To make your own tessellations at home (or wherever you might have the supplies), begin with a small square. We used a three-inch by three-inch square (which happens to have an area of nine square inches).  The square, of course, has four sides which we called the left, the right, the top, and the bottom.

With scissors, cut a non-straight line from the bottom to the top without cutting any pieces off.  You will be left with two pieces that fit together like a puzzle.

Now, keeping the pieces oriented as they are when the puzzle fits together (In other words, do not flip or rotate them.), slide the right piece over the left, so that the straight sides are touching.  Tape the straight sides together.

Beginning in the upper left corner of a full sheet of construction paper, line up the straight top of the taped shape with the top of the paper.  Trace the shape.  Sliding it to the right so that the left side of the shape fits within the right side of the tracing, keep tracing the shape.  When you have made it across the page, slide it down to make a second row.  Do the same until the larger paper is covered with the tessellated shape.  Trace over the pencil outline with a black marker.

Finally, alternating colors, use your crayons to neatly decorate the tessellated masterpiece.  Display it with pride; you have just tessellated!

​Augment the sentence below to greatly improve it.  Record your improved sentence on your paper.
​

I love this sound.  Twenty-five students.  All reading orally.  Books of their choice.  Simultaneously.  The room is abuzz with fluency practice.

We did this for 15 minutes on Wednesday, followed by 15 minutes of protected silent reading, during which students were encouraged to continue reading or reread the same books.  I also love this sound!

Throughout the year we will work on building stamina in our reading, extending the times for each of these activities. I want my students to have the ability to focus for longer and longer periods of time on reading for their own enjoyment.

Watch the short videos below to see both steps to this "activity".

Born on September 8, 1772, Manuel Lisa encountered some very prominent figures in our state's rugged history. Use your recording sheet to organize your thought as you read about Manuel Lisa.

The natives in North America also killed and used animals.  Watch the video here to get an idea for how all the parts of the buffalo (bison) was used for the good of the tribe.  The image on the left can also be enlarged with a click to show the uses of the buffalo's many parts.

You, too, may get in on the action.  The teacher has prepared a buffalo for your perusal.  Your task is to reach into the "carcass".  Take out an item, describe it (in writing), and tell us ways it could be used.

You notice, in the 1912 photograph of Olympic athlete Jim Thorpe, that he wears two different shoes.  It seems that earlier in the day, Mr. Thorpe discovered his own shoes had been stolen.  He found two shoes in the trash and slipped them on.  One of the shoes required extra socks, as well.

Then, he went on to win two gold medals, one in the pentathlon, winning four of the five strangely conglomerated events.  Now, we know that Jim Thorpe was racially profiled in the games (He was a Native American.), but the fact that he could run in two different shoes and extra socks should be a lesson to learners everywhere.

When I headlined this commentary, I thought I was going to write about the need for students to come prepared with the appropriate equipment for learning - including an appropriate attitude for struggle and perseverance - but upon considering Jim Thorpe's story, my focus soon changed.

You see, Mr. Thorpe was unprepared.  He knew what he needed, but he didn't have what it took to run a race against the world.  Isn't that the way we often find ourselves as we try to learn new things?  Oftentimes we don't know what we need.  We don't know where we're going.  We haven't stretched.  We don't even know how to train.

Students are like that, aren't they?  They come to us with insufficient training; they're not ready for what we have to impart.  But that doesn't stop us.  That shouldn't stop you.  Student, even when you feel like you can't and never will, you simply must toe the line.  Find some shoes, chock them into the starting block, and run when you hear the horn.  I'm not even interested in winning the race.  I'll be more impressed if you face the unknown.  Don't give up on yourself before you ever get started.

It's OK that you don't have the proper "shoes" (By shoes, of course, I mean whatever it is you need.); that's why I'm called a teacher.  Your lack of preparation means I get to do what I'm paid to do.  We simply need to start moving forward.  It's not always easy, but we work on these things together.

We would hope that students would master their basic multiplication facts, from 0x0 to 9x9, by the end of the third grade.

That said, we hear a lot of talk about how our students have little to no fluency in their times tables.  Fourth grade teachers often have to reteach these facts.

Frustrating?  Yup.

But it's also a place where I have some choices to make.  I am of the belief that I need to teach to the top of my class and bring others along for the ride, rather than teach to the middle.  That's easier said than done, but I'm constantly trying to do it.

In this case, while I know I need to reteach the times tables, I also need to make it interesting for the students have already mastered their third grade skills (and not forgotten them over the summer).  Ergo, I introduce exponents and square roots early in the fourth grade.  In this way, we can cover the same skills, but add a new way to look at them.

The first problems we work on are the squares (or doubles as some refer to them):  3x3, 4x4, 5x5, ..., 8x8, 9x9.  If parents want to help with this, they can reinforce the classroom by encouraging their fourth graders to constantly recite the square products:  9, 16, 25, 36, 49, 64, 81 (forwards and backwards).  For more, have you read Stepping Up to Multiplication?

Now, in addition to the standard multiplication sentence, students learn the proper way to write six to the second power, or six squared (which is 36, of course).  Then, to turn it around, these guys are ready for, What is the square root of 36?  The answer to that one is six.  Knowing these things forward and backward - and overlearning them - even with the "new" way of denoting these ideas.

Hopefully, while one student is internalizing squares and square roots, four others are mastering the products to basic multiplication problems.

