755 prompts matching "Structured question: three-part algebra question mixing methods"
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Learn: What closure means for a binary operation
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Quiz: Testing the odd numbers for closure under addition
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Practice: Testing a set for closure under multiplication
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Explain Back: Testing the integers for closure under division
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Spot My Mistake: Reading closure off an operation table
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Learn: What it means for an operation to be commutative
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Quiz: Reading commutativity off a symmetrical operation table
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Practice: An operation that is not commutative, with a counter-example
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Explain Back: What it means for an operation to be associative
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Spot My Mistake: Testing (a*b)*c against a*(b*c)
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Common Mistakes: Subtraction as an example of neither law
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Learn: What it means for one operation to distribute over another
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Quiz: Left distributivity and right distributivity
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Practice: Multiplication distributing over addition in ordinary arithmetic
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Explain Back: Showing distributivity fails by a counter-example
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Spot My Mistake: Checking distributivity from two operation tables
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Learn: What an identity element is
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Quiz: Finding the identity element from an operation table
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Practice: Why an identity element must work from both sides
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Explain Back: What an inverse element is
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