STEM EVIDENCE WORKBENCH
Audit ratio-table rows with cross-products and column scale factors while separating multiplicative equivalence from additive-looking patterns.
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
A row a:b matches base A:B when a times B equals b times A. The visible scale factors a/A and b/B should also match. Cross-products preserve exact decimal evidence better than independently rounded ratios. A zero-to-zero row is compatible but does not supply a useful nonzero scale factor by itself. A supported row agrees with both the entered claim and the reference ratio. Unequal factors show which column broke the multiplicative relationship. Ask the learner to name the common factor, draw a double number line, and connect each quantity with its unit before using the result as teaching evidence.
Confirm the prompt, source values, units, signs, notation, precision, and model required by the current course. Keep an untouched copy of observations or responses before changing a row.
Run the worked example first, inspect every intermediate row, and compare the table with a hand calculation, diagram, graph, periodic table, or approved laboratory method.
Record the method, assumptions, units, rounding, limits, and any row that needs review. Use the exported report as editable evidence and verify it independently before assessment or laboratory use.
How to interpret the result
Use this diagnostic after learners extend, shrink, or interpret a ratio table and need row-level feedback about multiplicative structure. It can distinguish equal column factors from adding the same amount. It does not decide whether a real context should use a ratio, validate measurement units, or diagnose the reasoning behind an incorrect row.
The paint-mixture example uses 2 to 5 as its base. Pairs 4 to 10, 6 to 15, and 1 to 2.5 have matching factors. The 8 to 18 row does not match even though both entries may look like additions. A 10 to 20 row is correctly labeled different because its second-to-first ratio is two instead of 2.5.
A row a:b matches base A:B when a times B equals b times A. The visible scale factors a/A and b/B should also match. Cross-products preserve exact decimal evidence better than independently rounded ratios. A zero-to-zero row is compatible but does not supply a useful nonzero scale factor by itself.
A supported row agrees with both the entered claim and the reference ratio. Unequal factors show which column broke the multiplicative relationship. Ask the learner to name the common factor, draw a double number line, and connect each quantity with its unit before using the result as teaching evidence.
Do not add the same number to both columns, scale one column only, reverse the base order, compare differences instead of factors, or round close ratios too early. Do not assume every pair of positive quantities is meaningful as a ratio; review units and context first.
Learning boundary
This browser-local workbench applies only the disclosed rules to entered values. It cannot diagnose learning, certify an experiment, establish a chemical fact, reconstruct missing evidence, or replace the method and judgment required by a teacher, curriculum, laboratory, or institution.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid names and other personal information, and retain authoritative records only in the system approved by the school.
No. A matched pattern describes the entered evidence under one disclosed rule. Ask for an explanation and review several evidence sources before deciding the next step.
Treat it as an editable calculation aid. Show your own reasoning, use the method requested by the course, cite required sources, and follow the applicable academic-integrity rules.
YOUR NIRMION
