Thursday, July 16, 2015

Welcome to Sixth Grade: Ratios

So, I'm blogging.  Why?  Because Julie told me to.  =)  Which is tough because I haven't really found my blogging voice.

Why Am I Blogging?

I don't feel confident just sharing the brilliant ideas I come up with because, frankly, I steal everyone else's ideas.  I think my contribution is in my execution.  Maybe I underestimate the role I play in it all, but I just don't feel there is much I could write about there.

And as much as I find Justin's vulnerability and transparency fascinating to read, I don't have the self-discipline to commit to the 180 day thing.

So, finding my purpose for even blogging is a bit tough.  I'm going to use it today to flesh out the ideas that I've been toying with all week because I think that will be useful for me.  But I suspect reading it will prove pointless for anyone else so consider that my disclaimer if you are still reading.  There are no fun pictures, video clips, or amazing ideas.  Just me tweaking my sequence and creating a repository for my thoughts.  Feel free to skip down to the Questions I'm Still Playing With if you wish to rescue me from my cognitive struggles.  ;)

My Plan for the Year

So, I mentally planned out my year.  I'm not a textbook teacher.  So, I used Geoff Krall's PBL Curriculum Map (here) as my starting point for my sequencing and modified it slightly to include an intensive revisit of multiplication fluency alongside NS.4 standard prior to working with Ratios. (Our state standards match CCSS pretty closely but here they are in case the numbers vary at all.) This led me to a schedule framework that looked like this:

First Nine Weeks
  • Introductory Unit - (2 weeks) Lots of work on expectations and group norms.  Definitely including the Marshmallow Challenge and some Get It Together activities.
  • Unit One: Integers/Coordinate Plane - (2-3 weeks) Covering NS.5-8
  • Unit Two:  Calculations, Calculations, Calculations - (4-5 weeks) Covering NS 1-3, including Critical Skill 2 (dividing fractions).
Second Nine Weeks
  • Unit Three: Multiplication Bootcamp - (2-3 weeks) Lots of activities to reinforce and build fluency with multiplication facts and cover NS.4 because it fits nicely here.
  • Unit Four:  Ratios - (6-7 weeks) Hmmmmmm.....what to do?  Besides cover all three RP standards and Critical Skill 1 (which I think may be the  most critical sixth grade skill).  Yikes!
Third Nine Weeks
  • Units idk...5-7 or so - (9 weeks)  Covering all of the Algebra standards here and may sequence them exactly as Geoff did but that is yet to be determined.  (That, and I am at a conference and my full calendar map is at home.) Critical Skill 3
Fourth Nine Weeks
  • Unit Eight - Geometry - (tbd)
  • Unit Nine - Statistics - (tbd) Or maybe I had it in the other order.  Clearly, I've spent more time on the first semester.  Critical Skill 4

So....let's talk about that Ratio unit.

My Ratio Unit

I find myself at a week-long Math Academy on Ratios and Proportional Reasoning.  A perfect time to flesh out what that unit could look like!  Plus, I am here with my collaborative Special  Education partner so it was a great opportunity to pick her brain on her perspective since she has taught sixth for a while.  (Her input is what caused me to embed that Multiplication Bootcamp here.)

I was hoping to keep it to six weeks.  And, we have a software program that we are expected to be using once a week so that would've meant 24 days of instruction.  That is definitely not going to happen.  I was super unfamiliar with how to teach ratios but I'd look at a lot of resources and had a general sense of what it entailed.  But I needed to break it down into subskills and get a sense for how to sequence instruction through it.  I also know that I'm planning to use Interactive Notebooks this year but don't always want to direct instruction and notetaking to proceed exploration and productive struggle.  Here is what I've come up with so far, though I am still tweaking the details:

