Today my eighth graders begin the Unit 2 Test on functions -- the F strand in Common Core. I'll write more about the eighth graders tomorrow, since my focus on each Tuesday will be my seventh grade math classes.
The seventh graders officially completed Unit 2 yesterday. Thus the students begin Unit 3 today. While Unit 2 is all about adding and subtracting positive and negative numbers, Unit 3 will concern multiplying and dividing them.
In some ways, multiplying signed numbers is easier than adding and subtracting them. The rule for multiplying integers is simple -- same signs are positive, different signs are negative. But of course, it always confuses students to see the multiplication rules right after the addition rules. Why is it that the sum of two negative numbers is negative, yet the product of two negative numbers is positive?
For its part, APEX motivates the lesson first by using repeated addition. Since the sum of -2, -2, -2 is -6, we conclude that 3(-2) = -6 -- but of course, this doesn't work if both factors are negative. At this point, the Distributive Property is used to motivate the product of two negative numbers. As (-3)(0) is obviously zero, we know that (-3)(-5 + 5) = 0, so distributing gives (-3)(-5) + -3(5) = 0. We already know that -3(5) is -15, and so (-3)(-5) must be its opposite, namely +15.
This week, third period is the designated class for tutorial. When the students arrive, I begin by having them finish the Unit 2 Test from yesterday -- even though I had this class start the test right away yesterday, some students still haven't started it yet. Much of this is due to how APEX works -- students can't progress until they pass the previous lesson. And so some students still have lessons to complete before the Unit 2 Test, so they can't start this test yet -- much less proceed to today's lesson, the first lesson of Unit 3.
After tutorial, the students leave their belongings behind for snack break, and then they return to class for third period proper. This is when I start the Lesson 3.1.1. Afterward I give time for students to work on APEX assignments, including Quiz 3.1.5. But of course, many students must make up previous quizzes or finish Test 2.4.2. The seventh graders are well-behaved for the most part, since they all have lots of work to do today.
One thing I've noticed so far about APEX is that, while eighth graders only need a score of 60% (that is, a D) to pass. seventh graders require a grade of 70% (a C) to pass. And since most quizzes contain only five questions, this means that they really need a grade of 4/5 (or 80%, a B) to pass. But I'm allowed to let students bypass the quiz after they've failed it three times. I'll often let students bypass the test if they're well behind and need to catch up, and their grade is 3/5 or 60%, just barely shy of passing.
Meanwhile in first period, one student is scheduled for in-person learning during hybrid, yet he logs in to Google Meet from home. It turns out that the student is sick -- before the virus, he'd just miss a day of school, but now he might as well take advantage of hybrid and just log in when he's ill.
The song for today is Square One TV's "Wanna Be," performed by Bobby McFerrin, a jazz singer:
Refrain:
Wanna be, wanna be,
Anything you wanna be.
Anything you wanna be,
You've got to know math.
Wanna be, wanna be,
Anything you wanna be.
Anything you wanna be,
You've got to know math.
First Verse:
You wanna be a doctor?
You wanna be a nurse?
You wanna fly a jet plane?
You've got to know math first.
You wanna coach football,
Or run a baseball team?
Operate computers,
Be whatever you dream? (To Refrain)
Second Verse:
You wanna be a stuntman,
A scientist?
A photographer,
An archaeologist?
A firefighter, detective,
Fighting fire and crimes?
You'll have to work with a lot of numbers,
Using math all the time! (To Refrain)
McFerrin sings this song in the key of F major. But in order to make it easier to play on the guitar tuned to EACGAE, I play this song in they key of G major, using the following chords:
G/D: xx2023
C: xx0030
D7: xx2232
The verses are played entirely over the D7 chord. I play a few running bass notes, D and A, along with the D7 chord. This is the first song I play with chord transitions (rather than getting away with only a G/B chord), which are tricky since I'm still trying to master the EACGAE chord shapes.
Interestingly enough, one of the problems in today's seventh grade APEX lesson is about a stuntman -- one of McFerrin's examples as someone who needs to know math. The stuntman receives positive points for each stunt and negative points for each fall, and so he needs to know how to add and multiply positive and negative numbers.
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