Over the past week, we’ve worked on strengthening our strategies for solving algebraic situations. Our scenarios have become less and less about direct exchange and more about looking at combinations with two distinct variables, and making sense of how to use what is known in the problem to determine the value of one of each variable. Once we know the value of one unit, it is easier to determine the value of any value for each variable.
A mixture of 3 cups of peanuts and 2 cups of raisins costs $3.30.
A mixture of 4 cups of peanuts and 3 cups of raisins cost $4.55.
What does it cost if you buy 5 cups of peanuts and 2 cups of raisins?
Understanding the relationships between the variables at this point is more important than knowing a procedure. Following steps does not mean that you understand why it works, and ultimately when we figure out the relationship mathematically, we gain stronger understanding. We will continue to practice solving for variables using our problem solving strategies and, sharing our strategies as a class to allow students multiple opportunities to see and try new strategies.
I also want to note, that students are still deliberately being given problems with numbers that are not complicated so that they can develop these relationships, and while students with strong number sense may immediately see relationships among numbers that lend themselves to quick ‘guess and check’ answers. Students are being encouraged to develop strategies that do not use ‘guess and check’ since relying only on that strategy in the future will slow them down.
This week we have already begun to look at situations with 3 variables and will add more strategies and tools to our bank. After break we’ll dust off the vacation cobwebs and jump back into our algebra work.
Have a happy, safe, and restful break!