# Linking Cubes

Canonical: https://manipulatives.org/manipulatives/linking-cubes/

Equal-sized cubes that connect into trains, groups, arrays, and three-dimensional builds.

![Colored cubes connected into trains of different lengths](https://manipulatives.org/_astro/linking-cubes.ZzZOViRN.svg)

Published: 2026-10-09
Reviewed: 2026-10-09

Topics: counting, operations, measurement

## What they teach

### Grouping

Join and break apart cube trains to show parts and totals.

### Equal groups

Build several trains with the same number of cubes.

### Measurement

Measure a length with repeated equal units placed without gaps.

## How to use them

1. **Check the connections.** Build and take apart a short train. Count cubes rather than connection points.

2. **Make equal groups.** Build four trains of three cubes and compare their lengths.

3. **Connect the model to symbols.** Count the whole collection and record 4 × 3 = 12, explaining what each number represents.

## Try an activity: Build every rectangle for twelve

Use twelve cubes to make single-layer rectangular arrays. Try one row, two rows, three rows, and other possibilities. Record rows and cubes per row for each complete rectangle.

## Decide what one cube represents

One cube may stand for one object, one length unit, or one cubic unit, depending on the task. Name that meaning before recording an answer. A train of five cubes is five units long when measured along its length, but it contains five cubic units of volume when each cube is the volume unit.

For measuring an object, line up the first cube with the object’s starting edge. Use equal-sized cubes, with no gaps or overlaps. A leftover portion is a reason to discuss an approximate measure, not to quietly change the size of the unit.

Cubes also offer a way to build tens before introducing fixed [base-ten rods](https://manipulatives.org/manipulatives/base-ten-blocks/). Learners can join ten separate ones, then compare their train with a rod that already represents that group.

## Choose your toolkit

Check how the cubes connect: some link on two faces and others on several. Choose a connection strength the learner can manage and enough repeated colors for your tasks.

- [hand2mind Centimeter Cubes, Set of 500](https://www.amazon.com/dp/B01D9KHOK6) — Connecting centimeter cubes can be joined into lengths, equal groups, and small arrays. Check cube size against your learners and storage needs.

### Manipulatives app

The cube preview offers a visual model for discussing groups. Use physical linking cubes when joining pieces by hand or building a three-dimensional structure is part of the task.

[Explore the app](https://apps.apple.com/us/app/manipulatives-hands-on-math/id6780701668)

## Related tools

- [Cuisenaire Rods](https://manipulatives.org/manipulatives/cuisenaire-rods/)
- [Base-Ten Blocks](https://manipulatives.org/manipulatives/base-ten-blocks/)
- [Two-Color Counters](https://manipulatives.org/manipulatives/two-color-counters/)