# Elimination (Lesson 2.3)

###### Unit 1: Sequences and Linear Functions

**Day 1:**Recursive Sequences**Day 2:**Applications of Arithmetic Sequences**Day 3:**Sum of an Arithmetic Sequence**Day 4:**Applications of Geometric Sequences**Day 5:**Sequences Review**Day 6:**Quiz 1.1 to 1.4**Day 7:**Linear Relationships**Day 8:**Point-Slope Form of a Line**Day 9:**Standard Form of a Linear Equation**Day 10:**Quiz 1.5 to 1.7**Day 11:**Unit 1 Review**Day 12:**Unit 1 Test

###### Unit 2: Linear Systems

**Day 1:**Linear Systems**Day 2:**Number of Solutions**Day 3:**Elimination**Day 4:**Larger Systems of Equations**Day 5:**Quiz 2.1 to 2.4**Day 6:**Systems of Inequalities**Day 7:**Optimization Using Systems of Inequalities**Day 8:**Quiz 2.5 to 2.6**Day 9:**Unit 2 Review**Day 10:**Unit 2 Test

###### Unit 3: Function Families and Transformations

**Day 1:**Interpreting Graphs**Day 2:**What is a function?**Day 3:**Translating Functions**Day 4:**Quiz 3.1 to 3.3**Day 5:**Quadratic Functions and Translations**Day 6:**Square Root Functions and Reflections**Day 7:**Absolute Value Functions and Dilations**Day 8:**Equations of Circles**Day 9:**Quiz 3.4 to 3.7**Day 10:**Unit 3 Review**Day 11:**Unit 3 Test

###### Unit 4: Working with Functions

**Day 1:**Using Multiple Strategies to Solve Equations**Day 2:**Solving Equations**Day 3:**Solving Nonlinear Systems**Day 4:**Quiz 4.1 to 4.3**Day 5:**Combining Functions**Day 6:**Composition of Functions**Day 7:**Inverse Relationships**Day 8:**Graphs of Inverses**Day 9:**Quiz 4.4 to 4.7**Day 10:**Unit 4 Review**Day 11:**Unit 4 Test

###### Unit 5: Exponential Functions and Logarithms

**Day 1:**Writing Exponential Functions**Day 2:**Graphs of Exponential Functions**Day 3:**Applications of Exponential Functions**Day 4:**Quiz 5.1 to 5.3**Day 5:**Building Exponential Models**Day 6:**Logarithms**Day 7:**Graphs of Logarithmic Functions**Day 8:**Quiz 5.4 to 5.6**Day 9:**Unit 5 Review**Day 10:**Unit 5 Test

###### Unit 6: Quadratics

**Day 1:**Forms of Quadratic Equations**Day 2:**Writing Equations for Quadratic Functions**Day 3:**Factoring Quadratics**Day 4:**Factoring Quadratics. Part 2.**Day 5:**Solving Using the Zero Product Property**Day 6:**Quiz 6.1 to 6.4**Day 7:**Completing the Square**Day 8:**Completing the Square for Circles**Day 9:**Quadratic Formula**Day 10:**Complex Numbers**Day 11:**The Discriminant and Types of Solutions**Day 12:**Quiz 6.5 to 6.9**Day 13:**Unit 6 Review**Day 14:**Unit 6 Test

###### Unit 7: Higher Degree Functions

**Day 1:**What is a Polynomial?**Day 2:**Forms of Polynomial Equations**Day 3:**Polynomial Function Behavior**Day 4:**Repeating Zeros**Day 5:**Quiz 7.1 to 7.4**Day 6:**Multiplying and Dividing Polynomials**Day 7:**Factoring Polynomials**Day 8:**Solving Polynomials**Day 9:**Quiz 7.5 to 7.7**Day 10:**Unit 7 Review**Day 11:**Unit 7 Test

###### Unit 8: Rational Functions

**Day 1:**Intro to Rational Functions**Day 2:**Graphs of Rational Functions**Day 3:**Key Features of Graphs of Rational Functions**Day 4:**Quiz 8.1 to 8.3**Day 5:**Adding and Subtracting Rational Functions**Day 6:**Multiplying and Dividing Rational Functions**Day 7:**Solving Rational Functions**Day 8:**Quiz 8.4 to 8.6**Day 9:**Unit 8 Review**Day 10:**Unit 8 Test

###### Unit 9: Trigonometry

**Day 1:**Right Triangle Trigonometry**Day 2:**Solving for Missing Sides Using Trig Ratios**Day 3:**Inverse Trig Functions for Missing Angles**Day 4:**Quiz 9.1 to 9.3**Day 5:**Special Right Triangles**Day 6:**Angles on the Coordinate Plane**Day 7:**The Unit Circle**Day 8:**Quiz 9.4 to 9.6**Day 9:**Radians**Day 10:**Radians and the Unit Circle**Day 11:**Arc Length and Area of a Sector**Day 12:**Quiz 9.7 to 9.9**Day 13:**Unit 9 Review**Day 14:**Unit 9 Test

#### Learning Targets

Solve linear systems using elimination.

Use elimination strategies to determine if a system has 0, 1, or infinite solutions.

Tasks/Activity | Time |
---|---|

Activity | 20 minutes |

Debrief Activity with Margin Notes | 10 minutes |

QuickNotes | 10 minutes |

Check Your Understanding | 10 minutes |

#### Activity: How Much is a Taco?

#### Lesson Handouts

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#### Answer Key

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#### Experience First

The goal of this lesson is that students use their problem solving skills to solve linear systems without a step-by-step procedure. Instead we want them thinking about how would they actually figure this out if they were Jacob or Amala. The questions were written with that in mind. It is our hope that students won't jump to graphing in their calculators or to solving with substitution. While they could do that, this system is actually much faster to solve without those methods, which is one of the reasons we like elimination. Sometimes it's a lot simpler than other methods.

So as students are working, keep in mind that we are trying to get them to see what the simplest way to solve is. Question 2b really gets at this. What are the differences in the orders? Ask students, "What more did Jacob and Amala get? How much more did they pay?"

Question 3 is going to be tougher for students. We want them to notice that they can double or triple Amala's order so that she has the same number of slices or cannolis as Jacob. So how do we get them to see that? You'll want to be ready with your guiding questions. Also, multiple groups may have this same question so trying to help a couple groups at a time can keep the class moving.

**Guiding Questions:**

- Why was I able to solve for the burritos before?
- How is this set up different from the last?
- Amala didn't buy the same number of slices as Jacob, but could we rewrite her equation so that it also contains 3 slices?

#### Formalize Later

The margin notes for this lesson are really cool because we're actually going to take the students work and show how the elimination works algebraically in the margin. So in question 1, when we ask about the differences in the orders, we're going to show how that is taking one equation and subtracting the other. That leaves us with an equation that we can solve because now we have one resulting equation with one variable. Now that we know one variable, we can solve for the other.

As you're debriefing the rest of the activity, try to highlight as many different approaches as possible. You may even ask multiple groups to write their solutions to the same problem on the board if they solved it in a different way. For example, some students might solve question 3c by eliminating the slices of pizza while others may have eliminated the cannolis.

One last thing...the last Check Your Understanding problem is modeled after a practice SAT item. These types of questions are VERY common on the SAT, and while students could find the correct answer by plugging in an answer choice and solving the system, they will save a lot of time if they notice the structure in the system and that we want coefficients that are multiples of each other.