STEM REASONING AND EVIDENCE WORKBENCH
Partition positive integer quantity pairs into identical primitive ratio groups and audit learner simplest-ratio claims.
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
The greatest common divisor of positive integers a and b gives the largest number of identical whole-number groups. Divide both quantities by that divisor to obtain the primitive ratio a over gcd to b over gcd. Cross-products show whether another pair is equivalent, while a greatest common divisor of one confirms the pair is in simplest form. A supported row names the exact primitive group in the same quantity order. An equivalent but nonsimplest response still represents the same multiplicative comparison but needs another common division. A conflict changes the ratio. Connect the primitive group with repeated table rows, a tape diagram, a double number line, and the context before generalizing.
Confirm the question, approved source, units, notation, signs, response coding, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner evidence.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, representation, periodic table, or approved laboratory method.
Record the method, assumptions, uncertainty, units, classifications, and flagged rows. Verify the editable report independently before instruction, assessment, or laboratory use.
How to interpret the result
Use when learners can populate a ratio table but need to explain the multiplicative structure beneath it. The model exposes how many identical primitive groups compose each pair and distinguishes an equivalent ratio from a simplest ratio. It does not process fractions, negative quantities, mixed units, additive patterns, rates with zero denominators, or causal claims.
Six to nine and fourteen to twenty-one both reduce to two to three, with scale factors three and seven. Eight to twenty reduces to two to five. The final twelve-to-eighteen pair also reduces to two to three, so the learner claim three to four changes the relationship rather than naming one identical group.
The greatest common divisor of positive integers a and b gives the largest number of identical whole-number groups. Divide both quantities by that divisor to obtain the primitive ratio a over gcd to b over gcd. Cross-products show whether another pair is equivalent, while a greatest common divisor of one confirms the pair is in simplest form.
A supported row names the exact primitive group in the same quantity order. An equivalent but nonsimplest response still represents the same multiplicative comparison but needs another common division. A conflict changes the ratio. Connect the primitive group with repeated table rows, a tape diagram, a double number line, and the context before generalizing.
Do not subtract the same amount from both parts, divide only one quantity, reverse the quantity order, compare labels with different units, assume any increasing table is proportional, or treat a simplified ratio as a fraction of the total without stating the whole. Label each quantity, identify one group, and multiply back to verify.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish a chemical structure, or replace teacher, laboratory, 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 school-approved system.
No. It describes entered evidence under one disclosed rule. Compare several evidence sources and ask for reasoning before drawing a conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow the course method and academic-integrity rules.
YOUR NIRMION
