# Equal and Opposite

I don’t know if this is the right title for this post…it feels like it is.  I get to its point at the bottom…

I was supporting an 8th grade teacher that was implementing the Classifying Solutions to Systems of Equations formative assessment lesson from Mathematics Assessment Project.

The students had not yet worked with linear equations in any form other than slope-intercept form.  The students already understood the different types of solution a system might have.

The students started out by completing the assessment task.  I wanted to focus on this part below:

I’ve encouraged this teacher to build a strong foundation for students being able to create and complete a table of values.  Creating a table should be a go-to strategy for students if all else fails.

I stood in the back of the room and I looked at the second equation…

I wondered if I could make a connection for kids…if it would be too much, or would they follow…Here is the gist of what I did:

I interrupted the class to pose a question.

Me: What do we know about an equation that is solved for y?

Students: We know the y-intercept and we know the change in y over the change in x.

Students: It’s solved for x.

Me: What do you think that might tell you?

Students: The x-intercept???? (Imagine a questioning tone here…) Is that a thing?

Me: Yes it is a thing. What about the coefficient of the y? What do you think that might tell you?

Students: The change in x over the change in y??? (Imagine a questioning tone again)

Me: Yep. Let’s pull up Desmos and check it out.

I remember being a math student that naturally made these sorts of connections~that if something happened mathematically one way, I could predict what would happen in an opposite direction.

I want the students to know and wonder about these things for themselves.  But, I think we need to make it obvious to them sometimes that they can do this thinking on their own.