Model, estimate, calculate, check.
Mathematical reasoning asks a student to use maths in a new problem. The official NSW information says calculators and rulers cannot be used in the OC test, so clear working and a reasonableness check are useful habits.
- Model: write or sketch what each number represents and the relationship between them.
- Estimate: predict roughly where the answer should sit.
- Calculate: complete only the operations the model requires.
- Check: put the result back into the story, including its unit.
Check the NSW Department of Education’s OC test information and official practice materials for current arrangements and examples.
Original worked example: show the relationship first.
Problem
A library puts 6 new books on each of 4 shelves. Then it gives 5 books to another room. How many new books remain on the shelves?
Work it through
- Model: books placed on shelves = 4 groups of 6; books remaining = that total minus 5.
- Estimate: 4 groups of about 6 is about 24, so the answer should be a little below 24.
- Calculate: 4 × 6 = 24, then 24 − 5 = 19.
- Check: 19 books is below 24 and answers “remain on the shelves”.
The answer is 19. The model prevents the common mistake of adding 5 simply because it is the last number in the problem.
Common error: calculating before identifying the target.
Students sometimes correctly combine numbers but answer the wrong question: the number added, the number removed or the original total. Underline the quantity being asked for, then label the result in words.
Self-check: can the answer live in the story?
After calculating, ask: “What does this number count?” and “Could it reasonably be this large or small?” If the answer has no unit or does not match the target quantity, revisit the model.
Use the method with fresh contexts.
The worked problem is original. Official OC format information checked 16 September 2026.