Unit 4, Lesson 3
Interpreting Inequalities
Extra Support Materials for Algebra 1
3.1
Warm-up
Standards Alignment
Building On
Addressing
6.NS.C.7.b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write to express the fact that is warmer than .
Materials
NoneActivity Narrative
This Math Talk focuses on solving inequalities. It encourages students to think about solving for a variable and to rely on what they know about solving equations to solve problems. The understandings elicited here will be helpful later in this lesson when students will need to be able to solve inequalities in order to match them with the appropriate graph and situation.
In explaining their answers, students need to be precise in their word choice and use of language (MP6).
Launch
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies, and record and display their responses for all to see.
- Before moving to the next problem, use the questions in the Activity Synthesis to involve more students in the conversation.
Keep all previous problems and work displayed throughout the talk.
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 for mentally.
Activity Synthesis
The goal of this discussion is to review students’ strategies for solving inequalities.
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
-
“Who can restate ’s reasoning in a different way?”
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“Did anyone have the same strategy but would explain it differently?”
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“Did anyone solve the problem in a different way?”
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“Does anyone want to add on to ’s strategy?”
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“Do you agree or disagree? Why?”
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"What connections to previous problems do you see?"
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. Examples:
Advances: Speaking, Representing
- “First, I because .”
- “I noticed , so I .”
Advances: Speaking, Representing
3.2
Activity
Instructional Routines
MLR2: Collect and DisplayMaterials
NoneActivity Narrative
The purpose of this activity is for students to practice solving inequalities and checking their solutions, especially those involving negative numbers. Students also practice representing inequalities written in natural language with symbols and number lines, and connecting the solution of an inequality with a number line. The work in this activity will be useful when students solve more complex inequalities in the associated Algebra 1 lesson. As students make decisions about solving and checking inequalities and make connections between situations and graphs, they make sense of problems and persevere in solving them (MP1).
This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.
Launch
Arrange students in groups of 2. Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to solve inequalities, check their solutions, and graph the inequalities. Display words and phrases, such as “same thing on each side,” “add,” “subtract,” “multiply,” “divide,” “open circle,” “closed circle,” and “change directions.”
3.3
Activity
Instructional Routines
Card SortMaterials
To Copy (from Blackline Masters)
What's the Situation Cards
Activity Narrative
Students sort different representations of inequalities during this activity. A sorting task gives students opportunities to analyze representations, statements, and structures closely and to make connections (MP2, MP7).
Monitor for different ways groups choose to categorize the representations, but especially for categories that distinguish between greater than and less than statements as well as those that distinguish between strictly greater or less than statements compared with those that can be equal to.
As students work, encourage them to refine their descriptions of their groupings using more precise language and mathematical terms (MP6).
Launch
Arrange students in groups of 2. Tell them that in this activity, they will sort some cards into categories of their choosing. When they sort the representations, they should work with their partner to come up with categories. Encourage students to find more than one way to sort the cards.