Kitchen floor tiling design
The task of your students is to design a floor tiling pattern for a room with given size using at
least two different types of ceramic tiles (having different sizes, or different shapes). In a less
open formulation students have to find floor tiling patterns using 2 types of square (or
rectangular) tiles and the pattern has to be independent of the size of the squares. The tiling
can be used for proving the Pythagorean Theorem (using square tiles) or the angle addition
formula for the sine (using rectangles) but it is also suitable for other mathematical content.
Tags
Discipline: mathematics
Target group: lower secondary education
Age range: 13-15
Time: one or two lessons
Role: tile installer, designer or salesman
Activity: in practice the design is the starting point for the cost calculation and most
professionals use predefined patterns and computer programs for 3D design and automated
cost calculation
End product:
Related profession: tile installer (or advanced DIY skills)
Problem (partially closed formulation)
In the context of moving to a new location you have to renew the ceramic tiles in the
kitchen. For this you want to design a pattern with at least two types of tiles. And of course
you want to calculate the costs as well.
Design a floor tiling using 2 types of square shaped tiles with different sizes. Make sure your
design is independent of the size of the tiles and can be used in an arbitrary large room.
Explore the possibility of using rectangular tiles instead of square tiles and the possibility of
using 3, 4 or 5 different types of tiles, eventually both squares and rectangular tiles.
cc by-sa mascil 2014
Author and Photos: Andreas Reichert; mascil team Freiburg in in
collaboration with vocational teachers who educate future bakers,
pastry chefs, butchers and salespeople
Pedagogic issues

Possible solutions are illustrated in the pictures above.

Tips: students may use paper tiles or work with a
computer
program
(for
example
geogebra)
to
investigate posssible patterns.

Stimulate students to make several different patterns
using the same tiles (see picture).

Geogebra presents the possibility of changing the dimensions of the tiles, students can
use this in their product.

Students may search on the internet or in flyers for the prizes of tiles. They can use this
information to calculate the costs for floors of different sizes. Note that when
calculatiing the costs students need to take into account the shape of the floor as well as
the waste material. In reality the design is also the starting point for the calculation of
the costs. Most professionals use predefined patterns and computer programs for 3D
design and automated cost calculation.

Extension: A possible use of a tiling for the proof of the Pythagorean Theorem is
illustrated below (and the corresponding Geogebra file is attached).
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p. 2

The activity can be used for several different purposes, depending on how deep you
want to involve mathematics, inquiry, or the Wow and gives the opportunity to
emphasize the connections between theoretical knowledge, contents and the
process of practical implementations.
Sample Lesson Plan
Lesson 1
10 minutes
Introduce the task by presenting the context. Discuss what students know
about tiles and tiling and about professions related to this. You may want to
show a video (or a photographs) of a tiler at work.
30 minutes
Students work on the task in pairs. See pedagogical issues for hints and
suggestions
10 minutes
Present and discuss intermediate results and findings in class.
Lesson 2
30 minutes
20 minutes
Students finish their design, you may have them make a poster or an other
type of product (a design in geogebra, a presentation, a brochure etc.)
Present and discuss students’ products and reflect on the mathematics they
used.
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p. 3