In a number series, you look for a rule connecting terms in order. In a number grid, sometimes called a matrix, you look for relationships across rows or columns. In both cases, a useful rule must fit all the relevant information—not just the first pair of numbers you try.
These original teaching examples are suitable for introducing pattern methods in Year 5 and Year 6 practice. They are not official Edutest questions and do not specify the content or rules of a particular school examination.
Start with simple operations
Check whether consecutive terms increase or decrease by a constant amount. Then consider multiplication or division by a constant factor. Doubling and halving are useful examples, but factors other than two are possible.
- 4, 9, 14, 19, 24: add 5 each time.
- 3, 6, 12, 24, 48: multiply by 2 each time.
- 81, 27, 9, 3, 1: divide by 3 each time.
- 30, 26, 22, 18, 14: subtract 4 each time.
Have your child state the rule in words and check every transition. A rule that works for 4 → 9 but fails for 9 → 14 does not explain the whole first sequence.
When the differences change
Consider 2, 5, 10, 17, ?
The differences are +3, +5 and +7. A simple consistent continuation increases the difference by two again, giving +9. Therefore the next term is 17 + 9 = 26.
Adding seven again would continue the last individual step but miss the pattern in the differences. Write the differences beneath the terms during practice to make the second pattern visible.
A finite list can be extended in more than one mathematical way. In a practice question, look for the simplest consistent intended rule and use the answer choices and question wording to test it. If several options remain equally supported, the question may need clarification rather than more elaborate guessing.
When two operations repeat
Consider 2, 5, 11, 23, ?
Multiplying by two and then adding one works at each step: 2 × 2 + 1 = 5; 5 × 2 + 1 = 11; 11 × 2 + 1 = 23. Continuing gives 23 × 2 + 1 = 47.
Order matters. “Add one, then double” would produce six from the first term, so it is not the same rule. Ask your child to test the exact order, not simply identify two operations that appear somewhere in the working.
When two sequences alternate
Consider 3, 20, 6, 17, 9, 14, ?
Separate the odd and even positions:
- Positions 1, 3, 5 and 7: 3, 6, 9, 12.
- Positions 2, 4 and 6: 20, 17, 14.
The odd-position terms increase by three; the even-position terms decrease by three. The missing term occupies position seven, so the answer is 12.
A sequence that repeatedly rises and falls is a reason to check alternating positions, not proof that this must be the rule. Confirm both smaller sequences before choosing an answer.
Number grids: test a rule across complete rows
Here is a three-by-three number grid, shown one row at a time:
- Row 1: 9 | 12 | 15
- Row 2: 16 | 20 | 24
- Row 3: 25 | 30 | ?
Within each row, the increase stays constant. Row one increases by three; row two by four; row three starts with an increase of five. Continuing the third row gives 30 + 5 = 35.
The row increments also follow an orderly pattern of three, four and five. Use the complete rows to check your idea before filling the missing entry.
A second grid with a different relationship
- Row 1: 4 | 3 | 14
- Row 2: 6 | 2 | 16
- Row 3: 5 | 4 | ?
A consistent row rule is: add the first two entries, then multiply the total by two. The first row gives (4 + 3) × 2 = 14. The second gives (6 + 2) × 2 = 16. The missing value is therefore (5 + 4) × 2 = 18.
Do not accept “multiply the first number by something” just because it fits one row. Testing another complete row is how you reject a rule that only works by coincidence. For this example, the stated row relationship gives the intended answer; more complicated alternatives are not useful teaching goals.
Number grids and shape grids are different practice
A number grid primarily asks you to test numerical relationships. A shape grid may ask you to track features such as rotation, shading or the number of objects. The grid layout alone does not tell you which skill is being tested.
Choose practice by the task described, rather than assuming that every resource labelled “matrices” teaches the same thing. Check the provider and school's current information for the relevant sitting. The Edutest practice-test information is a useful starting point for its own resources.
Review the reasoning before increasing speed
Ask your child to explain the rule, demonstrate it on the given values and then apply it to the missing value. If they can identify the rule but make a calculation error, practise that arithmetic separately.
Use the actual test instructions for timing, calculators, working paper and unanswered questions. This guide does not prescribe those rules.
Try the numerical reasoning sections in our QASMT Year 5 sample or QASMT Year 6 sample. For translating a written situation into a calculation, continue with maths word problems.