Tuesday, August 30, 2016

Learning Module 1: The Need for Speed (Days 11-12)

Tomorrow is my scheduled day off from blogging. This means that today will be my final post of the Blaugust challenge. And here is my last Blaugust prompt:

30. Theme song for the year? like your personal fight song?

Well, I've posted several songs during Blaugust, but none of them I'd consider to be a theme song for the whole year. Actually, maybe I could call the "Dren Song" and "Count on It" theme songs for the year -- both of them reflect the main idea that the students should learn math to be successful in life, but one of those is a song I wrote myself, while the other comes from Square One TV. These aren't songs that you can hear on the radio though.

Today we finally begin in the textbook. Learning Module 1 of the Illinois State Text is called "The Need for Speed." As the title implies, this module is all about measuring speed and other rates.

I've written about the Illinois State text in numerous posts over the last few months, but now it's time to take a closer look because we're actually starting the text. Recall that the first four modules are identical for all three middle school grades, as part of "Tools for Learning," or Unit 0 of the text.

The Illinois State text uses Project-Based Learning. (If you're a traditionalist, you might wish to stop reading this post right now.) The main project for Learning Module 1 is to build a mousetrap car and perform experiments to measure its speed as it travels down an inclined plane (formed using a board and a stack of books). By the way, it's called a "mousetrap car" because the miniature car really is propelled by a rat catcher.

But there are several problems as our class begins the project. First of all, there aren't nearly enough mousetraps to go around. There are nearly 80 students in my three classes (as I said above, this project appears in all three grades) and each group of four -- maybe five -- students is supposed to have a mousetrap car. There are definitely enough kits for the eighth graders and possibly for one of the other grades. It's difficult to get more kits because we must order them from Illinois State, which in turn obtains the items from England!

Not only that, but there aren't even textbooks to go around! As of now, I have only half the texts I need for the sixth and seventh grades. An order has been placed for the missing texts, but that order has yet to arrive.

So today the eighth graders attempt to construct their mousetraps cars. The instructions provided by Illinois State are a bit confusing for us -- we are supposed to use "rubber bands" to build them, yet we see nothing like rubber bands anywhere inside the kit. Still, we are able to put something together that looks like a mousetrap car.

I don't use my cell phone camera that often, but I just have to show pictures of the cars so far. This also fulfills a promise I made to Shelli, the leader of the Blaugust challenge -- by the end of this month, I would show picture from my classroom, and here it is. In the background, you can see the "Let's Talk" graphic I got from Shelli's website:

The hope is that tomorrow, the eighth graders will finish the mousetrap cars and start rolling them down a ramp in order to measure their speed. I might allow another grade to construct the cars -- probably sixth grade, as due to our confusing Common Planning schedule, seventh graders don't have STEM class on Wednesdays.

Here is the song that I played today in class:

The Need for Speed:

Life is full of patterns.
They show us the way.
School starts at the same
Time everyday.
The need for speed
To tell us every time
We can go how far
When we build a better mousetrap...
Mousetrap car!

Life is full of patterns.
Circumference follows patterns.
We can use math
To learn about patterns.
The need for speed
To tell us just how fast
We can be a star
When we build a better mousetrap...
Mousetrap car!

Looking at this song again, perhaps in a way this really is my theme song for the year! I actually created the lyrics from the introduction to this project in the Illinois State text. But in a way, it does summarize the theme that math is about patterns -- some of which involve measuring speed, time, and distance (including the distance around a circle).

But don't let the traditionalists Barry Garelick and SteveH hear that math is about patterns! Yesterday Garelick wrote a post criticizing that idea:


Now let's wrap up Blaugust with another visit to some other math bloggers! In creating Blaugust, Shelli challenged us to blog at least ten times this month. Well, I blogged eleven times, so yes, I did one-up her goal. Of course, she also said that we should try to blog everyday. I don't believe that anyone actually blogged all 31 days, but here's one teacher who came close:


Beth Ferguson calls herself "Algebra's Friend," so it figures she's an Algebra I or II teacher. She blogged 27 times during the month (and that doesn't include August 31st, so there's a great chance she can make it to 28). In her most recent post, she includes a link to a middle school math activity called "The Magic Circle":


During Blaugust, I was able to find another middle school math teacher, Jami Danielle, a sixth grade teacher in West Virginia:


In her most recent post, Jami Danielle has her students create a foldable about the eight mathematical practices found in Common Core (or the Mountain State's current version of them, as she explains):


By the way, I haven't had the opportunity yet to use foldables in my own classroom. It's possible that I might use them when we've finished the project and are ready for traditional math problems.

Before Blaugust ends (since I brought it up earlier this month) let me congratulate the seven American middle/long distance runners who managed to win medals in Rio (most since 1984). And in Little League, Chula Vista won only one game and was eliminated early, so for them it's back to school -- which has been in session since late July!

I enjoyed posting about my first dozen days of school for the Blaugust challenge. My next post will be on Thursday, September 1st.

Monday, August 29, 2016

Introduction to Coding (Day 10)

Here is today's Blaugust topic:

29. What are your best organizational tips?

Well, my school provides every teacher with a green file folder for each student. Within each folder -- hey, wait a minute, this sounds familiar! Oops -- apparently Prompts #19 and #29 are the same! But let's not blame Shelli -- we can all easily make mistakes when keeping track of 50 different prompts!

Speaking of those folders, I did finally obtain the folders, although I'm still a few folders short. So slowly but surely, I'm going to get completely organized.

For today, let's just do the previous Blaugust prompt instead:

28. Professional Growth Goal

This is my first year of teaching -- so my professional growth goal is just to have a successful first year and start to my career. The best way for me to become a better teacher is simply to teach -- until then, I can read books and write blog posts about the theory, but what matters is how I put it in practice in the actual classroom.

On the academic side, I'm learning how to teach to the Common Core Standards. Many of my blog posts so far are all about how to teach the standards, especially in Geometry (including the eighth grade standards relating to geometry). I hope that some of my ideas will be effective in teaching the students these new standards.

