PA.A.4.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form px + q > r and px + q < r , where p, q and r are rational numbers.
In a Nutshell
Students need to make the connection between an inequality and the real-world scenario that it represents. As students solve their inequalities, they should be able to represent it numerically, verbally, and graphically as well as apply the solution set in context of the problem.
Student Actions
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Teacher Actions
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Develop Accurate and Appropriate Procedural Fluency when writing linear inequalities with one variable in the form px + q > r and px + q < r, where p, q, and r are rational numbers.
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Develop Ability to Communicate Mathematically by using words to describe the solution to an inequality before writing it mathematically. Check answers using substitution.
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Develop a Deep and Flexible Conceptual Understanding when using words describing inequality solutions to explain how the graphical representation matches the problem.
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Develop Mathematical Reasoning by exploring tasks that require switching the inequality symbol and explain why that is done in context to the problem. (When you multiply or divide by a negative)
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Promote procedural fluency by using number lines when showing the solution to an inequality so students can see all possible answers and don’t intentionally leave out possible solutions.
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Make mathematical connections by relating solutions to inequalities to words that describe the solutions, which helps students make sense of the inequality symbols.
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Implement meaningful tasks that promote reasoning and problem solving and avoid telling students the rule, giving students opportunities to understand why the inequality sign changes direction when multiplying or dividing by a negative number.
- Implement meaningful tasks that promote reasoning and problem solving by allowing students to determine the rules for the direction of shading and for open and closed circles. This can be done through matching activities and multiple examples.
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Key Understandings
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Misconceptions
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Make connection to real world scenarios and inequalities.
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Represent inequalities numerically, verbally, and graphically.
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Explain the solution set, of the inequality, in the context of the problems.
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Students get confused and misinterpret the inequality symbols.
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Students may forget to switch the direction of the inequality symbol (aka "flip" the inequality symbol) when multiplying or dividing by a negative number when solving.
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Students may think that the inequality symbols indicate the direction of the shading of the number line.
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OKMath Framework Introduction
Pre-Algebra Introduction
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