Thursday, January 19, 2017

The MTBoS, Week 3: Middle School Math Links (Days 83-84)

This post fulfills Week 3 of the 2017 Blogging Initiative. This topic for this week's Initiative post is "Read and Share":

We will read blog posts by other math educators and then chose one (or many) to write about on our blogs.
You can either:
  1. Write about a single blogpost.  Please leave a comment on their post!
  2. Compile a bunch of blogposts that you love.  Here are some ideas to get you started:
    1. You can pick a bunch of various posts.
    2. You can blog around a theme.  Examples:
      1. A unit you are getting ready to cover
      2. Helpful classroom tools or ideas
      3. People or posts that inspire you
      4. And more and more!!
    3. You can read blogs by people who are in your area and blog about them. Yes, the #MTBoS has a search engine that can show you that!
Notice that I already do this -- link to other teacher blogs on this blog. In fact, after each of my posts in both the 2016 and 2017 Initiatives, my very next post (which I didn't submit to the challenge) was to link to some of the other participants. I didn't make such a post after Week 2, since I'd seen that the Week 3 topic is itself a linkfest.

On the other hand, I don't want to link back to Week 2 posts, since you (the readers of the Initiative) have already seen those. Instead, I link back to some of the participants of the other challenge that's going on now -- Tina Cardone's "Day in the Life" challenge.

No, there is no Cardone participant whose monthly posting day is today, the 19th. So instead, I'll follow suggestion #2 and blog around the following theme:

Middle School Blogs

It's no secret that most MTBoS bloggers are high school teachers. This makes sense, as many of those who currently teach middle school math don't even think of themselves as math teachers. (For example, the middle school math and science teacher at our sister charter school is in fact a natural kindergarten teacher.) So they are less likely to participate in something like the MTBoS.

But I found that several middle school teachers were participating in Cardone's project. And so in today's post, I'll link to these teachers. In each case, I begin with the number indicating that teacher's monthly posting day, and then a link first to the blog itself, and to the most recent "Day in the Life" post, which could be a December or January post. (The date on each post might not necessarily be the monthly posting date as we were to post the last day before, and first day, after winter break.)

6. Dawneen Zabinske's blog: http://mszmathmess.blogspot.com/
Her January 6th post:
http://mszmathmess.blogspot.com/2017/01/day-in-life-expanded-version-december.html

Ms. Z teaches sixth and seventh grades in South Carolina. Here's how she describes her blog:

This blog chronicles my journey as a middle school math teacher at a magnet school that is centered around a military theme. Mathematical Mess represents the chaos of mathematical thinking (and sometimes my classroom as we strive to be more creative in problem solving and critical thinking).

11. Bernadette Scheetz's blog: http://random-ah-ha-moments.blogspot.com/
Her January 11th post: http://random-ah-ha-moments.blogspot.com/2017/01/ditlife-11117.html

Scheetz teaches sixth and seventh grades in Maryland. One thing I notice in her January 11th post is that she often divides her class into "target groups" for more directed instruction. She writes that some of these groups are reviewing fractions or basic skills. This is something I need to work on in my own classes.

13. Kit Golan's blog: https://teachdomore.wordpress.com/
His December 13th post: https://teachdomore.wordpress.com/2016/12/13/whyistay-mfaproud/

Golan teaches sixth and seventh grades in New York. Here's how he describes his blog:

After my fifth year of teaching 8th grade math, I’m transferring schools and I’m going to be teaching 6th and 7th graders. I’m excited for the change in content/curriculum, and I’m hoping the switch will provide me an opportunity to innovate and revisit some of the things I’ve done in the past and consider how to do them better in the future.

15. Kathy Howe's blog: https://mathyesyoucan.wordpress.com/
Her First Day After Christmas Break post: 
https://mathyesyoucan.wordpress.com/2017/01/06/first-day-after-christmas-break/

Howe teaches sixth and seventh grades in Texas. Here's how she describes her blog:

My name is Kathy Howe.  I’ve taught Earth Science, Physical Science, Chemistry, Algebra, Pre-Algebra, and general math.  Right now I’m teaching general math and pre-algebra to sixth and seventh graders at a private school in Texas.

17. Mariam Brunner's blog: https://mbrunnermath.wordpress.com/
Her December 17th post: 
https://mbrunnermath.wordpress.com/2016/12/28/ditlife-december-17-2016/

Brunner teaches sixth grade in Georgia. I choose not to mention her "About Me" blurb, despite providing it to others, because she links to both her school and her church, and I don't want to reblog such personal information. Instead, I'll write about the project she describes in her December 17th post -- sixth graders learn all about financial literacy.

22. Jonathan Newman's blog: https://hilbertshotel.wordpress.com/
His November 22nd post: 
https://hilbertshotel.wordpress.com/2016/11/22/ditl-the-last-day-before-thankgiving/

Newman teaches eighth grade in Maryland -- yes, the first eighth grade teacher. on the list. Again I omit his "About Me" blurb since he actually links to his school website. Instead I mention that this post doubles as his "last day before Thanksgiving" post (the Tuesday before the holiday, which for personal reasons I call "Floyd Thursby Day"). His students take Benchmark Tests all day.

23. Alexandra Otto's blog: https://ottographblog.wordpress.com/
Her November 23rd post: 
https://ottographblog.wordpress.com/2016/11/30/ditlife-of-a-math-teacher-november-23/

Otto teaches sixth grade in Alaska. In this post, it's the day after Floyd Thursby Day, and there is no school that day. Instead, she writes about some conversations she has on her day off, when she tells other adults that she's a math teacher. Some of them have strong opinions of both math class in general and Common Core math in particular.

30. Kevin Cormier's blog: http://run-the-numbers.blogspot.com/
His December 30th post: 
http://run-the-numbers.blogspot.com/2016/12/relationships-beyond-classroom.html

Cormier teaches seventh and eighth grades in Massachusetts. This blog was a bit difficult to find for me, since Cardone provided us with an outdated link. Well, this post obviously occurs during winter break, so instead he writes about a former student of his that he meets that day. Now a college student, she tells Cormier about the ups and downs (too many) in the intervening years,

Before Cardone's project, the only middle school blog I knew was Fawn Nguyen's:

http://fawnnguyen.com/
http://fawnnguyen.com/these-twenty-things/

Nguyen is one of the better-known members of the MTBoS, so she needs no introduction. She teaches sixth and eighth grades right hear in my home state of California.

For once, the Week 3 prompt this year contains an image:


I used this search engine to find MTBoS results for the movie Hidden Figures, since our school went on a field trip to see the movie yesterday. (One of the posters I mentioned above, Mariam Brunner, watched the movie on a snow day and blogged about it.)

The first result is Max Ray's blog:

http://mathforum.org/blogs/max/
http://mathforum.org/blogs/max/a-hidden-figures-lesson-plan/

Max Ray is not a teacher. Here's how he describes his blog:

Hey, I’m Max. I work and blog at the Math Forum at Drexel University. My title is “Professional Collaboration Facilitator.” So what do I actually do?
  • I visit schools and teachers, observe, coach, co-teach and model lessons, mostly about teaching problem-solving skills, and teaching content through problem-solving.

In this link, Ray mentions a game students can play after watching the movie. I'd like to say that I spent today, the day after the field trip, playing Ray's game. Unfortunately, it was a day that was filled with arguments, with both seventh and eighth graders wondering why our school don't have a real science teacher -- and what I, as the "STEM" teacher, am doing and not doing to teach enough science this year. There were also complaints from all three grades about the new homework system, in which we are required to have students complete the homework online!

Here is today's Pappas problem:

361^(1/2) = x

The answer is the square root of 361, or 19 -- and today's date is the nineteenth.

This is a two-day post, and my day off from posting is Friday. (Good -- that will allow me to avoid politics in this post!) My next personal post is on Monday, and there is one week left in the 2017 Blogging Initiative.

Wednesday, January 18, 2017

A Field Trip Day (Day 82)

This post fulfills my monthly requirement for Tina Cardone's "Day in the Life" project. My monthly posting day is today, the 18th, and for once, it's not a weekend or holiday break.