On the behavior side, there is still much I need to improve there as well. As I mentioned in my last post, the school dean came in to my eighth grade class last Friday because he saw that these students aren't respecting me as a new teacher. He showed the students a PowerPoint slideshow on the importance of doing well in math and science.

Here in Southern California -- AKA Silicon Beach -- STEM grads can earn six-figure salaries. On the other hand, those without STEM degrees may find themselves unable to stay in their homes due to gentrification. Thus the point of this slideshow is to scare the eighth graders straight. (In fact, one student refused to respect even the dean as she talked during his presentation. He ended up having to call her mother, who came to fetch her.) Nonetheless, I want to improve my classroom management skills so that the students who want to learn can learn and work towards those six-figure salaries.

Due to the dean's slideshow, I didn't play Fraction Fever in class with my eighth graders. I want this blog to reflect accurately what I taught in class, with Grade 8 having priority. Therefore I've edited my last post to remove "Fraction Fever" from the title. I also removed some discussion of what Fraction Fever is from that post, but I kept the Fraction Fever song there because I actually did play it in class, as I had no other song prepared. Expect me to edit posts when I have two day posts -- such as that "Days 8-9" post -- and something unexpected occurs the second day.

In many ways, this is just as well. Fractions and rational numbers are more relevant to Grades 6-7, so at least I played Fraction Fever with my sixth and seventh graders. As for the eighth graders, science is more important, so at least I was able to give the Survival in the Desert activity, which is more relevant to science, to the eighth graders.

But let's get back to those high-paying jobs again. If my students want to be considered for these careers, they need to be successful in math, science, and coding (or computer programming). I provide the instruction in math and science. As it turns out, my school has a coding instructor, and he's present to teach coding to our students every Monday, starting today in fact.

Before I discuss what my school's coding class is like, let's see what the traditionalists have to say about coding. As it turns out, fellow California middle school math teacher Barry Garelick is opposed to teaching coding:


Again, I don't bite the hand that feeds me. I've said that I will quote Garelick when he's writing about the importance of learning math, not when he disagrees with our school's pedagogy. Our school will indeed teach coding, and so I don't cut-and-paste anti-coding statements from Garelick's blog. (Or actually, I should say Garelick and SteveH's blog, since SteveH frequently comments on the blog and indeed, SteveH's comments here are longer than Garelick's original post!) But I will summarize the post here and explain why I disagree with it.

First, SteveH hopes that the coding isn't done in math class. Well, unfortunately for SteveH, coding is indeed done during my math class, albeit taught by a special coding teacher.

Both Garelick and SteveH write about a pictorial language which contains commands for moving forward, turning a few degrees, and lifting the pen up and down. This language sounds very much like LOGO, which I've mentioned several times here on the blog (most recently in March).

Indeed, reflecting on my own coding experience, the first language in which I learned to code was indeed LOGO, back when I was in the first grade. The following year, I learned how to code in BASIC, on the same computer that played Fraction Fever (which was not at school). I believe that LOGO and BASIC are excellent training languages in which young students can learn to code before approaching the more powerful languages (such as Java, the target of the AP Comp Sci test).

SteveH repeats his usual comments that math classes should be focused on getting students to Algebra I in eighth grade and AP Calculus in senior year. But as usual, I counter that many students are going to be turned off by math. They ask questions like "Why do we have to learn this?" and I doubt that they'll accept "You'll need it for AP Calculus" as an acceptable response.

SteveH suggests that coding be taught after school instead of during the school day, because he feels that coding as currently taught in elementary and middle schools doesn't adequately prepare students for AP Comp Sci in high school.

At my school, the coding class varies by grade level. For example, one of the grades will be coding in Scratch, another visual language similar to what Garelick and SteveH are discussing. Since this blog focuses on the eighth graders, I'll tell you that Grade 8 is all about multimedia. The students are surprised when the coding teacher informs them that it takes hours just to create one minute of video!

Coding takes up nearly one hour out of the 80-minute block. This leaves me with only 25-30 minutes for math class. I've decided that this is just enough time to give the students a Warm-Up and a homework packet, with possibly some time for them to start the HW.

At our school, teachers are required to assign homework packets from special Daily Practice books. I notice that while the questions from the problem sets follow the Common Core Standards, they are taken from a mixture of strands through the year. For example, of the five problems on the Monday Week 1 problem set, Question #4 is "In a set of data, the difference between the greatest and least numbers is called the __________" (range), and the next is, "Which pairs of lines are perpendicular?"

Now if I know middle school students, they'll look at these questions and say to themselves, "I don't know the answer to #4, and I don't know what perpendicular means. The teacher never taught us this stuff, so I just won't do any homework at all."

Here is my compromise -- the 1-2-3-4 homework plan. I'll have students answer one question from Monday's set, two from Tuesday's, three from Wednesday's, and four from Thursday's. Then the students turn in the ten problems they answered on Friday. That way, there should always be enough questions the students do understand, and they get a choice. This should increase the likelihood that a student turns in the homework, as I'd much rather see the students answer 10 out of 10 questions than 0 out of 20 questions.

Furthermore, the Warm-Up contains a problem similar to one of the HW questions. For example, Question #1 on the HW is "Which sum is larger, 9,821 + 7,433 or 7,388 + 9,872?" So as a Warm-Up I ask, "Which sum is larger, 17 + 12 or 13 + 15?" This way, students won't be able to say "I don't know what sum means" as an excuse for not doing the homework. Moreover, the numbers are much smaller so that the answer can be 29, since today is the 29th.

For my fourth block of the day, I see the eighth graders again and they will be using the computer again, except that this time it's for Math Intervention. Students will visit a website and answer questions generated by a computer. The results are reported directly to me, so I can keep progress of how much the students are learning.

