There's no "Day in the Life" today, but I will point out that it's a block schedule with all three blocks being AP US History. The students learn about women's rights in the 19th century. They read Sojourner Truth's speech "Ain't I a Woman?" then watch a video. Here's a link to what they watch:
Afterward they are to begin working on a DBQ (Document-Based Question), which is great practice for the AP US History exam.
Today is Day 60, the day of the Chapter 5 Test. This is what I wrote last year about the answers to today's test:
Now here are the answers to my test.
1-2. constructions (or drawings). Notice that a construction for #2 is halfway to constructing a square inscribed in a circle for Common Core.
3. 95 degrees.
4. 152.5 degrees.
5. 87 degrees.
6. 86 degrees.
7. x degrees. This is almost like part of Euclid's proof of the Isosceles Triangle Theorem (except I think that his proof focused on the linear pairs, not the vertical angles).
8. 27 degrees.
9a. x = 60
9b. 61, 62, 58 degrees.
10. 25, 69, 128, 138 degrees.
11. polygon, quadrilateral, parallelogram, rectangle, square.
12. kite.
13. rectangle.
14. false. A counterexample is found easily.
15. Yes, the perpendicular bisector of the bases.
16. 46. Although I mentioned it briefly this year during Chapter 2, perimeter is a concept that could be developed more in these early lessons. My question actually defines perimeter since my lessons haven't stressed the concept yet. This is the simplest possible perimeter problem that I could have covered, where only the definition of kite is needed to find the two missing lengths. I could have given an isosceles trapezoid instead, where the Isosceles Trapezoid Theorem is needed to find a missing side length. Or since I squeezed in the Properties of a Parallelogram Theorem in our Lesson 5-6 (as part of proving that every rhombus is a parallelogram), I could have even put a parallelogram here with only two consecutive side lengths given.
17. The conjecture is true, and is a key part of the proof of Centroid Concurrency Theorem.
18. Statements Reasons
1. angle G = angle FHI 1. Given
2. EG | | FH 2. Corresponding Angles Test
3. EFHG is a trapezoid 3. Definition of trapezoid (inclusive def. -- it could be a parallelogram)
19. Statements Reasons
1. O and P are circles 1. Given
2. OQ = OR, PQ = PR 2. Definition of circle (meaning)
3. OQPR is a kite 3. Definition of kite (inclusive def. -- it could be a rhombus)
20. Figure is at the top, then below it is quadrilateral. Branching out from it are kite, trapezoid. Then below trapezoid is parallelogram. Kite and parallelogram rejoin to have rhombus below. (Once again, these are inclusive definitions!).
As today is a test day, it ought to be time for another discussion about traditionalists. The main traditionalists haven't posted anything major lately -- especially not Joanne Jacobs (and her frequent commenters like Bill), since she's been out of town without a guest blogger.
So instead, there will be a hodgepodge of topics for this traditionalists' post:
- Last night's tragedy in California
- California election results
- Geometry in my old district
- Fractions in the Number Talks book.
Let's start with the tragedy. Last night, there was a shooting at a bar in Thousand Oaks. There are a dozen casualties (including several college students) as well as the gunman. Meanwhile, there is also a major wildfire burning a short distance from the shooting.
Thousand Oaks in in Ventura Country. If I remember correctly, Fawn Nguyen lives and works in Ventura County, so she's probably close to both incidents. She hasn't blogged in months, and while she has tweeted recently, there's no mention of either incident on her Twitter account.
OK, let's move on to the election. Proposition 7 has been approved by almost 60% of voters, thus paving the way for Year-Round DST in California. The next step is for the state legislature to approve Year-Round DST, and then it will be up to Congress.
Once again, even though I voted for Prop 7, I say that it won't work unless Nevada follows suit. I hope that Nevada will consider Year-Round DST so that Congress can approve both states. I did find one article which discusses the passage of Prop 7 from a Vegas perspective:
Meanwhile, Marshall Tuck has a slight lead over Tony Thurmond for State Superintendent, but millions of absentee votes have yet to be counted:
And Gavin Newsom is now officially the Governor-elect of California. The following link discusses some of his campaign promises, including one year of universal preschool and two years of community college:
In the past, I've referred to "Presidential Consistency." Some people complain that presidents promote Common Core and other educational standards, then exempt their own children from them by enrolling them in private schools that don't adhere to the standards. Presidential Consistency solves this by automatically defining Common Core to be the standards used by the school where the president's own children are enrolled.
