Eighth Grade · Math · week 10

Function or not?

Determine whether a relation is a function, using the rule that each input has exactly one output.

A function is a rule where every input gives exactly ONE output. Check a table by scanning the input column for repeats: if an input repeats with two DIFFERENT outputs, it breaks the rule and is not a function. If outputs repeat, that is perfectly fine -- only repeated inputs with different outputs are the problem.

A real-life way to feel this: "person -> birth month" is a function, since every person has exactly one birth month. "Birth month -> person" is not, since many people share a birth month (one input, many possible outputs).

📋 For the teacher

Teach it (10–15 min):

State the one rule clearly: each input gives exactly ONE output. Repeated outputs never break it; repeated inputs with different outputs always do.
Scan a table by looking at the INPUT column only for repeats -- that is the whole test.
Use "person -> favorite color" (a function) versus "favorite color -> person" (not a function) to make the direction matter concrete.
Keep this playful with a guessing game: you are the machine, they feed you inputs, you answer, and they try to figure out your rule.

Talk about it:

Why does a repeated OUTPUT not break the function rule, but a repeated INPUT with two different outputs does?
Is "name -> favorite color" a function? What about "favorite color -> name"? Why the difference?
How would you check a big table for whether it is a function, without comparing every pair to every other?

Mastery looks like: Given a table, list of pairs, or description, they correctly decide function or not and justify it using the one-input-one-output rule.

Common stumbles: Flagging repeated outputs as a problem; missing a repeated input because the pairs are not listed in order.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →

Records attendance + 15 min of Math for this learner.

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