CCSS.Math.Content.8.F.A.1
The standard
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Common Core State Standards for Mathematics · Functions
What this standard means
Students need to decide whether a rule, table, mapping, graph, or set of ordered pairs is a function. The key test is simple: each input can have only one output. They also need to connect a graph to ordered pairs, seeing each point as one input matched with one output.
Mastery looks like students checking inputs first, not just looking for patterns. They can explain why repeated x-values with different y-values break the rule. Common trouble spots are mixing up input and output, thinking every graph is a function, and rejecting repeated outputs even though those are allowed.
Ways to teach it
- Give pairs of input-output cards and have students sort them into function and not function piles, then justify one card from each pile.
- Ask students to write: Can two different students have the same birthday, and how is that like a function?
- Show three tables and one graph, then have students mark yes or no for function and circle the evidence.
- Use a vending machine example where each button must give one item, then ask what would make the machine not function correctly.
Plan a lesson for CCSS.Math.Content.8.F.A.1
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