MATHS & ART WORKSHOP 1

Geometry for the First Cycle of Primary Education

Presentation for teachers

 The task of linking Art and
Mathematics may seem at first
glance somewhat artificial and
forced, but it is exactly the
opposite. Maths is essential, in
an obvious way in Architecture,
but also in Sculpture and often in
Painting and other Arts, which
sometimes are known as "minor
arts", but as we must not forget
the audience that the workshops
are directed to, I am going to
focus on the part of mathematics
whose relationship to art and
artistic expression is more
tangible and therefore easier to
visualize and understand by
children: that is Geometry.

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 This first workshop, which I have entitled: MATHS & ART
WORKSHOP, is firstly aimed at students in the first cycle
of primary education, working the foundations of
Geometry, focusing on flat shapes: Point, Line and
Plane, and within the latter, in Triangle, Circle, Rectangle
and Square.

 The way I am going to use to present these contents, can be
a little diffent to that in which they use to appear in
textbooks, but always encouraging children’s creativity.
I want to highlight that the objective is not to replace
that teaching, more academic, but to complement it.
On this way, the workshops will be appropriate to reinforce
some knowledges, to help to understand them if there are
any doubt, and to reach a more motivating learning.

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 The different chapters and sessions of this workshop, will
be always based in the same structure:
 Presentation.
 Geometric objects in our environment.
 Geometric objects in Art.
 Resources and activities of comprehension and
representation of geometric objects.

 In the original blog:
http://artedesermaestro.blogspot.com.es/
there are some videos included with certain advices, that
can help teachers and pupils to improve the process of
drawing of some geometric elements.
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1. Linguistic communication competence: With the use of
language, for listening and understanding contents to
communicate between themshelves and the teacher along the
development of the activities.
2. Mathematics competence: It is the most obvious of all of
them in this workshop, where Geometry, as an important part
of Mathematics, takes the main character.
3. Competence in Knowledge and interaction with the
physical world: With the comprehension of events, and the
prediction of consequences. It is also referred to the
progressive hability to investigate and scientific inquiry:
Identifying and posing problems, making observations, asking
questions and contrast hypothesis.
4. Dealing with information and digital competence: With
the use of TICs to present the workshop and to develop several
activities.
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5. Social and civic competence: With respect among all
the people, along the workshop and the group activities.
6. Cultural and artistic competence: Being conscious of
the artistic heritage in their environment, and about
significant masterpieces, as a reference and inspiration
for their own creations.
7. Learning to learn competence: With the purpose of
learning, enjoying in an effective way, with curiosity and
motivation to learn, responsability and personal
compromise, accepting mistakes and learning from and
with the others.
8. Sense of initiative and entrepreneurship: Which is
needed to approach several individual activities, and
taking part activily in group activities.

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 To understand and express basic concepts about Geometry.
 To know and value the presence of Geometry in Art and
our enviroment.
 To recognize the creative possibilities of Geometry, as well
as its contribution to all kind of disciplines.
 To know and understand the next basic elements of
Geometry:
 Point and straight line.
 Triangle.
 Rectangle and square.
 Circle and circumference.

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 To identify and understand the presence of the
mentioned basic geometric elements in our inmediate
environment.
 To identify and value the basic geometric shapes in all
kind of masterpieces.
 To improve the skill in drawing or tracing the basic
geometric shapes mentioned before.
 To make different activities from basic geometric
shapes, using traditional materials and computer
programmes.

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 Point and straight line.
 Point and straight line in our environment.
 Point and straight line in Art.
 To improve the drawing of straight lines.
representation of points and straight lines.
 Triangle.
 Triangle in our environment.
 Triangle in Art.
representation of triangles.
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 Square and rectangle.
 Square and rectangle in our environment.
 Square and rectangle in Art.
representation of squares and rectangles.
 Circle and circumference.
 Circle and circumference in our environment.
 Circle and circumference in Art.
 Drawing circles without compass and freehand drawing.
representation of circles and circumferences.
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 We observe the basic geometric elements (point, straight
line, triangle, rectangle, square, circle and circumference) in our
environment.
 We identify the basic geometric elements in different
masterpieces.
 We draw straight lines, triangles, rectangles and squares without
tools and with computer programmes.
 We draw circumferences with computer programmes, by hand
and with auxiliary elements different to the compass (we learn to
built and to use an auxiliary tool for this purpose).
 We develop our own artistic works, by hand and by
computer, from basic geometric shapes.
 We perform activities, traditional and computer games, based on
basic geometric shapes.
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 To show interest in the presence of basic geometric
elements, in our environment and taking part of
masterpieces.
 To respect and value our artistic and cultural
heritage.
 Interest in the performing of our own artistic
compositions, based on the use of basic geometric
shapes, both by hand and by computer.
 To respect and value the work and creations of our
classmates.
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 Each of these four parts can be developing in a work session along an
hour and a half or two hours. In all the cases, we will expend among
five and ten minutes to show and to talk the whole group the examples
of geometric shapes in our environment; and we will do the same about
Art. So, it will be about eighty minutes to develop the activities,
preferibly in the order that I state here, but with total flexibility,
depending on the circumstances of the class.
 Total estimated time for the workshop : 8 hours (4 work sessions).

