We returned to the question as I introduced solving linear inequalities and systems of linear inequalities. Students participated readily ... less pause than the first time around ...

What is a solution?

Student A: anything that satisfies the equation ...

Me: could someone add to that thought?

Student B: it's the numbers that solve the equation ...

Me: Hmmmm, I don't think we can use the root word in the definition ... any other thoughts?

Student C: it fits in the equation

Me: OK ... it satisfies, it solves, it fits ... any other thought?

Student D: it makes the equation true

Me: Yes ... to all of the above!

Me: Now, if I give you an equation with 2 variables, how might you represent the solution visually?

Student E: could you restate that question?

Me: (I write on the board) y = 2x + 3; How might I represent the solution to this equation visually?

Student F: (2, 7)

Me: OK, that point is true. How else might I represent the solution visually?

(pause)

Me: OK ... are there other solutions besides (2, 7)?

Several students: yes ... many of them ... infinite number

Me: Yes! So how might I represent those infinite solutions visually?

Student G: a line

Me: Yes! So how or why does a line represent the infinite solutions to that equation?

Student H: a line continues in both directions forever

Student I: a line is made of infinite number of points

Me: Yes!

We then extended our conversation to include inequalities ... talking about why we shade and what that tells us.

I want to get better at asking questions ... I want to ask better questions. I also want to develop strong math discourse in our class!

These are the "essential" questions suggested by our district curriculum document:

- Describe the solution to a system of equations with 3 variables.
- How do you determine the variables for a system of equations?
- How do you write a system of equations from information given in a problem situation?
- How do you know if your solution to a system of equations is reasonable?
- How do you connect the solution to a system of equations to the context of a problem
- situation?
- How do you decide which method to use to solve a particular system of equations?
- How do you solve systems with more than two variables?

These questions hit the surface and skim across the topic. I want something deeper, richer for my students.

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