Attached is a copy of my learning progression for CCSSM #A-SSE.B.3a with all of the visuals that would not display in the first post. This learning progression pertains to factoring quadratics. Benchmark & classroom assessments are also included. I plan to use the classroom assessment as a quiz near the end of this learning progression as a prep for the benchmark assessment which will be used as a conclusion to the learning progression. The way that I plan to communicate this learning progression with my school would be to post it on the district server for the school. This way, any teacher who wanted to use it at Davis would have access to it. This learning progression fit in perfectly with chapter 10 in the Carnegie Algebra 1 book. So, those who are teaching Carnegie Algebra 1 will be able to use it if they want to. This learning progression fits in with testing in the manner that it prepares them for factoring related question on the test. (The Learning Progression was revised on 7-31-13)
Learning Progression for CCSSM # A-SSE.3a (HW#1)
The learning progression connects the ideas from Carnegie Learning Curriculum with the CCSS Math. My only suggestion is to connect the idea of the Factor Theorem to the understanding of solving for zeros/roots. The idea that roots (x-intercepts) can be used to create the equations from factors. Example, if a and b are roots of an equation then the quadratic f(x) = (x – a)(x – b).
The benchmark assessment is very nicely written and the scoring criteria is complete.
Discuss either in the blog post or in the learning progression where the benchmark and classroom assessments will be used.
Lisa,
I chose to comment on your learning progression as it is similar to mine. I really liked the bridge problem that you included. A lot of the story problems that my curriculum uses are just silly. However, this is something that bridge architects and engineers really have to think about as they are planning. So problems like this may seem more valuable to students if they can see when in life this will ever be used.
There were two small suggestions that I have as additions to your progression. The first is that you have student’s factor equations that are in standard form to find roots, and you have them use roots to determine equations, but they are not encouraged to put them in standard form. I think it would be great to go that extra step because it encourages them to make the connection that factoring and FOIL are inverse operations.
My second suggestion has to do with the way Carnegie shows students to factor quadratics of the form ax2 + bx + c. It sounds like student make a list of all of the factors of ac that add to b, and then are required to guess and check (using FOIL) until they find which factors work in which positions. This is the same way that I learned how to factor quadratics in high school. However, it gets to be really time consuming for equations where ac has many factors, especially if a has lots of factors itself. Factoring by grouping would be a much quicker way for students to factor this type of quadratic, and it leads to less room for mistakes. Just a thought….Great job though!