 This workshop is initially thought for the First Cycle of Primary
Education, over all for pupils in the 2º year; but with little
corrections, especially about the activities, it could be equally
appropriate for the rest of the cycles of this stage.
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 Evaluation will be based on the continuous and
systematic observation of pupils’ work, and the
interest shown along the exposition of contents and in
the performing of the different activities.
 In this sense, many activities will leave a physical
record as an assessable material, such as drawings and
artistic compositions on paper, or computer files with
their digital works.
 Nevertheless, we mustn’t forget that the educational
possibilities of this workshop, are mainly based on
pupils perceiving it as a funny and less monotonous
way for acquiring knowledges.
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Workshop developed to be presented in the classroom. The
introductory texts can be appropriate as a help or reference for the
teacher, adapting the language to pupils’ level if necessary. You
can see more information :
http://artedesermaestro.blogspot.com.es/

 The original base of Geometry is the point; in anisolated way
it is nothing, it isn’t a physical object, but it is necessary to
form the rest of the basic geometric elements that we
know, everything around us. What is a straight line, but a
sequence of points all together in the same
direction? and is it not the point a way of representing
the intersection between two straight lines at the same
time? so, the straight lines and points are two of the main
elements of Geometry, as well as the plane, and these two first
elements are precisely those we are going to talk about in this
chapter.
 TIMING: 1 session=2 hours.
 You can see more complete information about this chapter in:
http://artedesermaestro.blogspot.com.es/2012/04/geometria-
para-primer-ciclo-de.html

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 In this video, recorded in Spanish, I show several advices, which can
be useful to transmit to your pupils how to improve the accuracy of
the drawing by hand. The video is directed to teachers, in order to
select what they consider appropriate, and adapt it to the resources
they have in the classroom (traditional blackboard, interactive
whiteboard, etc.) 27

http://www.pequejuegos.com/juego-cuatro-en-raya.html 32

 After finishing the first part of the workshop, about
points and straight lines, we are going to see now another
basic element for Geometry, such as the triangle. As the
rest of geometric shapes we will see along this
workshop, triangles are formed by points (vertices)
and straight lines (rectangle’s sides), and if we link
properly these concepts from the very
beginning, children will understand perfectly why we are
following this order.
 You can see more complete information about this
chapter in:
http://artedesermaestro.blogspot.com.es/2012/05/geome
tria-para-primer-ciclo-de.html

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 This new chapter about rectangles and squares, could
be developed before or after that about
triangles, without affecting the essence of this
workshop. As well as points and lines as constitutive
elements of all geometric shapes, there is no doubt about
that the most familiar ways for children, or at least
in a more prominent way, are rectangles and
squares, as we can see in the next examples, into the
school context.
chapter in:
tria-para-primer-ciclo-de-primaria.html
51

http://www.pequejuegos.com/juego-tetrix.html 62

 With this fourth chapter, about circles and
circumferences, the whole contents and activities of
this workshop will be completed. Talking about circles
and circumferences, we find basic geometric shapes
again, which are usually present in pupils’
environment, and that undoubtedly they know since
their first school years. We are going to see this with
some simple examples.
chapter in:
tria-para-primer-ciclo-de-primaria_18.html
64

 In this video I show several advices, in order to improve the drawing of
circles by hand and with auxiliary tools different from compass. At the
same time, I show step by step how to built and use a simple tool for
doing circumferences with 10 pre-defined radios. As well as the other
video we seen previously, this one is directed to teachers, in order that
they transmit these advices to their pupils on the way they feel
appropriate. 76

http://www.pequejuegos.com/juego-dispara-bolas.html 79


In my blog “El Arte de ser Maestro”, you can see an Spanish version
of this workshop. http://artedesermaestro.blogspot.com.es/

MATHS & ART WORKSHOP 1

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