But today is, in fact, a field trip day. You may recall our first field trip from my September monthly post -- my posting date was a Sunday, and the trip to the LA Country Fair was two days earlier. So that post was pure reflection post, but as the field trip occurred on the last school day before the post, it figured prominently in my reflection responses.

Today's field trip on the other hand, occurs on the actual 18th of the month itself. I could say that today, just like the PD Day on November 18th, is also not a real school day, and so I should just answer reflection questions. But instead, I think I'll actually do a "Day in the Life" for today, since I do actually interact with students. I'm sure Cardone didn't have a field trip day in mind when she came up with the project, but how could I've known there'd be a field trip on the 18th of a month?

The field trip is to see the movie Hidden Figures. I've already watched the movie on the 6th, the day it was released -- and in fact I blogged about the movie that day. I wrote that day that it would be a good idea for our students to watch it, and voila! That's what they watch today.

It's still January and the period of Disillusionment, but how can I be disillusioned on a day when my students are watching a movie? Actually, my disillusionment today has nothing to do with anything the students do.

7:45 -- I arrive at my school.

8:00 -- I report to the playground, where many students are beginning to arrive. The students are told to gather in a circle for the flag salute.

8:20 -- We don't even bother to send the students to any class. Instead, the students sit on the benches while we teachers check their permission slips. Students are required to wear uniforms on the trip, but many of them aren't wearing them. They are required to change into their uniforms or call their parents to bring their uniforms to school.

9:30 -- The fifth through eighth graders at our K-8 charter school have boarded the buses, and we are now on our way to the theater.

10:00 -- We arrive at the ArcLight movie theater in Culver City. We are actually not that far from where the TV shows Jeopardy and Wheel of Fortune are taped, and I tell the students this. Many of the students stand in line to purchase popcorn.

10:30 -- The movie begins. I wrote a full review of the movie in my January 6th post. I'll repeat parts of it here for the sake of Cardone and her readers -- and I'll add in a few student reactions as well. As this review may contain SPOILERS, those of you who haven't seen the movie yet may prefer to sjip the rest of this post.

The protagonist is Katherine Johnson (nee Goble), a mathematician and scientist. She is a real person, and in fact she's still alive -- she turned 98 just after the trailer was first released. We first meet the young Katherine as she is growing up in West Virginia. She is very smart, especially in math, but she can't attend her local high school because she is black. So a high school for African-Americans contacts her family to invite the girl to attend. Her parents are shocked, because she's just getting ready to complete the sixth grade. But the administrators are impressed when they see Katherine solve a complicated algebra problem on the board. As a math teacher, I can tell you that all the math in the movie appears to be genuine. Katherine solves a quartic, or fourth-degree, equation that has already been factored into two quadratics. The girl explains how she used the Zero Product Property to find all four solutions.

The scene jumps to the early 1960's. The now middle-aged Katherine is riding in a car with her two companions, Dorothy and Mary, when the car breaks down. A police car arrives on the scene, and the cop is impressed when he finds out that the three women work for NASA. This is right after the Soviet launch of Sputnik, and thus the Americans are now working hard on their own launch of a space capsule.

Naturally, Katherine faces several challenges due to both her gender and her race. She's assigned to assist her white coworker Paul, who resents her so much that doesn't even want to let her drink from the coffeepot. My own students often ask to go to the restroom during class, and so does Katherine during her work -- but the nearest colored bathroom require her to walk a full mile round trip, in high heels! Unlike my students, though, Katherine carries her work with her. Mr. Harrison is annoyed when she has to leave for forty minutes at a time.

At this point, Runnin', a Pharrell Williams song, plays, and one of my students recognizes it -- from yesterday's music break. I sang its first verse as my song of the day.

We also learn a little more about Katherine's family. She is a widow who has to raise three daughters with only her own mother to help out. After NASA learns that a Russian, Yuri Gagarin, has orbited the earth, Katherine and the others must spend long hours working away from their families. Despite this, she meets a new guy, Colonel Jim Johnson, whom she eventually marries. Jim's ring comes from his parents, whose marriage lasted 52 years. It's revealed that as of 2016, the colonel is also still alive, and the couple has just celebrated their 56th wedding anniversary.

At this point, a few of my students hoot and holler as Katherine and Jim share their first very passionate kiss.

The climax of the movie is when astronaut John Glenn is set to orbit the earth. The engineers must calculate the "go/no go" point where the space capsule would reenter earth's atmosphere. Glenn is worried that the calculations are incorrect, and so NASA calls in the only mathematician whom he trusts to find the exact point of reentry -- Katherine. Glenn is launched into space, and he's supposed to orbit the earth seven times, but instead orbits it only thrice. He's afraid that he will burn up upon reentry, but with the help of Katherine and the other engineers, his capsule safely lands in the water near the Bahamas. By the way, the real John Glenn fell short of seeing his depiction in the movie, as he died about a month ago.

As a math teacher, I enjoyed this movie greatly! I recognized more actual math in the movie. For example, to calculate the "go/no go" point, I see Katherine multiply a certain number of degrees by pi/180 -- that is, she converted the degrees to radians. And I also liked seeing actual clips from the 1960's of the Friendship 7 capsule, President Kennedy, and Martin Luther King, Jr. Many of the students cheer when they recognize King.

In fact, I loved the movie even better watching it the second time! I like how two fifth graders sitting behind me -- black girls, so they're in the target demographic, pick up on some of the hidden symbolism of the movie that even I missed the first time. The girls notice the scene where Katherine is handed a piece of chalk and asked to calculate the "go/no go" point to impress the white men who are in the room with her. The fifth graders compare it to the opening scene where Katherine is handed a piece of chalk and asked to solve the equation to impress the teachers at her new school.

Of course, both the girls and I notice the more obvious symbolic moments. It's Paul who must run the mile round trip to fetch Katherine when Glenn is about to launch. The fifth graders are upset when Paul never gives Katherine credit for her work, He insists that "computers don't author reports," but after the astronaut's safe landing, he lets her include both their names on the report. And at the end of the movie, Paul is the one serving Katherine coffee.

12:45 -- The movie ends. At our school, this would be lunchtime -- and today it's again lunchtime as my support provider and the fifth grade support provider provide us with pizza and water! I talk to one of my sixth graders. He tells me that this is his first ever visit to a movie theater, and so he definitely enjoys the experience!

1:00 -- The buses arrive to return us to the school.

1:45 -- Wednesdays are Common Planning days at our school. So once the students return to school, they're dismissed -- and the easy part of my day is over. The more difficult part of the day is dealing with the Common Planning meeting, since the topic of the day is the Illinois State math text.

I've alluded to the Illinois State text several times in my "Day in the Life" posts, including back in my August PD day post. That day, I met the person who created some of the projects that actually appear in the STEM text. Well, at today's meeting the actual curriculum developers have flown in all the way from England to discuss the implementation.

You see, the reason that they keep flying in that our school is considered a pilot school for the text, yet we aren't actually the first to adopt it. Another school has already done so -- and its scores on the Common Core tests rose dramatically. And so the administrators keep flying the developers in over and over in order to make sure that our implementation is complete. If our school doesn't show sufficient gains on the test scores, the assumption will be that it's due to the failure of us teachers to implement the curriculum completely.

And so today, all the teachers except those in the middle school who teach English/history are required to give a ten-minute report on what we'll do to implement the Illinois State curriculum. The emphasis is on whether we're including all the extra bells and whistles that are part of the program.

2:30 -- My counterpart -- the middle school math and science teacher at our sister charter school -- presents first. She includes the Illinois State pre-assessment and post-assessments for each unit, but she hasn't given all the STEM projects yet. She's afraid that the first project in the text -- where students are asked to build mousetrap cars -- won't go well.

3:00 -- The dreaded moment has come -- it's now my turn to present. Let me include a little of what I wrote in my written report. Pay special attention to the extra components that I haven't included yet, but am now required to. (Now there's that Disillusionment!)

-- Assessments

Illinois State Level 1 questions will be used for Daily Assessments.
Level 2-3 questions are 50-point quizzes and 100-point tests.


Quizzes and tests will be given on a 3-week rotation as follows: the first week is a Dren Quiz, the second week is a 100-point test covering that week's and the previous week's standard, and the third week is 50-point quiz covering only that week's standards. 

