# Dice

Canonical: https://manipulatives.org/manipulatives/dice/

Objects with numbered or dotted faces for generating values, playing number games, and collecting chance data.

![Two six-sided dice showing different dot arrangements](https://manipulatives.org/_astro/dice.BLcKVxXo.svg)

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

Topics: probability-and-data, counting, operations

## What they teach

### Dot quantities

Recognize and describe small groups arranged as familiar dot patterns.

### Operations

Combine rolled values through addition, difference, or another agreed rule.

### Chance and data

Record repeated outcomes and compare possible results.

## How to use them

1. **Inspect the faces.** Check the die’s labels and list possible outcomes before rolling.

2. **Set the rule.** Decide whether a roll represents a number, a move, a sum, or another quantity.

3. **Record consistently.** Make one tally for each trial and compare the observations with your prediction.

## Try an activity: Which sum appears most?

Roll two standard six-sided dice and record each sum for thirty trials. Compare the results with a table of all 36 ordered face pairs. Explain why sums have different numbers of combinations.

## Outcomes and sums are different things

With two standard six-sided dice, 1 then 6 and 6 then 1 are two distinct ordered outcomes, both giving a sum of seven. A sum of two has only one ordered pair, 1 and 1. If the dice are fair and independent, the 36 ordered pairs are equally likely; the eleven possible sums are not.

Thirty rolls will rarely match theoretical proportions exactly. Treat a short experiment as a set of observations to compare with a model, rather than as a guarantee of what must happen next.

For younger learners, a single die can prompt a simpler conversation. Ask how a pattern of five dots is grouped. Someone may see four and one, while another sees two, one, and two. Place counters to reproduce each explanation.

## Choose your toolkit

Check face labels, legibility, size, and how many dice a task needs. Dot dice, numeral dice, and ten-sided dice support different starting points.

- [jrceliy Six-Sided Colored Dice (50 pieces, 14 mm)](https://www.amazon.com/dp/B09VZ6N9GL) — Fifty six-sided dot dice in ten translucent colors, with a storage box for number games and probability investigations. Each die measures 14 mm.

- [Bicycle Six-Sided Dice (5 pieces, 16 mm)](https://www.amazon.com/dp/B000BUUTKU) — Five white six-sided dice with black dots, each measuring 16 mm. A smaller set for number games, comparing totals, and collecting results from repeated rolls.

### Manipulatives app

Use the dice model for a short counting or chance experiment. Record each result and compare the observations with your prediction. Physical dice let learners explore the roll itself as well.

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

## Related tools

- [Probability Spinners](https://manipulatives.org/manipulatives/probability-spinners/)
- [Two-Color Counters](https://manipulatives.org/manipulatives/two-color-counters/)
- [Hundred Charts](https://manipulatives.org/manipulatives/hundred-charts/)