Activity 01
Card Sort: Relations vs Functions
Prepare cards with inputs and multiple possible outputs for relations, and single outputs for functions. In small groups, students sort cards into two piles and justify choices using arrow diagrams. Discuss edge cases like empty sets as one group.
Compare and contrast a general relation with a function.
Facilitation TipDuring Card Sort: Relations vs Functions, ask groups to first categorise cards silently, then discuss disagreements aloud to surface misconceptions early.
What to look forPresent students with 3-4 sets of ordered pairs. Ask them to write 'Function' or 'Not a Function' next to each set and provide a one-sentence justification for their answer, focusing on the input-output rule.
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Activity 02
Vertical Line Test Relay
Display graphs on the board or handouts. Pairs take turns drawing vertical lines at different x-values and checking intersections. Switch roles after five lines; the first pair to identify all functions correctly wins a point.
Justify why a vertical line test is effective for identifying functions.
Facilitation TipFor Vertical Line Test Relay, have students rotate roles between tester, sketcher, and recorder so every learner stays engaged.
What to look forGive students a simple function rule, e.g., f(x) = x² + 1. Ask them to calculate f(3) and f(-2). Then, ask them to draw a quick sketch of the graph and perform the vertical line test, stating their conclusion.
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Activity 03
Function Machine Game
One student acts as the 'machine' with a secret rule like f(x) = x + 3. Others input numbers and guess the output. Rotate roles; class compiles a table to verify if it behaves like a function.
Predict the output of a simple function given an input and its rule.
Facilitation TipRun Function Machine Game with a timer to create urgency, then pause for peer checks before revealing answers.
What to look forShow students an arrow diagram where one element in the domain maps to two elements in the codomain. Ask: 'Why is this not a function? What would need to change for it to become a function?' Facilitate a brief class discussion on the uniqueness requirement.
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Activity 04
Mapping Table Challenge
Provide tables with inputs and mixed outputs. Individually, students rewrite tables to make them functions by choosing one output per input, then share and vote on creative solutions.
Compare and contrast a general relation with a function.
Facilitation TipIn Mapping Table Challenge, insist students write the rule in words before coding it numerically to strengthen conceptual bridges.
What to look forPresent students with 3-4 sets of ordered pairs. Ask them to write 'Function' or 'Not a Function' next to each set and provide a one-sentence justification for their answer, focusing on the input-output rule.
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Generate Complete Lesson→A few notes on teaching this unit
Teach functions by starting with real-life examples like student roll numbers mapping to names, which naturally enforce one-to-one output. Avoid rushing to formal definitions; instead, let students discover the uniqueness rule through guided exploration. Research shows that multiple representations—arrow diagrams, tables, and graphs—strengthen flexible thinking, so rotate between them deliberately. Watch for students who confuse input with output order; gentle prompts like 'Show me the input and output in this pair' often clarify confusion.
By the end of these activities, students will confidently identify functions using multiple representations. They will explain the one-to-one output rule, apply the vertical line test correctly, and justify their reasoning using ordered pairs, arrow diagrams, tables, and graphs without hesitation.
Watch Out for These Misconceptions
During Card Sort: Relations vs Functions, watch for students who label any pairing as a function without checking for unique outputs.
Have them physically count arrows from each domain element; if two arrows leave one element, prompt them to reclassify it as a relation first.
During Vertical Line Test Relay, watch for students who apply the test only to straight lines.
Provide a parabola graph and ask them to sketch vertical lines at three points to verify the output uniqueness rule applies to curves too.
During Mapping Table Challenge, watch for students who assume tables are always functions without checking rows for duplicate inputs.
Ask them to scan input columns aloud and circle any duplicate values before deciding if it is a function or not.
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