# Operations

Canonical: https://manipulatives.org/topics/operations/

Use materials to explain joining, separating, grouping, sharing, and comparing.

An operation describes a relationship or a change. A collection may be joined to another, shared into equal groups, or compared with a larger collection. Materials are useful when their arrangement makes that situation clear.

Use [linking cubes](https://manipulatives.org/manipulatives/linking-cubes/) for equal groups, [math bars](https://manipulatives.org/manipulatives/math-bars/) for parts and comparisons, or a [number line](https://manipulatives.org/manipulatives/number-lines/) for jumps and differences. Ask what each piece, group, and movement represents.

Record an equation alongside the model and connect each symbol to something visible. Different models can represent the same calculation, but some make a particular question easier to discuss. Choosing the model is part of the mathematical work.

## Tools

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

- [Cuisenaire Rods](https://manipulatives.org/manipulatives/cuisenaire-rods/)

- [Dice](https://manipulatives.org/manipulatives/dice/)

- [Fraction Circles](https://manipulatives.org/manipulatives/fraction-circles/)

- [Fraction Tiles](https://manipulatives.org/manipulatives/fraction-tiles/)

- [Linking Cubes](https://manipulatives.org/manipulatives/linking-cubes/)

- [Math Bars](https://manipulatives.org/manipulatives/math-bars/)

- [Number Lines](https://manipulatives.org/manipulatives/number-lines/)

- [Play Money](https://manipulatives.org/manipulatives/play-money/)

- [Rekenreks](https://manipulatives.org/manipulatives/rekenreks/)

- [Sketch Pad](https://manipulatives.org/manipulatives/sketch-pad/)

- [Ten Frames](https://manipulatives.org/manipulatives/ten-frames/)

- [Two-Color Counters](https://manipulatives.org/manipulatives/two-color-counters/)

## Articles

- [A small space for a good math conversation](https://manipulatives.org/blog/adapting-an-activity-for-home/)

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