Common Core Algebra Planning (Part 2)

Wow!

It's truly amazing that we have the technology to connect with so many people so very quickly!  Thank you for visiting my blog, and for the positive feedback from all of my fellow teachers and professionals in Twitter and the MTBoS!  As promised, I will continue my musings of how I envision the first couple weeks of school.

Outline

Distributive Property

I plan on continuing my work with the real numbers as Topic B outlines, but rather than the exact lessons I hope to talk about the distributive property first.  What I love about this approach is that it ties in a lot of what the elementary grades are currently doing with the properties.  Essentially, it is "filling in the gaps" of my students, since the work we do in Algebra assumes this understanding, but based on where my students are in the education system, they have not had the instruction.  I absolutely LOVE the pictorial references of distributive property to area.  Using the below picture, instead of having my little arcs connecting the 4 to each of the addends to show distribution, it is easy for any student to grasp since they can count the squares and relate it to the expression.  The picture below that, where I show distributive property with subtraction, shows the natural progression of the area model, which gets more abstract with area.

Math Progressions

This brings up a good point about the mathematical progressions.  If you have not looked at these, and you teach Common Core math, I highly suggest that you check it out.  Though the reading is at times dense, it completely puts things in perspective when it comes to the progression of mathematics with coherence across grade levels.  I am a secondary teacher and I thought I knew elementary math (what they teach in elementary school).  I was wrong.  Digging into common core math at the most basic level makes things so much easier for me to tackle the Algebra curriculum, which looks so different than the Algebra we are used to.  One suggestion: read these progressions a little at a time before bed; if you're having trouble sleeping, it'll put you right to sleep!

Commutative Property

I love the idea of having the students interact with the operations here rather than telling them there is a commutative property of addition and one for multiplication.  Have them explore all four since we have already dug into the operations earlier in the unit.  Most likely they will recognize that they have seen the properties before, and that is okay.  I doubt they have done much more than mention the properties and not use them again except perhaps on a quiz or in passing.  I love having cutouts representing length for addition and area for multiplication.  This way they can see the commutativity!

Associative Property

I like the explanation I use in the picture for associative property.  When I was learning these properties in school, I never really saw a need to mention associative since it was similar to commutative in my opinion.  I think that having visuals really made the distinction for me, and perhaps for my students it will as welll.  I plan on making the analogy of driving down the street: the number of houses is the same, but depending on which direction you are traveling, the grouping of houses is perhaps different.  In the picture above, it would be easy to have concrete blocks for students to build numerical expressions.  Again, going back to the concrete-->pictorial-->abstract flow of mathematical progression.

In looking at module 1, there is a flowchart in Lesson 7 of the properties that kind of confused me.  I tried to make it my own, by adding color to distinguish the variables.  However, it was still very cumbersome.  At first I thought I liked it, but I am rethinking that now.  Anyone who has taught this lesson: what did you do to tie in the properties?  Did you teach lesson 7?  How did you adapt it?

What other lessons do people have for the properties that really gets students engaged and thinking about structure?

Common Core Algebra Planning (Part 1)

First Blog!

So here I am, starting a new job as an Algebra teacher; 1 section Common Core, some sections of year 1 of a 2-year algebra course, and some lab sections in the second year of a 2-year algebra course.  I have been completely transformed by what I have seen online on other teacher blogs, the MTBoS, and Twitter Math Camp.  People like Dan Meyer, Sarah Rubin, and Sarah Hagan have completely transformed how I view teaching math.  I know this year is going to be the best year yet, and I will only continue to learn more!

I am overwhelmed with ideas of classroom posters, interactive notebooks, three-act-math tasks, and first day math activities.  So far, I have begun my notebook, but I am trying to adapt our New York State modules to fit my style and my approach to laying the foundation for algebra.  

Sorry for the faintness of the writing, I feel nervous to commit to the outline!

Outline

For those of you using modules, I have really been able to dig into the progressions of K-HS math and the structure of the modules themselves.  I have even ordered myself a color, teacher copy of the modules that can be found here! Anyways, based on how things have worked for others this year and what I know, I have decided to not do Topic A.  Instead I have decided to modify Topic B and consulted an algebra textbook from the 1950s similar to the one below...

...in order to review the deep-down basics of numbers, properties, and operations.

1. I want to review math as a language.  Music, German, and Klingon are all languages.  "Like other languages, Mathematics has its own vocabulary, grammar (principles that govern the correct use of a language), syntax (the part of grammar that concerns rules of word order), synonyms, negations, conventions, abbreviations, and sentence structure" (Esty).  I love, love LOVE this quote!  So inspiring and relevant!
2. What is a number?  Is "12" a numeral?  What is the value?  Why wouldn't we use "(8-5)*4" to represent "12"?  I want to have rich discussions, or even arguments, over what a number is.  In 9th grade, students think they know what math is about, but I guess I want to shatter that illusion.
3. Sets.  What is a set?  A set of dishes, a set of tools, a set of numbers...I think this a good flow into the different number sets like the natural numbers, whole numbers, integers, etc.  I am not afraid to use the notation as in college either, I have made a poster!
4. Operations I love this progression found on the math page here.  Again, kids think they know what operations are and how they work, but they really don't!  I also think this is paramount for making connections from integers to polynomials like the modules do.  As for the Order of Operations?  Forget PEMDAS!  I love love LOVE the "Boss Triangle" (also on my math posters).  I got the idea from this article from NCTM.

I am also going to start a weekly student blog for my math journals, called "Writing Fridays".  I know it's not a catchy title, but I think that it is a good way to instill some literacy in the math classroom.  So on Fridays I am thinking of posing a task, or question to the students.  They have parameters to answer over the weekend (due Monday) and respond to at least two other students (due the following Friday).  We will develop a rubric, but I love the idea of allowing the students to be creative with their responses and "critique the reasoning of others".  I, of course, will monitor responses and posts to make sure it is appropriate.

For instance, the first Friday I have a "Write your Mathology".

Students can pick from these prompts (borrowed from here):

• How do you feel about math? Do you like or dislike it? Why do you feel that way?
• Are you "good" at mathematics? Explain.
• Do you like some areas of mathematics better than others? If so, which ones do you like or dislike? Why do you like or dislike them?
• What makes math great or horrible for you?
• What experiences in math have you liked? Why?
• Describe your most memorable experience in learning math (good or bad).
• How do you feel about taking the math class you are taking this year? What do you expect to learn about?
• What type of things do you think are important to help students learn math?

The next week, they will answer "Is math the language of the universe? Why or why not?"  Here is a cool article that references this video that students can watch to whet their appetites:

I will have to write another blog on the entire next week I have planned, including properties, equality, expressions...

I told you, my mind is SPINNING with ideas from the #MTBoS!!!!

Esty, Warren. "The Language of Mathematics." (n.d.): n. pag. AugustMath. Web. <http://augustusmath.hypermart.net/LMSection1p1.pdf>.