So far, I have the students work on identifying ratios -- this is fairly easy, but the computer asks increasingly difficult questions as the score approaches 100. My top eighth grader, of course, did exceptionally well. Of course, this is the perfect time for me to give her some Algebra I questions on the computer. The first section is about classifying numbers (rational, irrational, etc.) -- and naturally she does a great job with these questions as well.

Thus ends my computer-filled day.

Thursday, August 25, 2016

Survival in the Desert (Days 8-9)

Here is today's Blaugust topic:

25. What are your go to quotes?

Back in my Father's Day post, I mentioned the quote "If you don't know the answer, at least know where to find it." I consider it to be part of my classroom motto.

I've also quoted the famous MTBoS blogger Sarah Carter, especially with regards to her three function-related mnemonics (Slope Dude, DIX-ROY, and HOY-VUX). She explains these three at the following link:


Actually, according to the following more recent link, DIX-ROY should be DIXI-ROYD, with the extra I and D standing for "independent variable" and "dependent variable":


I probably should use Carter's DIXI-ROYD now, especially since "dependent variable" showed up in one of my eighth grade Benchmark Testing Week questions.

Speaking of which, my students have finished their Benchmark Tests. And so I have two extra days left over for special activities before lessons start in earnest next week. I decided that I wanted some science to break up the math testing, and so I decided to right back to Sarah Carter, especially since now she's teaching science in addition to math:


As for my physical science class, I had to plan an entirely different lesson for Day 1 since almost all of my physical science students are also enrolled in one of my math classes.  

We started the "Survival in the Desert" activity from Kagan's Cooperative Learning book (affiliate link).  Though, a search for this activity on google shows that it is included in numerous books.

I won't post the link to the activity, since you can get it right from Carter's website.

This activity goes well in my eighth grade class -- maybe because it's the smallest class. I divide my 14 students into three groups of four and one group of two. I definitely enjoy the discussions among the groups as they decide which items they wish to rank higher.

The activity doesn't work as well in the larger sixth and seventh grade classes. Many students are loud and fail to listen to my instructions -- which would not be terrible if they follow the steps given on Carter's worksheet, but of course they don't. Common errors include labeling almost every item on the list "1" or "14." Then when I try to explain that they must rank the items, they just go in order, labeling the pistol "1" just because it's first on the list, the animal book "2" because it's the second item, and so on.

Meanwhile, I'll only play Fraction Fever if the students show that they can handle it. Otherwise, I may just convert it into a worksheet. There's also a possibility that our dean will have to come in to speak to my eighth graders.

Fraction Fever is also the inspiration for today's song. I made up the lyrics, but the tune is the intro song from the actual 1980's game (to the best of my memory):

Fraction Fever:

Hey, if you never
Played Fraction Fever
To get in the action
You gotta get the right fraction!

Choose the wrong one and down you fall
(Down you fall!)
Through the hole and that's not all!
(That's not all!)

If you find the right one later
(Right one later!)
You'll go up in the elevator!

When you get to Floor 20
(Floor 20!)
You'll win plenty!

Fraction! Fever!
Fraction! Fever!

My next post will be Monday, August 29th.

Wednesday, August 24, 2016

Benchmark Testing Week, Continued (Day 7)

Here is today's Blaugust topic:

24. What is your focus/theme/mantra for the year and why?  Create and share a notecard for your desk as a reminder.

Actually, my school doesn't have a theme for the year -- it has an aspiration of the month. For the month of August, our aspiration is Commitment:

"A Committed Scholar is responsible, a person of character who lives with integrity, is honest, reliable, and loyal."

And come to think of it, a committed teacher is also a responsible person of character. During my first year of teaching, I definitely want to show that I'm committed to my profession and my students.

The Blaugust prompt asks for a "notecard." Well, here is a sign that all teachers are to post to represent the monthly aspiration. Due to the Disclaimer at the start of the year, the initials of my school have been blacked out:

As Benchmark Testing Week continues, I've seen which students are excelling on the test due to their prior knowledge. One eighth grader in particular is doing very well on the tests. Yesterday, I gave Part Two of my exam, which contains questions from the Functions and Geometry strands of the eighth grade Common Core Standards. The geometry questions were mostly on graphing and transformations -- the cornerstone of eighth grade geometry. I tried to explain what reflections and translations were -- but to my pleasant surprise, this girl had already figured out all of the transformations and graphed them!

As I wrote on the blog earlier, I may attempt to give my top eighth graders some Algebra I -- and in particular, I may do so during the Statistics strand. This girl will be a prime candidate for giving extra Algebra I work. Today, I tell her that if she does well on my Algebra I questions, I will write her a letter of recommendation to her future high school (whichever school that may be) -- to recommend her for Geometry next year.

On the opposite side of the spectrum, some students had trouble just with the graphing -- even without trying to translate the figure. This is another issue that I've mentioned on the blog before -- is it a good idea to attempt teaching transformations without graphing? We've seen that it's not really necessary to perform transformations on the coordinate plane, and in fact, some properties of the plane ultimately depend on transformations.

Meanwhile elsewhere on the MTBoS, fellow middle school teacher Fawn Nguyen posted the "seven deadly sins of teaching":


1. Giving extra credit (especially right at the end of the term).
2. Giving timed multiplication drills.
3. Giving out the equation.
4. Teaching from one source.
5. Talking, talking, you're still talking.
6. Keeping up with the Joneses.
7. Being an a-hole.

Sin #2 is similar to something I plan on doing, via my Dren Quizzes. But as Nguyen explains, the problem is the word "timed." She writes that this perpetuates the myth that faster is smarter. I suppose that Sin #3 is avoided by using a progressive text such as the Illinois State text. Of course, I shouldn't be completely dependent on the Illinois State text, lest I commit Sin #4.

Still, Nguyen's "sins to avoid" are things I'll keep in mind as I begin to teach.

