The idea in brief. The rule of a pattern is the gap between two neighbours, found by one subtraction, and it is applied in the direction the sequence is already moving: a falling sequence keeps falling. When the gaps alternate, the rule is the pair of gaps, and the term asked takes whichever gap its place in the pair says.
Lesson video, with the working
Number patterns: find the rule
3 min 27 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
How can I help my child find the rule in P4 number patterns?
Your child learns to recognise and continue patterns in number sequences, the MOE Primary 4 whole numbers outcome 1.4.
What your child learns here
Your child learns to recognise and continue patterns in number sequences, the MOE Primary 4 whole numbers outcome 1.4. A rule must account for the terms already given as well as the next answer. Comparing several neighbouring terms helps your child distinguish a steady change from steps that alternate.
Compare neighbouring terms to test a repeated addition, subtraction, multiplication or division, keeping track of whether the sequence increases or decreases.
Test a possible rule on more than one pair of terms before using it to fill a blank or extend the sequence.
Recognise when two different changes take turns, and keep their order when a missing term interrupts the visible pattern.
Work backwards from a known term using the reverse operation when the blank is at the beginning or inside the sequence.
Explain the numerical relationship in words, so that another person can use the same rule to generate the next few terms.
Does the answer make sense?
After filling a gap, your child can calculate the changes on both sides of the new term. In an alternating pattern, those changes must continue in the same order as the earlier pairs, rather than merely produce a number between its neighbours.
How to practise these questions
The Basic pattern uses a steady additive step. Intermediate practice includes more than one missing term, repeated multiplication and repeated division, so your child should test the kind of change before extending the sequence. Challenge questions ask for a later term in an alternating pattern or recover a starting term from two known positions. Count the intervals between those positions carefully; a position number is not itself a count of increases. After calculating, reconstruct enough of the sequence to check the supplied terms. If the rule remains unclear, compare the worked solution's first decision with your child's proposed rule before trying the calculation again.
Questions parents ask
Is one pair of numbers enough to identify a pattern? One pair suggests a possible change, but the remaining terms must support it. Encourage your child to calculate several gaps and compare them. A rule that explains only the first pair may fail when the sequence uses alternating changes or follows another repeated arrangement.
What helps when the missing term is first? Use an uninterrupted part of the sequence to establish the rule, then reverse the relevant step. If counting forwards adds an amount, counting backwards subtracts that amount. With alternating steps, your child also needs to decide which of the two steps comes immediately before the known term.
Should my child describe a pattern or just give the answer? The question determines what must be written, but a spoken explanation is useful during practice. Ask your child to name what changes and when it changes. That explanation makes it easier to check a later term and to return to a sequence after a blank.