Within each week, here is the daily plan:
Monday: Coding
Tuesday: Illinois State STEM Project
Wednesday: Begin Traditional Content (Illinois State Student Journal)
Thursday: Finish Traditional Content (Illinois State Student Journal)
Friday: Weekly Assessment

Of course, Illinois State daily assessments are given throughout the week.

-- Manipulatives

DIDAX manipulatives can be given the same weeks as the Basic Skills Quiz. It is said that DIDAX is for struggling students, so those who fail the Basic Skills Quiz can use DIDAX in order to reinforce those basic skills.

-- Focus Tutorials

Focus Tutorials are given same weeks as 100-point tests. With at least two standards to be covered, Focus Tutorials can be completed on whiteboards to prepare students for the tests.

-- Die-Cuts

The die-cut can be given same weeks as 50-point quizzes. As of now I don't even know how to use the machine, so hopefully I can figure it out by February 3rd. I've heard that die-cuts can be used for fractions and 6th grade has a fractions lesson then. I also know that die-cuts are to be used for some "art projects." [Note, after I say this, one of the developers shows me how to use the machine.]

-- Centers

I know that with both my support provided and a Bruin Corps member in my room everyday (save Monday, which is for coding), I must divide the class into three centers. I can discuss with the others who exactly will be assigned to each center. We must watch out for behavior issues -- for example, if Bruin Corps arrives late and that group consists of students who don't work well together.

-- Homework

I don't assign the Interactive Homework System directly online for two reasons. First, the students have never been assigned individual TPS passwords. Second, I don't trust them to do the assignments even if they had the passwords -- they'd come up with all sorts of excuses, beginning with "I forgot my TPS password" and going up to "I can't access TPS from home." So instead, I print the Interactive Homework System pages and include them in packets, along with the daily practice workbooks that we were given at the start of the year. [Note, after I say this, the developers tell me that giving the online homework is required, and our director/principal tells me that only two students, a brother and sister, lack Internet access.]

3:30 -- It's our fifth grade teacher's turn to go. Before the presentations, she tells me that neither one of us really has time to complete the report, since we're both on the field trip all day. Still, her lessons meet Illinois State specifications much better than mine, since she incorporates the DIDAX manipulatives, Focus Tutorials, and Die-Cuts into her lessons. Instead of using the daily practice text for homework (since that's not from Illinois State), she uses it as a Warm-Up instead.

4:00 -- After the fourth grade teacher gives the final presentation, the meeting ends. Overall, today was a good day, marred only by my getting a little sick/cold, especially during the meeting time. I go home to type this blog entry.

I obviously don't assign any students any math problems since there are no classes today. But I'll still post the Pappas Question of the Day, written in ASCII:

6 * sqrt(6+sqrt(6+sqrt(6+... = ?

You don't have to be a Katherine to solve this problem. If we denote the square root by x, notice that adding 6 and taking its square root produces itself again, so sqrt(6 + x) = x. Solving this gives x = 3, but we ask for 6x due to the extra factor of six. So the answer is 18 -- and today's date is the 18th.

After the movie, our director/principal gives us a packet for Hidden Figures, which we can discuss with our students. The packet actually comes from the following website:

https://b0f646cfbd7462424f7a-f9758a43fb7c33cc8adda0fd36101899.ssl.cf2.rackcdn.com/teaching-guides/TG-9780062363596.pdf

which I found by following a link from Denise Gaskins -- a teacher whose blog I found during the other MTBoS challenge (the 2017 Blogging Initiative). Unfortunately, this packet is based on the book Hidden Figures, not the movie -- and the book covers so much more than the film. Judging by the questions, we see that the book begins in the 1940's, back when NASA was called "NACA" -- and Katherine doesn't even appear until Chapter 8. The events of the movie all correspond to the second half of the book. Now imagine asking these questions to our students, who of course only watched the movie!

I'll include one of Cardone's special reflection questions today:

4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year.  
First post: What is a goal you have for the year?  
Subsequent posts: What have you been doing to work toward your goal?  How do you feel you are doing?
What if each T set a goal of some sort for the yr that they could reflect on? Then we ask: How have you been working toward your goal?

My goal is to become the ideal classroom manager. Well, yesterday an assistant arrived in my classroom to help me reach that goal. She has experience in all grades K-12 and beyond, and she's already helping me establish some new rules and routines with my sixth graders -- and even using Interactive Modeling (as in the Responsive Classroom training, see my November and December monthly posts) to explain the new rules. For example, she suggests that I hold up two fingers on my right hand and place my left finger on my lips to indicate silence.

The assistant goes to the sister charter school today -- which is just as well, since our school is on a field trip. Tomorrow she may return, and it will be just like my second day of school, where I ask the students to come up with rules (and those rules, of course, failed, hence my need for an assistant),

Tomorrow will be my last post for the week, so it's by default my Week 3 Blogging Initiative post. I point out that my next monthly post will be February 18th -- oops, a Saturday!

Friday, January 13, 2017

The MTBoS, Week 2: Two Important Soft Skills (Days 80-81)

This post is being submitted to the 2017 MTBoS Blogging Initiative. It fulfills the requirements for the Week 2 topic: "Soft Skills."

Before I begin this week's topic, let me announce some good news on this Friday the 13th (that's right, no triskaidekaphobia here). Our school has just announced that we'll all be going on a field trip to the movie theater to watch -- you guessed it -- Hidden Figures. I've already been working on an extra credit assignment to those who see the film, and this field trip gives me the opportunity to extend this assignment to the entire class. I'm hoping that the movie will motivate our students to learn math and science.

Now for today's prompt. The idea comes from Riley Lark, a former teacher who's now a programmer:

I’ve organized a ‘conference’ to focus more specifically on the soft skills we need to be effective teachers.  Not the killer worksheets, or the progressive grading systems, but on the skills of raising children.  This conference is a great opportunity for us to share the way we bring out the shy kids in our classes, handle teasing, build confidence, create opportunities for leadership, and acknowledge the beauty and significance of the blossoming lives for which we are responsible.

Even though Lark hasn't posted in years, the idea of "soft skills" is nonetheless our topic. The challenge is to go to the 2010 online conference and choose one of the links, and then expand upon the ideas mentioned there. I ended up choosing David Cox, since he's a fellow California middle school teacher (who even shares my first name):

http://coxmath.blogspot.com/2010/07/creating-culture-of-questions.html

Cox's post is about the importance of asking questions. He writes:

I learned how to learn when I was in college.  No one told me.  It just happened.  As a teacher I have tried to help this process along a bit for my students because it kinda pissed me off that I spent 14 years in school and no one actually told me, "Learning is about the questions you ask, not the answers."  So that pretty sums up my teaching philosophy.  It hasn't  changed much in 16 years.

Cox tells us that he makes the students learn by avoiding direct answers of their questions. But not all of his students are enamored with his teaching style:

It takes some students quite a while to adapt to my questioning style in class.  I've had kids want to drop my class (especially when I was at the high school) because "he doesn't give me the answers" "he never answers my questions."  It's tough sometimes because kids are resolute.  They'll try to corner you into taking the pencil out of their hand.  The key is consistency.  The more questions I ask, the more willing they are to ask.

I admit that in my middle school classroom, I don't always adhere to Cox's style. Many times, I'm tempted just to give them the answers myself.

But there is one time when I use Cox's "answer a question with a question approach" -- namely when we are working on STEM projects. You see, at our school the math curriculum comes from Illinois State, and the Illinois State text is project-based. Back in October, I even met Dr. Brad Christensen of Illinois State, who told me not to answer any project questions -- in fact, he often says there's no point, as the students won't listen to the answer anyway. Clearly Christensen and Cox share the same attitude towards direct answers to questions.

As it happens, my classes are working on STEM projects today. The sixth graders are doing a project called "Movin' On." Notice that this is officially a math project that extends into science -- the students are to research animals that migrate long distances depending on the season. Then they are to create a chart that displays migration data and a map that shows where the animals migrate.

Cox and Christensen's predictions prove true during this project. Some students ask, "How do we draw the chart?" and complain when I reply, "What does it say in step 1?" Or some of the students choose a bird as their animal to research, and then I point to some words in the text and ask, "What do these words say?" The answer, by the way, is, "Avoid using bird migration." As Cox writes, the key is consistency -- I must keep answering a question with a question every time we do the STEM projects.

