11 plus Place Value & Ordering questions

What a Place Value & Ordering question looks like

Place Value & Ordering is one of the number topics in 11 plus maths, and every question in it turns on the same thing: which column a digit is sitting in. The numbers run from four digits up to six, so 4628 at one end and 900,009 at the other. Nothing here goes below zero and nothing carries a decimal point. That is what marks the topic out from its neighbours: whole numbers above zero, read, written, compared, ordered and rounded, with the rounded number as the answer rather than a step towards one.

Four shapes come up again and again. The first asks what a single digit is worth. The second gives a number in words and asks for it in figures, which is mostly a test of whether a child remembers the zeros that hold the empty columns open. The third gives a set of numbers to compare or put in order, or asks which of them is nearest to a round target. The fourth asks for a number rounded to the nearest 10, 100 or 1,000, and often runs the rounding backwards: what is the smallest number that could have been rounded to give this?

A smaller group puts the numbers somewhere other than the stem. Some sit in a table of town populations or race times, so the values must be read off first. Some sit on a number line, where the real work is deciding what one gap is worth. A few give the clues in reverse, describing a six-digit number whose ten-thousands digit is worth 30,000, with five candidates to test against the description. It is the quietest of the eleven plus number topics and the one most of the others lean on.

Example one: what is one digit worth?

What is the value of the digit 6 in the number 4628?

Split the number into columns, working from the right: 8 ones, 2 tens, 6 hundreds, 4 thousands. The 6 is in the hundreds column, and 6 hundreds is 600.

The answer is 600.

The wrong option that catches the most children is 6. It is the digit sitting on the page, and reading it straight off feels like answering. The other trap is 6000, one column too far left. Saying the columns aloud from the right keeps a child in the right one.

Example two: putting numbers in order

Order these numbers from smallest to largest: 2309, 2039, 2930, 2390.

All four start with 2, so the thousands column settles nothing and the work moves one place to the right. The hundreds digits are 3, 0, 9 and 3. The 0 is the smallest, so 2039 goes first. The 9 is the largest, so 2930 goes last. That leaves 2309 and 2390, which both have 3 hundreds, so move right again: their tens digits are 0 and 9, so 2309 comes before 2390.

The answer is 2039, 2309, 2390, 2930.

The tempting wrong order begins 2309, 2039, from comparing the tails, 09 against 39, and seeing 9 as smaller. Comparing from the left is the only order of work that holds, because a digit is always worth more than every digit to its right added together.

Example three: reading a number line

A number line runs from 300,000 to 400,000, with a tick mark every 10,000. An arrow points to the middle of the gap between the 310,000 tick and the 320,000 tick. What number is the arrow pointing to?

Find what one gap is worth before doing anything else. The line covers 100,000 in ten equal gaps, so each gap is 10,000. The arrow is halfway across a gap, and half of 10,000 is 5,000. Start at the tick behind the arrow and add: 310,000 + 5,000 = 315,000.

The answer is 315,000.

The option that catches a child here is 320,000, and it comes from counting whole ticks and carrying on to the next one rather than reading the space in between. The other near miss is 312,000, from judging the arrow by eye instead of halving the gap. On a number line the gap is the unit, so working it out first turns guesswork into arithmetic.

How to answer it

1. Decide which of the four jobs you have: the value of a digit, words into figures, a comparison or an order, or a rounding.
2. Say the columns from the right before answering: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands. Almost every wrong answer here is a slip of one column.
3. For the value of a digit, find the column it is in and read off what that column is worth. A 6 in the hundreds column is 600.
4. For comparing and ordering, line the numbers up and compare from the left. Stop at the first column where they differ; where they match, move one place right.
5. For rounding, find the column you are rounding to, then look at the digit immediately to its right. Five or more rounds up, four or less leaves it alone, and every column to the right of it becomes a zero.

Common mistakes

• Giving the digit rather than its value. The 6 in 4628 is worth 600, not 6. It is a reading slip rather than a gap in the maths.
• Being one column out. 6000 for 600, or 60 for 600. The method is right and the counting is not.
• Dropping a zero that is holding a column open. “Six thousand and fifty-two” is 6052, not 652 and not 6520. There are no hundreds in it, so a zero holds the column open.
• Rearranging a long number given in words. “Three hundred and four thousand and seventeen” is 304,017. Children write 340,017, because the two phrases sound close read at speed.
• Looking at the wrong digit when rounding. To round 3847 to the nearest 100, the digit that decides is the 4 in the tens column, so the answer is 3800. A child who looks at the 7 in the ones column rounds up and writes 3900.

How to practise 11 plus Place Value & Ordering questions

This is worth returning to in short bursts rather than in one long sitting, because the errors are habits rather than gaps: a child who is one column out today will still be one column out next week unless the counting is made deliberate. Two things help more than extra questions. Ask your child to say the columns aloud, from the right, before they answer, and when they get one wrong, ask them which number their answer would have been correct for. Nine times in ten they spot the slip themselves. 11+ Daily has a Place Value & Ordering project alongside the other number topics, on laptop, tablet or phone, and the full list is on our 11 plus maths practice page. Short and regular beats long and occasional, and the reasoning is in how much 11 plus practice a child needs each day. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

Questions parents ask