South African Geometry Construction Awarded A World Record


A little while ago, we reported on the attempt to break a world record for the Largest Menger Sponge. We are excited to tell you that it was successful.

The Level 3 Menger Sponge built in Cape Town on 10 May 2019 has been confirmed as the new world record title holder for the Largest Menger Sponge. This is a wonderful Proudly South African achievement!

15 mathematics education students from the University of Stellenbosch worked with 45 Grade 4, 5, and 6 students from Rosmead, Prestwich and St Agnes primary schools to build the world record setting Level 3 Menger Sponge. 18,048 tabbed cardboard squares where joined together by 36,096 rubber bands to build the record setting sponge which measures a whopping 1.9m x 1.9m x 1.9m. The tabbed squares used in the construction form part of the GeoGenius Construction Kit.

The record attempt was hosted at Cape Town’s incredible Zeitz MOCAA (Museum of Contemporary Art Africa) as part of the 2019 NumberSense User Group Conference.

Image taken by Domenic Gorin, Infinity Studios 2019 ©

What did Aarnout, the project leader, have to say?

Aarnout Brombacher, the project leader of the Largest Menger Sponge activity makes the point that, “Although building the sponge was primarily a fun activity and challenge, the project provided the opportunity to showcase students from public schools in Cape Town that are participating in the Shikaya/Standard Bank NumberSense Mathematics Programme. The project also allowed us to showcase the GeoGenius Construction Kit and its versatility in building beautiful mathematical objects which plays an important role in the study of geometry”

Image taken by Domenic Gorin, Infinity Studios 2019 ©

The GeoGenius Construction Kit is a South African invention that supports the development of geometric thinking, by enabling students to easily build a wide range of geometric objects using only cardboard geometric shapes and rubber bands.

What is the GeoGenius Construction Kit?

It is an integral resource of the NumberSense Mathematics Programme. The NumberSense Mathematics Programme was developed by Aarnout Brombacher and the team at Brombacher and Associates as a uniquely South African mathematics programme that seeks to address the crises in South African mathematics education. Every year 1.2 mil students start school in South Africa. 12 years later fewer than 45 thousand of these students pass mathematics with a C-symbol or better – a success rate of less than 1 in 30! The problem, argues Aarnout Brombacher, “Has nothing to do with the mathematics that we teach, and also nothing to do with the students.” He goes on to say: “there is nothing wrong with our students, the problem is in how we teach mathematics. When children experience mathematics as the memorisation of rules and formulae to be applied to produce answers without understanding, they soon suspend any attempt at sense-making. By contrast when children experience mathematics as a meaningful, sense-making, problem solving activity they recognise the value of mathematics and are intrinsically more motivated to learn it.

What is the Menger Sponge?

A Menger Sponge, first described by Karl Menger in 1926, is 3-dimensional geometric shape. It can best be understood by thinking about a large cube that is divided into 27 identical smaller cubes – in the same way that a Rubik’s cube consists of 27 cubes. If the small cube at the centre of the large cube and the small cube in the middle of each face is removed, 20 cubes remain and the resulting shape is called a L1 Menger Sponge. If the process is repeated on each of the remaining 20 cubes, 400 still smaller cubes remain and the resulting shape is called a L2 Menger Sponge. If the process is then repeated on each of the 400 smaller cubes, 8 000 still smaller cubes remain and the resulting shape is called a L3 Menger Sponge. This process can be continued with the Level describing the complexity of the sponge. The Menger Sponge has a lot of fascinating properties, but more than anything it is very beautiful.

Image taken by Domenic Gorin, Infinity Studios 2019 ©

In addition to the many schools across South Africa that subscribe to and use the NumberSense mathematics programme, more than 4 500 students at 12 schools (8 in the Western Cape; and 4 in the Easter Cape) are supported to use the NumberSense programme through funding provided by Standard Bank to the Shikaya school improvement activities. In addition to supplying the NumberSense workbooks to the students in the school, Standard Bank and Shikaya also support the effective use of the programme by providing in-class coaching support to the teachers. The impact of the NumberSense Programme in these schools is apparent in a number of different ways e.g. improved school performance on the WCED (Western Cape Education Department) systemic assessments. The impact is also evident in the confidence with which the participating students contributed to the success of Largest Menger Sponge project.

Having set the world record for the Largest Menger Sponge, the attention of Aarnout and his team has turned to exploring ways of working with schools across the country to manufacture a Level 4 Menger Sponge which when completed will measure more than 6m x 6m x 6m. “Our vision” reports Aarnout Brombacher, “is to provide 400 schools across the country with enough GeoGenius squares and rubber bands to build their own Level 2 Menger Sponge and then to bring these to a central venue for assembly.” Schools that are interested in participating should make contact with the NumberSense and GeoGenius teams (

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Kids Connection was successfully launched in March 2006 by Wendy Beaufort for distribution to parents and teachers in the local Port Elizabeth market. The comprehensive directory for young families from newborn to 12 years, was born because, Wendy, a mom of three, understood the importance of having detailed information related to children that is aimed at assisting young families spend less time PLANNING and more time PLAYING….READ MORE