Part One - What is a Ratio?
  1. The Fightin' ____________ - A lesson from our training (I think from Carnegie Learning) that has them explore different ways that comparison statements are made.  I may modify this to take advantage of the fact that we are in the midst of a consolidation and will be looking at new school mascot names soon.
  2. Direct Notes for Interactive Notebook - Still determining what these might look like
  3. Cube Ratio
  4. Comparing Two Quantities - from the Carnegie Training book
Part Two - Scaling Up and Down
  1. Mixing Paint (Carnegie 5.1)
  2. Direct Notes for Interactive Notebook - Use Frayer model type of foldable with four representations: Scale Up/Down, Table, Double Number Line, Graph
  3. Frayer Model Group Practice - I give one representation, they create others.
  4. Muffin Man - from Carnegie Training book
 I also know a few things that I want to include during this section, including having them get into groups by distributing cards with fractions written on them (find all of the equivalent fractions) a lot of equivalent fraction skill practice (Homework?), and some practice with completing tables of equivalent fractions with parts are missing.  
Part Three - Comparing Ratios
  1. Which cup has lighter color? 
  2. Direct Notes for Interactive Notebook - Still determining what these might look like
  3. Hot Chocolate Sales - from Carnegie Training book
  4. Quiz Bowl - from Carnegie Training book
  5. Grocery Store Gas Points
  6. Nana's Hot Chocolate
  7. Nana's Paint MixUp
Part Four - Unit Rates
  1. Ticket Prices
  2. Direct Notes for Interactive Notebook - Will include graphic organizer from Carnegie Training book
  3. Partial Product
  4. Print Job
  5. A Special on Unit Rates in Aisle 9 - from Carnegie Training book
Part Five - Percentages
  1. Activity tbd
  2. Direct Notes for Interactive Notebook - Still determining what these might look like
  3. Amazon Percent Discount - Accessible on Dan's Three Act Spreadsheet
  4. Activity tbd
  5. Activity tbd
  6. Activity tbd
This is clearly where I need to put some more work in.  I figure I will need to embed some skills practice here as well.
Part Six - Unit Conversion

  1. The Height Dilemma
  2. Direct Notes for Interactive Notebook
  3. Sugar Packets
  4. Huckleberry Trail Mix
  5. Super Bear
  6. Bone Collector
I am not set on the sequence of the four post-note activities.  I'm also not set on including all of them.  Most of my time today was spent focusing on HOW I wanted to teach unit conversions.  Thanks to a heck of a lot of bounce back from Casey and some others, I've settled on using dimensional analysis.  It is the method that makes the most sense to me but I am going to need to flesh out how to scaffold it for sixth graders without falling into the Tricks.  And I'll be honest, Glenn's endorsement was pretty much all I needed to finalize my decision here because, let's face it, he is a math teacher god among men. 

Questions I'm Still Playing With

I had really planned to include Dan's Cost of Liquid thing in here somewhere...but I'm not sure where or if it is useful at this point in the curriculum.  If so, do I make them do all of the unit conversions and include it in Part Six?  Do I not trudge them through the calculations and just use it as a teaser to introduce the need for unit rate?  Or the need for unit conversions?  Not sure yet.

Are there other lessons in Carnegie's materials that I would prefer to some of what I've listed?

How can I possibly keep this to 6 or 7 weeks?

How much skills practice will I need to embed?  And where?  I'm planning to give students a homework choice between a Math Forum POW and a skills practice, but only assigning once per week so I don't think that is sufficient skills practice even if they do it.

Am I planning a culminating assessment of any kind?

What about Mathalicious?  They have some cool stuff for sixth grade ratios!  Don't I want to include at least one lesson somewhere in the unit?

And then, there's this MARS task.  I've never met a MARS task that I didn't love so I would think I'd want it...but they usually take me a few days.  

What exactly do I want my notes to look like for INB and which ones might include foldables or other such things?

Do I want to include a culminating INB lesson for key vocabulary as I'm thinking of doing with other lessons?

Do I want to give them some online game practice?  Or just send a Remind note recommending it to parents or for home?

At what point do I introduce the distinctions between part:part, part: whole, rates, etc.?

I'm using Smart Board so I still need to create slides and embed all of these activities into that in preparation, as well as choosing openers and summarizing closing activities to help make sure each of these goes off well.  My kids are (hopefully!) going to be seated in groups but I'd like to change up grouping on occasion so a few different strategies for that which reinforce the concepts (i.e. find the equivalent ratios or find another representation of your ratio) will be nice.

Oh, and that Percent stuff....need to flesh that out.


  1. I, too, often blog for my own benefit and know it's pretty dull reading for anybody else. It's still useful to me to see that yea, other people are wondering "how can I give them enough actual practice?" I mean, if you're going to have a multiplication "boot camp," you are recognizing the need for fluency... in my experience, building in "more than I think I should have to" at the beginning ends up meaning that later, when things that should be automatic are, I can move at a faster clip. It pays off. I think it's got other benefits -- students start *expecting* math to get easier and ... that's a good feeling. They're less resistant to it.
    Happy Blogging!

  2. I think that it is incredibly helpful when others post their plans+rationale for a unit or year. I think globally, and thus hearing about cool lessons or a snapshot of a day is not nearly as useful as something like this. Throwing in all the links is a huge service for the community as well by not just stating what you think, but how you intend to incorporate what other people think. I have doubts about the value of my own blogging as well, and mainly keep doing it for the same reason I eat vegetables (the people I respect think it is important), but I think this goes beyond just that. So thanks :)

    1. Thanks, Andy. I always think it terms of big picture and unit plans so this is just kind of my process. Then I zoom in and finetune details as I go. Ultimately, I'm looking at about 10-11 of these unit type chunks to plan.