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
Loading resource...

Solving Problems in Two or More Unknowns

Unit 9: Systems of Equations
Lesson 1 of 20

Objective: SWBAT practice solving problems with two or more unknown values. To start, they'll use Guess and Check, which will soon lead to more formal algebraic methods for solving systems of equations.

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.

  Print Lesson
10 teachers like this lesson
u5 l1 ducks and cows sw gac
Similar Lessons
Formative Assessment: Systems of Equations and Inequalities
12th Grade Math » Matrices and Systems
Big Idea: A quick assessment will give you and your students feedback about the second half of the unit.
Troy, MI
Environment: Suburban
Tim  Marley
Solving Linear Systems of Equations with Substitution (Day 3 of 3)
Algebra I » Systems of Linear Equations
Big Idea: Students will create a system of equations from a real world scenario and interpret the solution. Students will use linear substitution to solve systems of equations.
Washington, DC
Environment: Urban
Noelani Davis
REVIEW: Systems Review and Word Problem Practice
Algebra I » Systems of Equations and Inequalities
Big Idea: Students have the opportunity to review and practice solving systems of equations, including those with inconsistent and dependent systems
Boston, MA
Environment: Urban
Amanda Hathaway
Something went wrong. See details for more info
Nothing to upload