How to teach place value

Place value is the idea that a digit's worth depends on its position in a number. In 472 the 4 means 400, the 7 means 70 and the 2 means 2, even though 4 is the smallest digit. This positional system underpins all multi-digit reading, writing and arithmetic.

Use base-ten blocks to build numbers first, then practise the value of each digit, such as the 7 in 472 being 70. Move on to expanding numbers into the sum of their parts, and finally to comparing and ordering numbers using place value.

Place value begins in Grade 1 with tens and ones, and develops through Grade 5 to include thousands, then decimals. Each year the range of numbers grows, but the core idea, that position sets a digit's value, stays the same throughout.

Place value underpins every multi-digit method: lining up columns for addition, carrying and borrowing, long multiplication and division, rounding, and decimals all depend on knowing what each digit is worth. Without it, children treat digits as loose numbers and make regular column errors.

Common signs are reading digits without regard to position, misplacing zeros that act as placeholders, and struggling to compare numbers of different lengths. Base-ten blocks and a place-value chart, where each digit sits in a labelled column, make the position and its value visible and usually fix these errors.

A placeholder zero holds a place open so the other digits keep their correct value. In 508 the zero shows there are no tens, keeping the 5 in the hundreds place and the 8 in the ones. Drop it and the number wrongly becomes 58, so the zero is not 'nothing'.

Expanded form, comparing and ordering numbers, rounding, and column arithmetic all build directly on place value. Later, the same positional idea extends to the right of the ones to give decimals, so a secure grasp of place value carries through most of primary maths.