11 plus Complete the Sum questions

What a Complete the Sum question looks like

Complete the Sum gives your child a number sentence with one value missing, marked as (?), and five options to choose from. The job is to work out which option makes both sides of the equals sign come to the same amount. It belongs to the number reasoning group of the 11 plus verbal reasoning paper rather than to maths, which surprises most parents the first time they meet it.

The arithmetic itself stays small: times tables, and addition and subtraction a Year 5 child can already do. What is being tested is whether they can see the shape of the sentence. One side can be worked out completely, and the other side holds the gap. Finish the side you can, then undo whatever is being done to the gap.

Example one: 4 x 9 = 24 + (?)

Options: 10, 11, 12, 13, 14.

The left side has no gap in it, so start there. 4 x 9 = 36. The sentence now reads 36 = 24 + (?). Something added to 24 makes 36, and taking away undoes adding, so the missing number is 36 - 24 = 12.

Two of the wrong options, 11 and 13, sit either side of the right answer. They are there for the child who counts up from 24 in ones and loses their place by one along the way. Taking 24 away from 36 in a single step is much safer than counting on.

Example two: 18 ÷ 2 + 6 = 3 x (?)

Options: 3, 4, 5, 6, 7.

The left side is again the complete one, but this time it has two steps in it and the order matters. Divide before you add: 18 ÷ 2 = 9, then 9 + 6 = 15. The sentence becomes 15 = 3 x (?). Three lots of something make 15, and dividing undoes multiplying, so the missing number is 15 ÷ 3 = 5.

The tempting wrong option is 3. That is what you get if you do the division, look up at 9 = 3 x (?), and answer before finishing the left side. The + 6 was still waiting. Option 6 catches a different slip: it is 18 ÷ 3, which is what you get by grabbing the first number on the left and the first number on the right and pairing them up.

Example three: (?) - 9 = 6 x 3

Options: 18, 22, 24, 26, 27.

The gap is at the very start of the sentence this time, so the side you can finish is on the right: 6 x 3 = 18. That leaves (?) - 9 = 18. Something with 9 taken off it leaves 18, and adding undoes taking away, so the missing number is 18 + 9 = 27.

Option 18 is there for a good reason. It is the value of the side that was just worked out, and a child who finishes 6 x 3, feels the relief of finally having a number, and glances down at the options will find it waiting for them. Working out one side is only half of the question.

How to answer it

1. Find the (?) and see which side of the equals sign it is on. The other side is the one you can finish.
2. Work that side out to a single number. If it has more than one step, do the times and divide parts before the add and take away parts.
3. Write the sentence out again with that single number in place, so you are left with something short like 36 = 24 + (?).
4. Use the opposite operation to get the missing value on its own. Adding undoes taking away, taking away undoes adding, dividing undoes multiplying, multiplying undoes dividing.
5. Put your answer back into the original sentence and work both sides out. They should match. It takes a few seconds and it catches almost every slip.

Common mistakes

• Working straight along the line. In 18 ÷ 2 + 6, doing 2 + 6 first gives 18 ÷ 8, which does not divide neatly. Times and divide come before add and take away, on either side of the equals sign.
• Stopping halfway through. A side with two steps in it invites an answer after the first step. The gap is not going anywhere, so there is time to finish the side properly before looking at the options.
• Answering with the total instead of the missing value. When the finished side comes to 18 and 18 is sitting there as an option, it is very easy to pick. The question asks for the value of the gap, not the value of the side.
• Using the same operation instead of the opposite one. Seeing 3 x (?) and multiplying by 3 rather than dividing by 3 is the most common cause of an answer that is far too big.
• Assuming the gap is always on the right. It can be the first thing in the sentence, as in (?) - 9 = 6 x 3, and a child who has only met the other version often stalls on it.

How to practise 11 plus Complete the Sum questions

Two things carry most of the marks here, and neither of them is really about this question type. The first is quick, confident times tables, because every step of the working rests on them. The second is knowing which operation undoes which, well enough not to have to stop and think. Ten minutes on tables does more for these questions than an hour spent on the questions themselves.

After that, what builds speed is meeting the different shapes in a mixed order: gap on the left, gap on the right, one step on the finished side, two steps. Complete the Sum is one of around 25 verbal reasoning formats used in the eleven plus, and it is a good one to keep in rotation rather than to block out for a week. 11+ Daily has a Complete the Sum project that mixes those shapes, and it sits alongside the other 11 plus verbal reasoning question types so a child keeps meeting them. Every question is original to 11+ Daily, nothing is a past paper, and the bank is re-checked in rounds. The same undo-the-operation thinking runs right through 11 plus maths practice, so time spent on one repays the other. If you are working out how much time to give it, we have written about how much 11 plus practice a child needs each day.

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