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This guide tackles distinguishing a germinated count from the proportion that germinated. Ask: Were the same numbers of seeds tested, or must each germinated count be related to a different starting total? The goal is a portable decision, not a memorised surface pattern.
Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. The sections build this model through mechanism, contrasting cases, misconception repair, practice, delayed transfer and examination control.
Use the complete Learner’s Guide volume directory, the original PSLE Learning Guide, and the Science hub. Current format information is available from the official SEAB PSLE formats examined in 2026.
Mechanism before method
Mechanism 1
A germinated count states how many seeds sprouted. A germination proportion relates that count to the number originally tested. The denominator is part of the scientific comparison.
Mechanism 2
If 8 of 10 seeds germinate and 8 of 20 germinate, the final counts match but the proportions differ. The first setup has 80 per cent germination and the second has 40 per cent.
Mechanism 3
When starting counts are equal, comparing germinated counts is sufficient because both counts use the same denominator. State that condition rather than treating it as automatic.
Mechanism 4
Fair comparisons also require relevant controlled conditions such as seed type, observation period, water, temperature and a consistent criterion for germination.
Mechanism 5
A percentage does not repair weak experimental design. Very small samples, damaged seeds or unequal observation times can limit what the result supports.
Use four moves: name the job, select controlling evidence, apply the relationship, and reject the nearest alternative with a reason. A correct answer without its evidence is too fragile for transfer.
Worked decision laboratory
Case 1: Setup A starts with 10 seeds and Setup B with 20 seeds. Exactly 5 germinate in each. Is the proportion equal?
Answer: No. The results are 5/10 and 5/20. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 2: Setup A has 9 of 15 seeds germinate and Setup B has 15 of 25. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 3: Two setups each start with 20 seeds. 7 germinate in one and 5 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 20, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 4: Setup A starts with 25 seeds and Setup B with 10 seeds. Exactly 8 germinate in each. Is the proportion equal?
Answer: No. The results are 8/25 and 8/10. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 5: Setup A has 18 of 30 seeds germinate and Setup B has 9 of 15. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 6: Two setups each start with 10 seeds. 10 germinate in one and 8 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 10, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 7: Setup A starts with 15 seeds and Setup B with 25 seeds. Exactly 11 germinate in each. Is the proportion equal?
Answer: No. The results are 11/15 and 11/25. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 8: Setup A has 12 of 20 seeds germinate and Setup B has 18 of 30. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 9: Two setups each start with 25 seeds. 5 germinate in one and 3 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 25, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 10: Setup A starts with 30 seeds and Setup B with 15 seeds. Exactly 6 germinate in each. Is the proportion equal?
Answer: No. The results are 6/30 and 6/15. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 11: Setup A has 6 of 10 seeds germinate and Setup B has 12 of 20. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 12: Two setups each start with 15 seeds. 8 germinate in one and 6 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 15, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 13: Setup A starts with 20 seeds and Setup B with 30 seeds. Exactly 9 germinate in each. Is the proportion equal?
Answer: No. The results are 9/20 and 9/30. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 14: Setup A has 15 of 25 seeds germinate and Setup B has 6 of 10. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 15: Two setups each start with 30 seeds. 11 germinate in one and 9 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 30, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 16: Setup A starts with 10 seeds and Setup B with 20 seeds. Exactly 10 germinate in each. Is the proportion equal?
Answer: No. The results are 10/10 and 10/20. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 17: Setup A has 9 of 15 seeds germinate and Setup B has 15 of 25. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 18: Two setups each start with 20 seeds. 6 germinate in one and 4 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 20, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 19: Setup A starts with 25 seeds and Setup B with 10 seeds. Exactly 7 germinate in each. Is the proportion equal?
Answer: No. The results are 7/25 and 7/10. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 20: Setup A has 18 of 30 seeds germinate and Setup B has 9 of 15. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 21: Two setups each start with 10 seeds. 9 germinate in one and 7 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 10, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 22: Setup A starts with 15 seeds and Setup B with 25 seeds. Exactly 10 germinate in each. Is the proportion equal?
Answer: No. The results are 10/15 and 10/25. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 23: Setup A has 12 of 20 seeds germinate and Setup B has 18 of 30. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 24: Two setups each start with 25 seeds. 10 germinate in one and 8 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 25, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 25: Setup A starts with 30 seeds and Setup B with 15 seeds. Exactly 5 germinate in each. Is the proportion equal?