Monday, August 22, 2016

Benchmark Testing Week (Days 5-6)

Here is today's Blaugust topic:

22. Be the Change.. what will you do this year to impact the culture of your school and/or classroom?

Well, I want the culture of my classroom to be one in which every student knows that he or she can be successful in math and science. The first step in establishing this culture is to determine the students' level of previous understanding as part of the current Benchmark Testing Week. Only after I find out what the students already understand can I help them expand their knowledge.

The Benchmark Tests have been provided by Illinois State, since as I've said before, we are currently using the Illinois State text. In the past, I've posted tests and other materials that I've developed on the blog, but in order to avoid copyright issues, I don't post Illinois State material on the blog...

...that is to say, I don't post correct Illinois State material on the blog. I can and will post questions that contain errors -- and I found so many all over the middle school tests.

Most of the sixth grade errors involve the lack of an accompanying picture that contains information necessary to solve the problem. The following are given using the Illinois State Database ID number:

68. 24 science books are shown as what percent of books on a shelf?
a) 10%
b) 15%
c) 20%
d) 50%

79. What is the ratio between fruit and nuts in this chart?
a) 1:2
b) 2:1
c) 1:4
d) 2:4

81. What would the next number of cups and ounces be in the chart?
a) 6 cups, 48 ounces
b) 48 cups, 6 ounces
c) 4 cups, 32 ounces
d) 32 ounces, 4 cups

If you couldn't solve any of the above problems -- don't worry -- neither could I.

32. A student is trying to see if 3:15 is equivalent to 12:60. Complete the missing number and confirm if they are equivalent or not.

a) 55, Yes
b) 60, Yes
c) 60, No

Notice that it's possible to show that 3:15 and 12:60 are equivalent without a picture -- it's only required to "complete the missing number." According to the key, the "missing number" was 60 (most likely, it was to complete a proportion like 3/15 = 12/??). Fortunately, hardly any of my sixth graders tried to mark a) 55 as the answer anyway.

200. The opposite of the opposite of 3 is:
a) 0
b) -3
c) 3

This problem is a classic -- "the opposite of 3" is -3, but "the opposite of the opposite of 3" is +3. I am not surprised that many of the sixth graders (who are new to integers) would be confused and choose b) -3, but I am surprised that Illinois State would give -3 as the correct answer!

On the first day, the eighth grade Benchmark Test contains 32 questions given from the first two strands of the Common Core Standards -- The Number System and Expressions and Equations. And just as with the sixth grade test, the eighth grade test contains errors!

1202. Which of the following is an irrational number?
a) 1/10
b) 1.75
c) 0.001
d) pi

Obviously the correct answer is d) pi -- yet believe it or not, Illinois State gives b) 1.75 as correct!

1262. Evaluate x^3 = 21
a) (+ or -)2
b) 2
c) (+ or -)3
d) 3

First of all, the students aren't supposed to evaluate the equation -- they're to solve it. But much more importantly, Illinois State gives the solutions as d) 3 -- but none of the answers are correct. (And ironically, the very next question on the test asks students to find the cube root of 27.)

The plan is for the eighth graders to answer questions about Functions, Geometry, and Statistics and Probability during the rest of this week. Still, this doesn't give me faith in the Illinois State text when my very first interaction with the text involving correcting numerous errors. (Fortunately, there appears to be no errors with the seventh grade test.)

Going back to my Blaugust prompt -- well, I don't impact the culture of my classroom and convince the students to be successful by handing them tests riddled with errors.

By the way, here is the song that I played for my students:

Benchmark Tests -- by Mr. Walker

Verse 1:
Why do we take Benchmark Tests?
It's the start of the year so let's
See how much we know, know know!

It's much new stuff on Benchmark Tests.
If we don't know it, we take a guess.
We leave none blank, oh no, no, no!

The teacher sees our Benchmark Tests,
Knows what to teach more or less.
That's the way to go, go, go!

This counts as the first verse of this song. I'll write and play the second verse in January for the second Benchmark Test, and the last verse in May for the third Benchmark Test.

This is a song that I made up myself. I mentioned back in my Pi Approximation Day post that I would invent songs by choosing a random number and then assigning digits to each note, as Michael Blake did with pi and a few other irrational constants (not including the "irrational" 1.75, though).

The number I chose at random was:


I decided to use the key of C major. On the guitar, certain other keys are often easier to play, such as G or D major, or if we want to go minor, A or E minor. But for this song, all the chords are easy to play in C major.

I use Michael Blake's trick -- 1 = C major, 2 = D minor, 3 = E minor, 4 = F major, 5 = G major, and Blake uses 0 to denote a rest. This gives the chord progression as:


I then add a melody that seems to fit these chords, and then finally lyrics that fit the melody and describe what the students are doing today and tomorrow -- the Benchmark Tests, of course.

Elsewhere in the MTBoS, I notice that Elissa Miller uses a Benchmark Test system similar to ours, where she gives the same test three times during the year:


We ended the week by taking our end of course exam which will be given again in December and May. I spent my time making answer keys and updating my spreadsheet data.

Lucky her -- she uses a spreadsheet, but we're expected to put our Benchmark Test data into student folders (then again, there's nothing stopping us from placing the data onto a spreadsheet anyway).

Meanwhile, I found something interesting written by Sarah Carter, one of the most famous members of the MTBoS:


Tomorrow's our last PD day before kids start on Monday.  Having kids come in and out of my room helped to make the fact that school is starting soon actually sinking in.  It also reminded me of how much I have missed interacting with my students.  I've enjoyed my break, but I'm ready to get back to teaching some math.  And physical science.  That part is going to be an adventure.

In other words, Sarah Carter -- just like me -- finds herself teaching a science class! She's a high school teacher and I'd thought that something like that would never happen in high school. But, as she explains, she teaches in rural Oklahoma, and so the issues that occur at my small charter school can also happen in small rural high schools like Carter's.

