A1.A.2.1 Represent relationships in various contexts with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.
In a Nutshell
Students will solve linear inequalities and graph their solutions on a coordinate plane while interpreting and communicating their solutions. Students will also write inequalities of given graphs and interpret the solutions.
Student Actions
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Teacher Actions
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Students will develop a deep and flexible conceptual understanding by examining various models of linear inequalities and discovering relationships between these models.
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Students will develop accurate and appropriate procedural fluency as they connect different models of inequalities to algebraic representations and begin to use inverse properties learned in pre-algebra to solve these inequalities.
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Students will develop strategies for problems solving as they work with models of inequalities, including number lines and coordinate planes, and then apply those understandings to begin solving problems algebraically. Students will also understand their solutions in the context of the problem, understanding that a range of values will be the solution in these situations.
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Students develop mathematical reasoning as they draw connections between various models of a situation involving an inequality and as they interpret their solutions correctly in context and check for reasonableness of those solutions.
- Students will develop the ability to communicate mathematically by interpreting and translating verbally and graphically the solutions of inequalities using correct mathematical notation and by explaining their reasoning and solutions to teachers and peers.
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Use and connect mathematical representations by providing students with many models (verbal, sketches, number lines, coordinate plane) of one and two variable inequalities.
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Build procedural fluency from conceptual understanding by helping students discover the connections between various models of inequalities and applying previously taught ideas of equality to solving inequalities.
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Pose purposeful questions while working with individuals, small groups the whole class to guide students’ exploration of a variety of models of inequalities, finding patterns in the models, and connecting them to real-world situations.
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Implement tasks that promote reasoning and problem solving by introducing real-world problems that involve inequalities, encouraging creative methods for solving (including relying on models), and expecting students to interpret their solutions in the correct context.
- Elicit and use evidence of student thinking by asking students to explain their reasoning and processes to both teachers and peers, building on their explanations to guide them toward deeper thinking.
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Key Understandings
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Misconceptions
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For Example:
Graph the inequality y≥−x+1.
Solution:
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For Example:
8x -2y < -2
-2y < -8x - 2
Incorrect answer: y < 4x + 1*
Correct answer: y > 4x - 1 *Here a student may forget to reverse the symbol while dividing by -2 in the previous step.
- Students may not identify the correct side of a boundary line area as a solution.
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Students may not consider the shaded region and its boundary line together as multiple solutions possible.
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Students may confuse the differences of solid and dashed lines and their meanings in a linear inequality.
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OKMath Framework Introduction
Algebra 1 Introduction
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