## Reflection: Developing a Conceptual Understanding Solving Problems in Two or More Unknowns - Section 1: Opener: Ways to Make 50 Cents

Starting with today's lesson and continuing over the next few days, I hope to show how to use the Guess and Check strategy to motivate students toward the formal algebraic methods for solving a system of equations.  To get started, I will show how organizing a list of possibilities is a useful precursor to Guess and Check.

Efficient, thoughtful use of Guess and Check requires a problem solver to notice patterns and make use of the structure in a problem (ie, "If I change my guess, then what happens to my check?"), so being organized is a means toward that end.  Additionally, listing possibilities is a way to get kids thinking about tables and graphs.  A table is a just an ordered set of points, and a graph is the visual depiction of those points on the coordinate plane.  That's what an equation in two variables is: a representation of all possible values.  As students will see, once we have two equations, we have a system we can solve.

If you've never tried giving your students a problem like today's Lesson_Opener, then I recommend it. I've had equal success using this problem with freshmen and seniors, and I can imagine it working earlier than high school.  What's great about the problem is that anyone can get started listing ways to make 50 cents, but to "prove" that the list of possibilities is complete is a more exciting achievement.

Developing a Conceptual Understanding: Starting with an Open Ended Exploration

# Solving Problems in Two or More Unknowns

Unit 9: Systems of Equations
Lesson 1 of 20

## Big Idea: The reason systems of equations exist as an algebra topic is that they're a tool to be used when a problem has more than one unknown variable.

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Subject(s):
Math, Systems of Equations and Inequalities, Algebra, problem solving, guess and check, modeling
43 minutes

### James Dunseith

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