So I'll definitely be looking at Carter's blog more often for hints on teaching science. But here's something on Carter's blog that I'm able to use right away:


I had posted a number line on the wall in my classroom, with the words "forever" printed on either end of the number line. One student asked my why the word "forever" was printed there -- apparently she must be a Buzz Lightyear fan because she thought "infinity and beyond" would make more sense than "forever."

And that very same day, Carter posted Infinity Posters on her blog. So of course I had to put the infinity signs up on my own wall. So far, that student hasn't reacted to them yet, since she was so busy with the Benchmark Tests.

My next post will be on Day 7, which is Wednesday, August 24th.

Friday, August 19, 2016

Drawing in Perspective (Day 4)

This is my "A Day in the Life of..." post for August 18th, the third day of school:

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.

8:25 -- My first class, a seventh grade class, arrives. Today there is a confrontation with one of the seventh graders. She refuses to do her work, then argues with my student support aide, who asks her to leave the room. I am the teacher, so I should have tried to intervene sooner, though it still might not have made much difference. It is only Day 3, but I already know there's one girl I'll need to watch out for this year.

9:45 -- My seventh graders leave and my eighth graders arrive. Throughout the entire first week of school, I am giving the same activities for all three grades. I begin with a warm-up:

What comes next? 2, 4, 6, 8, 10, 12, 14, 16, _____

The answer is 18 -- and of course today is the 18th. Most students answer this one correctly.

9:55 -- The previous day we discussed the classroom rules. Today I pass out Behavior Contracts for all of the students. Each student writes down the rules we agreed to, and then the students take them home for the parents to sign. In this way, each student is to be made accountable for his or her own behavior throughout the year -- and if a parent requests a conference, I can just take out the contract and let the parents know that their child has violated that contract.

10:25 -- I move on to the Music Break. Today I play the Square One TV song "Count on It," another song about the need to learn math.

Here are the lyrics, courtesy the following link:


Count On It

Lead vocals by Larry Cedar

Sooner or later, you’re gonna see some math
You can count on it
Sooner or later, those numbers cross your path
You can count on it
You may be hoping it will go away
But let me tell you, math is here to stay
You can count on it, hoo, yeah
You can count on it
Everywhere you look, they’re measuring the action
You can count on it
Everywhere you look, they’re even using fractions
You can count on it
They’re keeping time, and they’re keeping the score
They draw the line, and they’re running the store
You can count on it, hoo
Yeah, you can count on it
Look at the dial; look at how far
Look at how much; look where we are
Look at the gauge; look at the graph
Check out the numbers; you’ve got the last laugh
‘Cause it ain’t mystery; there’s nothing tough about it
You can count on it, that’s right
Soon you’re gonna see that you couldn’t live without it
You can count on it, hoo
Don’t take a genius or a great magician
To make a pretty good mathematician
You can count on it, hoo, yeah
Yeah, you can count on it, whoo
Oh, you can count on it, whoo
Baby, you can count on it
(fade out over Larry singing skat)
In the video the song is played on saxophones, but the only instruments I'll ever play in class are drums and a guitar. Today I play the song on drums.

10:35 -- Finally, the main lesson is another Opening Activity, on number patterns. In this lesson, students use inductive reasoning to find patterns in sequences of numbers, letters, and names.

My number patterns worksheet is better organized, since I've added two simpler sequences to the top to make the worksheet more inviting. Students enjoy the challenge of trying to be the first person to get a question right to earn the participation point. Question 1 is just the sequence of odd numbers -- similar to the even numbers from the Warm-Up, while Question 5 is the famous Fibonacci sequence.

On this worksheet, I had to help my students out with Exercise 7, which refers to George Washington, John Adams, Thomas Jefferson, and James Madison, so the correct answer is another James (Monroe), another John (Quincy Adams), and then Andrew (Jackson).

Exercise 8 looks similar, but this time it refers to money -- George Washington ($1), Thomas Jefferson ($2), Abe Lincoln ($5), and Alexander Hamilton ($10). So the correct answer is Andrew (Jackson again, $20), Ulysses (Grant, $50), and then it's all about Benjamin (Franklin, $100). I also point out that in ten years, the next name after Alexander won't be Andrew, but Harriet -- as in Harriet Tubman, who will be on the $20 bill soon.

10:55 -- I give the students the following Exit Pass:

I will turn in my Behavior Contract with a...

The answer, of course, is "parent signature." I try to give those with the correct answer a stamp -- except that my stamp pad is missing. I see one student covered in blue ink, and the missing pad is on her desk. Other girls sitting next to her say that she's stolen my stamp pad. But I can already tell that the ink-covered girl isn't very popular with her classmates. She might have taken the pad, but it's possible that the student sitting next to her took it and stamped the poor girl in order to frame her. It is something I will watch out for as the year proceeds.

11:05 -- My eighth graders leave for nutrition.

11:25 -- My sixth grade class arrives. I repeat the same activities as I did with the older students.

12:45 -- My sixth grade class goes out to lunch.

1:25 -- The students dress for P.E. for the first time. Due to a quirk in the schedule, the students get dressed for P.E., yet have one more class to attend before P.E. actually starts!

1:35 -- My eighth grade class returns for a special "Math Intervention" class. Just as with the sixth graders back on the first day of school, there is special software for the class, but I spend the entire period acquainting the students with the laptops, including making sure that the students all have the correct password.

2:35 -- My eighth graders go out to P.E. class.

4:00 -- I go home for the day.

Teachers make a lot of decisions throughout the day. Here is today's Blaugust topic, in which I discuss a decision I made that will help me be organized:

19. What are your best organizational tips?

Well, my school provides every teacher with a green file folder for each student. Within each folder we are to put all of the student's work, beginning with the Behavior Contracts that I mentioned in the previous post, followed by the results of next week's Benchmark Tests. So as you can see, the file contains both academic and behavior information. This way, if a parent asks about a specific student, all the necessary information is right there in the folder.