If you oppose the idea of national standards and prefer state standards only, then I've also mentioned "Gubernatorial Consistency" in earlier posts. Governor-elect Newsom and his wife have four young children, ages two to nine, but I don't know what school they currently attend. Under Gubernatorial Consistency, the standards used at their school would be the new California Standards. This includes Newsom's preschoolers, since the Governor-elect is a proponent of universal preschool.
Let's move on to our third topic. In the old district, I've yet to sub in any math class (except for a few days of co-teaching), much less a Geometry class. But for some reason, today's history teacher has some texts for other subjects, and I found a Geometry text. I'm not sure whether it's the official text for this district, but let's assume for now that it is.
The publisher is McDougal Littell, and it's dated 2005 -- so it's a pre-Core text. I've mentioned McDougal Littell texts in earlier posts, but none of them are today's text.
Here's the table of contents:
1. Basics of Geometry
2. Segments and Angles
3. Parallel and Perpendicular Lines
4. Triangle Relationships
5. Congruent Triangles
6. Quadrilaterals
7. Similarity
8. Polygons and Area
9. Surface Area and Volume
10. Right Triangles and Trigonometry
11. Circles
Even though this is a pre-Core text, the four major Common Core transformations -- translations, reflections, dilations, and rotations -- all appear in the text. They appear as the last lesson of four different chapters -- 3, 5, 7, and 11 respectively.
Once again, I don't know whether this district uses this text, but I can imagine how I'd adapt this text to the Common Core Standards. For starters, we might move the four transformation lessons so that they're the first lesson in each chapter, not the last chapter.
Here are tables of contents for two of the chapters that end with transformations:
Chapter 3:
3-1. Relationships Between Lines
3-2. Theorems About Perpendicular Lines
3-3. Angles Formed by Transversals
3-4. Parallel Lines and Transversals
3-5. Showing Lines Are Parallel
3-6. Using Parallel and Perpendicular Lines
3-7. Translations
Chapter 5:
5-1. Congruence and Triangles
5-2. Proving Triangles Are Congruent: SSS and SAS
5-3. Proving Triangles Are Congruent: ASA and AAS
5-4. Hypotenuse-Leg Congruence Theorem: HL
5-5. Using Congruent Triangles
5-6. Angle Bisectors and Perpendicular Bisectors
5-7. Reflections and Symmetry
We can imagine moving these lessons up -- for example, covering Lesson 5-7 before 5-1. This allows us to define "congruent" as "having an isometry (or composite of reflections) mapping one to the other," which is the Common Core definition. Then we can show how SSS and SAS (Lesson 5-2) are related to reflections.
Notice that as this text is written, very few proofs of theorems appear in the text -- not even the standard proofs found in most pre-Core texts. For example, the Corresponding Angles Postulate (Consequence) appears in Lesson 3-4 followed by the Alternate Interior Angles Theorem, yet there's no proof of AIA (not even the usual one derived from Corresponding and Vertical Angles). And Lesson 5-3 mentions both the ASA Postulate and the AAS Theorem, but the usual proof of AAS (using ASA and Triangle Sum) doesn't appear.
Meanwhile, the Pythagorean Theorem appears very early -- Chapter 4. This is before both similarity (Chapter 7) and area (Chapter 8), and so neither is used to prove Pythagoras. But at least the Distance Formula appears in the same lesson as the Pythagorean Theorem (as opposed to those infamous texts that place the formula in the first chapter, well before Pythagoras).
The only proofs that do appear are simple ones, such as the Vertical Angle Theorem. Interestingly enough, the Perpendicular Bisector Theorem is proved, and students are asked to fill in steps to complete the Angle Bisector Theorem. Otherwise, with so few proofs, this text might as well be Michael Serra's Discovering Geometry and label postulates and theorems as "conjectures." At any rate, this leaves the door open to fill in the missing proofs with Common Core derivations.
In this text, translations appear before reflections. In some ways this is good, since translations are easier to understand than reflections. But this rules out defining translations as the composite of two reflections in parallel mirrors. (The word "vector" doesn't appear either -- instead, a translation is merely defined as sliding all points the same direction and distance.) Also, dilations appear before rotations, which is unusual. But I can see why we might wish to place rotations with circles.
