Today is Tuesday, and so this post is all about the seventh grade class. But unfortunately, the Math 7 class is a big mess today -- mainly because of the Benchmarks.
I begin the third period class with a short "review" of two-step equations -- but it's more like a preview, since we haven't fully taught two-step equations yet. Then we start the Benchmarks, which the students complete online through Canvas.
After the Benchmarks, we begin the main APEX lesson -- and this is when the problems begin. This lesson, on simplifying and rewriting algebraic expressions, contains a hodgepodge of topics -- combining like terms, adding/subtracting linear expressions, factoring via GCF, expanding by distributing, and percent increase. With so much of the period dedicated to the Benchmarks, I end up having to rush through all of these topics -- and I know that this confuses the students. Only two students are able to pass the APEX quiz today.
As soon as the class ends, I immediately run next door to see the math department head -- she's the one who came up the idea of doing both Benchmarks and a lesson today. Earlier, she warned me about how APEX presents so many topics at once in Unit 4, and I now know exactly what she means. Yet she tells me today that her own seventh graders struggled more with Lessons 4.2.1 and 4.3.1 than 4.1.1.
Fortunately, she explains where I went wrong with this week's lessons. Yesterday, I played three videos for the students (the ones I linked to on the blog that day) -- but now she tells me that I should have presented only one of the three videos. Afterwards, I should have started a two-step equations lesson myself -- this lesson would have had nothing to do with APEX. I actually could have taken some two-step equations from the eighth grade lesson or worksheet, or else just make some up myself.
Then I wouldn't have needed as much time to review/preview two-step equations today. I could have used a few minutes to review them, and then needed only 20 minutes for the Benchmark Test itself. This would have left at least an hour for the APEX lesson, and so I wouldn't have needed to rush.
I do wish to improve this lesson for tomorrow, even though I'm loath to make significant changes for the other cohort of the same third period class. (When both cohorts meet together on distance Mondays, I don't want one cohort to be ahead of the other.) The plan is to shave a few minutes off of both the review/preview and the Benchmarks so that they take 40 minutes together. This leaves a full hour for the lesson in APEX. Today I had trouble accessing the printed study guide for 4.1.1, but the department head tells me that I could just give examples from the online lesson instead (which are sometimes, but not always, the same as the printed examples).
But Thursday's Math 7 class will be second period, not third, so I don't mind changing it up for a whole different period. For APEX on Thursday, I'll go back to the printed study guide but skip up to Example 6, since the Quiz 4.1.5 questions come from #6-11 on the study guide. The first few questions are about key vocabulary terms -- in order to combine like terms, students should know what "combine," "like," and "terms" mean. But I'd rather spend more time on actual math questions so that students aren't frustrated on the quiz -- only when I have the luxury of time do I teach vocabulary.
Students report to fifth period for tutorial, with those having three or more D/F grades seeing a counselor instead. Two students are absent today, and you can probably figure out who one of them is -- yes, it's the student who earned one D- and the rest F's for first quarter.
With the remaining students, I give them all ten of my resolutions, since these can inspire them to improve in their classes. (In case you're curious, the resolution assigned to today is #9: "We pay attention to math as long as possible." This applies to other classes, not just math.)
Then I ask each student to come up with goals for the fourth quaver. Of the four students who remain in class today, two girls have one D and one F each (with the failing grade in English). So their goals are to raise those grades to C or better, and keep up with the reading. One guy (whose online) has only a single D in his Math 8 class (with another teacher). I remind him that I'm a math teacher, so I can give him extra help in that particular subject. The last guy has all C's except for a B+ in science. Since he has no D/F grades, his goal is simply to maintain his current grades.
OK, so today I make my decision for what song to sing. The song for the week is "Solve It," since both classes (especially the eighth graders) are solving equations this week. The version I sing is the one I came up with during Summer 2019.
SOLVING EQUATIONS
1st verse:
When you see an equation,
Or problems that involve it,
All you have to do,
Is solve it!
A letter alone on the left side,
A number alone on the right side.
That's all you have to do,
To solve it!
2nd verse:
When you see an equation,
Or problems that involve it,
All you have to do,
Is solve it!
Whatever you do to the left side,
The same done to the right side.
A letter alone on the left side,
A number alone on the right side.
That's all you have to do,
To solve it!
3rd verse:
When you see an equation,
Or problems that involve it,
All you have to do,
Is solve it!
Move the variables to the left side,
Move the numbers to the right side.
Whatever you do to the left side,
The same done to the right side.
A letter alone on the left side,
A number alone on the right side.
That's all you have to do,
To solve it!
4th verse:
When you see an equation,
Or problems that involve it,
All you have to do,
Is solve it!
Combine like terms on the left side,
Combine like terms on the right side.
Move the variables to the left side,
Move the numbers to the right side.
Whatever you do to the left side,
The same done to the right side.
A letter alone on the left side,
A number alone on the right side.
That's all you have to do,
To solve it!
5th verse:
When you see an equation,
Or problems that involve it,
All you have to do,
Is solve it!