But I still have some work to do before my file folders are completely organized. You see, I looked into the teacher's desk and saw that there aren't enough folders for every student. I see a filing cabinet that might contain some folders -- except it's locked and I don't have the key -- oops! Hopefully, I'll get organized in my class, eventually. Once that happens, I should have a very strong organized system, especially if I can get into that filing cabinet.

Oh, and here's one more organizational tip -- if you have trays for the students to turn in work, keep it away from the doors so that the wind won't blow papers around. I found that out the hard way in my class today.

Speaking of class, today I gave the last of the opening week activities previously posted on the blog -- Designing Buildings. This is what I wrote earlier about this activity:

And as it turns out, Nguyen covered something similar to this in her class as well:


Nguyen's lesson takes a different approach to drawing three-dimensional figures. For one, the focus on this lesson is on buildings. Her lesson begins by having some buildings already drawn and the students counting the "rooms" and "windows." (As it turns out, one "room" is one cubic unit of volume, and one "window" is one square unit of lateral area.)

I like the way that Nguyen's lesson begins. Unlike the bridge problem, where I wanted to avoid beginning the school year with a problem that's impossible to solve, here we begin with a very solvable problem. The only issue I have is with the second question, because it requires materials. I work from the assumption that most classrooms don't have the blocks and isometric dot paper that Nguyen's classroom has.

(As an aside, notice that cubes drawn on isometric dot paper are definitely not in perspective. This is because, while edges perpendicular on the cube intersect at 120 degrees on the iso dot paper, edges parallel on the cube remain parallel on the paper. Therefore there are no vanishing points.)

Then again, my worksheet is very similar to Nguyen's. On the front side, I gave the same example as she did and the three buildings for the students also come from the Ventura County teacher. I used two of her easier buildings -- A and B -- and the more challenging Building F.

The back side of my worksheet differs slightly from Nguyen's, though. Her worksheet specified the number of rooms and windows and asked the students to draw the buildings. Mine, on the other hand, simply has the students draw four different buildings with eight rooms and then asks them to count the number of windows in each one.

Now that I'm giving this activity in an actual classroom, I don't have any interlocking cubes (which I can only assume means "Lego bricks"), but I did find some small manipulative cubes. There weren't enough for me to give every group eight cubes (as specified in the assignment) -- instead I gave five to each group of sixth graders and seven to each group of seventh graders. (Half the seventh graders were absent because they hadn't satisfied California's 7th grade vaccination requirement.) The eighth grade groups did receive the full set of eight cubes. I believe that having actual blocks certainly helped the students visualize the three-dimensional buildings.

By the way, here are the rules the middle school classes came up with as part of the Rules Posters. At last I'm done discussing the rules here on the blog:

1. Raise your hand
2. Be silent and listen when it's someone else's turn to speak
3. Stay in your seat
4. Keep your hands to yourself
5. Keep the desks free of drawing
6. Treat the books, papers, and any other resources like you would treat your own items
7. Keep your voice at a conversational level
8. Allow the speaker to finish before you raise your hand
9. Speak in a respectful manner
10. Stay on task, work hard, and do your best!

Here I post the same worksheet that I gave in the past, since the only change I made was the number of cubes (which was on the fly).

Wednesday, August 17, 2016

Activity: Number Patterns (Days 2-3)

Remember that now I'm a full-time teacher, I no longer have time to post every school day. My plan is to skip every third day. So I'm posting today, Day 2, but my next post won't be until Day 4. The result is that I should be posting approximately three times every week during the school year -- this week I'm posting Tuesday, Wednesday, and Friday.

Let's begin with the Blaugust prompt for today:

17. The best teacher I ever had was …. because ...

Hey, I just wrote about my favorite teachers at the end of the previous school year! I usually don't like reblogging to satisfy MTBoS challenge prompts, but then again, the following prompt encourages it:

26. Reblog an old post - reflect how you see/use it now?

So let me fulfill both Prompts #17 and #26 by reblogging my favorite teachers. From June 2016:

-- My favorite elementary teacher was my second grade teacher -- who later became my fifth grade teacher as well. She was one of the first to notice that I was good at math, and so she came up with the idea of having a Pre-Algebra teacher from the high school (which went from Grades 7-12 in my district) send me a textbook. As a second-grader I would work on the assignments independently, then my teacher would send my work to the high school before I worked on the next assignment. By the time I reached the fifth grade and was in her class again, she had convinced the high school teacher to send me the textbook for "APA," or Advanced Pre-Algebra.

-- Incidentally, my favorite math teacher was that teacher who sent me the advanced work. I finally met her when I was placed in her Algebra I class in the seventh grade. I was the only seventh grader in a class full of eighth graders, but she made me feel welcome in her class.

-- Just like Fawn Nguyen, I had my favorite history teacher when I was an eighth grader. He was also in charge of the Thespian Club at our school, and so he decided to teach history in a unique way -- he would dress up as a historical figure and lecture as if he were that character. Therefore his lectures were more memorable to the students. A few years ago, he retired from teaching, and many of my classmates held a big party for him.

-- My favorite science teacher was my junior-year teacher. I was an up-and-down student when it came to science -- the first two years of Integrated Science were more biology-leaning and I struggled a little, but the third year had more emphasis on physical science, which is more closely related to my strongest subject, math (as we spent over a month discussing with Kline's book). And so I did very well in this teacher's class -- indeed, she told me that I would finish the whole test in a few minutes and spend the rest of the time making my writing neat, and of course my answers were correct. She wondered why I wasn't enrolled in the magnet program, and I replied that I had moved to my new district as a freshman, while magnet students are recruited in the eighth grade. And so my science teacher convinced the school to admit me to the magnet program as a junior. Even though I was no longer in her class, she was still my most memorable science teacher for this reason.