Answer: No. The results are 5/30 and 5/15. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 26: Setup A has 6 of 10 seeds germinate and Setup B has 12 of 20. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 27: Two setups each start with 15 seeds. 7 germinate in one and 5 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 15, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 28: Setup A starts with 20 seeds and Setup B with 30 seeds. Exactly 8 germinate in each. Is the proportion equal?
Answer: No. The results are 8/20 and 8/30. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 29: Setup A has 15 of 25 seeds germinate and Setup B has 6 of 10. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 30: Two setups each start with 30 seeds. 10 germinate in one and 8 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 30, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 31: Setup A starts with 10 seeds and Setup B with 20 seeds. Exactly 10 germinate in each. Is the proportion equal?
Answer: No. The results are 10/10 and 10/20. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 32: Setup A has 9 of 15 seeds germinate and Setup B has 15 of 25. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 33: Two setups each start with 20 seeds. 5 germinate in one and 3 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 20, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 34: Setup A starts with 25 seeds and Setup B with 10 seeds. Exactly 6 germinate in each. Is the proportion equal?
Answer: No. The results are 6/25 and 6/10. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 35: Setup A has 18 of 30 seeds germinate and Setup B has 9 of 15. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 36: Two setups each start with 10 seeds. 8 germinate in one and 6 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 10, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 37: Setup A starts with 15 seeds and Setup B with 25 seeds. Exactly 9 germinate in each. Is the proportion equal?
Answer: No. The results are 9/15 and 9/25. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 38: Setup A has 12 of 20 seeds germinate and Setup B has 18 of 30. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 39: Two setups each start with 25 seeds. 10 germinate in one and 8 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 25, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 40: Setup A starts with 30 seeds and Setup B with 15 seeds. Exactly 12 germinate in each. Is the proportion equal?
Answer: No. The results are 12/30 and 12/15. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 41: Setup A has 6 of 10 seeds germinate and Setup B has 12 of 20. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 42: Two setups each start with 15 seeds. 6 germinate in one and 4 in the other during the same period. May counts be compared directly?
Answer: Yes, if the other relevant conditions are controlled. Both results use the same starting total 15, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 43: Setup A starts with 20 seeds and Setup B with 30 seeds. Exactly 7 germinate in each. Is the proportion equal?
Answer: No. The results are 7/20 and 7/30. Equal germinated counts give equal proportions only when the starting totals are also equal. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Case 44: Setup A has 15 of 25 seeds germinate and Setup B has 6 of 10. How should they be compared?
Answer: Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Apply the model: Equal germinated counts represent equal success only when the starting counts match; otherwise compare germinated proportions. State what condition would have to change for a different conclusion.
Common misconceptions and targeted repair
1. Equal germinated counts prove equal success.
The starting number must also match. Repair the habit by naming the denominator, syntax, table unit or local key and citing one visible cue.
2. More germinated seeds always means a better proportion.
A larger starting group can yield a larger count but a smaller fraction. Repair the habit by naming the denominator, syntax, table unit or local key and citing one visible cue.
3. Percentages make every experiment fair.
Conditions and observation time still matter. Repair the habit by naming the denominator, syntax, table unit or local key and citing one visible cue.
4. Ungerminated seeds should be removed from the denominator.
The original tested count remains the denominator unless a justified exclusion is stated. Repair the habit by naming the denominator, syntax, table unit or local key and citing one visible cue.
5. Equal starting counts prove causation.
Other variables must still be controlled. Repair the habit by naming the denominator, syntax, table unit or local key and citing one visible cue.
6. One-day and seven-day results are directly comparable.
Observation periods must match. Repair the habit by naming the denominator, syntax, table unit or local key and citing one visible cue.
Independent practice with explained answers
1. Setup A starts with 10 seeds and Setup B with 20 seeds. Exactly 5 germinate in each. Is the proportion equal?
No. The results are 5/10 and 5/20. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
2. Setup A has 9 of 15 seeds germinate and Setup B has 15 of 25. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
3. Two setups each start with 20 seeds. 7 germinate in one and 5 in the other during the same period. May counts be compared directly?
Yes, if the other relevant conditions are controlled. Both results use the same starting total 20, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
4. Setup A starts with 25 seeds and Setup B with 10 seeds. Exactly 8 germinate in each. Is the proportion equal?
No. The results are 8/25 and 8/10. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
5. Setup A has 18 of 30 seeds germinate and Setup B has 9 of 15. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
6. Two setups each start with 10 seeds. 10 germinate in one and 8 in the other during the same period. May counts be compared directly?
