A number pattern is a sequence with a rule. Discovering the rule helps children predict what comes next and explain why an answer fits. The simplest place to start is the change between two neighbouring numbers.
Patterns appear in counting, shapes, music and everyday routines. In a number sequence, the terms might increase, decrease, double or alternate between two steps. Look at several neighbouring terms before deciding on a rule; the first two alone can fit many possible rules.
Growing patterns
In 2, 4, 6, 8, …, each number is 2 more than the one before. The next numbers are 10, 12. In 5, 10, 15, 20, …, the step is 5, so the next number is 25.
Ask a learner to say the rule aloud, then check it at every step. A rule that only works once is not enough.
Shrinking patterns
In 20, 17, 14, 11, …, subtract 3 each time. The next number is 8. To check, work backwards: 8 + 3 = 11.
For a missing middle term, use both neighbours. In 4, 7, □, 13, a step of 3 gives 10; it works from 7 to 10 and from 10 to 13.
Multiplying patterns
Some patterns grow by multiplication instead of a fixed addition. In 3, 6, 12, 24, …, each term is twice the previous one, so the next term is 48. The differences are 3, 6 and 12; because those differences change, “add 3” cannot be the rule for the whole sequence. Try naming both what changes and what stays consistent.
Alternating patterns
Not every pattern uses the same step every time. In 5, 8, 6, 9, 7, 10, …, the steps alternate: add 3, subtract 2, add 3, subtract 2, and so on. The next term is 8. Marking each jump above the sequence can reveal the repeating pair of instructions. Check at least two full cycles before predicting the next number.
Why patterns matter
Describing a rule strengthens careful observation and mathematical language. A child learns to compare neighbours, test a hypothesis and revise it when one term does not fit. Those habits support skip-counting, multiplication and later work with sequences; they are more useful than guessing a number that merely looks plausible.
Teaching and common challenges
Begin with concrete groups or a number line. Let the learner move objects or make visible jumps, then write the numbers, identify the rule, predict a term and finally create a new pattern for someone else. Ask “What changed from this term to the next?” and “Does the same rule work all the way through?”
If a child mistakes a doubling pattern for an adding pattern, compare several steps and write the differences. If the pattern alternates, use two colours to mark the two kinds of jump. If a middle number is missing, test the proposed value against both neighbours. These checks make errors useful clues about the rule.
Patterns are not limited to worksheets. Look for repeating rhythms in music, regular dates on a calendar or rows of tiles. Count steps while walking or group objects in twos and fives. The aim is to help a child recognise structure in a real situation, then explain it in numbers.
Try making your own
Choose a starting number and a small step. Write four terms, hide one, and ask someone else to find it. Then switch roles. A simple drawn number line can make the repeated jumps visible.
MathApex has addition practice, subtraction practice and number-line activities that support the skills behind these examples.