-- My favorite English teacher was my senior-year teacher -- or to be precise, one of two English teachers I had that year. You see, the magnet program I'd entered a year earlier was a year ahead in English -- that is, junior-level English for neighborhood students was equivalent to sophomore English within the magnet. This meant that I would have to double up on English my senior year in order to graduate from the magnet -- and I didn't look forward to this, since my strongest subject was math, not English. So even though I was the only senior in a class full of juniors, I enjoyed this English teacher's class the most. This teacher allowed us to be creative in our writing -- I remember that for extra-credit, I wrote parodies of the literature we were reading, except with my friends and me as the characters. There was also an essay contest for seniors in which we were to write about a journey we had taken -- I wasn't going to participate, except that the junior English teacher whose class I had to take decided to assign the same topic for an in-class grade! I was in the unique position of writing an essay for class and submitting the same essay to the contest.  So I wrote about my journey through my education (much of which I just wrote about in this post) -- and won $200.

When I reflect upon my favorite teachers, I notice that they have some traits in common. Two of my teachers taught subjects I didn't enjoy, English and history -- and made them enjoyable by presenting them in a unique way. The other teachers taught my stronger subjects, math and science -- and they recognized that I was talented enough in those subjects to move me up to the next level.

Some traditionalists lament the fact that the Common Core accountability movement encourages teachers to focus on the weaker students at the expense of the stronger students. They say that some strong students want to move ahead in their classes, but the teachers, who claim their hands are tied by Common Core, won't let them.

I'm torn whether I should focus on my stronger or weaker students as I get ready to teach in the middle school classroom this year. On one hand, neglecting the weaker students is why many people spurn tracking, so I want to help my weaker students get ahead. But on the other hand, I myself am the beneficiary of certain teachers noticing my special talents and allowing me to succeed in more challenging classes. Therefore I owe it to my stronger students to support them and celebrate their talents just as my own teachers celebrated my own talents.

This is so important that it bears repeating. I owe it to my stronger students to support them and celebrate their talents just as my own teachers celebrated my own talents.

Recall back on Square Root Day the story I told about teaching my second grade friend the square roots of 0, 1, and 144. I admit that this incident, along with my admiration of my second grade teacher, formed the foundation of my desire to become a teacher. At first I didn't know that Grades 7 and higher even existed -- I knew that my elementary school was K-6, and I'd always believed that students went directly from sixth grade to college. I remember that as a kindergartner, to me the sixth graders looked like grown-ups, and so I expected that they were nearly college students.

Naturally, it was the arrival of my Pre-Algebra text that alerted me to existence of 7th grade. I wasn't sure whether I wanted to be a teacher because I wasn't sure I'd be good enough at any subject other than math, but the benefactor who gave me the Pre-Algebra text was a single-subject teacher who taught math and nothing else. And so I knew at that moment that I wanted to become a single-subject math teacher -- which meant that I'd most likely teach in a high school.

Now I will be working in a K-8 school, just like Nguyen, But while I will have three preps, Nguyen has just two -- interestingly enough she teaches 6th and 8th grade, but not 7th. This means that my new K-8 school will actually be more like what I thought school was like when I was a little kid, with 6th grade as (one of) the highest grades.

The Blaugust prompt directs us to reflect on this old post, so let me do so. First, as it happens, I was checking the website of my old elementary school and -- believe it or not -- my second/fifth grade teacher still teaches there, nearly 30 years after I was a student in her classes! (At least, she taught there last year, when the site was last updated.) And according to the website, she still teaches both second and fifth grade! (The only other teacher I recognize is my kindergarten teacher.)

Now as I wrote in that old post, I want to focus on my stronger as well as my weaker students. I won't truly know who my strongest students are until after the first Benchmark Testing Week. But I am aware of the best way to protect the top students in the class -- with rules.

As I wrote in yesterday's post, the middle school English teacher came up with the idea of having the students write about the rules. And so this is most of what we're doing on Days 2-3 in the classroom.

I begin by giving each group of four students a sheet of poster paper. Students divide the paper into four quadrants, and each quadrant is labeled with the four rules mentioned earlier on the blog:

1. The Teacher Respects You
2. Respect Your Honesty
3. Respect Yourself and Each Other
4. Respect Your Class Equipment

As it happened, I only had the sixth and eighth graders create rules blogs -- this is due to a mix-up in the Wednesday Common Planning Day schedule. On Wednesdays the students take music, but music lessons don't actually begin until next week. So I gave the seventh graders an alternate assignment.

All three middle school teachers have the students create rules posters. Afterwards, the three of us discuss what the students write, and then the English teacher prints up a common list of rules for all three of us to use. The ultimate rules list will be given to the students tomorrow, and from it we create a Behavior Contract for the parents to sign. We haven't discussed the final rules list at the time of this post, since tomorrow is the day I don't post to the blog.

Because of this, let me post my lesson plans for tomorrow. After passing out the Behavior Contract and spending half the period discussing the rules, I move on to the Music Break. Tomorrow I will play the Square One TV song "Count on It," another song about the need to learn math:

Here are the lyrics, courtesy the following link:


Count On It

Lead vocals by Larry Cedar

Sooner or later, you’re gonna see some math
You can count on it
Sooner or later, those numbers cross your path
You can count on it
You may be hoping it will go away
But let me tell you, math is here to stay
You can count on it, hoo, yeah
You can count on it
Everywhere you look, they’re measuring the action
You can count on it
Everywhere you look, they’re even using fractions
You can count on it
They’re keeping time, and they’re keeping the score
They draw the line, and they’re running the store
You can count on it, hoo
Yeah, you can count on it
Look at the dial; look at how far
Look at how much; look where we are
Look at the gauge; look at the graph
Check out the numbers; you’ve got the last laugh
‘Cause it ain’t mystery; there’s nothing tough about it
You can count on it, that’s right
Soon you’re gonna see that you couldn’t live without it
You can count on it, hoo
Don’t take a genius or a great magician
To make a pretty good mathematician
You can count on it, hoo, yeah
Yeah, you can count on it, whoo
Oh, you can count on it, whoo
Baby, you can count on it
(fade out over Larry singing skat)

In the video the song is played on saxophones, but the only instruments I'll ever play in class are drums and a guitar. I like to play each song over two days, so I'll play the song on the drums on Thursday and the guitar on Friday.