In my classes, I often sing songs in order to break-up the monotony of our 80-minute blocks. Today's song is called GCF, since the sixth graders were learning about greatest common factor yesterday:

GCF!
Greatest Common Factor
GCF!
List every factor
GCF!
Circle the ones in common
GCF!
Choose the biggest one

LCM!
Least Common Multiple
LCM!
List some multiples
LCM!
Circle the ones in common
LCM!
Choose the smallest one

I made up the tune as I played it on my guitar. Of course, I couldn't resist the temptation of basing the tune on the actual musical notes G, C, and F.

The seventh graders' project is a classic -- that is, I've done this project a student myself back when I was in either freshman World History or sophomore Health class. I divide the class into two groups -- one of which has only two students, and the other with everyone else. The group with only two students represents the United States. Now the U.S. consumes 25% of all energy in the world, and so I give the two "Americans" two whole energy bars and six to the rest of the "world." Here all the students other than the two lucky Americans complained -- and I don't mind them complaining this time as this is by design. The U.S. not only consumes the most energy per capita, but our country also produces the most waste, represented by the energy bar wrappers.

There is one problem with this project. Some of the energy bars were peanut butter and there's one girl whose throat itches after eating it -- oops! The rule of thumb is to assume that all students are allergic and thus avoid any foods with the most common allergens.

Now in the eighth grade class I take the direct opposite approach from Cox. But first, let me provide some explanation. My small charter school has no middle school science teacher -- instead, I, as the math teacher, must include some science into the lesson. Notice that some STEM projects, like the ones I gave sixth and seventh, already contain some science. But I want to be sure that the eighth graders receive sufficient science content since this is a tested subject here in California.

And so I go to our online software that we use for science, and download a worksheet based on questions that they may see on the state test. The hope is that next week, they can go to the online program itself and answer the questions correctly. The lesson is on the environment, because there is an upcoming science unit that will begin next month. It is called Green Team, and the students will be learning about energy and water conservation.

But then one girl -- the top student in math -- begins to complain. She argues that at the very least, science should be project-based, and so she wants to have some project rather than a worksheet. I assume that she had her hopes up all week when she saw that we'd be doing science, only to be disappointed when she sees the worksheet today. She says that she enjoys the science projects that she performed at her old school, before she transferred to our school over a month ago.

There are several issues at play here. In sixth and seventh grades we have the Illinois State "STEM" projects in math, but "STEM" projects are not actually science projects. At our charter school, there is neither a science teacher nor a specially designated time for science. But at our sister charter, there is an actual science period, even though there's no separate science teacher there either. At our last meeting, the math/science teacher at the other school tells me that there are separate texts published by Illinois State for actual science projects, distinct from the STEM projects. She says that her students enjoy the real science projects more than the STEM projects.

My top student wants to do actual science projects. She isn't satisfied by the STEM projects -- which isn't surprising, since the students at the sister charter feel the same way. Even traditionalists like California middle school teacher Barry Garelick, who disparages math projects (like our STEM projects), acknowledges that science projects are fine:

https://traditionalmath.wordpress.com/2017/01/08/articles-i-never-finished-reading-dept-4/

What isn’t mentioned is that such approach has been the purpose of science labs for years. The difference now, is turning much of instruction–including math classes– into one big science lab.

In the end, we agreed that next week, we'd do one of her favorite projects from last year -- the Edible Cell Model. I decided to change "cell" to "atom," but this is problematic. There is still a debate between California and the federal government regarding whether the state testing will be based on the old California standards or the new Next Generation Science Standards -- and the final decision may still be a month or so away. Teaching the eighth graders the model of an atom makes sense under the California standards, where physical science is the eighth grade focus -- but not under the NGSS, where this is a seventh grade standard. Likewise the model of a cell is taught in the seventh grade under the old standards but sixth grade under the new standards. I fear that I could be having the students do a project on a topic they won't be tested on in May. (There was a similar scuffle between the state and federal governments at the adoption of the Common Core Standards.) But at least this project doesn't waste any class time -- the preparation for the edible models takes place at home.

You may wonder why I didn't just provide time for science projects in the first place. Well, first, if I took our 80-minute blocks for each of the three grades and divided it in half for math and half for science, I'd essentially have six preps. Even my current three preps are a bit daunting for a first-year teacher like myself, so six preps would have been overwhelming. The second is that many science projects require many materials with which I'm not comfortable using, especially considering that I came into teaching thinking that I'd teach math, not science.

In the end, maybe four preps wouldn't have been that much tougher than three -- I count eighth grade science (the tested year) as the fourth prep and let sixth and seventh get any science that happens to fall in a STEM project. And note that my counterpart teacher at our sister charter was originally a kindergarten teacher. If even a kindergarten teacher can handle the middle school science projects, then surely so can I.

OK, by this point I'm rambling, so let's wrap up this post. Hey, I began by talking about the soft skill of asking questions and I ended with a different soft skill, namely listening to the students. They had concerns about the way the class is taught, and I address these concerns.

In fact, today's whole lesson demonstrates why soft skills are so important. I've been trying to develop the soft skills of asking the students questions and listening to what they have to say, but these are still a work in progress. My lack of soft skills means that the students don't like or respect me as much as they would a teacher who already has those skills -- and it shows.

Here's the problem -- some are my eighth graders already say that they don't want to participate in Green Team or watch Hidden Figures. In theory, they should at least be looking to forward to the Green Team, since they will be working on exactly the type of projects that they say I should have more of. But I've only mentioned "Green Team" in conjunction with the worksheets, which they don't want to see more of.

But more importantly, they don't look forward to Green Team or Hidden Figures because they associate those with me -- the teacher they don't like or respect. If it was another teacher with the necessary soft skills to gain their respect, that teacher could make them look forward to Green Team as a project they'll enjoy or be inspired by the Hidden Figures movie. A more respected teacher can say more personal things to the students and have them actually listen to me.

After the Edible Atom project, but before the Green Team project, I may be able to find some projects in the Illinois State science text. Fortunately, I have only one copy of the science text, so I can just Xerox it -- the students may be turned off by the sight of an Illinois State text and assume that it's one of the math projects that they don't like. I can also get projects from the science book that I purchased last week (and mentioned in my Week 1 post). I did buy that book for a reason.

(Speaking of which, I bought one more book from Barnes and Noble today as Educator Appreciation Week draws to a close. It is Euclid in the Rainforest, written in 2005 by Dr. Joseph Mazur, who is a math professor in Vermont. His book discusses the relationship among math, science, and logic.)

Don't forget that I'm still participating in Tina Cardone's "Day in the Life" challenge! Since today is (Friday) the thirteenth ,the participant whose monthly posting date is the 13th is Kit Golan, a fellow middle school teacher:

https://teachdomore.wordpress.com/2016/12/13/whyistay-mfaproud/

Today's math problem can also be used in science, since Venn diagrams can be used to compare tand contrast the traits of, say, two different organisms. (I write it here in ASCII as sets, but pretend that it's a Venn diagram.)

How many elements are in the universe of this Venn diagram?

Universal set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {0, 3, 6, 9, 12}
B = {0, 2, 4, 6, 8, 10, 12}

The answer is 13 -- and today's date is (Friday) the thirteenth.

This is a two-day post. Monday is Martin Luther King Jr, Day and Tuesday is the day I don't post, so my next post will be on Wednesday the 18th. Hey, that's my own monthly posting day for "Day in the Life," and it's also the day of the field trip. That will make for an interesting post indeed.

Thursday, January 12, 2017

Student Journals: Rotations (Day 79)

With so many blogging challenges going on now, today is one of the few posts that isn't part of one of the challenges. And as you know, in most of the non-challenge posts I write during challenge time, I end up linking to other participants. So expect me to mention challenges in every single post I write in January.

In particular, today I'll link to some of the other 2017 Blogging Initiative Posters. But first, let's start with the Pappas Question of the Day:

12 trillion = 12 * 10^?

