STEM PRACTICE AND EVIDENCE WORKBENCH
Compare unit rates from two ordered pairs and audit learner constants and proportional or not-proportional classifications.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Calculate k1 = y1/x1 and k2 = y2/x2. The pairs are proportional when their difference falls within the entered percentage tolerance. The learner constant is checked against k1 with the same tolerance. A response is supported only when both the numerical constant and proportional or not-proportional classification agree with the disclosed calculations. Supported means the learner response matches the two entered pairs, not that a whole dataset or causal model has been validated. A correct label with an incorrect constant suggests calculation or unit-rate evidence needs review. Consider whether the relationship includes the origin, whether a fixed fee creates a nonzero intercept, whether signs and units are meaningful, and whether rounding or measurement uncertainty justifies the tolerance.
Confirm the learning question, authoritative source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence and remove learner names or identifiers.
Run the worked example first, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method. Correct input evidence before interpreting a flag.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently, connect the numerical signal with learner reasoning, and document any teaching or laboratory decision outside this tool.
How to interpret the result
Use when a learner must decide whether two points are consistent with y = kx and explain the constant of proportionality. The workbench separates the unit-rate calculation from the classification label, which helps distinguish arithmetic from concept errors. It does not prove that all possible observations follow one rule, fit an intercept, infer units, read a graph image, or decide whether proportionality is appropriate for the real context.
The recipe pairs 2 to 6 and 5 to 15 both give k equals 3. Distance-time pairs give 4. The fee example produces rates 7 and 11 divided by 3, so the not-proportional claim is supported even though the first entered rate is 7. The final pairs both produce 2.5, but learner k is 5, so its otherwise correct classification is flagged.
Calculate k1 = y1/x1 and k2 = y2/x2. The pairs are proportional when their difference falls within the entered percentage tolerance. The learner constant is checked against k1 with the same tolerance. A response is supported only when both the numerical constant and proportional or not-proportional classification agree with the disclosed calculations.
Supported means the learner response matches the two entered pairs, not that a whole dataset or causal model has been validated. A correct label with an incorrect constant suggests calculation or unit-rate evidence needs review. Consider whether the relationship includes the origin, whether a fixed fee creates a nonzero intercept, whether signs and units are meaningful, and whether rounding or measurement uncertainty justifies the tolerance.
Do not compare y-values alone, divide x by y after defining k as y per x, use an x-value of zero, declare proportional from a constant difference, ignore units, treat two approximate rates as exactly equal without a threshold, or claim that any straight line is proportional. Write both ratios with labels and test whether the model also makes contextual sense.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish assessment validity, or replace teacher, laboratory, curriculum, accessibility, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
