11 plus Estimation & Approximation questions

What an Estimation & Approximation question looks like

Estimation & Approximation is one of the number topics in 11 plus maths, and it does two related jobs. One is judging whether an amount is a sensible size: how much water a mug holds, how much a pencil weighs, how long a classroom door is, which container is nearest to 240 ml. The other, and the larger part of the topic, is using a rough answer as the route to an exact one, then checking the exact one looks right.

That second job separates these from ordinary rounding work. A rounding question asks a child to round a number, and the rounded number is the answer. Here the rounded number is nearly always in the options as a trap, and the mark goes to the child who rounds, does the tidy sum, then puts back the bit they moved.

A smaller group asks a child to read a value off a number line, a table, a bar chart or a line graph and work from what they see. Estimating is one of the most transferable habits in eleven plus maths: a rough answer held in the head catches mistakes in every other topic.

Example one: is this a sensible size?

About how much does a new pencil weigh? 5 g, 50 g, 500 g, 5 kg, 50 kg

Picture something that weighs a kilogram, such as a bag of sugar. A pencil is nothing like that, so both answers in kilograms go out. That leaves 5 g, 50 g and 500 g, and 500 g is about a big hardback book, so that goes too.

The answer is 5 g.

The tempting wrong option is 50 g: a small number, in grams, and grams feel right for a pencil. But 50 g is roughly a small chocolate bar. These questions reward a child who pictures a real object rather than taking the middle option.

Example two: round, then put back what you moved

Theo runs 4 laps of a track. Each lap is 397 m. What is the total distance he runs? 1564 m, 1588 m, 1597 m, 1600 m, 1612 m

397 is close to 400, and 400 is easy: 4 × 400 = 1600. That is the rough answer, and it already rules out 1564 m as too far away.

Now put back what you moved. Each lap was treated as 3 m longer than it is, and there are 4 laps, so the rough answer is 4 × 3 = 12 m too big. 1600 - 12 = 1588.

The answer is 1588 m.

Two wrong options catch children here. 1600 m is the rough answer left standing as the final one. 1597 m comes from taking off 3 m once instead of once per lap, the commonest slip in the topic: the adjustment is made as many times as the number appears.

Example three: working from a table

The table shows the number of visitors to a museum over four days. What is the total number of visitors across the four days? 1098, 1300, 1400, 1500, 1600

Every value is near 300 or 400, so a rough total is 1400. Now do it properly, pairing values that make round numbers: 302 + 398 = 700 and 296 + 404 = 700, so the total is 1400.

The answer is 1400.

The rough and exact answers agree, which is the point of doing both. 1600 tempts a child who rounds all four days up to 400 and stops. 1098 comes from adding only three of the four rows, an easy slip when the eye skips a line, and it shows why the rough answer earns its keep: it is nowhere near 1400, so it goes without recalculation.

How to answer it

1. Decide what the question wants. If it asks “about how much”, the rough answer is the answer. If it gives a real calculation, the exact number is wanted and the rough answer is only a stepping stone.
2. Make the numbers friendly. Move each to the nearest easy value and note how far you moved it and which way: 397 up by 3, £4.98 up by 2p, 49 up by 1.
3. Do the easy sum: 4 × 400, 6 × £5, 50 × 3. This is your target, and any option nowhere near it can be crossed off now.
4. Put back what you moved. Multiply the amount you moved by how many times that number appears, then take it off if you rounded up and add it on if you rounded down.
5. Hold your answer next to your target. If they are not close, you have adjusted the wrong way or the wrong number of times.

Common mistakes

• Choosing the tidy round number. 1600, £30, 1000 and £360 all appear as wrong options here, each a rough answer left standing as a final one. It is how you check, not what you write down.
• Adjusting once instead of once per item. Six books at £4.98 are each 2p short of £5, so the adjustment is 12p, not 2p. Answers built this way look almost right, which makes them easy to pick.
• Adjusting the wrong way. If you rounded up, the easy sum came out too big, so the adjustment is taken off. Adding it gives 1612 m where the answer is 1588 m.
• Rounding so hard the target stops being useful. Turning 51 × 19 into 40 × 20, or £4.98 into £4, moves the numbers further than they need to go, and the target is too loose to test an answer against.
• Slipping a decimal point or a unit. 142.1 m written as 1421 m, millilitres read as litres, grams read as kilograms. In the sensible-size questions that is the whole difficulty: the digits are right and the unit is wrong.

How to practise 11 plus Estimation & Approximation questions

This improves through a habit more than through drilling. Whenever your child does a calculation, in any subject, ask for the rough answer before the exact one, then ask whether the two agree. That one question catches most of the errors above. For the sensible-size questions, real objects beat any worksheet: weigh a pencil, fill a mug from a measuring jug, pace out the hall. Short and regular still beats long and occasional, as we set out in how much 11 plus practice a child needs each day. 11+ Daily has an Estimation & Approximation project alongside the rest of the number work, on laptop, tablet or phone, and the full list is on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the maths bank has been re-checked in five rounds since April 2026.

Questions parents ask