One trillion is the 12th power of 10. So the answer is 12 -- and today's date is the twelfth. This isn't the actual question I gave today in any class (and you'll see why later on), but I could have given it in my eighth grade class earlier. Notice that this isn't true scientific notation (it should be 1.2 * 10^13), but the Illinois State text mentioned forms like 12 * 10^12 en route to teaching scientific notation.

I need to mention my eighth grade class today, especially since they're learning about transformations on this Common Core Geometry blog. In the end, I decided to delay the science lesson to tomorrow and teach transformations today. The main reason is that today's Bruin Corps member is a molecular biology major. But yesterday, I received a second Bruin Corps member whose major is atmospheric and oceanic sciences. This is more in line with the Green Team, and so I will wait until she's here tomorrow for the eighth grade science lesson.

This means that this week I had three full days to cover the three transformations. On the first two days, the translations and reflections went well, and most students appeared to understand. But I worried as today's lesson approached, because rotations are probably the most difficult of the three transformations for students to understand.

Now keep in mind that I'm using the Student Journals that are part of the Illinois State text. We know that rotations can be centered either at the origin or away from the origin. Rotations centered at the origin have easier formulas -- for example, the rotation of 180 degrees centered at the origin maps the point (x, y) to the point (-x, -y).

But none of the rotations mentioned in the Illinois State text are centered at the origin. Most of the questions direct a student to rotate a line segment around one of its endpoints. This at least makes it a little easier, since every rotation maps its center to itself.

And so here's what I dis today -- on the first page, the students are asked to rotate AB 90 degrees clockwise about point A, The coordinates are A(2, 3) and B(7, 3). I had the students change A to "the origin," and then I show them the 90-degree rotation about the origin. To do this, I had the students the paper 90 degrees counterclockwise -- that is, the opposite direction from the rotation. Then they drew the image A' by going 2 units on the new x-axis and 3 units along the new y-axis. They did the same to find B', and then they restored the paper to its original position. The new segment A'B' now appears to be the clockwise rotation image of AB.

Of course the students are confused by this at first, but in the end, I believe that they're starting to get the hang of this. I like teaching rotations this way because it sets them up nicely to learn the slopes of perpendicular lines later on. By the end of class, I think the most confusion came from changing all the questions in the Illinois State text, which were geared towards the rotation centered at A rather than the origin.

On the second page, I kept the original question intact. This time, the students are asked to rotate a segment 90 degrees around its midpoint rather than an endpoint. But they appeared to figure out quickly that the preimage and image together would form a cross.

At this point, you may be wondering why I didn't just create my own worksheets rather than modify the Illinois State text. (Recall that the worksheets I posted the first two years of the blog are not valid for this lesson as I didn't emphasize the coordinate plan enough.) The reason is that we teachers are required to use the Illinois State material as much as possible.

I must warn you that if you're a traditionalist, you may wish to stop reading this post, since you won't like anything that I'm about to say next. (Hopefully, traditionalists were already scared away by the word "rotations" in the post title, since they don't like transformation geometry in the first place.)

We are one of the first schools to use the Illinois State text. That's why the curriculum developers keep flying in over land and oceans to introduce the program to us. But we're not the very first school to pilot the program. A few other schools used it last year, and supposedly, those schools' scores on the Common Core tests skyrocketed from around 20% to near 80% proficiency. It doesn't matter whether I trust these claims or not -- what matters is that the administrators believe them.

And this was drilled home at yesterday's Common Planning meeting. We (and by "we," I mean the elementary teachers plus myself) have been told, basically, that if our test scores fail to rise by a significant amount this year, it's because we didn't fully implement the Illinois State program. And then next year we'd have to double down on our efforts to stick to the program. (I did warn the traditionalists that they won't like anything in this post!)

Each day, we should begin with an Illinois State "daily assessment," which I can find on the Illinois State website, and I use the projector to show the class. This is why I couldn't use the Pappas question today, since most of the time I'm using Illinois State questions whose answers aren't the date. (Today's question was to define "reflection," and so the answer isn't even a number, much less the date.)

The Illinois State text also provides some "Interactive Homework." Most of the rotation questions are of segments being rotated about an endpoint. I'm now wondering whether it was better for me to keep the first page in the journal intact (since its rotations are also centered at an endpoint) and change the second page to the origin (since rotations centered at a midpoint don't appear in the homework). Of course, I couldn't create my own worksheet since I must use the text.

But there are some poor questions included in the homework as well. One type of question gives students two segments and asks whether a translation, reflection, or rotation maps one segment to the other segment.

Now here's the problem -- the answer usually isn't unique! In particular, if AB and A'B' are segments and there exists a reflection mapping AB to A'B', then there must also be either a translation or a rotation mapping AB to A'B'! Proof: Let m be the mirror of the reflection mapping AB to A'B'. Now, we know by the Segment Symmetry Theorem (found in the U of Chicago text, mentioned during the first two years of the blog) that the reflection image of AB over its own line, AB, is itself. And so we have two mirrors, line AB and m, and reflecting AB first over line AB and then m produces A'B'. This is a composite of reflections mapping AB to A'B'. If line AB is parallel to m, this composite is a translation mapping AB to A'B', otherwise it's a rotation mapping AB to A'B'. QED

Most of the mirrors in these problems are either the coordinate axes themselves or at least parallel to an axis, and most of the rotations are centered at an endpoint of the segment being rotated. So if the segment and its image have a common endpoint, the intended answer is "rotation," even though reflection over the bisector of the angle formed by the two segments also works. In particular, if the segment and its image are parallel, then the intended answer is "translation," even though a reflection may sometimes work as well. (Most of the time it doesn't, since the composite of a translation and a reflection is usually not a reflection, but a glide reflection instead.)

One blatant error gives the students the line x + y = 1 and asks them which one of three given lines is the reflection image of the original line. As it turns out, all three lines are the images of x + y = 1 -- one is the image over the x-axis, one the image over the y-axis, and one the image over y = -x. In fact, we can show that in 2D, there exists a reflection mapping any line to any other line! If the two lines are parallel, the mirror is parallel to both and halfway between them. If the lines intersect, then there are two mirrors possible, each one a bisector of an angle formed by the lines. (This fails in 3D, because the lines could be skew.) Even one of my students figured out that there was no single correct answer to this homework question!

One of the curriculum developers provided us with a list of the "major content" (MC) standards for each grade level -- that is, the standards most likely to be test on the SBAC. And I have a huge problem -- I haven't covered enough of the standards yet, especially not in sixth grade.

The problem is that my pacing plan was to cover one STEM project every two weeks -- and each STEM project is linked to various standards. But too many projects that I've covered link to standards that aren't MC, and some that do link to MC standards are near the end of the STEM text. At the meeting, the administrators told that we must submit to them a new pacing plan to demonstrate how we plan to cover all the MC standards before the SBAC.

As it turns out, in sixth and seventh grades, all of the MC standards are either Ratios and Proportional Thinking, Number Sense, or Expressions and Equations -- none are from the Geometry or Statistics and Probability strands. In fact, in seventh grade this is simple -- every single RP, NS, or EE standard is MC, while again, no Geo or SP standard is MC.

On the other hand, some of the sixth grade NS standards are not MC. To my surprise, decimal division -- after I made such a big deal about it in previous posts -- is not MC, and neither is whole number long division or any decimal arithmetic. The only NS standards that are MC are fraction division and introduction to negative numbers.

In eighth grade, the NS standards are not MC. All of the EE standards are MC, as are most of the Function standards, Eighth grade is the only year with Geometry standards that are MC -- the only one that isn't MC is volume -- and we can see why, since this is the introduction to transformation geometry that is critical to high school Geometry classes.

The big culprit for my failure to cover enough MC standards in time are the first four Learning Modules -- the infamous Unit 0: "Tools for Leaning" projects that are only linked to Mathematical Practices rather than any content standard (much less any MC standards). In fact, there are 15 modules in the eighth grade text (and fewer in the other grades) that are linked to MC. Hey, didn't I say earlier that there's just enough time for 15 projects? Of course, none of these are the "Tools for Learning" projects -- and yet I wasted nearly an entire trimester on them!

