contrast with the Roman), even though Phoenician has nothing to do with Hindu-Arabic. So in the end, I don't know what numerals Carthaginians might have used.
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