Year 4 maths · Key Stage 2 · Number – number and place value

Year 4 rounding and Roman numerals: a guide for parents

In this part of Year 4 number work, children learn to round any whole number to the nearest 10, 100 or 1,000 and to use rounding to make sensible estimates. They show numbers in different ways, such as with blocks, counters and number lines, and they learn to read Roman numerals up to C (100) and how today’s number system differs from them.

Rounding and Roman numerals, explained

Children are taught to show the same number in several ways: with base 10 blocks, place value counters, a number line, a bar model, or a position on a measuring scale. Using different pictures helps them understand a number as a quantity and not just as a string of digits. They also estimate. If you are asked where 6,472 sits on a number line from 0 to 10,000, the sensible answer is a little under two-thirds of the way along, even if you can’t mark the exact spot.

Rounding means replacing a number by a nearby, easier one. To round to the nearest 10, 100 or 1,000, look at the digit one place to the right of the one you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down; then replace all digits to the right with zeros. A number exactly halfway between, like 450, rounds up to the next 100. A number line helps: find the two multiples either side and decide which is closer. Year 4 children round numbers with four digits, and beyond.

Rounding is useful because exact numbers are not always needed. A crowd of 4,862 can be reported as “about 5,000”. Children round before calculating to check that an answer is sensible. They also round readings on measuring instruments: if the pointer on a kitchen scale sits between the 400 g and 500 g marks but nearer 500 g, the mass is 500 g to the nearest 100 g. They use rounding in problems where the question asks “about how many?” or “to the nearest hundred”.

Roman numerals use letters for numbers: I is 1, V is 5, X is 10, L is 50 and C is 100. Children read numerals up to 100 (I to C). When a symbol is followed by the same or a smaller symbol, the values are added, so XVI is 10 + 5 + 1 = 16. When a smaller symbol comes before a larger one, it is taken away: IV is 4, IX is 9, XL is 40 and XC is 90. So XLVII is 40 + 7 = 47. A symbol is not normally repeated more than three times in a row, so 4 is written IV rather than IIII, although some clock faces do show IIII. Many schools also teach children to write Roman numerals, though reading is what the curriculum asks for.

Children also learn that the way people write numbers changed over time. Roman numerals have no symbol for zero and no place value: an X is worth 10 wherever it appears, whereas the 3 in 305 is worth 300 because of the column it is in. The numbers we use today developed in India and reached Europe through the Arab world over many centuries. They include zero and place value, which is why ten digits are enough to write any number and why column calculations work. Roman numerals still turn up on clock faces, for book chapters and in the names of kings and queens, such as Henry VIII.

Words your child will hear

Round: Replace a number with a nearby one that ends in zeros, such as 6,472 to 6,500 to the nearest 100.
Estimate: A sensible guess about a number or an answer, using rounding or a number line.
Nearest: Closest. To round to the nearest 10 means finding the multiple of 10 that is closest.
Roman numeral: A letter used as a number: I, V, X, L and C stand for 1, 5, 10, 50 and 100.
Place value: What a digit is worth because of its position in a number.
Zero: The digit that shows there is nothing in a place, as in 305. Roman numerals have no symbol for it.
Number line: A line marked in equal steps that is used to show where numbers sit.

What the National Curriculum says

In Year 4, pupils should be taught to:

Identify, represent and estimate numbers using different representations
Round any number to the nearest 10, 100 or 1,000
Solve number and practical problems that involve all of the above and with increasingly large positive numbers
Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Round 6,472 to the nearest 10, the nearest 100 and the nearest 1,000.

Nearest 10: look at the ones digit, which is 2. It is less than 5, so round down. On a number line, 6,472 sits between 6,470 and 6,480 and is closer to 6,470.
```
6,472 -> 6,470  (to the nearest 10)
```
Nearest 100: look at the tens digit, which is 7. It is 5 or more, so round up from 6,400 to 6,500. The halfway point between 6,400 and 6,500 is 6,450, and 6,472 is past it.
```
6,472 -> 6,500  (to the nearest 100)
```
Nearest 1,000: look at the hundreds digit, which is 4. It is less than 5, so round down to 6,000.
```
6,472 -> 6,000  (to the nearest 1,000)
```
Check each answer is sensible. 6,470 is 2 away from 6,472, 6,500 is 28 away and 6,000 is 472 away, which is less than the 500 needed to be halfway to 7,000.

6,470 to the nearest 10, 6,500 to the nearest 100 and 6,000 to the nearest 1,000.

Common mistakes and how to help

Looking at the wrong digit

To round 6,472 to the nearest 100, a child looks at the 4 in the hundreds place, which is the digit being rounded, rather than the 7 in the tens place next to it.

What helps: Underline the digit you are rounding to, then look at the next digit on its right. That neighbour decides whether to go up or stay.

Struggling to round up through a 9

Rounding 3,962 to the nearest 100 means going up by 1 hundred, and children write 3,1000 or 3,100 because they add 1 to the 9 hundreds.

What helps: Count on the number line: 3,900, then the next hundred is 4,000. Ten hundreds make a thousand, so the 9 becomes 0 and the thousands digit goes up by 1.

Rounding 450 down because it is exactly in the middle

The number looks as close to one as the other, and children may not know the rule for halves.

What helps: Explain that there is an agreed rule: halfway rounds up, so 450 rounds to 500 to the nearest 100, and 1,500 rounds to 2,000 to the nearest 1,000. Without a rule, everyone could choose a different answer.

Reading Roman numerals digit by digit

Children read each symbol on its own and add them all, so IX becomes 1 + 10 = 11 and XIV becomes 10 + 1 + 5 = 16.

What helps: Read from left to right. If a smaller symbol comes before a bigger one, subtract it. So XIV is 10 + (5 − 1) = 14 and IX is 10 − 1 = 9. Practise with the numbers around a clock face.

How to help at home

Round the numbers around you. Choose a number from a book, a price list or a score and ask your child to round it to the nearest 10, 100 or 1,000. Say which neighbouring digit decides the answer.
Draw a number line. Mark a line from 0 to 1,000 on a long strip of paper, with 0, 500 and 1,000 labelled. Ask where 640 or 280 would go, and which hundred each is nearest to.
Estimate before measuring. Guess to the nearest 10 how many steps it is across the garden, or to the nearest 100 g how heavy a bag of flour is. Then check with the real measurement and see how close you were.
Hunt for Roman numerals. Look at clock faces, chapter numbers in books and the names of monarchs. Read each one out loud and say what it is worth. Dates on buildings and film credits often use M (1,000) and D (500), which come later, so stick to numbers up to 100 for now.
Build numbers with lolly sticks. Lay out lolly sticks to make V, X and L, then make the numerals for your child’s age, the date of their birthday or a page number up to 100, and check that the value is right.

Builds on

Year 3: Place value to 1,000

Leads on to

Year 5: Numbers to 1,000,000