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This chapter shows the research results of the analysis of how Colombian Year ten students built mathematical models, through the measurement of area and volume, in the context of the flooding of their school. This situation allowed the creation of mathematical models associated with the quadratic and cubic functions, which were obtained from the environmental situation that allowed the students their application. The study was a qualitative case study focussing on two pairs of students. It took into account the everyday environment, communication, prior experiences and the interaction of each member with the group. The aim of the study was to explore and analyse the different ways students build models and apply mathematical elements arising in an authentic context.

International audience; Traditionally, for thousand of years, masonry techniques were commonly used for the building of homes,monuments, walls, and retaining walls. Masonry is one of the oldest construction materials. Since masonry is a composite structure, however, failure of these structures will depend on the properties of the materials (mortar, bricks, etc.), as well as on the characteristics of the bonding between the various components. Two main methods of modeling masonry structures have been developed in the literature. The first method involves macroscopic models and homogenization techniques: the wall is assumed to be a single structural element characterized by a non-linear response when it is exposed to external forces. The second method has been developed for predicting the evolution of cracks and damage at the interface brick-mortar or brick-brick. This chapter deals with two families for the modeling of brick-mortar interface. The first part of this chapter deals with the experimental characterization of the materials (bricks and mortar) and the brick-mortar interface. Hereafter, we describe experimental studies on the shear behavior of masonry on the local scale, in the case of two different assemblies composed of two and three full/hollow bricks, with or without confinement. Two other structures are presented: a small wall made by seven bricks and the classical problem of a small wall under diagonal compression. The second part of this chapter deals with a phenomenological model of interface. The mechanical modeling approach (and in particular the RCCM [10] adhesive model adopted) is first presented. The model is based on the concept of adhesion variable due to Frémond [12]. A variation equation of this variable is introduced and the coefficients are identified experimentally. The numerical procedure used is then described. Lastly, some numerical examples are given and compared with the experimental data. The third part presents a multi-scale model of interface. The method is based on homogenization theories and asymptotic analysis. In the present work, we assume the existence of a third material: the brick-mortar interface, which is considered as a mixture of brick and mortar with a crack density. To obtain the effective properties of the damaged intermediate material, three aim steps are performed. First, we calculate the exact effective properties of the crack-free material using homogenization techniques for laminate composites, and thus define a first homogeneous equivalent medium. In the second step, we assign a crack density to the material. To model the macroscopic behavior of the cracked material, we use the Kachanov model [18] and then define a new homogeneous equivalent medium. Finally, in order to be sandwiched between the brick and mortar, this material is given a small thickness, and its mechanical behavior is derived using asymptotic techniques to shift from the micro to the macro level. A variation law of the crack length is introduced. The numerical procedure used is then described. Lastly, some numerical examples are given and compared with the experimental data.