Yes, if the other relevant conditions are controlled. Both results use the same starting total 10, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
7. Setup A starts with 15 seeds and Setup B with 25 seeds. Exactly 11 germinate in each. Is the proportion equal?
No. The results are 11/15 and 11/25. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
8. Setup A has 12 of 20 seeds germinate and Setup B has 18 of 30. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
9. Two setups each start with 25 seeds. 5 germinate in one and 3 in the other during the same period. May counts be compared directly?
Yes, if the other relevant conditions are controlled. Both results use the same starting total 25, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
10. Setup A starts with 30 seeds and Setup B with 15 seeds. Exactly 6 germinate in each. Is the proportion equal?
No. The results are 6/30 and 6/15. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
11. Setup A has 6 of 10 seeds germinate and Setup B has 12 of 20. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
12. Two setups each start with 15 seeds. 8 germinate in one and 6 in the other during the same period. May counts be compared directly?
Yes, if the other relevant conditions are controlled. Both results use the same starting total 15, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
13. Setup A starts with 20 seeds and Setup B with 30 seeds. Exactly 9 germinate in each. Is the proportion equal?
No. The results are 9/20 and 9/30. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
14. Setup A has 15 of 25 seeds germinate and Setup B has 6 of 10. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
15. Two setups each start with 30 seeds. 11 germinate in one and 9 in the other during the same period. May counts be compared directly?
Yes, if the other relevant conditions are controlled. Both results use the same starting total 30, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
16. Setup A starts with 10 seeds and Setup B with 20 seeds. Exactly 10 germinate in each. Is the proportion equal?
No. The results are 10/10 and 10/20. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
17. Setup A has 9 of 15 seeds germinate and Setup B has 15 of 25. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
18. Two setups each start with 20 seeds. 6 germinate in one and 4 in the other during the same period. May counts be compared directly?
Yes, if the other relevant conditions are controlled. Both results use the same starting total 20, so the larger count is also the larger germination proportion. Equal denominators make the count comparison meaningful. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
19. Setup A starts with 25 seeds and Setup B with 10 seeds. Exactly 7 germinate in each. Is the proportion equal?
No. The results are 7/25 and 7/10. Equal germinated counts give equal proportions only when the starting totals are also equal. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
20. Setup A has 18 of 30 seeds germinate and Setup B has 9 of 15. How should they be compared?
Compare the fractions or percentages. The starting totals differ, so raw counts do not use the same denominator. Relating each germinated count to its own starting count creates the fair numerical comparison. Attempt before opening. If wrong, classify the fault as reading, evidence selection, relationship, execution or checking.
Three-round independence ladder
Round 1: visible model
Solve five items with the mechanism visible and add a short evidence tag beside each answer.
Round 2: hidden model
After twenty minutes, reconstruct the rule and solve five new items before checking explanations.
Round 3: mixed transfer
Mix four new items with unrelated topics and include one boundary case where a condition changes.
Delayed transfer
The next day, retrieve the controlling question, principle and two contrasting examples. Invent and solve a fresh case.
Three days later, change one condition and predict what changes before solving. This tests the model rather than memory.
Keep a four-column correction record: cue, first decision, missed evidence and repaired rule.
Examination control
- Name the exact job.
- Mark controlling evidence.
- State the relationship.
- Execute the comparison or interpretation.
- Check denominators, periods, units, syntax and keys.
When uncertain, compare the two most plausible readings against explicit evidence and reject the one that contradicts the setup.
Target the final check: unequal starting totals mistaken for equal success, or a question mark treated as punctuation inside a table or equation.
For parents and tutors
Ask what evidence controlled the answer before correcting. This reveals whether the need is knowledge, context selection or execution.
Replace “be careful” with “compare each count to its starting total” or “read the mark’s local syntax and key.”
Frequently asked questions
Must I memorise every case?
No; learn the relationship.
Why explain?
It separates reasoning from guessing.
Can a changed condition reverse the answer?
Yes; state the dependency.
Does appearance settle meaning?
No; use labels and conditions.
How fast?
Accuracy first, then timed retrieval.
What is mastery?
Delayed retrieval, new-case solution and boundary recognition.
Next routes
Continue through the complete directory, the original guide, and the Science hub.