Edutest number series questions

It's a list of numbers made by a rule, and your child works out the rule to choose the number that comes next.

4, 11, 18, 25, … Each number is 7 more than the one before, so the next is 32.

Series are one of the kinds of question Edutest names in Numerical Reasoning. Harder ones change the gaps, multiply, or have two series take turns. In our questions the wrong options come from a nearly right rule, so a rough sense of the pattern won't be enough.

Start with the gaps between neighbours, then move on to multiplying or splitting only if the gaps don't settle it. Gaps come first because they're quick to find and they show at once whether the rule is steady, growing or something else.

Our series questions use one of the patterns below, sometimes two at once. Knowing the list lets your child test the likely ones in turn instead of staring at the numbers.

Two of these are easy to misread. Multiply-then-add looks like a changing gap, and both views work: the gaps in 2, 5, 11, 23 double too. Squares and cubes look random until your child recognises them, so learning them by heart pays off.

A rule can fit the first few numbers and still be wrong. Take 1, 2, 4, …: doubling gives 8 next, but adding 1, then 2, then 3 gives 7. Only another number can settle it, and a fair question shows enough.

So never skip the check: if the rule breaks anywhere, it's the wrong rule. The near-miss option is there for exactly the rule that half works.

When two different rules both fit every number and give the same next one, as in the second and fourth examples below, your child can choose with confidence.

We wrote these in the style of the Edutest test, from easier to harder. Each one shows the answer and the working. Read them with your child, and have your child say each rule out loud, then check it against the working.

Write the gaps under each series together and compare them with the working. If your child's rule and the gaps part ways, that is the step to practise.

Each slip below leads to an option beside the answer. Name the slip with your child, then use its check on the next few series.

• Using the last gap again. When the gaps shrink by one each time, the next gap is smaller still. Repeating the last one gives the option just beside the answer.
• Dropping the extra step. "Double and add 3" is easy to shorten to "double". The answer then misses by the extra amount.
• Answering the number after next. When two series take turns, the next number belongs to the other one. Count positions before choosing.
• Stopping at the cube. In a series that is a cube number plus 2, the bare cube is one of the options.
• A slip in the last sum. Edutest doesn't allow calculators, rulers, dictionaries, working-out paper, mobile phones, smart watches and fitness trackers, so the final addition is worth checking twice.

Not long, once the habits are in place. Edutest's practice page gives the sizes: 20 practice questions per test; real tests have 40 to 60. A real test fits all of its questions, series included, into 30 minutes, so there's little time to stare at a stubborn one.

If gaps, multiplying and splitting have all failed, your child should shade a guess and move on. Edutest says there are no marks lost for wrong or blank answers. Coming back later with fresh eyes can show the pattern straight away.

Make series for each other at home. One person writes four numbers with a hidden rule; the other finds the rule and adds the next number. Inventing series teaches the patterns too.

Number facts make patterns visible: times tables, squares, the first few cubes, and doubling from 1. In the app, the number series lesson has an Interactive version and Notes. There are also drills by section and topic; a free account drills the free test's questions, and a paid plan opens the rest.

Four questions show the method; the Numerical Reasoning section of Practice test 1 shows whether your child can use it against the clock. Afterwards, results by skill show whether series are costing marks. Series sit with the other kinds on the Numerical Reasoning sample questions page, and number matrices use the same rule-finding on grids and pairs.