Solving Linear Systems Using Elimination (Lesson 4.4)
Unit 1: Generalizing Patterns
Day 1: Intro to Unit 1
Day 2: Equations that Describe Patterns
Day 3: Describing Arithmetic Patterns
Day 4: Making Use of Structure
Day 5: Review 1.1-1.3
Day 6: Quiz 1.1 to 1.3
Day 7: Writing Explicit Rules for Patterns
Day 8: Patterns and Equivalent Expressions
Day 9: Describing Geometric Patterns
Day 10: Connecting Patterns Across Multiple Representations
Day 11: Review 1.4-1.7
Day 12: Quiz 1.4 to 1.7
Day 13: Unit 1 Review
Day 14: Unit 1 Test
Unit 2: Linear Relationships
Day 1: Proportional Reasoning
Day 2: Proportional Relationships in the Coordinate Plane
Day 3: Slope of a Line
Day 4: Linear Equations
Day 5: Review 2.1-2.4
Day 6: Quiz 2.1 to 2.4
Day 7: Graphing Lines
Day 8: Linear Reasoning
Day 9: Horizontal and Vertical Lines
Day 10: Standard Form of a Line
Day 11: Review 2.5-2.8
Day 12: Quiz 2.5 to 2.8
Day 13: Unit 2 Review
Day 14: Unit 2 Test
Unit 3: Solving Linear Equations and Inequalities
Day 1: Intro to Unit 3
Day 2: Exploring Equivalence
Day 3: Representing and Solving Linear Problems
Day 4: Solving Linear Equations by Balancing
Day 5: Reasoning with Linear Equations
Day 6: Solving Equations Using Inverse Operations
Day 7: Review 3.1-3.5
Day 8: Quiz 3.1 to 3.5
Day 9: Representing Scenarios with Inequalities
Day 10: Solutions to 1-Variable Inequalities
Day 11: Reasoning with Inequalities
Day 12: Writing and Solving Inequalities
Day 13: Review 3.6-3.9
Day 14: Quiz 3.6 to 3.9
Day 15: Unit 3 Review
Day 16: Unit 3 Test
Unit 4: Systems of Linear Equations and Inequalities
Day 1: Intro to Unit 4
Day 2: Interpreting Linear Systems in Context
Day 3: Interpreting Solutions to a Linear System Graphically
Day 4: Substitution
Day 5: Review 4.1- 4.3
Day 6: Quiz 4.1 to 4.3
Day 7: Solving Linear Systems Using Elimination
Day 8: Determining Number of Solutions Algebraically
Day 9: Graphing Linear Inequalities in Two Variables
Day 10: Writing and Solving Systems of Linear Inequalities
Day 11: Review 4.4- 4.7
Day 12: Quiz 4.4 to 4.7
Day 13: Unit 4 Review
Day 14: Unit 4 Test
Unit 5: Functions
Day 1: Using and Interpreting Function Notation
Day 2: Concept of a Function
Day 3: Functions in Multiple Representations
Day 4: Interpreting Graphs of Functions
Day 5: Review 5.1-5.4
Day 6: Quiz 5.1 to 5.4
Day 7: From Sequences to Functions
Day 8: Linear Functions
Day 9: Piecewise Functions
Day 10: Average Rate of Change
Day 11: Review 5.5-5.8
Day 12: Quiz 5.5 to 5.8
Day 13: Unit 5 Review
Day 14: Unit 5 Test
Unit 6: Working with Nonlinear Functions
Day 1: Nonlinear Growth
Day 2: Step Functions
Day 3: Absolute Value Functions
Day 4: Solving an Absolute Value Function
Day 5: Review 6.1-6.4
Day 6: Quiz 6.1 to 6.4
Day 7: Exponent Rules
Day 8: Power Functions
Day 9: Square Root and Root Functions
Day 10: Radicals and Rational Exponents
Day 11: Solving Equations
Day 12: Review 6.5-6.9
Day 13: Quiz 6.5 to 6.9
Day 14: Unit 6 Review
Day 15: Unit 6 Test
Unit 7: Quadratic Functions
Day 1: Quadratic Growth
Day 2: The Parent Function
Day 3: Transforming Quadratic Functions
Day 4: Features of Quadratic Functions
Day 5: Forms of Quadratic Functions
Day 6: Review 7.1-7.5
Day 7: Quiz 7.1 to 7.5
Day 8: Writing Quadratics in Factored Form
Day 9: Solving Quadratics Using the Zero Product Property
Day 10: Solving Quadratics Using Symmetry
Day 11: Review 7.6-7.8
Day 12: Quiz 7.6 to 7.8
Day 13: Quadratic Models
Day 14: Unit 7 Review
Day 15: Unit 7 Test
Unit 8: Exponential Functions
Day 1: Geometric Sequences: From Recursive to Explicit
Day 2: Exponential Functions
Day 3: Graphs of the Parent Exponential Functions
Day 4: Transformations of Exponential Functions
Day 5: Review 8.1-8.4
Day 6: Quiz 8.1 to 8.4
Day 7: Working with Exponential Functions
Day 8: Interpreting Models for Exponential Growth and Decay
