Connect a Dependent Variable to a Table and Rule
Use the supplied rule and input count to calculate the output.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: A fictional printing model uses y=5x, with x sheets and y seconds, for nonnegative whole x.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A relationship can define one quantity from another. The independent input is chosen within a stated domain; the dependent output follows the rule. A table records input-output pairs and a graph locates them. Units and model limits explain what the symbols mean and when the rule applies.
Use the supplied rule and input count to calculate the output. Build at least three labeled table rows and identify which quantity is dependent. Check an output against the rule rather than drawing a trend without numerical support.
Label both variables with units and domain restrictions. A fictional rule does not certify how a real device behaves. Make a table whose first column is the chosen input and second is the calculated output.
- Make a table whose first column is the chosen input and second is the calculated output.
- Work through the supplied example and label what each number or attribute represents.
- Use the supplied rule and input count to calculate the output.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
A fictional printing model uses y=5x, with x sheets and y seconds, for nonnegative whole x. For x=0,2,4, outputs are 0,10,20 seconds. Time is dependent in this model. The rule says nothing about an actual printer’s pauses or behavior outside the stated exercise. Label both variables with units and domain restrictions. A fictional rule does not certify how a real device behaves. Make a table whose first column is the chosen input and second is the calculated output.
Check your reasoning
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Helpful tips
- Label both variables with units and domain restrictions.
- A fictional rule does not certify how a real device behaves.
See the answer and explanation
12
Substitute the independent packet count into the four-cards-per-packet rule. The result is 12.
Take it further
For y=3x+2 at x=0,1,3, expected outputs are 2,5,11.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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