Start from a connected problem
You may know formulas or individual operations and still be unable to connect them into an answer. The Suite helps make those connections: what information a construction must retain, what another method can do with its result, and where a changed question makes earlier work worth revisiting.
| What you need to do | Follow the worked connection |
|---|---|
| Split or change a calculation while keeping its answer meaningful | Change a combining rule (MATH — MP-COMBINE-RESULTS): expose the lost distinction, construct a summary and operation, prove their compatibility, then use and revise them. |
| Decide a question without reconstructing every hidden detail | Obtain a sufficient answer (MMP — MMP-SUFFICIENT-ANSWER): expose what reduction loses, bound its effect, interpret the result and obtain more where it changes the answer. |
| Decide whether another observation will improve an action | Connect intervention, information and choice (MMP — MMP-INTERVENTION-AND-INFORMATION): derive the relevant consequences, compare the report’s benefit with its burden, and make the subsequent choice depend only on timely information. |
| Replace expensive component models and still obtain a usable joint answer | Replace and couple models (MMP — MMP-REPLACE-AND-COUPLE): retain the required responses, connect their meanings and error bounds, and refine only what prevents the answer. |
| Develop a physical prediction and decide which observation matters | Connect physical accounts and observations (PHY — PH-PREDICT-AND-DISTINGUISH): constrain the law, derive a consequence, compare the observations that matter and revise the affected premise. |
| Construct an algorithm and adapt it when the required answer changes | Keep construction and output consistent (CMP — CP-ANSWER-UNDER-LIMITS): construct the recurrence, share results, use bounds where they reduce search, and revisit what may be discarded. |
| Carry a changed instruction through several expressions | Keep meaning and change connected (NOT — NT-CHANGE-TOGETHER): recover references and interpretation, expose translation losses, and update the affected expressions. |
| Connect mathematics to changes in working methods | Understand and change a construction (Foundational.Reference:3.2): retain the distinction a later operation uses and connect it to the general Methods of methodological development in Core. |
| Make reasoning available to other contributors and develop its next use | Continue and distribute thinking (Foundational.Reference:3.5): recover a missing relation, arrange explanation or support, change the work and preserve the method for further development. |
These examples use several patterns together. Their short sequences show dependencies; worked explanations give calculations and return points. Start at a later contribution when its inputs are available. Each DPF’s Table of Contents also gives direct help for other questions.
The vertical of ongoing work (Foundational.Reference:3.9) asks a complementary question: what larger work is being performed through this action now, and what constituent abilities and resources make it possible? It helps locate a missing intermediate Method or capability even when the elementary operations and the intended whole are familiar.