Finally, I am introducing the measurement of area.  This week, we learned the formula for finding the area of a rectangle - Length times Width.  With this, we have an instant application for our multiplication skills.  I've been proud of the way this year's class has reacted so far, and I've seen some faces light up with understanding.  Some students just need to feel like they are worth the efforts that I put in to help them learn difficult things and make them seem simple.

I no longer believe the halls or the cafeteria of a school have to be deathly silent.  What a double standard from the start!  Do the adults follow the Zero-Voice-in-the-Hall rule?  No, we do not!  In fact, we can often be heard talking to the other adult at the other end of the hallway, joking and teasing with him, asking her about her weekend.

I do like to look at the positive side of things, and I try to give people the benefit of the doubt in most occasions. Not that I don't go negative from time to time - even daily - but I try to keep things positive.  And I'm getting better.  No really, I am!  Stop looking at me like that.

I believe that a properly engaged student is the learning student.  That means she is engaged with the material before her, as well as with the peer sitting across from her or beside her.  And that means our classroom is not always so silent you can hear a pin drop.

I had a sixth grade teacher, Mrs. Langham, who insisted just that:  the class was to be so silent we could hear a pin drop.  And then she would pull said pin out of her industrial teacher tesk and proceed to drop in onto the tile floor.  If she couldn't hear it, the class (yes, the entire class, even the ones of us who adhered to her edicts) would stay in for recesses, writing 100 very, very long sentences.

The pin dropped often.

And we often had to write those paragraph-long sentences.

It made people strongly dislike this lady, who probably was very amiable in her life outside of the school; either that or she was akin to the evil queen in Sleeping Beauty!

What was she thinking?  Did she have any idea what she was doing to us?

The only things I remember about her class were:

• This kid, Duane, had a very curved backbone, and he was kind of a jerk, but that he was the best sixth grade artist I can remember in a school that didn't have art classes.
• Someone took another kid's yearbook and scribbled and drew all over the pages during Langham's class.  I confess that I was the one who subtly reported to the authorities who it was.

More educators and parents should realize this.  For some, it will be a challenge.  Some of us are not cut out to be chipper in the morning, and some just have displeasing auras that hang about us all the livelong day.

​Last year, my students, being trained and well-practiced in the art and social grace of looking people in the eyes, delivering firm shakes of the hand, and expressing gratitude, did all of that with one of the adults overseeing an activity.  When the sour-pussed adult scowled at them and refused to shake their hands, some of my students were distraught.  They didn't know what to do with this.

A parent standing nearby witnessed the situation.  Upset that the adult was not a partner in teaching these kids proper manners and would not accept thank you's, the parent expressed her displeasure with me.  What was I to do?  I suppose living on a planet with other human beings means that some of those beings are not as nice as others.  The sad part is that I have to teach my students about those people, as well.  They need to be ready to be shunned and shut down by people, all the while not squelching their own enthusiasm and positivity in the process.

The Bloggatteer Experience is up and running.  That's our classroom blog (separate from this website) where all students are expected to contribute to the community.

Ultimately, the Bloggatteer Experience provides a safe place for students to write about their thoughts and respond to the activities of their day - and now they are doing it in a forum that allows them to do so for a real audience.

In the short time we had at the of Friday, four students made it to the point of publishing.  Obviously, some grasped the purpose a little better than others, but we'll continue to work on that.  Right now, they are getting used to the process of logging in to their blog and using the iPads for this purpose.

We use the Seesaw app for this.  This is an amazing portfolio program in which students can publish writings, photographs, videos, and drawings.  Once a student begins a writing, whatever the subject, s/he has a choice to put it into one of three electronic folders I've set up for them.  The first folder is for ideas and drafts.  The second is for items receiving ongoing editing for publication.  Items are held in these folders until a child is ready to publish them.  Once ready, the student can put the item in the ready-for-publication folder and ultimately publish the item to the public blog.  Once there, other students can like and comment on their work.

We have some guidelines for the blog.  They are simple rules, but they are in place for student safety.  With this in mind, I ask them not to publish their last names or any other personal information like phone numbers or addresses.  Since I have to approve items before they are made public, this should not be a problem anyway, but I'd like for my students to get used to thinking about what they are making public.  We also do not talk about plans for the weekend and the like.  Finally, I allow students to use some emojis.  Emojis are not my favorite thing in the world, but they can be fun, and they do express things that aren't more easily expressed in words.  I limit the number of emojis to exactly one per post or comment.  We might be able to loosen the ropes on this one a little bit in the future, but I do not want Hoggatteers to spend more time choosing just the right emoji when they should be concentrating on the quality and contents of their writings.

So there you have it.  They're excited to get started.  Check out the Bloggatteer Experience from time to time to get another glimpse into our classroom - this time from the fourth grader's point of view.

After the initial logic activity is completed, we will begin a deeper study about the rocks and minerals.  We will also conduct an artifact analysis based on the paper pictures of real artifacts from the mounds near St. Louis.  And all of this will lead us straight into the depths of a quaint little hole in the ground that we like to call Hoggatt Cave.

Maybe I just like to torture myself.  Days like these often result in a teacher pulling out his own hair.  The room is louder than usual.  Kids are all over the place.  Kid's forget the procedures for both the classroom and for the current activity.  The bottom line is this:  I desperately seek creative ways to present the same old information and lessons to my students.  This is the first time for this particular activity, so I'm going to reevaluate this one for next year.  Is there anything I need to do differently?  Was it too complicated?  Too convoluted?  Too time-consuming? Was it less exciting than it should have been?  What could be done to tweak the wow factor?