Monday, July 1, 2013

Units for Algebra 1

I had SBG and Learning Targets forced on me (and I don't mean that in a bad way) this past year.  The school I started at had been working to implement these for somewhere around 5 years (not exactly sure since I wasn't there).  And the teacher that left didn't leave anything for me.  So I fumbled around a lot at the beginning of the year trying to figure out what other teachers did, why they did that, what the benefits were, and how to apply it to my classroom.  What I ended up with are some poorly organized units with learning targets that are OK.  One of my goals this summer is to create some more solid units (with assessable learning targets) that are organized, teachable, and centered around the standards.

Our district's guideline for core math classes is Appendix A [pdf].  (I really don't want to get into an argument over whether this is a good choice or not.  I was not at the district when the choice was made, therefore I have little say.  Also I don't hate it.)  This means that the standards Appendix A suggests for Algebra 1 are the standards I have to teach, and I need to make sure my students demonstrate them to the level that Appendix A recommends.

I do not have to teach the Appendix A units, but it seems like a good place to start.  However Appendix A units are big, so I wanted to break them down into sections/modules/something smaller and more manageable.  What makes sense to me is to group certain standards together and create learning targets from there.  However I have kind of hit a wall trying to do this.  I've been working with Unit 1 and trying to break it into 2 or 3 sections/modules/whatever, but I am hesitant as to what is best.

The goal of Unit 1 is to continue students' work with linear equations and increase fluency/adaptability.  Students should already be able to solve linear equations and some simple systems.  Students analyze the process of solving and practice moving between forms of an equation (summarized from the Appendix A document).  To me, Appendix A is an opportunity for students to apply and play with linear equations and expressions.

Here are the recommended standards:

  • N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  • N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
  • N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 
  • A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
  • A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s lawV = IR to highlight resistance R.
  • A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

(Sorry for the list--please don't stop reading! I think you need this to tell if my grouping makes sense.  I'll try to not blabber much more.)

Group 1:  N.Q.1, 2, 3/A.CED.3
Mostly focused on precisely modeling and appropriately using units to assist with this.  (More "simple" modeling situations.)  Could get into expression vs. equation as that is an important distinction, but a lot of modeling situations could be solved either way.

Group 2:  A.CED.1, 2, 3, 4/A.SSE.1/A.REI.1, 3
Focused both on modeling and on the "pure" algebra.  Would get into more "complex" modeling situations where restraints on domain/range may come into play.

I have also thought of breaking a few from Group 2 to form
Group 3:  A.CED.4/A.REI.1, 3
This would allow a section focused on the algebra outside of modeling (not always, but a little bit more). Not sure if I want this or not...

Ok, so what do you think?  Two groups or three?  What are the pros and cons of each?  Would you do it a completely different way?  I am not an expert, so please tell me what you think.  I need something to help me continue moving forward in my planning for next year.  Thanks!

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