I highly recommend finding some sort of curriculum to use as a foundation for your lesson planning. I say this with a word of warning, however. Textbook and curriculum publishers have been notorious for placing whatever sticker they need to on the cover of their publication and selling it to states. This means that just because it says "Common Core Aligned," or "TEKS Aligned," etc., does not necessarily mean it is. [You can check out EdReports for an independent review of educational materials.]
Even if it is properly aligned, often the material isn't rigorous enough to be used without any modifications. Sometimes the questions are posed as "higher order thinking questions," but provide too much information to the students, and end up being a simple substitution problem. Other times, it is marked as a "modeling problem," but, again, all of the information is provided for the students. Here is a great example from Dan Meyer's blog:
Mathematical modeling is defined in similar terms by the Common Core State Standards, the modeling cycle, or the IB:
- identifying variables in the situation and selecting those that represent essential features,
- formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables,
- analyzing and performing operations on these relationships to draw conclusions,
- interpreting the results of the mathematics in terms of the original situation,
- validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable,
- reporting on the conclusions and the reasoning behind them.
In the above problem:
- Who is identifying essential variables? Where?
- Who is formulating the model for those variables? Where?
- Etc.
This does not have to be the awful question it appears to be. This is asking students to decompose numbers and then regroup. For example, the student can rewrite the problem to be 8+2+3, which would result in 10+3. Or the student can rewrite the problem to be 3+5+5, which would result in 3+10. This is a bad question because of how it's asked, but not because of the underlying math the problem is trying to get at.
The standards are not a curriculum. They are standards students are expected to meet to help to close achievement gaps and prepare them for college and the workforce. The way teachers (or schools or districts) put in place curriculum and meet those standards is entirely their own, so there is no such thing as a "Common Core math problem," just like there is no such thing as a "TEKS math problem."
It is our job to make sure the questions we're asking our students align to the standards of our states and help our students master the skills outlined in those standards. If the textbook or curriculum we have been directed to use (or have chosen to use) does not meet that criteria, it is our job to modify when necessary.
What challenges have you faced with your curriculum?
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