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.
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.