Classroom dice: two large dice for maths practice

How to use the dice on this page

Above are two large dice, sized to be read from the back of the room when the page is on the interactive whiteboard. Before rolling, set two things:

• The operation: addition, subtraction or multiplication. The page takes the two numbers rolled and writes the calculation underneath the dice.
• The type of dice: d6 (six faces, with dots), d10 (ten faces) or d12 (twelve faces). Changing the dice is the way to raise the level without changing the activity.

To roll, press Roll, or pick the dice up with the mouse or your finger and release them with a flick over the tray. When they stop, the calculation appears with a question mark in place of the answer, for example 4 × 6 = ?. Pupils think, answer aloud or on mini whiteboards, and then you press Show the answer to check.

Two details worth knowing:

• In subtraction, the larger number always comes first. If a 2 and a 9 come up, the page writes 9 − 2 = ?, so negative answers never appear. If both dice match, the answer is 0.
• On the d10, the 0 face counts as 10. That is the usual convention for a ten-sided die used on its own, so the d10 gives numbers from 1 to 10.

Why dice work in the classroom

Dice have been part of primary maths in many countries for decades, and maths education research gives clear reasons for it. These are the arguments that come up again and again in teacher-training material.

Recognising amounts without counting

The faces of a six-sided die are fixed dot patterns. Young children start by counting dot by dot, but with practice they recognise five or six at a glance from the shape. That move from counting in ones to seeing structure, often called subitising, is one of the foundations of calculation, and German maths educators work on it with dice and domino patterns. Instant recognition of very small amounts, up to about four, appears before school; recognising larger amounts arranged in patterns is something children learn in class.

Mental maths with a reason to do it

A worksheet of twenty sums and a roll of the dice ask for the same calculation, but the roll changes the mood. The teacher does not choose the numbers, every calculation is different and there is a small moment of anticipation before each roll. The University of Cambridge's NRICH project points out that these games combine calculation, estimation and strategy, and that the target can be raised or lowered to suit each group.

Seeing what each pupil knows

While they play, pupils explain what they are doing. The teacher can hear who counts on their fingers, who counts on from the larger number and who simply recalls the fact. NRICH recommends dice games as a formative assessment tool at the start of the school year for this reason: you see what each child can do without it feeling like a test.

Turn-taking, rules and talk

Waiting your turn, accepting the result of the dice and explaining a move are all learning in their own right. In pairs or small groups, the dice share out luck neutrally, so nobody argues that they were given the hard question.

A bridge to probability

A die is the textbook example of a random experiment. In England, the Key Stage 3 programme of study asks pupils to record, describe and analyse the frequency of outcomes of simple probability experiments, and dice are the obvious place to start. Pupils move from «I think 7 comes up more» to counting, recording and comparing.

There is also research with control groups. In studies by Robert Siegler and Geetha Ramani (2008), pre-school children from low-income families played a linear board game numbered 1 to 10 four times a week for two weeks, moving with a number spinner. Afterwards they placed numbers on a number line more accurately than children who had played a colour version of the game. A straight-line board worked better than a circular one.

Which dice to choose for each level

The type of dice sets the size of the numbers. This table, worked out by going through every possible combination of the two dice, shows the range of answers each one gives:

A useful detail when planning: the d6 gives only 18 different products, because several repeat (6 comes from 1 × 6 and 2 × 3, 12 from 2 × 6 and 3 × 4). The d12 gives 59.

Twelve dice activities by age and year group

Early years and Reception (ages 3 to 5)

Years 1 and 2

Years 3 and 4

Years 5 and 6

• Chain calculation. With the d12. Roll three times in a row, changing the operation each time (add, multiply, subtract), and the class carries the result forward mentally. Everyone writes the final answer and it is checked at the end.

Key Stage 3

• Experimental probability with the sum of two dice. Addition with the d6. Each pupil rolls a set number of times and records the totals in a frequency table. Pool the class results and compare them with the calculated probability (see the next section).
• Is this game fair? On multiplication with the d6, player A wins if the product is even and player B if it is odd. Before playing, ask pupils whether it is fair. After a few rolls, count up: the product is odd only when both dice are odd, 9 cases out of 36, so A wins 27 rolls in 36 (75%).

Probability experiment: the sum of two dice

This is the most widely used probability activity in schools because the result surprises pupils. Two six-sided dice give 36 equally likely combinations, but the totals are not equally likely: 7 can be made six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while 2 and 12 can be made only one way each.

How to run it

1. Set the dice to d6 and the operation to addition.
2. Before starting, each pupil predicts which total will come up most. There are usually votes for 12 and for «lucky» numbers.
3. Share out the rolls: in a class of 30, twelve rolls each makes 360 in total. Each pupil records their totals in a table from 2 to 12.
4. Pool the data on the board and work out the relative frequency of each total (number of times it came up divided by the total number of rolls).
5. Compare with the table of expected frequencies.

Expected frequencies

What to expect from real data

The class results will not match the table exactly, and that is part of the lesson. In 36 rolls, the chance of getting exactly six 7s is only about 18%, and there is a 36% chance that a total of 2 does not appear at all. In 100 rolls, the number of 7s falls between 12 and 21 in 82% of cases. In 360 rolls, it falls between 50 and 70 in 86% of cases. The more rolls, the closer the relative frequencies get to the probabilities. This is the law of large numbers, and it shows up best when you compare one pupil's results with the whole class's.

Classic dice games for the classroom

Many traditional games practise number skills with nothing more than one or two dice and paper. These are the ones most often used in schools:

Dice facts to share with the class

Practical tips: interactive whiteboard and lesson routines

How to show the dice on an interactive whiteboard

On-screen dice have practical advantages in a classroom: they do not roll off the table, they make no noise and the whole class sees the same result at the same moment.

Getting the most out of it in lessons