Rekenrek (Arithmetic rack)

• NUMBER: Counting, operations

The name Rekenrek literally means calculating frame. The development of the Rekenrek is attributed to Adrian Treffers from the Freudenthal Institute in Holland. The Rekenrek is basically a bead frame where the beads are grouped in fives. Five beads of one colour alternate with five of a different colour. It is felt that young children anchor on five and then ten and use these numbers to support calculation.

Mathematical Language

Addition, calculate, counting number names, subtraction, sum, total.

Using a Rekenrek

In order to use a Rekenrek students will need to have mastered the five counting principles.

1. The one-one principle – The matching of counting words to the items being counted.

2. The stable order principle – Counting words are always said in the same order.

3. The cardinal principle – The final number in the count represents how many in the set.

4. The abstraction principle – The counting procedure may be applied to any counting situation.

5. The order-irrelevance principle – The order in which items are counted does not affect the count.

Eventually students need to be able to count on from any given number and to be able to count in multiples of numbers such as 2, 5 and 10. Students should be able to stop a count part-way through the count and then recommence the count. For example, three beads might be moved and counted 1, 2, 3, at which point the count is stopped and the students are asked how many beads have been moved. The students are then asked what the next number in the sequence is when counted from that point on, 4, 5, 6 … Later the same process may be repeated with the three beads covered so that the students have to remember or hold the three in their short term memory.

Typical Classroom Requirements

A class set:

– One Rekenrek per pair of students. A class of 32 students would require a kit of 16 Rekenreks. If using Beadstrings (see below), then the students could have one each.

Support and Complementary Materials

There are a variety of Rekenrek related materials such as beadstrings. The smaller beadstrings (up to twenty beads) are typically configured in fives.

Larger beadstrings (100 beads) are configured with ten beads of each colour. Students anchor on the ten rather than the five.


 Bead Frame Abacus

 Tens Frame