Abacube (Abaku dice) is a set of ten dice with numbers arranged as follows::

First dice – numbers 1-2-3-4-5-6
Second dice – numbers 7-8-9-0-1-2
Third dice – numbers 3-4-5-6-7-8
Fourth dice – numbers 9-0-1-2-3-4
Fifth dice – numbers 5-6-7-8-9-0

The five dice have different colors which means there are two dice from each color in the set.

Children should check the dice before using them. It is recommended to have at least one set of dice per two students.

Games with cubes

0-9

Children are making an ascending sequence from 0 to 9. They have to look for the right numbers. It is recommended for children to use both hands and thus develop their fine motor skills symmetrically, especially left-handed children. Then, tell them to make a descending sequence (9-0) and observe how each one of them is dealing with this task. Whether they simply turn the sequence upside down or rearrange it, or whether they start from the beginning. This may seem as an activity only for the youngest children but you can try it with the older ones for starters.

Build Differences

Children place dice in front, behind, or next to each other according to your instructions how big is the numeric difference of the dice.

Children put three dice on the desk, no matter which ones. Look at the first picture on the left where you may see a solution with numbers differing by one. The dice with number 5 was added ON the first dice on the left, dice with number 8 BEHIND the dice in the center, dice with number 5 IN FRONT of the dice on the right, and dice with number 7 on the RIGHT of the same dice.

Build As I Did

One child secretly prepares his/her own combination of dice and describes it to his/her classmate using the prepositions in front of, behind, on etc. In the end they compare their dice. This activity is similar to the previous one; children work in pairs or in small groups where one of them is describing and the others are working.

Basic Sequences

Children shuffle the dice and without any more adjustments they make basic sequences. If they get dice with the same numbers they use them to expand the sequence to sides. The numbers have to be arranged in the left-right or top-bottom direction. Point out creating numeric rows even though some numbers may be missing. Such row are not in orderly sequence.

Triplets

Children shuffle the dice and without any further adjustments they start to form arranged groups of numbers. This is not a free choice anymore; children are limited by the roll. The groups consist of two addends and their sum, or subtrahend and minuend and their difference. Even though the first combinations are usually triplets, we encourage children to make multiple-digit numbers as well. The numbers have to be arranged in the left-right or top-bottom direction. This task is quite difficult and depends heavily on the roll. However, it is always possible to create at least one equation.

Simple Multiples

Children work in pairs with one set of dice. One child throws a random dice. The second one chooses one dice from the remaining dice, gives it to the first child and says what multiple should the first child make. So the first child turns with the dice looking for the right number to create the desired multiple with both dice.

Example: The thrown number is 2. One of the children chooses multiples of 7 and the other child looks for number 1 (21) or 8 (28) or 4 (42). This task is more suitable for multiples of smaller numbers (up to 5) that always have a solution. With highest numbers the task may not have a solution but even discovering this option is important for children.

Absolute Values

Student rolls all the dice, randomly picks three of them, and creates three-digit number (see 938 in the left picture). Then looks for a dice with value equalling absolute value of the difference between the first and second dice of the triplet (|9-3|=6) and does the same thing with the second and third dice (|3-8|=5) and places both dice below the triplet. By following this principle the student places one last dice below the second row and creates so called difference cluster.

This activity is a great way to teach the concept of absolute value, when only the raw difference is important. There is actually no need of mentioning the term absolute value, we ask only by how much the numbers differ. In this way children also easily learns to deal with number zero.

The top row may be formed also from four dice. The exercise then gets much harder and requires several combinations and rearrangements of the dice to find the valid solution. Yet from experience children prefer this over the former three-dice setting. Keep in mind that in this case children must use all ten dice and it might not always have a valid solution (probably, we have never saw such a case).

How to

Abaku Spider

A child throws all the dice and doesn’t turn them any further. He/she makes groups of equations so that each number is a part of an equation. The dice follow up each other and part the equations may be mixed together. In the picture you may see 2 + 8 = 10 and 10 – 4 = 6 in the horizontal line, 6 + 2 = 8 and 2 x 8 = 16 in the vertical line. There is also 23 = 8. Zero cannot be used as an independent number and thus it cannot be a result of an equation. It can only be used as a part of some multiple-digit number (10, 20, 101…).

As soon as the child uses all dice we let him/her read out loud all the equations. This is a valuable feedback and important correction check. Children usually find their mistakes themselves when reading out loud the equations. After that each child changes their dice with a classmate and tries to make equations from different dice. Children are usually surprised that they find totally different equations in the same task..

How to

3x3

Children create a square 3×3 with the dice so that the three numbers in each direction create equations.

This task can be limited to addition and subtraction (see the picture on the left), or you can allow all arithmetical operations. This task is suitable for individual work. Children have to realise that the number they need doesn’t have to be on the remaining dice and that they might need to replace some dice, or change the equations. The task can be modified with several exactly defined dice (in the center, in corners, in the first line etc.) In this case it is recommended to use a layout from a prepared solution just to be sure that the task could be solved. For example we can define that there will be 1, 7, 9, 3 in the corners because we know that this task has a solution according to the picture on the left.

How to