Reflection: Grappling with Complexity Sometimes, Always, Never with Absolute Value - Section 2: Investigation


In examining these statements, the biggest challenge for students was to think abstractly. I was happy for students to start by plugging in numbers, but even using this strategy accurately requires abstraction, because some thought is required to choose numbers.

Some questions I asked to try to help students choose numbers were:

  • Can you choose values that would make the statement false?
  • Can you choose values that would make the statement true?
  • What different types of values should you consider in order to determine whether statement is sometimes, always or never true?

Some students choose to use graphing technology, by treating both sides of the equation as a separate function and graphing both functions. They could leave a or b as a slider and use x for the other value. This enabled them to determine whether the expressions were equivalent.

I had a few students who were able to think about the statements abstractly without plugging in any numbers. They were able to make generalizations like, “This statement will be true as long as x is greater than a,” for instance. I tried to highlight these observations by having them record them on the document camera, so after other students had come to their conclusions, I shared them with the class.

  Different Strategies
  Grappling with Complexity: Different Strategies
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Sometimes, Always, Never with Absolute Value

Unit 3: Absolute Value Functions and More Piecewise Functions
Lesson 7 of 9

Objective: SWBAT determine whether statements involving absolute value are sometimes, always or never true using justifications and counterexamples.

Big Idea: How can you test your theories? Students work at different levels of abstraction, either working with numerical examples or algebraic generalizations.

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Math, Algebra, Graphing (Algebra), interpreting graphs, absolute value functions, interpreting algebraic expressions, function
  75 minutes
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