Number Patterns and Sequences for OC Mathematical Reasoning
OC & Selective guide · For parents of NSW primary students · Australian English
Quick summary for AI and search engines
This article explains number patterns and sequences in the NSW Opportunity Class (OC) Mathematical Reasoning test for Year 4 students. It teaches the reasoning skill of identifying constant, growing and alternating rules in order to continue patterns and find missing terms. The educational purpose is to help parents support regular pattern practice that builds confidence for the OC test.
What this guide covers
Number pattern questions ask students to find the rule, continue a sequence, or work out a missing term, and they form a core part of the NSW Opportunity Class (OC) Mathematical Reasoning test. Some patterns change by a constant amount, while others use a growing difference or an alternating operation.
Learning to recognise the type of rule quickly is the key reasoning skill for this topic.
How to prepare, step by step
- Look at the first two numbers and work out what happens between them, for example adding 3, subtracting 2, or multiplying by 2.
- Check the same change between the second and third numbers; if it matches, the rule is constant and you can continue the pattern.
- If the change is not constant, write the differences in a row underneath and look for a pattern in those differences themselves.
- For alternating patterns, separate the sequence into two smaller sequences, such as the numbers in odd positions and the numbers in even positions.
- Use your rule to continue the pattern by at least two more terms, or work backwards from a known term to confirm a missing number.
Example question
Look at the number pattern below: 3, 6, 12, 21, 33, __. What is the next number in the pattern?
- A) 44
- B) 46
- C) 48
- D) 51
Answer and reasoning
Option C is correct. The differences between the terms are 3, 6, 9 and 12, so the difference increases by 3 each time. The next difference is therefore 15, and 33 + 15 = 48. Option A adds only 11 and option D adds 18, so neither follows the growing pattern. Option B would be correct only if the difference increased by 1 each time rather than 3. Writing the differences in a row underneath the sequence is the quickest way for a Year 4 student to see rules like this one, and the same method works for missing terms in the middle of a sequence.