So far, I've only covered three modules (numbered 5-7) linked to MC standards. This leaves me with 12 MC modules to cover -- forcing me to speed up to one module per week! Here is the pacing guide that I plan to send to my administrator:

Week of 1/17: Module 8 (MC standards covered: G3, G4, G5)
Week of 1/23: Module 9 (G6, G7, G8)
Week of 1/30: Module 10 (EE7a)
Week of 2/6: Module 11 (SP2 -- not MC, but appears on 2nd Trimester Benchmarks)
Week of 2/21: Module 12 (EE8a, EE8b)
Week of 2/27: Module 13 (EE8c)
Week of 3/6: Module 20 (F3 -- appears on 2nd Trimester Benchmarks)
Week of 3/13: Module 14 (EE5, EE6)
Week of 3/20: Module 15 (EE4)
Week of 3/27: Module 17 (F1)
Week of 4/3: Module 18 (F2)

This leaves us with a little extra time to cover a few more modules before the last Benchmark Test leading up to the SBAC. Notice that Module 16 is skipped -- I unwittingly included EE1 and EE2 during "Tools for Learning," in order to prepare for EE3 in Module 5.

Also, we see that EE7a is included, but not EE7b. The STEM text mentions EE7b very late -- it's in the last two modules, 24 and 25, But those STEM projects are on matrices, which I feel are not appropriate for eighth grade. (I'm glad they're at the end of the text so I don't have to teach them.) So I must sneak in EE7b in somehow. After EE7a is logical, but keep in mind that EE7b (which is on solving multi-step equations with like terms, parentheses, etc.) is much more difficult than EE7a (on solving one- and two-step equations.) As a student teacher, I've seen freshmen struggle with the multi-steppers -- how much more trouble, then, will my eighth graders have? In this case, it's okay for me to bleed EE7b into the following week -- SP2 is only for Benchmarks, not MC, and notice that I put some leeway in around the five-day President's Day weekend.

A typical module week will look like this:

Monday: Coding
Tuesday: STEM Project (however much can be finished in one day)
Wednesday: Student Journals
Thursday: Student Journals
Friday: Quiz or Test, followed by Science

I also have to figure out how the quizzes and tests are going to work out. I'm almost considering going back to my original three-week rotation of Dren Quiz, Regular Quiz, Test (though it won't be staggered among the three grades).

The sixth grade pacing plan looks even worse, since I covered so many standards -- long division, and the current standard (GCF and LCM) -- that are not MC. I'll begin with Learning Modules 8, 9, and 10, then skip to 24 and 25. Recall that Modules 24 and 25 are about water, which is related to the Green Team. I actually had a meeting today with the Green Team leader. She tells me that the Green Team projects should begin in earnest in February, so I schedule Modules 24-25 for those weeks.

In seventh grade, we must skip around immediately -- tomorrow I'll begin Module 14. The only MC module remaining before 14 is 9 -- and since it includes circumference and area of a circle, and we're skipping around anyway, I might as well save it for March, close to Pi Day. Notice that circle measures are not MC, but Module 9 also includes EE6, which is MC.

By the way, you may be wondering about my Algebra I pacing plan with my new eighth grader. Well, she still hasn't been given an IXL account, so I can't start yet. Actually, today would have been a bad day for Algebra I anyway -- for reasons that I choose not to disclose on the blog, some of my seventh graders were in my classroom for the first half of IXL time along with the eighth graders. With over 30 kids in the room, there weren't enough laptops for everyone -- and the class was so noisy that the new girl wouldn't have been able to concentrate on algebra. This at least gives us an extra week for her to be given the IXL account.

Okay, now that I've gotten all of this out of the way, let's see those Blogging Initiative links. As it turns out, there are three fellow middle school teachers participating in the Initiative:

https://matheasyaspi.wordpress.com/2017/01/06/minions-in-math-my-favorite-thing/

Cheryl Leung is a seventh grade teacher. (I couldn't find her state easily.) The Week 1 topic was "My Favorite" -- and her favorite is programming robots! My school doesn't having robots, but programming would fall under the purview of our Monday coding teacher.

https://mnmmath.wordpress.com/2017/01/07/one-of-my-favorites/

Melynee Naegele teaches all three middle school grades (again, state unknown). Her favorite is a "bellringer" activity at the start of each class. I also have "bellringers," and I call them Warm-Ups -- these are either a Pappas date question or an Illinois State question.

http://iamamathteacher.blogspot.com/2017/01/mtbos-2017-blogging-initiative-my.html

Anna Pacura is a New Yorker who teaches all three middle school grades. (Wow, three of us four middle school teachers cover all three grades!) Her favorite consists of online resources. This again highlights the problem I have with Illinois State -- if I try going to online resources (including those on MTBoS), I'm made to feel guilty for not choosing an Illinois State resource instead!

I will make my own 2017 Blogging Initiative post for Week 2 tomorrow.

Tuesday, January 10, 2017

A California "Snow" Day? (Days 77-78)

This post is being submitted to Tina Cardone's "Day in the Life" project. It fulfills the requirement for the special day "after Christmas break," since due to our three-week winter break plus an extra day for PD, today was the first day back for the students.

But before I begin, let me explain something about California weather. You see, another one of Cardone's special days to post is "Snow day." Now as it turns out, it almost never snows here in the city of Los Angeles. The closest snow is in the mountains. Some cities in the northern part of our state, such as San Francisco, receive the occasional snow flurry.

I'm actually not quite sure what Cardone means by a "snow day" anyway. She could mean a day on which a blizzard or nor'easter cancels school completely -- meaning that the resulting post describes not interactions with students, but what the teacher does at home once the school is shut down. Or Cardone could mean a day on which the school is still open, but there are enough flurries to affect school in some way, such as a late start or the cancellation of outdoor activities.

Here in California, the closest we get to a "snow day" is a rainy day. So far this season, there hasn't been much rain here. It actually started to rain more in mid-December -- and it was right on first day of winter break, so the weather hasn't really affected any days of school so far.

My original plan was to submit a rainy day and claim it as the closest I'll ever get to a "snow day" here in California. I was hoping to post a rainy day in February or March, since my regular posting day of the 18th falls on the weekend in those months. But it's definitely raining today, and this is a post I'm submitting to the project anyway. And so I'll no longer make an extra post in February or March, as there's nothing about the weather in those months that is significantly different from what is happening today.

Keep the weather in mind as you read today's "Day in the Life" post. Most of the "Disillusionment" I feel today is related to the weather and its effects.

7:45 -- I arrive at my school.

8:00 -- I report to the playground, where many students are beginning to arrive. The students are told not to gather in a circle for the flag salute, but to go straight to the classrooms due to the rain.

8:25 -- My first class, a sixth grade class, begins. As it turns out, two students -- one boy, one girl -- are celebrating birthdays today.

The class is learning prime numbers and GCF. I begin by telling the class that if I am a PRime, then 1 and ME are my only factors -- an idea I got from the fifth grade teacher at our K-8 school. Then I play a short game where students earn participation points for naming primes, one for each digit. So students earn one point each for 3 and 7, two points each for 13 and 17. One student impresses me by giving the three-point answer 113. I trick one girl into giving a four-point answer by asking her to name the new year, since 2017 is prime.

Then I mention a prime that would earn eight points -- 74207281. But this number is nowhere near the largest known prime. That number is the subject of a Numberphile video that I show the class:


This number is 2 to the power of the eight-digit prime I gave earlier, minus 1 -- a special number called a Mersenne prime. This number requires three notebooks to print -- and each notebook contains a ream of paper. It's so huge, yet its only factors are 1 and itself. If one of my students could have come up with that number when I ask for a prime, that student would have earned over 22 million participation points!

Someday, we might discover a prime with 100 million, or even a billion, digits. I tell my students that those primes are worth $150,000 and $250,000 respectively -- not points, but dollars:

https://www.eff.org/awards/coop

Of course, I warn my students that if they find the prime, they'll have to share the prize with the person who wrote the computer program.

9:45 -- My sixth graders leave and my seventh graders arrive. In this class, the students are learning about angles, as well as how to draw a triangle given its three angles. I start out by telling the class about a movie I watched over the weekend, Hidden Figures, whose main theme is that black girls can do math, too. I'm offering extra credit points to anyone who watches the movie, brings me the ticket stub, and answers five questions about the movie. I'm hoping that my students -- especially the black female students -- will watch the movie.

