Here is today's Pappas question of the day:
A circle is inscribed in a square of side length 6. The area of the circle = ?pi sq. units.
Notice that the side of the square equals the diameter of the circle. So the diameter is 6, the radius is three, and so the area is 9pi. We fill in the blank with a 9 -- and of course, today's date is the ninth.
This question may be a bit tricky for middle school students just learning about circles. For seventh graders, it's best just to state directly that the diameter is 6 (or even that the radius is 3). I give this problem today as it's convenient for the ninth, but in reality, I'll give this sort of problem closer to the actual lesson on circles -- which I'm hoping will be on Pi Day next month.
Today is the day that I need to establish the Illinois State learning centers. Well, I do try it -- and of course it leads to mixed results.
Seventh grade is always tricky due to the schedule. There is no seventh grade class on Wednesdays, and so they haven't had any real math lesson this week yet (after Monday's coding lesson and Tuesday's STEM project). Other factors conspire against my doing lessons in seventh grade. My Bruin Corps member, who leads one of the centers, isn't scheduled to arrive until right around the time that seventh grade leaves. Finally, the leader of Green Team comes in to deliver T-shirts to all participating students, and that takes about half the period.
And so it's easier just to teach the lesson -- and this is a big one. Today the students learn how to add integers for the first time. During music break, I get out a song I first learned as a student teacher:
ADDING INTEGERS SONG
Same sign, add and keep.
Different signs, subtract,
Keep the sign of the bigger number,
Then you'll be exact!
My master teacher would sing this to the tune of "Row, Row, Row Your Boat," so I do the same. I point out that the Illinois State begins by having the students draw a number line. Some students, of course, figure out the answers without a number line, and so they end up using the rule mentioned in the song.
The learning centers work out much better in eighth grade. I'm still not able to figure out what to do with the die cut machine and art projects, but I do set up a center for manipulatives, which Illinois State calls "DIDAX." There are some algebra tiles provided, and so I set up some simple one-step algebra equations to be solved using the tiles.
I divide the class into three groups. My Bruin Corps member and my support staff member take the other two groups, and they work ahead in the Student Journals. I take the DIDAX group for my own, since I avoid having to explain to the other adults how algebra tiles work. Naturally, I take the lowest achievers for the DIDAX group.
In the end, I feel that the learning centers are more or less successful. My group finally gets to see one-step equations rather than the multi-step equations dominating the Student Journals.
By the way, some of the other groups remember what my predecessor teacher (on his visit to the campus yesterday, as well as last year) taught them about equations like 2x = 8. Usually, we have students divide both sides by 2, but he had the students multiply both sides by 1/2 instead. It's easy to see why he taught it that way -- for an equation like (2/3)x = 8, we have to explain why we multiply both sides by 3/2. With his method, any equation with multiplication is always solved by multiplying by the reciprocal.
In the name of continuity, I'll probably try to use my predecessor's method with these equations. And yesterday, he actually pulled some seventh graders (yes, from another class, as they didn't have my class that day) and gave them a sneak peek at solving equations, using his method. So I'll extend use of his method into next year as well.
In the sixth grade class, learning centers did not go well at all. The students are learning about percent, and so yesterday I gave them questions where calculate a percent of a whole. But subsequent pages in the Student Journals have problems where students are given a percent and a part and are asked to find the whole. The students haven't learned enough where they can solve these problems independently, and so I'm forced to continue the traditional lesson today.
During music break, I sometimes plan songs where one verse is about the sixth grade lesson and another is about the seventh or eighth grade lesson. Technically, today's song qualifies -- I've written in earlier posts about the "Mode, mode, mode the most..." song that also follows the "Row, row, row your boat" tune. And so I sing this song -- but then go to YouTube and play the Square One TV song about percents, as this is actually relevant to the song.
Near the end of class, I attempt to implement the centers. I see some old 100-blocks in my cabinet -- I'm not sure whether these are actually DIDAX manipulatives or something left by a teacher who worked in my room in years past. Anyway, the 100-blocks are relevant to percents -- especially considering that some questions in the Illinois State text direct the students to shade a certain percentage of a square divided into 100 smaller squares.
But the centers quickly fall apart. My Bruin Corps member makes plans to go to lunch with his fellow college students, who are working in classrooms of other grades (who don't all have the same lunch time). They leave 15 minutes before middle school lunch -- which was right around the time I had the centers set up. And so I quickly showed my students how to form 50% on the 100-tiles before having to return to the full class. It's a shame though -- if only I could have had the main lesson completed before today, it might have been helpful to rotate the groups through all the centers.
We'll see whether I can get the centers to work better next time. Tomorrow will be the Dren Quiz on 6's, and I have the luxury of time to check what the students learned during the centers.
This is a two-day post. My next post will be on Monday. Notice that the LAUSD and my charter school observe only President's Day -- unlike either of the schools I subbed at last year which also observe Lincoln's Birthday. So Monday is still a school day for us.
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