Unit 2, Lesson 16
Elimination
Extra Support Materials for Algebra 1
16.1
Warm-up
Standards Alignment
Building On
Addressing
Building Toward
HSA-REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Instructional Routines
Which Three Go Together?Materials
NoneActivity Narrative
This Warm-up prompts students to compare four systems of equations. It gives students a reason to use language precisely (MP6) and gives the opportunity to hear how they use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the systems of equations. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three systems of equations that go together and can explain why. Next, tell students to share their response with their group and then together to find as many sets of three as they can.
Activity
NoneWhich three go together? Why do they go together?
A
B
C
D
Student Response
Loading...
Building on Student Thinking
Activity Synthesis
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure that the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “coefficient,” “variable,” or “constant,” and to clarify their reasoning as needed. Consider asking:
- “How do you know ?”
- “What do you mean by ?”
- “Can you say that in another way?”
16.2
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity, students find intercepts and slopes for pairs of equations. They should notice that the equations in each pair are multiples of one another and, therefore, are equivalent equations. Students look for and make use of structure (MP7) when they notice the relationships between the pairs of equations.
Launch
Ask students what they remember about - and -intercepts. One useful thing to remember is that the -intercept of a graph occurs where the -coordinate is zero. (Demonstrate using a graph, if needed.) So, to find the -intercept of a graph representing an equation, you can replace with 0 and solve the equation for . (And vice versa to find the -intercept.)
Ask students how they can use two points like and to find the slope of a line. (Using a formula like , or a less-formal version like “subtract the y’s, subtract the x’s, then divide.” For this example the slope is -8 since .)
Action and Expression: Develop Expression and Communication. Provide access to a blank pre-formatted table for students to keep track of the key features of and what they notice about the equations.
Supports accessibility for: Visual-Spatial Processing, Fine Motor Skills
Supports accessibility for: Visual-Spatial Processing, Fine Motor Skills
16.3
Activity
Instructional Routines
MLR8: Discussion SupportsMaterials
NoneActivity Narrative
In this activity, students multiply an equation to get a specified coefficient to a target value. In the associated Algebra 1 lesson, students will need this skill for solving systems of equations by elimination. Since students are using the same skills to determine the new equation, this is an opportunity to express regularity in repeated reasoning (MP8).
Launch
Ask students to recall the meaning of the term coefficient. Display the equation and ask students to find the coefficients. (The coefficient of is 6. The coefficient of is . Regarding the 18, sometimes this is called “the constant term.”) Consider referring to the display created using Collect and Display from earlier lessons.