STEM MODEL AND EVIDENCE WORKBENCH
Build exact partition, area, and reciprocal-step models for fraction addition, subtraction, multiplication, and division.
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
Addition and subtraction use ad plus or minus cb over bd, then reduce. Multiplication uses ac over bd. Division uses ad over bc when c is nonzero. The greatest common divisor reduces numerator and denominator, while the least common multiple supplies the smallest common partition for addition and subtraction evidence. The result connects the exact operation with a count statement and reduced fraction. Ask learners why equal wholes matter, why both parts scale in a common partition, why area dimensions multiply, or why division asks how many divisor-sized groups fit. A correct result alone does not demonstrate those connections.
Confirm the task, approved source, units, notation, signs, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner responses.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, physical model, 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 need a representation behind fraction algorithms. Common partitions support addition and subtraction, area counts support multiplication, and reciprocal reasoning supports division. The builder does not draw measured geometry, infer the intended whole, assess an explanation, or decide which visual representation is developmentally appropriate.
The example adds two thirds and one fourth using twelve common parts, subtracts one third from five sixths using sixths, models three fifths times two thirds as six of fifteen area cells, and divides four sevenths by two fifths through multiplication by five halves. Every result is reduced visibly.
Addition and subtraction use ad plus or minus cb over bd, then reduce. Multiplication uses ac over bd. Division uses ad over bc when c is nonzero. The greatest common divisor reduces numerator and denominator, while the least common multiple supplies the smallest common partition for addition and subtraction evidence.
The result connects the exact operation with a count statement and reduced fraction. Ask learners why equal wholes matter, why both parts scale in a common partition, why area dimensions multiply, or why division asks how many divisor-sized groups fit. A correct result alone does not demonstrate those connections.
Do not add denominators, scale only numerators, cancel across addition, invert the first fraction, divide by zero, or hide an unreduced ratio. Keep the shared whole explicit, preserve signs, and connect each symbolic step to equal partitions, an area model, measurement, or grouping context.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose learning, certify an experiment, identify a substance, establish a 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
