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Function Intro9-12 · Function Intro: Conjecture and justification challenge

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Structured investigationAlgebra I

Function Intro: Conjecture and justification challenge

Function Intro focus: functions as input-output relationships. A conjecture fits familiar cases but its domain is not yet justified.

What representation and justification make a Grade 9 claim about functions as input-output relationships valid within its stated domain?

CourseAlgebra I

RigorOn-level

Performance artifactModel and justification portfolio

Evidence minimum2 evidence forms

Connect a table, graph, or diagram to a symbolic relationship and state its domain.

variable
representation
equivalence
conjecture

1Conjecture
2Represent
3Test
4Analyze assumptions
5Revise
6Justify
7Generalize

Model

Representations, assumptions, and quantities

Test 3 cases using a visual model, table or graph, and symbolic rule. Record assumptions and a boundary value.

Represent: Function Intro visual model, table or graph, symbolic rule
Justify: Connect equivalent representations and justify each inference about Use Function Intro to investigate functions as input-output relationships and produce a defensible mathematics explanation, design, interpretation, or decision.
Counterexample: A universal claim must survive a boundary case or be revised to state its domain.
Assumptions: Name the domain, parameter constraints, and whether a computed case establishes or merely illustrates the claim.

Input quantity50Model parameter28

Select the conjecture that can be tested across representations and boundary cases.

Evidence

Cases and counterexample check

Commit a falsifiable model and run the repeated trials to generate the dataset.

Model and justification portfolio

linked representations
valid computation
assumption or counterexample check
generalized justification

Original World tools

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