7.A.3.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x+p>q and x+p<q, where p, and q are nonnegative rational numbers.
In a Nutshell
Use real-life and mathematical situations and represent them using algebraic symbols, and graphs as inequalities. The inequalities should only have a rate of change of one and a positive constant. Graphing should take place on a vertical or horizontal number line. Solve problems involving >, <, ≤, and ≥ symbols by isolating a single variable.
Student Actions
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Teacher Actions
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- Develop strategies for solving and graphing inequalities.
- Develop accurate and appropriate procedural fluency when solving inequalities.
- Develop a deep and flexible conceptual understanding of linear inequalities with one variable, by selecting which forms of single-variable equation represents a given real world situation.
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- Use and connect multiple representations of inequalities such as tables, symbols, graphs, and inequalities.
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Pose purposeful questions to students that probe whether solutions make sense, scaffold for help and extend inequalities for students ready to continue.
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Implement tasks that promote reasoning and problem solving beyond just basic problem solving.
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Develop a productive mathematical disposition as students explore strategies.
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Elicit and use evidence of student thinking to ensure the properties of inequalities (especially the reversal and addition/subtraction properties) are clear and not overgeneralized.
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Key Understandings
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Misconceptions
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Be able to identify the symbols by their name and understand the meaning of >, <, ≤, and ≥.
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Algebraically solve 1 or 2 step inequalities for an unknown value. (May require simplification before using algebraic properties of inequalities.)
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Identify areas on a number line by shading that would satisfy all the terms of an inequality.
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Operations on an inequality should be done in a certain order.
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More than one answer, and sometimes an infinite number, will satisfy an inequality.
- Write inequalities by a rate of change of one and identify a positive, constant value from a real-world situation.
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Students may confuse the words “at least” and “at most”.
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Students may not see infinite solutions that make the inequality true.
- Students may have difficulty graphing solutions to inequalities where the variable is not presented first. Example 2<a instead of a>2.
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Students may have difficulty algebraically representing the words at least, at most, not more than and not less than.
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OKMath Framework Introduction
7th Grade Introduction
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