Mathematics

This module targets the four skills relating to the mathematical processes listed in the documents Compétences disciplinaires attendues à la fin de la classe de 6^e et à la fin de la classe de 4^e (Discipline-specific skills expected at the end of 6^e and at the end of 4^e) and Compétences disciplinaires attendues à la fin des classes de 7G-6G-5G (Discipline-specific skills expected at the end of 7^eG, 6^eG and 5^eG) issued by the Ministry of Education. These four skills are as follows:

1. Problem solving: As explained in the Discipline-specific skills document, solving mathematical problems “is characterised, on one hand, by the implementation of general strategies, and, on the other, by the implementation of specific strategies”. This is exactly what the pupils are led to do in this module: they start by discovering the game through testing a few examples, then they follow the strategy given in the module. This module is a wonderful example that demonstrates that you can practice problem solving by “working actively on problems and then reflecting on problem-solving methods and strategies”.
2. Modelling: In this module, the pupils are first led to simplify the problem, then model it in graph form. This process accurately corresponds to the description of the skill to be modelled: “It is a matter of first simplifying the real situation and then mathematising it, i.e. describing it with mathematical tools”.
3. Present your arguments: This skill is described as follows: “Mathematical argumentation starts with exploring situations, looking for structures and relationships and by formulating conjectures about the mathematical relationships.” This is exactly what happens in challenges 3 to 8 in 1.3 Teaching materials. In the first exercise, the pupils are asked to formulate a conjecture, then in the following exercises, they are led to prove their conjecture.
4. Communicate: The exercises proposed in this module are not the typical exercises you would usually find on a mathematics course, but they need reasoning and argumentation to be proven. The pupils must, therefore, “explain mathematical content in an appropriate way using everyday language and mathematical language”.

To be more precise, this module enables work to be done on a skill in the chapter on literal calculation in the new provisional mathematics curriculum for the 6^eC. This skill reads as follows: decode a literal expression into an ordered series of calculation instructions and understand how to formalise this algorithm.

The Involution© game can also be used to illustrate central symmetry and rotation concepts. The game’s crank handle movement is nothing more than central symmetry or 180-degree rotations. The geometric transformations are taught in 5^e and 4^e in Luxembourg and often pose problems for pupils: axial symmetry is much more natural to them and they find visualising these new transformations rather difficult. Involution© is another method of visualisation.

In lower technical secondary school, the pupils have already started to familiarise themselves with probabilities. Involution© enables the pupils to count and enumerate (how many different configurations exist?) and to calculate probabilities in many different ways.

Finally, this module prepares the ground for proof by induction. In challenges 4 to 8 of 1.3. Teaching materials, the pupils are led, stage by stage, to do proof by induction (without mentioning the mathematical term itself).

Geography

Using navigation algorithms (such as Google Maps), we can make the connection with the maps used by navigation apps. Directions and maps feature in the geography curriculum for the 7^eC and 7^eG.