Halfway during class, I give the students a "music break" and I sing a song from Square One TV that's appropriate for this lesson, "Angle Dance":


This is one of the oldest videos on YouTube -- in fact, tomorrow will mark 11 years since it was uploaded there! I do not play this video in class. but instead I sing and dance it myself. I find that the students enjoy the songs when I sing them much more than when I play them on YouTube. Still, I post the lyrics to the song here, courtesy Barry Carter:

http://wordpress.barrycarter.org/index.php/2011/06/07/square-one-tv-more-lyrics/#.WHW0BxsrKUk

Angle Dance

Lead vocals by Larry Cedar

Featured vocals by Reg E. Cathey

The following song includes graphic descriptions of obtuse and acute angles.
Viewers who might be offended by this subject matter should not view this program.
I know all the angles
Angle Dancing’s the latest fad
Make two lines meet, add a throbbing beat
The results’ll drive you mad
If you learn all the angles
You can dance to my angle song
To start bend your knees forty-five degrees
Everybody crawl along
Angle Dance, Angle Dance
Find the point where two lines merge
Angle Dance, Angle Dance
Come, let’s make our paths converge
Once you know all the angles
A two-person square’s a breeze
It’s quite cut-and-dried; stretch one arm to the side
Raise the other one ninety degrees
Next hang a friend from the ceiling
If he loves you I know he won’t care
Grasp his hands real tight, get those angles right
There you’ve done it; you’ve made a square
Angle Dance, Angle Dance
Help me measure these angles please
Angle Dance, Angle Dance
We’re all doing it by degrees
Angle Dance, Angle Dance
Make a circular turn on your toe
Angle Dance, Angle Dance
In degrees spin three six zero
If you try you can make any angle
If you don’t there’s no excuse
This little beaut is called acute
And this wide one is obtuse
Now I’ve taught you the angles
You’re Angle Dancing hip
And if you’re inclined, you can go out and find
A spatial relationship
Angle Dance, Angle Dance
Come and join me, hun
Angle Dance, Angle Dance
Have some geometric fun
Angle Dance, Angle Dance
Let’s hope our math’s correct
Angle Dance, Angle Dance
Gee it’s great when lines connect
(Fade out, repeating last refrain)
I offer the students a participation point for dancing along with the song. Several students take me up on my offer, including two black girls -- the target demographic of Hidden Figures.

11:05 -- My seventh graders leave for nutrition. It is raining outside, and I tell the students that they my stay inside my room for the break, but they decide to go out anyway.

11:25 -- My eighth grade class arrives. I begin the class the same way I start all my classes, with a Warm-Up question, which I form from the digits of the new year:

Question: 2 + 0 + 1 + 7 = ?

The answer is 10 -- and of course today is the 10th.

11:35 -- The students are now learning about translations, rotations, and reflections. These are at the heart of the new transformation geometry that is taught under Common Core. The name of my blog is "Common Core Geometry" because for the two years before I became a full-time teacher, I devoted most of my blog posts to these transformations and how they affect the way eighth grade and high school Geometry are taught.

Of these three, translations are the easiest to understand, so I begin with these. Working from the Illinois State text, students are given a line segment and a direction and they are to graph the image.

12:00 -- A seventh grade boy and his sixth grade sister arrive in my classroom. As it turns out, they are leaving to go to a different school. The boy wants to join a middle school football team but our school doesn't offer competitive sports.

12:15 -- At this point, the students are now working on questions where they are given a preimage and image and they are to give the translation mapping one to the other. The only trouble is when students miscount the number of steps -- otherwise they do well with this lesson.

12:35 -- This is a good time to end the period with an Exit Pass. Students redo one of the translation problems from the text:

What translation maps y=6 to y=-6? (Answer: 12 units down)
12:45 -- My eighth grade class goes out to lunch. At this point, we actually require the students to go right back to my room to eat lunch, rather than let them stay outside again.

1:00 -- The dean comes in to explain why lunch must be in the classroom. He asks, what would happen if a student gets sick and must go to the doctor? The parents would complain to the school for letting the child go outdoors in the rain. (Note to non-Californians -- I know that in other states it rains so often that parents and teachers let the children play in the rain.)

During this time, I receive an email from the Green Team. (I explained what the Green Team is in my November and December "Day in the Life posts.) The leader of the program wants to meet with both the fifth grade teacher and me to discuss implementation of the program. The two of us look forward to our students learning about energy, water, and science!

1:10 -- A girl takes out her cell phone -- which is forbidden at our school, even at lunch. She tells me that she's using it to look up movie times, and so I inform her that she can use the phone only if she's looking up times for Hidden Figures, not Sing.
1:25 -- My sixth grade class returns for a special "Math Intervention" class. There is special software for this class, IXL. But first, I let the students sign up for the Green Team online. By doing so, they will get a T-shirt when the program leader arrives on Thursday. Afterwards, they may complete any sixth grade math lesson on IXL.

2:25 -- My support staff member is also in charge of P.E. for sixth grade. Of course, P.E. is cancelled, and so she shows the students the movie Good Burger in my classroom.

3:20 -- After school, all of the middle school teachers plus the fifth grade teacher (at our K-8 school) gather in the classroom of the history teacher. We discuss various things -- Green Team, the two students who are moving away, and the cancellation of music tomorrow due to the injury sustained by the music teacher.

3:50 -- We receive an email informing us that tomorrow's Common Planning meeting will be held at our sister charter school. The topic of discussion is the Illinois State text -- which means that the curriculum developers are flying in all the way from England.

4:00 -- I go home for the day and head for my computer to type up this blog entry.

This concludes my "Day in the Life" post for both "After Christmas break" and, um, "Snow day." My next monthly post is scheduled for Wednesday, January 18th. Since that will be a school day, let me squeeze in one of Cardone's special Reflection Questions into this post:

3) We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

This is followed by two sub-questions:

How did someone help you today?
Describe a relational moment you had with a student/admin/teacher/support staff today.

And here are my answers:

1. Several people helped me today. My support staff member and Bruin Corps member (which I explain in my Day Before Thanksgiving DITL post) helped me keep the class under control and allow me to assist other students with the work.

I also had to ask the English teacher next door for several things -- first the paper telling us what we're supposed to say at the morning circle (as I was the one to lead the circle today before it started to rain), then a projector because the sound stopped working when we tried to play Good Burger (though it was working fine for the Numberphile video earlier), and then some scotch tape (so I could tape up a poster of Martin Luther King, Jr., whose holiday is next week). All of this is after I had to borrow her laptop yesterday during PD, since I'd forgotten my charger.

2. In previous posts, I wrote that I yell too much at my students. Today I tried to avoid yelling and worked at establishing a more respectful relationship. When a girl told me that she got sick during winter break, I made sure that I looked her in the eye before asking "Are you OK now?" The girl who had the cell phone out informed me that she has a friend who goes by the name "Dren." The name "Dren" is short for something else -- and it's not pronounced the same as the word "dren" I use to describe a reverse-nerd who doesn't know basic math! And so I asked her more about her friend.

I've also gave high-fives to my students as they enter the room -- quickly today, though, so that they aren't stuck in the rain -- to welcome them back. I wished my students a "Happy Birthday" and tried to call on those students so they could earn extra points on their special day. (The girl I let give the prime 2017 celebrated her birthday yesterday.) And overall, I tried to do a better job checking for understanding before moving on in the lesson. All of this is to build a relationship with my students that's based on mutual respect, not yelling.

My next weekly post for my other challenge, the MTBoS 2017 Blogging Initiative, is on Friday.

My next personal post (that is, one that's not submitted to a challenge), is on Thursday, since this is a two-day post.

Saturday, January 7, 2017

The MTBoS, Week 1: My Favorite Game

It's time for Week 1 of the 2016 Blogging Initiative. I'm hoping that this is being submitted in time -- I just barely found out that this is due Saturday at "the end of the day." It's already past midnight Eastern Time, but I'm hoping that before midnight Pacific Time still counts as on time, or I've already blown the challenge!