In some ways, this fits an old idea that I once proposed on the blog -- not only do we place each Common Core transformation in a different unit, but we name each unit after the transformation. For this text, we obtain the following:
Unit 1 (Chapters 1, 2): Basics of Geometry
Unit 2 (Chapters 3, 4): Translations
Unit 3 (Chapters 5, 6): Reflections
Unit 4 (Chapters 7, 8): Dilations
Unit 5 (Chapters 9, 10): ??? (What transformation do volume and trig have in common? In this past, I might have just put "Glide Reflections" here since nothing else fits.)
Unit 6 (Chapter 11): Rotations
Three units make up each semester. (If you're at the rare high school that has trimesters, then two units make up each trimester.) The sixth unit contains only one chapter -- this might be a great time to squeeze in probability (included as part of the California Common Core Geometry course).
Finally, I wish to wrap up today's traditionalists' debate post with someone I mentioned back in my last traditionalists' post. Recall that in Chapter 8 of her Number Talks book, Cathy Humphreys wrote about a sixth grader in her class, Anthony, who had trouble with fractions. He said:
"Mrs. Humphreys, we had fractions in third grade and fourth grade and fifth grade. We didn't get them then, and we don't get them now."
Let's imagine having a hypothetical conversation with Anthony. So far, this is what he's said:
Finally, I wish to wrap up today's traditionalists' debate post with someone I mentioned back in my last traditionalists' post. Recall that in Chapter 8 of her Number Talks book, Cathy Humphreys wrote about a sixth grader in her class, Anthony, who had trouble with fractions. He said:
"Mrs. Humphreys, we had fractions in third grade and fourth grade and fifth grade. We didn't get them then, and we don't get them now."
Let's imagine having a hypothetical conversation with Anthony. So far, this is what he's said:
- In third grade, I tried to learn fractions, but I didn't understand them.
- In fourth grade, I tried to learn fractions, but I didn't understand them.
- In fifth grade, I tried to learn fractions, but I didn't understand them.
Suppose we were to say to Anthony, "Today we won't learn fractions. Instead, you only have to answer one question -- and the answer will be a whole number. Just fill in the blank:
- In ______th grade, I will try to learn fractions, and yes, I'll finally understand them!
What number do you suppose Anthony will fill in this blank? Well, Humphreys tells us that Anthony goes on to say, "And we don't want to do them anymore!"
So in other words, what Tony really wants to say is:
- I'll never understand fractions. I'll take my lack of fraction understanding to the grave.
Or more to the point:
- I shouldn't have to spend time doing things I find difficult. I should be able to spend all of my time doing only things I find easy.
But if everyone stopped doing difficult things instead of trying and trying again, then the Chicago Cubs wouldn't have won its first championship 108 years, nor would the Eagles have won its first championship in 57 years, and so on.
Of course, Tony would probably reply that winning the World Series or Super Bowl are good things, while learning fractions is a bad thing. Every athlete wants to win a championship, but there's nothing wrong with never learning fractions.
It reminds me of what I wrote last year on the day of the Chapter 5 Test:
Imagine the following hypothetical conversation:
Teacher: What do you want to be when you grow up?
4th Grader: A nurse.
Teacher: To be a nurse, you have to get A's and B's in all your classes, especially science and math.
4th Grader: Boo! I hate math!
Teacher: You know the nurses you see at the hospital? All of them are great at math. They won't let you be a nurse unless you're good at math.
4th Grader: But math is so hard!
Teacher: Don't worry -- there's still time. For the next ten years, you'll have to work hard on these p-sets.
4th Grader: That's no fun!
Teacher: I know that they're boring, but it's the only way you'll ever be good at math. Work on these p-sets, and ten years from now you'll be able to say, "Yes, I'm good at math!" Then they'll let you become a nurse, or anything else you want to be.
4th Grader: Um, OK.
Teacher: What do you want to be when you grow up?
4th Grader: A nurse.
Teacher: To be a nurse, you have to get A's and B's in all your classes, especially science and math.
4th Grader: Boo! I hate math!
Teacher: You know the nurses you see at the hospital? All of them are great at math. They won't let you be a nurse unless you're good at math.
4th Grader: But math is so hard!
Teacher: Don't worry -- there's still time. For the next ten years, you'll have to work hard on these p-sets.
4th Grader: That's no fun!
Teacher: I know that they're boring, but it's the only way you'll ever be good at math. Work on these p-sets, and ten years from now you'll be able to say, "Yes, I'm good at math!" Then they'll let you become a nurse, or anything else you want to be.
4th Grader: Um, OK.
- In 6th grade, I will try to learn fractions, and yes, I'll finally understand them!
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