First Week: Tiling Pools & Notebooking

I love teaching, but boy does it wear me out.  Especially the first week.  I was talking with one of my coworkers after school last week and she said the following, “I’m coming to realize that what we do is exhausting! We spend all day trying to entertain a room full of teenagers . . . with math.  And we’re fairly successful at it for the most part.  But it takes a lot of energy.”  I completely agree.  I’ve already spent a good chunk of my holiday weekend sleeping, reading, and just laying on the couch in zombie mode.  I love my job, but I’m looking forward to October when I’ve rebuilt my teaching endurance.

That being said, I really did have a great first week.  And thanks to Sunday Fundays, I have the motivation to write and reflect about it on my blog.  Like I did last year, I’m spending the first two weeks teaching about multiple representations using the tiling square pools problem.  What I did differently this year, though, is I spent Thursday of last week setting up Interactive Notebooks with my students.  It blew my mind how difficult it was for some of my classes to follow my directions.  But I got better at the directions by the end of the day and it went much more smoothly.  Right now their notebooks look something like this:


I modified a rubric that I found online to include a self-evaluation. I forgot to take a picture of the next few pages.  But imagine a page of notebook rules (bring your notebook ever day, use it only for math, no off-topic doodling, write down everything Miss Moore writes, etc) glued in behind the title page. Then they filled out three Table of Contents pages behind that (date, pages, topic).  After the Table of Contents, they have this: Image

I had them fill out a multiplication chart and also fill out the Order of Operation stairs on the next page. (Pet Peeve: Let’s start a coalition of math teachers against PEMDAS. It drives me nuts! I have to reteach order of operations every year because of the misunderstandings it creates.)  Students glued in a copy of my disclosure on the next page.  Since it has the learning goals for the year on it, I plan to have students refer back to this and ‘check off’ the learning goals as they master each of them.


In the back of the notebook, we are using word-webbing to build a glossary of vocabulary words.


And this is what they did in class yesterday.  I spent the first part of class explaining how to use the left side.  They will glue in daily warm-ups on the left side and also keep a record of any Aha’s or Questions/Wonderings.  I’m also opening this page up for illustrated notes for any of my students who would learn best taking notes in pictorial form. They just have to be able to explain or it needs to be obvious how the pictures relate to the content.

On the right-hand page I had them start building a list of equivalent equations that all work for the Tiling Pool problem.  I offered a prize to the group who can come up with the most unique equations by the end of the unit.  Two interesting topics that arose from this activity:

  • What makes an equation unique?  Students asked about uniqueness of the following pairs of equations: n=4s +4 and n= 4*s + 4;  n=4(s+1) and 4(s+1)=n; n=s+s+s+s+4 and n=4s+4.  Also, since I had introduced the equation n=4(s+2) – 4, one group of students realized that you could use addition and subtraction to create an infinite amount of equations (ie n=4(s+10) – 36).  So we’re going to have to discuss that one as a class on Tuesday.  Since the focus of the unit is connecting multiple representations, I probably will guide the class to a discussion about whether these types of equations can be represented using the pool picture.
  • How do we know if two equations are equivalent? If you look eat Joshua’s #8 equation, you can see that it isn’t actually equivalent to the others.  Which is awesome!  Totally going to bring that up for discussion on Tuesday.  I think Joshua’s group intuitively knew that they equation wasn’t equivalent – which is why they asked me about it. But since it had given them the correct number of tiles for a 5 ft pool, they couldn’t figure out why it wasn’t equivalent to the others.  I’m not planning to introduce simplifying equations until term two, so we’ll talk instead about how to show this strategy on the picture and whether it would give the correct number of tiles for a different sized pool.

All in all, I’d say it was a pretty good first week and I’m looking forward to the follow-up discussions on Tuesday.  I have some other fun ideas to share that I used with my 9th grade math lab, but that will have to wait for a later time.

As a side note, what would you say about the equation pairs I listed above? Are they unique? Why or why not?


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