The Supposition or Assumption Method is a PSLE Mathematics heuristic for problems with two kinds of objects, people or outcomes where the total number and total contribution are known. The classic family is “chickens and rabbits”: every item belongs to one of two categories, and the categories contribute different amounts.
Students searching for assumption method PSLE, chickens and rabbits, heads and legs problems or Primary 5/6 heuristics often memorise a trick such as “assume all are chickens”. The deeper method is baseline → discrepancy → correction per switch → number of switches.
This page is the canonical Supposition owner under the PSLE Mathematics Heuristics hub.
Quick answer: the four-step method
- Assume every item is one type.
- Calculate the total under that assumption.
- Compare with the actual total to find the discrepancy.
- Divide by how much one switch changes the total.
Worked example 1: chickens and rabbits
Problem: There are 18 animals, all chickens or rabbits. Altogether there are 50 legs. How many rabbits are there?
Assume all 18 are chickens: 18 × 2 = 36 legs.
Actual legs = 50, so discrepancy = 14 legs.
Changing one chicken into one rabbit adds 2 legs.
Rabbits = 14 ÷ 2 = 7. Chickens = 11.
Check: 7 × 4 + 11 × 2 = 28 + 22 = 50.
Why the method works
The assumption gives a clean baseline. Every time one assumed item is replaced by the other type, the total changes by a fixed amount. The total discrepancy therefore tells us how many replacements are needed.
Total discrepancy = number of switches × change per switch.
Worked example 2: ticket prices
Problem: 30 tickets were sold. Adult tickets cost $12 and child tickets cost $7. Total sales were $285. How many adult tickets were sold?
Assume all 30 are child tickets: 30 × $7 = $210.
Actual total is $285, discrepancy = $75.
Changing one child ticket to an adult ticket adds $5.
Adult tickets = 75 ÷ 5 = 15.
Worked example 3: marks
Problem: A quiz has 20 questions. A correct answer earns 4 marks and an incorrect answer loses 1 mark. A pupil answered every question and scored 50 marks. How many were correct?
Assume all 20 are incorrect: 20 × (−1) = −20.
Actual score is 50, so discrepancy = 70.
Switching one answer from incorrect to correct changes the score by 5 marks.
Correct answers = 70 ÷ 5 = 14.
The important phrase: change per switch
Do not divide by the larger category value. Divide by the difference between the two category contributions.
Chicken 2 legs → rabbit 4 legs: change = 2.
Child $7 → adult $12: change = 5.
Incorrect −1 → correct +4: change = 5.
Which type should I assume?
Either type can work. Choose the baseline that makes the arithmetic simpler.
- Assume the lower contribution if you expect to add discrepancy.
- Assume the higher contribution if subtraction is cleaner.
- Choose values that reduce mental load.
When the method applies
- exactly two categories
- fixed contribution per category
- total number of items known
- total contribution known
- every item belongs to one category
When not to use it
- three or more categories without additional information
- contribution per item is not fixed
- total number of items is unknown and no second relationship exists
- categories overlap
- a ratio or constant method gives a much simpler representation
The algebra hiding underneath
Supposition is a Primary-friendly form of solving two linear relationships. If x is one type and y the other, then x + y = total items, while ax + by = total contribution. The heuristic eliminates one unknown by assuming a baseline.
This is why the method transitions naturally into simultaneous equations later in Secondary Mathematics.
Common errors
- divides by one category value instead of the difference between categories
- forgets negative scoring in quiz problems
- does not check that category counts add to the total
- assumes a category but applies the wrong baseline total
- gets the switch direction backwards
- stops after finding switches without interpreting what they represent
A visual correction model
Imagine 18 chicken icons. The assumed model has 36 legs. To reach 50, replace chickens with rabbits one at a time. Each replacement adds two legs. Seven replacements add fourteen legs. The discrepancy literally counts how many model corrections are needed.
Transfer practice
Practice 1
Structure: 24 vehicles are bicycles or tricycles; 62 wheels total.
Reasoning: Assume bicycles: 48 wheels. Gap 14. Each switch adds 1 wheel. 14 tricycles.
Practice 2
Structure: 40 tickets cost $5 or $8; total $248.
Reasoning: Assume $5: $200. Gap $48. Each switch adds $3. 16 higher-price tickets.
Practice 3
Structure: 25 questions score +3 or 0; total score 54.
Reasoning: Assume all 0. Gap 54. Each switch adds 3. 18 correct.
Practice 4
Structure: 16 animals have 54 legs; each has 2 or 4 legs.
Reasoning: Assume 2 legs: 32. Gap 22. Each switch adds 2. 11 four-legged animals.
Frequently asked questions
Why is this called supposition?
Because we begin by supposing all items are one type, then correct the assumption.
Can I assume either category?
Yes. Both are valid if the correction is done consistently.
What do I divide the discrepancy by?
The change created when one assumed item is switched to the other category.
Is this the same as simultaneous equations?
It solves the same two-relationship structure in a Primary-friendly way.
Where does this sit in Atlas?
This is the canonical Supposition/Assumption owner under PSLE Mathematics Heuristics.
The final Assumption rule
Create a simple baseline, measure how wrong it is, then ask how much one correction changes the total. The discrepancy tells you how many corrections are needed.