Distribute on the left side,
Distribute on the right side.
Combine like terms on the left side,
Combine like terms on the right side.
Move the variables to the left side,
Move the numbers to the right side.
Whatever you do to the left side,
The same done to the right side.
A letter alone on the left side,
A number alone on the right side.
That's all you have to do,
To solve it!
And in addition to playing this on the guitar, I also added some dance moves. I perform the following moves using the left and right sides of my body, depending on which verse I'm singing:
First verse: hold up one finger (for "letter alone" and "number alone")
Second verse: slap the arm (for "do to one side" and "done to the other side")
Third verse: move the whole body (for "move the variables" and "move the numbers")
Fourth verse: grasp both hands together (for "combine")
Fifth verse: point one finger farther and farther ahead (like distributive arrows)
In the seventh grade class, yes, I decided to sing "Benchmark Tests" for this class only. Here's is the version that I sang:
Benchmark Tests -- by Mr. Walker
Verse 2:
Why do we take Benchmark Tests?
The first three months are done so let's
See how much we know, know know!
It's some new stuff on Benchmark Tests.
If we don't know it, we take a guess.
'Cause there's still time to grow, grow, grow!
The teacher sees our Benchmark Tests,
Knows what to teach more or less.
That's the way to go, go, go!
For this version, I replace "first trimester" with "first three months," since this middle school doesn't have trimesters. In Math 7, I sing "Solve It" at the start of class to lead to the equations review/preview, and "Benchmark Tests" after they complete said tests.
In Math 8, I only since "Solve It" during the usual music break. Indeed, I complete Lesson 4.1.1 on solving multi-step equations before music break, and then set them loose to work on a Kuta worksheet that has already been posted in Canvas. This is probably a waste -- I go through the lesson without singing the song (since I'm waiting for music break), and then I don't get to use the song to teach the actual lesson. Instead, for tomorrow I will keep on solving two-step equations from the worksheet and singing the song as we do them.
As I reflect on all of my failures, often it feels as if I'm the only struggling teacher in the world. But in reality, even the Queen of the MTBoS, Fawn Nguyen, has her struggles. (I will add the "MTBoS" label to this post in order to honor the Queen.)
http://fawnnguyen.com/reviewing-for-a-test/
There’s not enough time or humility for me to share my teaching fails, but here’s a test review routine that worked well with my students.
I pass out the review questions near the end of class and say:
Chapter 3 Test is scheduled for _____. To review for it, I need you to look through the ten problems on this paper. You’re more than welcome to work on the questions, but you don’t have to, not for me anyway. I need you to just examine them enough to identify two questions on there that you feel confident about, that you have no problem solving them.
Then, I need you to identify two questions that you would like to get help on most. That’s it.
Hey, I could have used this post last week, back when my classes were reviewing for the Chapter -- uh, Unit 3 Test. The only test I'm giving my seventh graders this week is the Benchmark -- and the only "review" I'm giving is actually previewing two-step equations.
Nguyen's idea here is compatible with our Go Formative review assignments. I can ask our students which questions students understand and need more help with, and then go over those problems.
In the current pandemic era, I'm wary of passing out slips of survey papers. Nguyen also mentions how to do something similar on Desmos. I wonder whether this will work in my class -- the students would have to see the practice questions on Go Formative, and then answer the survey on Desmos. And this is in addition to Canvas, etc., just to do one assignment. The proliferation of websites to visit might become a turn-off.
After discussing Chapters 3-5 of Eugenia Cheng's latest book on Twitter, I'm now ready to return to blogger to do a longer summary of Chapter 6.
Chapter 6 of Eugenia Cheng's x + y is titled "Leaning Out." Here's how it begins:
"I eventually realized that I was unhappy with the standard ingressive academic environment, unhappy with how my character was being influenced by it, and unhappy with the effect I perceived it to have on students. So I left the standard academic career path and built myself a congressive new career --"
Yes, there are those two words that Cheng likes to use, "ingressive" and "congressive." She defines these words back in Chapter 4:
"The etymological idea is that 'ingressive' is about going into things, and 'congressive' is about bringing things together."
By the way, the author's main idea is that males tends to be more ingressive while females tend to be more congressive -- and society's ingressive bias is why females aren't as successful in math as males.
Here are some more key points of this chapter:
- Congressive Role Models: Cheng lists Michelle Obama (who worked on community relations for the U of Chicago), Prof. John Baez, and Prof. Emily Riehl as congressive role models.
- Reframing Ingressive Assumptions: To the author, ingressive strength is rigidity, but congressive strength is flexibility. Ingressive self-confidence tends toward arrogance, while congressive confidence tends toward self-awareness.
- Risk-Taking: Taking risks is definitely an ingressive behavior. Cheng recommends that congressive people build big safety nets to reduce the risk.
- Congressive Responses to Ingressive Energy: When ingressive energy is incoming, the author tells us that we choose to respond in either an ingressive (escalate), passive (enable), or congressive (neutralize) manner.
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