Reply To: How do you define solutions?

[Mary Manske]

I like that start–we’ve done similar and I use Racing Cars as well! I used both of the two intro activities in the Systems bundle (Systems of two linear equations and Solutions to Systems of Equations)–I felt like my students were getting closer to identifying what a solution actually is, but struggling to connect that across multiple representations. We can identify that its the price of each with a problem in context (with or without manipulatives) and we can find where the y values are the same in a table or the lines cross on a graph. We can usually then restate that matching part in context as a solution–but how all of that fits together is unclear for most of them. 

My big issue though is how to better define that distinction. I think there’s a big difference between making that link or connection & being able to see how it carries through many representations and having done problems with solutions from tables/graphs/words/whatever and be able to identify a solution in any of those contexts. (Or maybe there isn’t and I should get over it.) Its pretty conceptual though so its hard to discuss with my team so we can get some more clarity (that usually works) because of it turning into “so we’ll give them tables!” “We’ll make sure they answer in a sentence!” “If I can teach them to say ____, would that work?”

I know this needs to be addressed starting now (or yesterday) and it seems like there is something about solutions to one variable or linear equations that is an useful connection, I just can’t quite get it.