Translate the story
- Write the quantities with their units.
- Show how they are related: total, difference, equal groups or rate.
- Calculate, then put the answer back into the model.
Worked example
A garden has 24 seedlings in 3 equal rows. Four seedlings are moved away. How many are left in each row if the remaining seedlings are rearranged equally?
Model: 24 seedlings − 4 seedlings = 20 seedlings. Then 20 ÷ 3 does not make equal whole rows. The information cannot produce equal rows of whole seedlings, so do not force an answer. A model can reveal a problem condition that needs checking.
A common error
Using every number in a calculation just because it appears in the story. The diagram should explain why each operation matches a relationship.
Independent self-check
Read your equation aloud in words. If it does not tell the same story as the question, change the model before solving further.
Use the method in practice
Quantity models are useful for NSW Selective and Opportunity Class mathematical reasoning. Begin with the free test and continue through the public study methods.