[[TASK NO. 4]]
How does a building constructor calculate how many bricks are needed to build a brick house? Students work to solve this authentic task from the construction industry using a photo and eventually, their own observations of real objects (houses).
In order to construct a mathematical model, students need previous knowledge in calculating and geometry, especially in how to calculate area and the surface content of objects.
Before a construction company builds a house of brick, the employees responsible for building the house shell first need to have an approximate idea of how many bricks will be needed.
How many bricks are needed, for example, to build the exterior walls of the house shown in this photo?
Photos: Wienerberger / www.aktion-pro-eigenheim.de
TAGS
Discipline and curriculum area:
Mathematics; Strands: Counting and understanding number, measuring, space and shape
Educational level:
Lower secondary (ISCED 2), Age: 11 and up (Year 6)
Mathematical prerequisites:
Basic arithmetic operations, calculating area, calculating the surface content of objects
Inquiry-based learning:
This is an underdetermined task. Students use a provided photo and can observe real objects (houses) to make assumptions and estimate size and quantity.
CC BY-SA MASCIL 2013
Idea from: Katja Maass, Mathematisches Modellieren. Aufgaben für die Sekundarstufe I (Mathematical
Modelling. Tasks for Lower Secondary School Students), Berlin 2007, p. 104.

[[TASK NO. 4]]
Connection to the world of work:
This task poses an authentic question from the construction industry.
Class time needed:
Circa one class lesson.
POSSIBLE SOLUTION
Estimating and counting bricks on the photo show that the longer side (back) of the house depicted has a height of about 14 bricks and a width of about 40 bricks. That gives a total of circa 600 bricks.
The other, gable side of the house depicted seems to be somewhat narrower than the longer side. However, when one considers the design of gable side of the house (about half of it protrudes from the rest), then it seems realistic to estimate that the amount of bricks needed for the gabled side (up to the bottom edge of the roof) is about the same as the quantity needed for the longer side. The amount of bricks needed for the triangular part of this wall (beneath the roof ridge) remains to be estimated. This area can be modelled as a triangle with sides of 40 bricks and a height of 15 bricks. This model results in about
1
2 of 600 + 300 = 900 bricks.
𝑥 40 𝑥 15 = 300 bricks. Therefore, the entire gable wall needs an estimated total
Now the areas taken up by the windows must be estimated to determine how many bricks will be ‘saved’ – meaning not needed for the walls. For the broader side, 9 𝑥 11 + 6𝑥 10 ≈ 160 bricks will not be needed and for the gable side, the amount of 2 𝑥 9 𝑥 4 + 2 𝑥 9 𝑥 6 = 180 bricks can be subtracted from the total needed for the wall. The small window at the top is not included in this calculation. As to the other house walls that cannot be seen in the photo, it can only be assumed that these walls will need about the same amount of bricks as the other two. In total, 2 𝑥 ((600 + 900) − (160 + 180)) ≈ 2300 bricks will be needed for the house in the photo.
This result is based on relatively imprecise estimates and in so far, not very exact. It does, though, provide a general idea of the house dimensions that can be used as a basis for ordering bricks. It should also be noted that in reality, bricks for construction purposes are normally ordered by the pallet and the amount of bricks on one pallet varies according to brick size and weight.
This task can be made more ‘real’ by having students observe (as a class, in groups, or individually) examples of actual brick homes. In doing so, they can count the number of bricks needed to estimate how many bricks were needed to construct the entire house using calculations like those described above. This task might even be combined with a visit to a house being constructed to observe the process of brick-laying – and perhaps even have a short talk with someone from the construction site about all the mathematics ‘found’ in a house! A follow-up homework activity could be reporting on the type of material(s) used to build the house or flat where they live – including an estimate of how much of a particular building material was needed.
PRACTICAL EXPERIENCE S FROM TEACHING AND SUGGESTIONS
This task was tested in a German middle school with Year 9 students (Ages 14 to 15). The facts and circumstances that need to be considered are quite easy to grasp and the task is well-suited for practicing modelling.
In countries where bricks are not commonly used for home building purposes, other types of building materials, such as natural stone, wood, cement blocks, etc. could be used instead (and an appropriate photo substituted for the one included here).
CC BY-SA MASCIL 2013
Idea from: Katja Maass, Mathematisches Modellieren. Aufgaben für die Sekundarstufe I (Mathematical
Modelling. Tasks for Lower Secondary School Students), Berlin 2007, p. 104.