This week's idea comes from Julie Reulbach, a North Carolina high school teacher:

https://exploremtbos.wordpress.com/2017/01/05/new-year-new-blog/

Called a “My Favorite,” it can be something that makes teaching a specific math topic work really well.  It does not have to be a lesson, but can be anything in teaching that you love!  It can also be something that you have blogged or tweeted about before.  Some ideas of favorites that have been shared are:
  • A lesson (or part of one) that went great
  • A game your students love to play
Reulbach lists more options here, but this is the "My Favorite" that I wish to post. I've mentioned My Favorite Game here on the blog a few times before. In the following description, this game is set up for a Geometry lesson on quadrilaterals, but it can be adapted to any lesson.

Oh, and I've noticed that based on the blogs I've glanced at so far, many teachers' "My Favorite" posts involve computer programs. I seem to be behind the times as my activity uses pencil and paper.


(Yes, I know that's the image for the 2016 initiative, but no image for 2017 was provided to us!)

The point of this lesson is to get the students thinking about the properties of special quadrilaterals without worrying about how to prove them. In other words, I want to get the students engaged and thinking about the quadrilateral properties so that they can make the conjectures.

We begin by dividing the class into groups -- say of three or four students. Each group is assigned a worksheet -- or the members can write down answers on a common blank sheet. Then my usual set of ten questions are assigned -- but there are some differences between this and the usual individual worksheets that I post.

First of all, let's look at the first two questions:

1. What is the teacher's __________?

2. What is the teacher's __________?

Beforehand, the teacher fills in the blanks with words -- I'd fill them in with age and weight. I have no problem with giving this much information to the students -- but many people, especially women, are highly sensitive to revealing such personal data. This is why I left blanks in the questions -- so that the teachers fill in the blanks with words that they are comfortable revealing in class.

The teacher asks the question, "What is my age?" (or whatever is in the first blank). The groups signal when they want to answer. The teacher calls upon the group that signaled first to answer -- and since this answer will almost certainly be wrong, the teacher then calls upon another group. When a group finally gives the correct answer, the teacher awards this group a point. (In case you're as curious as the students are about my age, I am currently 35 years old.)

Notice several things about this game so far. The first team to give a correct answer -- and the answers in my version of this activity are numerical so far -- is the one to get the point. And after the first two questions, two groups have one point each -- or possibly one team already has two points -- and the rest have none.

Certainly the groups without points so far are eager to earn one. And so they are faced with the next question in the activity:

3. True or false: the diagonals of a rectangle are always equal in length.

Recall that this activity is all about conjectures. The students have already spent time making conjectures (that is, educated guesses) about the teacher's age and weight -- now it's time to make a conjecture about geometry!

This question serves several purposes. First, the students in groups that are trailing in points -- the same students who would have complained about doing math after the long exam -- now suddenly want to answer a math question because they want to catch up to the leaders. Second, this question is a true-or-false question, so students who might have tuned out if given an open-ended question will want to try this one at least since there are only two possible answers. The students are likely to guess at the answer -- and they're encouraged to do so, because a conjecture is a guess! Third, the conjecture in question involves rectangles -- and students who tend to forget what a rhombus or trapezoid is will still remember what a rectangle is. The only problem word that might be a barrier to participation is diagonal -- so the teacher reminds them that the two diagonals of a rectangle run from a corner to the opposite corner.

In my activity, every third question (that is, the third, sixth, and ninth) is a true-or-false question. I use these to give the students more opportunities to earn points. The teacher allows every group to give an answer of true or false before revealing the answer, and every group that gives the correct answer earns a point. In this way, groups can earn points without worrying about being the fastest group to get the answer.

Of course, the answer to Question 3 here is true. Hopefully, most, if not all, of the groups were able to guess that the diagonals of a rectangle are equal, so that every group is on the scoreboard. Now we move on to the next questions.

4. The diagonals of a square always divide the square into four triangles of __________ size.

5. The diagonals of a kite are always __________.

Now these questions are open-ended, just like the first two questions (but there are no more personal questions -- from now on, all are geometric). So we return to having the groups compete, and only one group will receive the point.

Now we move on to our next true-or-false question:

6. True or false: consecutive angles in a parallelogram are always equal.

And the game continues in this fashion. At the end of this post is a worksheet containing all ten questions plus a Bonus Question.

I'll let the teachers decide what prizes to award the winning team -- or teams, since I prefer to give the reward to the top two groups.

Now returning to the present, let me say that when I first posted this activity last year for the 2016 Initiative, I was just a substitute teacher. Now that I'm a full-time middle school teacher, I had the opportunity to play this game in my class a month ago, on December 7th. Here's how it went, as I first recorded on my blog:


Now I decide to play this game today in all my classes. And you may ask, why today? Well, I actually played this game as a sub one year ago today -- and I did it for one very particular reason.

The answer to the first question "What is the teacher's age?" is 36. That's because today is -- you guessed it (or remembered from last year) -- my 36th birthday! And so I knew that if I was going to play a game which starts with my age, it might as well be on my birthday.

What lessons do I include in today's game? Well, just as in the version of the game I posted as a sub, I want to focus on geometry questions. As it turns out, the game fits the current seventh grade lesson like a glove. Yesterday, the students cut out triangles out of straw, and Illinois State even asks the students to make conjectures about the triangles they created. So it's easy to fit some of those right into the game.

Today is Wednesday -- always a scheduling adventure at our school. For once, we actually follow the same schedule as last week -- but again, it means that I don't see the seventh graders as much as the other grades. I try having them come up with Triangle Inequality as a conjecture. A few of them are able to get on the right track, especially after I give them the hint (or "lead them by the nose").


For eighth grade, I notice that the STEM project mentions the measures of angles that are vertical, adjacent, corresponding, and so on. So I play the game using these conjectures. One big problem is that some students can't use a protractor correctly, so many don't arrive at the conjecture that vertical angles have the same measure. (Actually, the seventh graders also had to conjecture Triangle Sum, but I don't even try to reach that conjecture, knowing that if the eighth graders won't use the protractor correctly, neither will the seventh graders.)

Meanwhile, for sixth grade, the animals project ultimately relates to guessing how much room animals need, so it fits into the game as well. They are learning about how to find the dimensions of a rectangle given its area -- that is, factoring.

I like this game as a sub because it gives the students something to do. But if I use it in the regular classroom, it might be better to do some preparation. Once again, I just took the STEM project and added my own "What is the teacher's age?" questions. But instead, I could have come up with some questions such as just measuring random given angles. If I award points in the game, then the students should be motivated to find them. Then after that I segue to finding specific angles such as vertical angles or those of a triangle. That should lead them to make the conjectures.

So as you can see, my game works best for discovery or conjecture lessons to begin a new unit. I found out the hard way that it doesn't always work well for review. Groups with smart yet talkative students end up dominating the game, while quiet students who need extra help fall behind. In this case, it may be helpful to award extra points for behavior. Therefore, this is "My Favorite" lesson for introducing a new topic.

For those who have come to read my 2017 Blogging Initiative post, thanks! I'd like to inform you that there's another active MTBoS challenge, Tina Cardone's "Day in the Life," and I'm participating in that challenge too! Here is a link to Cardone's website explaining what "Day in the Life" is:

http://drawingonmath.blogspot.com/2016/08/day-in-life-book-plan.html

As today's the 7th, here's a link to Brianne Beebe, the blogger whose monthly posting date is the 7th:

http://busybeebe.blogspot.com/2017/01/january-7-2017-monthly-post-ditl.html

(And yes, Beebe is also participating in the 2017 Blogging Initiative!)

My own monthly posting date is the 18th, and here's a link to my December 18th post:

http://commoncoregeometry.blogspot.com/2016/12/mtbos-day-in-life-post-december.html

My next post will be on January 10th -- that's not my posting date, but it's our first day back from winter break and Cardone wants us to post on special days, too.

This week, Barnes and Noble is having another Educator Appreciation Week, which means discounts for us teachers. Since I teach both math and science, today I purchased a science book, STEM to Story: Enthralling and Effective Lesson Plans for Grades 5-8. It is published by 826 National and edited by Jennifer Craig. I hope I'll be able to find some ideas for science activities in this book.

Finally, I conclude this post with a math problem:

sin 97 degrees = cos theta

As cosine is sine shifted 90 degrees left, the answer is 7 degrees -- and today's date is the seventh.