Day 9: Constructing Exponential Models
Day 10: Rational Exponents in Context
Day 11: Review 8.5-8.8
Day 12: Quiz 8.5 to 8.8
Day 13: Unit 8 Review
Day 14: Unit 8 Test
Learning Targets
Given a system of two equations, write new equations by adding, subtracting, or scaling the given equations.
Choose an appropriate strategy for eliminating one variable by adding the equations or scaling and subtracting the equations.
Tasks/Activity | Time |
---|---|
Activity | 20 minutes |
Debrief Activity with Margin Notes | 10 minutes |
QuickNotes | 5 minutes |
Check Your Understanding | 15 minutes |
Activity: Gas Station Snacks
Lesson Handouts
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Answer Key
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Homework
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Experience First
Today students will look at elimination as a strategy for solving linear systems. The ideas are very similar to when students reasoned about slope in Lesson 2.4 and considered what was different about the KFC orders (only the number of sides and the price) and how that could be used to identify the price of each side. In question 1, though students are dealing with two different items, and thus two variables, the only difference between the orders is the 2 extra Combos, so the price difference must reflect only the price of 2 Combos. It is critical for Algebra 1 students to establish this line of reasoning before they have to scale equations. Question 2 has students creating more true equations by finding the cost of various orders. Students learn to write related equations to the ones given, by adding or scaling orders. Finally, in question 3, students must make use of 2 of the equations and do this in a way so that the only difference can be attributed to one variable. Remember that students are new at this, so they may struggle with solving question 3, or even realizing that they can use two of the given or created orders to find the answer. It’s important to not rush to the procedure here, but to give students time in their groups to figure it out. Note that students actually have multiple options for choosing their two equations. They could pick the 4 M&Ms/2 Starbursts order and the 4 M&Ms/6 Starbursts order OR they could pick the 2 M&Ms/3 Starbursts order and the 2 M&Ms/1 Starbursts order. They could of course also continue scaling the equations to make other true equations. Your use of assessing and advancing questions will be critical in this lesson as a way to understand students’ thinking and extend their thinking without giving away answers! Guiding Questions:
Formalize Later
Much like in Unit 3 when students solved equations, elimination can be seen as a comparison strategy. The goal is to rewrite an equation so that the only difference between the two equations can be attributed to one variable. This is the reasoning behind why two equations in a system might be subtracted. Furthermore, adding two equations together results in another true equation, and this is intuitive when you think about combining two orders. This equation that represents the sum is always true, but it is especially helpful when adding the two equations eliminates one of the variables. This will only happen if one of the coefficients is negative, which is harder to see in a contextual scenario. Note that we don’t usually tell students explicitly what method to use for solving the system. We want students to be strategic about which method they choose based on a conceptual understanding of what each method does. If we want to assess a particular method, choose a context where one method is more convenient than another. The CYU questions in Lessons 4.3 and 4.4 are specifically tailored to apply the method learned that day.