Finally, the main lesson is another Opening Activity, on number patterns. It's time for me to reblog again, since I wrote about it last year:

During the year, I pointed out that many texts begin with a lesson on inductive reasoning, which often entails completing number patterns. I like this sort of lesson at the start of the school year.

In this lesson, students will use inductive reasoning to find patterns in sequences of numbers, letters, and names.I began with some simple sequences where students had to find the next two terms. Notice that Exercise 5 is the Fibonacci sequence -- a nod to Fawn Nguyen, who gives her Geometry students a worksheet on that famous sequence on the first day of school.

Speaking of Fawn Nguyen, yes, many of my opening activities are based on Nguyen's. As it turns out, one of her best known lessons is on patterns -- except these are visual, not numerical, patterns:


Exercises 7 and 8 on my worksheet don't come from Nguyen. Instead, they come from the texts used by the students I tutored. Those students enjoyed trying to figure out the patterns in these lists of names. I know that I've spent so recent posts about future presidents, but these lists are all about past presidents. Exercise 7 refers to George Washington, John Adams, Thomas Jefferson, and James Madison, so the correct answer is another James (Monroe), another John (Quincy Adams), and then Andrew (Jackson).

Exercise 8 looks similar, but this time it refers to money -- George Washington ($1), Thomas Jefferson ($2), Abe Lincoln ($5), and Alexander Hamilton ($10). So the correct answer is Andrew (Jackson again, $20), Ulysses (Grant, $50), and then it's all about Benjamin (Franklin, $100). As it turns out, one can actually extend this sequence. I was recently watching old 1960's episodes of the game show Let's Make a Deal on the new BUZZR channel, and often the host Monty Hall would offer contestants $500 bills (William McKinley) and $1000 bills (Grover Cleveland). There was even an episode when Monty showed a contestant an extremely rare $5000 bill that the bank had allowed him to show on that episode only -- had the contestant won it, she would have received a check for $5000 as the bill would have to be returned to the bank. James (Madison, not Monroe) was on the $5000 bill, so the sequence would continue Benjamin, William, Grover, James. It may be a good idea for teachers to give the related number sequence 1, 2, 5, 10, 20, 50, ..., as a hint.

The worksheet was getting long, so I stopped here. but notice that there are still many other types of problems that I could give:

Quatros: 4, 108, 60, 52, 36, 144
Not Quatros: 2, 29, 106, 18, 15, 22, 6
Which are Quatros? 86, 737, 42, 72

Semirps: 2, 13, 11, 23, 53, 97, 71, 47
Not Semirps: 15, 25, 209, 21, 190
Which are Semirps? 123. 67, 51, 27

Notice that "Quatros" are simply multiples of four. The word "Quatro" comes from the Latin word for four -- and we'll see that root later on in Geometry when we cover quadrilaterals. As it turns out, the modern Portuguese word for "four" is quatro [yes -- the Rio Games are still going on now -- dw] A few other Romance languages pronounce the word for "four" identically to the Portuguese, albeit with a slightly different spelling.

As for "Semirps," any nerd -- or even a dren -- can see that "Semirp" is "primes" spelled backwards. I do find it a bit awkward that the text pluralized "prime" to "primes," reversed it as "Semirp," then pluralized it again to "Semirps." Then again, one advantage to calling them "Semirps" rather than "emirps" is that the extra s- may trick readers into thinking about the prefix semi-, which is Latin for one-half -- especially right after seeing the Latin root for "four" in the previous question.

I was also considering including the first two sequences from the "Improving Reasoning Skills" section, which contains some bonus problems:

1. 18, 49, 94, 63, 52, 61, ...
2. O, T, T, F, F, S, S, E, N, ...
3. 4, 8, 61, 221, 244, 884, ...

I was able to figure out the first one, and I'd seen the second one before, but the third question stumped me -- and I suspect that it will stump our students as well. (The second one in the sequence is as easy as One, Two, Three!)

One of my favorite websites when considering number sequences is the On-Line Encyclopedia of Integer Sequences:


The OEIS is one of the oldest sites on the Internet. Notice that it was first created in 1964 -- long before the Internet existed as we know it! Back in the 1960's, users had to submit queries by sending it a primitive form of e-mail. Nowadays, of course, it is web-based like most other sites.

Many famous sequences are entries in the OEIS. Here they are:

180,360,540,720 (Notice the geometrical interpretation -- sum of the angles of an n-gon!)
1,3,6,10,15,21 (triangular numbers)
1,3,4,7,11,18 (Lucas numbers, similar to Fibonacci)
1,3,7,15,31,63 (sometimes called Mersenne numbers)
2,6,15,31,56,92 (given by the polynomial that generates these, (n+2)*(2*n^2-n+3)/6)
3,12,48,192,768 (there are some signed sequences in the database, but here the signs were ignored)

In fact, the only sequences I didn't enter were the ones containing letters or fractions, since this is in fact an integer sequence database.

Here's a sequence related to one of the lists of dead presidents that I entered:


Finally, here are the answers to the bonus questions:

18,46,94,63,52,61 (but I really did figure this one out before entering it into the OEIS)
4,8,61,221,244,884 (too hard for me, no problem for OEIS)
2,3,6,1,8,6,8 (too hard for me, no problem for OEIS)

The last sequence did stump the OEIS, however. Neither one of us figured out the sequence:

6,8,5,10,3,14,1, ...

Maybe you can figure it out, then try submitting it to the OEIS! Unfortunately, the OEIS has been swamped with submissions for months. Still, you can see why I enjoy the OEIS as a handy resource for integer sequences.

I hope the students will enjoy tomorrow's activity.

I am not posting tomorrow -- the title of the post includes the notation (Days 2-3) to remind the readers that the next post won't be until Day 4, which is Friday.