# Place Value

Canonical: https://manipulatives.org/topics/place-value/

Make the grouping of ones, tens, hundreds, and smaller units visible.

Place value depends on groups of ten and on the value assigned to each position. A written digit can look unchanged while its contribution changes: the 4 in 42 represents four tens, while the 4 in 24 represents four ones.

[Base-ten blocks](https://manipulatives.org/manipulatives/base-ten-blocks/) provide fixed groups, and [linking cubes](https://manipulatives.org/manipulatives/linking-cubes/) let learners assemble those groups. Move between a model, a spoken description, and a written number. Each representation should refer to the same quantity.

Allow nonstandard representations, such as two tens and fourteen ones for 34. Exchanging pieces without changing value gives regrouping a meaning beyond a written procedure. State the unit explicitly before reusing the same blocks for decimals.

## Tools

- [Base-Ten Blocks](https://manipulatives.org/manipulatives/base-ten-blocks/)

- [Hundred Charts](https://manipulatives.org/manipulatives/hundred-charts/)

## Articles

- [Make the exchange visible](https://manipulatives.org/blog/place-value-with-base-ten-blocks/)