Singapore School Mathematics Operating Manual · Chapter 55
Change assumptions or parameters systematically, compare resulting mathematical states, and distinguish a controlled what-if scenario from an unsupported prediction.
This is a cross-topic operating-control chapter for the Singapore Mathematics spine. It complements existing BTT owners and is intended to connect Primary reasoning, PSLE, SEC G1/G2/G3, E-Math, A-Math and JC Mathematics without replacing their topic-specific teaching.
1. A scenario changes specified inputs while holding others controlled
Make a scenario changes specified inputs while holding others controlled explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
2. Baseline comes first
Make baseline comes first explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
3. One-factor changes isolate effects
Make one-factor changes isolate effects explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
4. Multi-factor scenarios reveal interactions
Make multi-factor scenarios reveal interactions explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
5. Counterfactuals ask what the model would imply under a different condition
Make counterfactuals ask what the model would imply under a different condition explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
6. Scenario analysis is conditional not predictive certainty
Make scenario analysis is conditional not predictive certainty explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
7. Parameter ranges are stronger than one alternative point
Make parameter ranges are stronger than one alternative point explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
8. Best-case and worst-case scenarios need explicit definitions
Make best-case and worst-case scenarios need explicit definitions explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
9. Threshold scenarios identify regime changes
Make threshold scenarios identify regime changes explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
10. Sensitivity and scenario analysis are related but different
Make sensitivity and scenario analysis are related but different explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
11. Discrete scenarios suit categorical assumptions
Make discrete scenarios suit categorical assumptions explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
12. Continuous sweeps suit numerical parameters
Make continuous sweeps suit numerical parameters explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
13. Scenario tables preserve comparability
Make scenario tables preserve comparability explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
14. Use the same output metrics across scenarios
Make use the same output metrics across scenarios explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
15. Do not change hidden assumptions between rows
Make do not change hidden assumptions between rows explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
16. Interactions can make combined effects non-additive
Make interactions can make combined effects non-additive explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
17. Scenario results inherit model assumptions
Make scenario results inherit model assumptions explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
18. Extreme scenarios can stress-test conclusions
Make extreme scenarios can stress-test conclusions explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
19. Return to the baseline after each isolated test
Make return to the baseline after each isolated test explicit before calculation. Use a small worked example, preserve the active domain and units, and check the result against an independent representation, bound or baseline where possible. The purpose is to control reasoning across topics rather than introduce a competing topic owner.
20. A scenario-analysis audit
Ask what must remain consistent, what is allowed to change, which bound or comparison is global, and what evidence would make the conclusion auditable from the original problem.
21. Worked examples
Example 1. If category percentages are exhaustive, their total should be 100% apart from justified rounding. A larger discrepancy signals a missing, duplicated or misclassified part.
Example 2. If a minimisation candidate uses 8 containers and a capacity argument proves at least 8 are necessary, the lower bound and construction match; 8 is optimal.
Example 3. In a what-if table, change one named parameter from the baseline while keeping the remaining assumptions fixed before interpreting the difference.
Example 4. Translating coordinate axes changes point coordinates but does not change the physical distance between the same two geometric points.
22. Independent practice
1. Give one mathematical total that can be reconciled in two ways.
2. Explain how a lower bound plus a matching feasible construction can prove a minimum.
3. State the difference between a baseline and a scenario.
4. Name one quantity preserved when a coordinate system is translated.
5. Explain why all compared scenarios must use consistent definitions.
23. Worked answers
1. Examples include probability branches summing to 1, frequencies summing to sample size, or component areas summing to total area.
2. No feasible answer can be below the lower bound, and the construction attains it, so nothing better exists.
3. The baseline is the reference set of assumptions; a scenario changes specified assumptions or parameters relative to it.
4. Distance between fixed geometric points.
5. Otherwise differences can be caused by hidden definition changes rather than the named scenario change.
24. Continue through Batch 14
Return to the BTT Mathematics Hub for Batch 14.