“IQ-game design” – teacher guide – Happy Cube
Abstract
The original Happy Cube puzzle consists of several models,
each of one has 6 pieces with different shapes that can be
joined to form a cube (for more on Happy Cube see
http://www.happycube.com/ ). The aim of the activity for
each group of students is to design and to produce their
own Happy Cube style puzzle (from polyfoam or only a
model of the Cube from cardboard) and then to classify
these puzzle according to their difficulty level.
Discipline: mathematics
Duration: 2x90 minutes
Target Group: lower and upper secondary but it can be adapted also to primary
Age range: 9-18
A student handout is provided for this task. It describes the task as it is designed for the main target
group, i.e. lower and upper secondary level, whereas the adaptation to the primary level is given in
the possible scenarios below.
Possible scenarios with different age groups
Primary
Teachers need to prepare beforehand 5x5 polyfoam squares with a meshgrid on it. The unit for the
meshgrid is the thickness of the polyfoam, so it is recommended to use polyfoam with 6-8 mm
thickness. It is also recommended that teachers prepare some ready-made patterns as examples, for
instance some original pieces of Happy Cube (see http://www.happycube.com/) or pieces obtained
from elsewhere.
Let the students work in pairs. Each pair of students will receive 6 pieces of those 5x5 polyfoam
squares with a meshgrid on it. They then have to mark the small 1x1 squares that will be cut from
these squares following the ready-made patterns, and to draw on a paper the obtained design. In the
second part teachers have to cut the corresponding pieces and students will play with the cubes in
order to rank them by difficulty. After gathering sufficient data for a “proper ranking” students can
discuss about how to obtain a final ranking from the individual rankings.
Lower secondary
Students are asked to design cubes satisfying different criteria: an easy one (that can be assembled
easily), a hard one, a didactical one (where you can easily explain how to assemble it), a cube with
several possible solutions. After designing the cubes they have to be manufactured (from polyfoam)
and students will design an experiment for ranking the designed cubes.
The mascil project has received funding from the European Union’s Seventh Framework Programme for research, technological
development and demonstration under grant agreement no 320 693
CC BY-NC-SA 4.0 mascil 2015
Upper secondary
Starts as in lower secondary, but ends with a deeper analysis of the designed cubes. For more
information on the analysis you may read the paper produced in Primas:
http://www.nieuwarchief.nl/serie5/pdf/naw5-2011-12-2-121.pdf (in dutch) or the English version at
http://simplexportal.ro/cikkek/happycube.pdf
These pictures are from an activity performed with 13 year old students, who did not learned about
solid geometry (they knew only what means “unfolding a cube”).
One of the models is made from polyfoam while the other is from a cardboard (150 g/m2).
WoW context
Several extra requirements that are relevant for WoW can be added: pack the pieces into a rectangular
shape, produce a software that can solve such a puzzle, etc. The most relevant aspect is related to the
classification of the different designs; this is a real task from the work of a game designer.
Equipment
Polyfoam with thicknes 6-10 mm, which is cut to squares 5units x 5 units, where 1 unit is the thickness
of the polyfoam. Tools for drawing the grid on the squares and tools for cutting the polyfoam (a cutter
is an excellent choice).
The mascil project has received funding from the European Union’s Seventh Framework Programme for research, technological
development and demonstration under grant agreement no 320 693
CC BY-NC-SA 4.0 mascil 2015
Teaching notes
You may propose several different specifications to students: to produce an easy cube, a difficult cube,
to produce a cube which is analyzed from the viewpoint of possible solutions. It is almost sure that if
student know that the cubes will be ranked according to the difficulty level by their colleagues, they
will focus on producing a difficult one (we had this activity for several times with several different
groups and this was the general trend). However, in many cases they will not be able to produce a
difficult cube, because they do not analyze the way the cube is assembled from all possible starting
pieces. This is a strong motivation for understanding how important is the analyzed cube (which
probably is not chosen by any of the groups). If you want students to be familiar with Happy Cube, you
may organize an introductory activity where they only play with the real Happy Cube set.
The mascil project has received funding from the European Union’s Seventh Framework Programme for research, technological
development and demonstration under grant agreement no 320 693
CC BY-NC-SA 4.0 mascil 2015