Unit 4, Lesson 9
Testing Points to Solve Inequalities
Extra Support Materials for Algebra 1
9.1
Warm-up
Instructional Routines
Worked ExampleMaterials
NoneActivity Narrative
The purpose of this activity is to examine how to solve an inequality using a test point.
This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.
Launch
Arrange students in groups of 2. Tell them to close their books or devices (or to keep them closed). Reveal the prompt and the first step. Give students a brief quiet think time, and ask them to give a signal when they have read the step and are ready to see the next. Once most students have given the signal, reveal the next step. Repeat until all steps have been revealed.
If previous work indicates that most students will struggle to make sense of a step, pause and give students 1 minute to discuss with their partner and formulate a question about the step. Ask 1–3 groups to share their questions, inviting other groups to answer while recording responses next to the step for all to see. Once questions have been answered, continue to the next reveal.
Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Supports accessibility for: Memory, Organization
Activity
NoneSolve the inequality and use a test point to check your answer.
Step 1:
Step 2:
When .
, so 0 is not a solution.
Step 3:
, so all solutions are .
Activity Synthesis
The purpose of this discussion is to analyze the steps taken by the solver to solve an inequality and use a test point.
Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.
- “Why did the inequality become an equation?” (Solving for in the equation shows where the endpoint of the inequality is. All of the solutions will either be greater than or less than that number.)
- “Why did the solver choose 0 as their test point?” (The solver could choose any number that is not -3 as their test point. 0 is usually a number that is nice to work with.)
- “Why did the solved inequality have a different inequality sign from the original inequality?” (Since 0 is not a solution to the inequality and 0 is greater than -3, the solutions must be the numbers that are less than -3, which changes the inequality sign.)
Ask partners to compare their responses to each question and decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.
If time allows, consider displaying a second worked example next to the first that either:
- Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7).
- Shows the same method with an error that students can critique and correct (MP3).