Foundations for Algebra Concept Map

I’ve spent all day creating the following concept map.  It depicts many of the arithmetic properties, operations, rules, and structures students must master to succeed in algebra; in other words, the foundations for algebra.  It is extremely busy, and too much information for one handout.  However, it helps me relate various concepts together as I plan out detailed lessons for the first unit of a Common Core State Standards (CCSS)-based curriculum.  Plus, I enjoyed the challenge of showing most of the foundational concepts used in algebra on one page.  You will need to click on the following figure to have any hope of reading the details.

Any comments related to concepts to add, delete, or modify?  Or on anything else?

I expect to revise this single map view several times then extract it into multiple maps with one overview map tying the lower level ones together.  I might even try putting this into a Prezi format.

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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17 Responses to Foundations for Algebra Concept Map

1. Impressive!!!

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2. Glenn says:

I am doing a rather large project using the Exeter Math and CCSS. This kind of mapping will be very useful to me. I actually sat down today to create something similar! Thank you for saving me some work.

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• You are quite welcome, Glenn. Please share any derivative works so the larger community benefits!

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• Glenn says:

Always. I post things on my blog, blog.mrwaddell.net. thank you!

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On first glance terrific, I will study it carefully. A similar idea is a review grid for IA regents. It’s a very frustrating experience to teach very weak IA students in a summer schools (23 days and for som e only 11 days) program as you can’t thoroughly teach evrything.

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• What would the review grid for IA look like?

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4. Cal says:

I’m unclear on how an algebra unit could be CCS based. And yes, I’ve seen the standards, which are nothing more than reorganized fundamentals of algebra. We discussed the standards yesterday in our staff meeting, and good lord. If it takes a group of five math teachers 3 minutes to hunt down the standard for slope-intercept–which, by the way, is supposed to be found using similar triangles? I don’t think so—then there’s something annoyingly precious about the standards. It’s exactly like a corporate re-org. Most of them happen just to change things around, with no real objective.

Not that it matters,because CC ain’t happening, baby. (g)

Let’s do breakfast again.

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• Agree that the standards per se, whether CCSS, CA 1997 standards, or other, are all very similar, and mostly a reshuffling and rewording. The real value of CCSSM, in my opinion, is the emphasis on the mathematical practices, which are a mixing of the NRC five strands of mathematical proficiency and the NCTM mathematical process standards. If instruction emphasizes the mathematical practices, along with the proper “essential standards,” then students’ mathematical capabilities should be improved after developing them over the course of twelve years. Emphasizing the practice requires a thinning of the content standards, which has not happened in my view for CCSSM. And HOW to deliver the practices effectively is more art than science, so like anything in life, the success of CCSSM falls largely on those responsible for ensuring teachers know the practices pedagogically. Additionally, students must invest in their learning or the best efforts of any teacher, CCSSM-based or not, will be minimally effective.

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6. Sarah White says:

I am starting my third year as a high school math teacher. This will be my second year teaching Algebra 1. Last year, as a final project, not test, I had the class split into groups of 3-4 and they created a concept map of the course. This helped me see what the students thought of as relevant, and what they didn’t remember.

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• Great idea, Sarah. It can be a great formative assessment. Question: did it really indicate relevance? Or more like recall, as you state in the negative? I think it might be more the latter.

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7. Alysca says:

Love it! I was just starting to put something similar together myself. Thank you for sharing!

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• My pleasure!

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8. This concept map is spot on. I am curious about the diagram’s effect on students. Can anyone comment on that?

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