8.F.1 Functions and the word "Rule"

Home Forums Questions about the standards 8–12 Functions 8.F.1 Functions and the word "Rule"

This topic contains 1 reply, has 2 voices, and was last updated by  Bill McCallum 4 years, 2 months ago.

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    I’m seeking clarity on the definition of the word rule in the first sentence of standard 8.F.1.

    When I first read it, without hesitation, I thought of the definition:
    rule – a prescribed guide for conduct or action (merriam-webster)

    While arguing with a friend =), he defined rule as in a pattern rule (Grade 4.OA.5). Leading the the following claims:

    Ex.1 Suppose a function sends 1 to 3, 2 to 7, 3 to -1.
    Me: “The ‘rule’ (the guidelines for conduct, the accepted procedure) is send 1 to 3, 2 to 7, and 3 to -1.”
    Friend: “The function has a mapping but no rule because there is no pattern.”

    I think it’s an interesting topic for educators that have spent years with function machines and finding patterns to determine the ‘rule.’ Hopefully our debate can provide clarity for others.

    #2189 Reply

    Bill McCallum

    Your debate has nicely captured the way the meaning of rule evolves over the grades. In Grade 4 it means what your friend says: a prescribed sequence of arithmetic operations. The rule could be either recursive (start with 1 and keep adding 3s) or explicit (think of a number, double it and add 1). This leads to the Grade 8 notion of using a rule to define a function. At some point the concept of a rule becomes merged into the concept of a function. Your example illustrates this.

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