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# Algebraic Nuts and Bolts: Solving Systems

Lesson 13 of 20

## Objective: SWBAT demonstrate mastery of the algebra skills they need to solve systems of linear equations at various levels of difficulty.

Today's class opens with an example of a system of equations. This is a system that could be solved by either substitution or by elimination; for today we're calling it an example of "Level 3" substitution.

My goal in providing this opener is to get a quick picture of which of my students are comfortable solving this system and which students need help. Today is all about practicing with solving systems, and I find that this one can can help me and each of my students decide where they should start. If this is too hard for a student, I'll get them going on Levels 1 and 2, in which at least one variable is already isolated. If it's too easy, then it's on to Level 4.

Starting with yesterday's homework, here is how I've defined the four levels of substitution practice:

- Level 1: Two equations in which y is isolated, so students just have to set the two sides equal and solve.
- Level 2: Either x or y is isolated in one equation, but not the other, so students must make a substitution step before solving.
- Level 3: Two equations in standard form. At least one variable in one equation has a coefficient of 1, so it takes one step to isolate a variable. From there, it becomes a "Level 2" problem.
- Level 4: Two equations in standard form. No variables have a coefficient equal to 1. (
*Wait a minute. Isn't substitution kind of annoying in this case? There must be another way to solve a system like this...right?*)

I give students just a few minutes started here, before using this opener as an example of what students might work on today. I'll leave the example on the board as everyone gets to work.

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After spending a few minutes on today's straightforward algebra opener, it's time for some straightforward algebra practice. As I describe in this narrative video, making time for this sort of practice is a great way to meet students where they are.

There are a few things that might happen right now. For most students, this will be time to either finish last night's homework, or to "level-up" to a more difficult sort of substitution problem.

Other students may want to spend a little time continuing to practice graphing lines, or we may have some loose ends to tie up on the "Commission-Based Salary" problem (see today's lesson notes or yesterday's lesson). I circulate to check in with each table of students, and to make sure everyone has a plan for the 20 minutes or so.

I tell everyone that if they finish what they're working on, to let me know right away, so we can decide what to do next.

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Just as there were leveled versions of last night's substitution homework, there are leveled versions of today's Mastery Quiz. The point of a mastery quiz like this is to give students credit for as much as they can do. I see what I can see, kids practice what they can, and we can all a plan for moving forward.

I tell students that can choose to take a quiz consisting of levels 1 and 2, 2 and 3, or 3 and 4. Of course, to earn a 4 on learning target 5.3, they'll have to give me perfect work on the "Level 3 and 4" quiz. I use Kuta's Infinite Algebra software to create today's quiz.

In addition to serving as evidence of what kids know about solving systems by substitution, this quiz will set the stage for tomorrow's class. Usually, the quiz gets kids fired up to do even better tomorrow, when there will be some practice time like there was today. This helps make it clear to students what they know so far, and helps them goals for what they'd like to be able to do.

I also use what I see on this quiz to create the leveled groups in which students will work tomorrow.

#### Resources

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- UNIT 1: Number Tricks, Patterns, and Abstractions
- UNIT 2: The Number Line Project
- UNIT 3: Solving Linear Equations
- UNIT 4: Creating Linear Equations
- UNIT 5: Statistics
- UNIT 6: Mini Unit: Patterns, Programs, and Math Without Words
- UNIT 7: Lines
- UNIT 8: Linear and Exponential Functions
- UNIT 9: Systems of Equations
- UNIT 10: Quadratic Functions
- UNIT 11: Functions and Modeling

- LESSON 1: Solving Problems in Two or More Unknowns
- LESSON 2: Organizing a List and Guess & Check
- LESSON 3: What's In an Intersection?
- LESSON 4: Solving Systems by Graphing
- LESSON 5: Mastery Session: MP1, 5.1, and 5.2
- LESSON 6: From Guess and Check to Graphing Systems
- LESSON 7: Graphing Lines and Getting Stuff Done
- LESSON 8: Linear Equation Drills (Computer Lab)
- LESSON 9: Three Ways to Solve a Problem
- LESSON 10: From Graphing to Substitution
- LESSON 11: REALLY BIG IDEAS! Graphing vs. Substitution
- LESSON 12: An Intersection Point, and What Happens Around It
- LESSON 13: Algebraic Nuts and Bolts: Solving Systems
- LESSON 14: The Most Important Algebraic Idea of the Year
- LESSON 15: How Far Can Substitution Take You?
- LESSON 16: Sweet Problems with Two Variables
- LESSON 17: Many Lines Through One Point
- LESSON 18: Solving Systems by Elimination
- LESSON 19: Three Days of Review, Problem Solving, and Achieving Mastery
- LESSON 20: Unit 5: Systems of Equations, Two Day Exam