Implementation of  “Pythagorean Theorem”  (SOI-RO-360)

Author: Andrei Roxana, teacher

School/Organization: Secondary  School No.28, Galati, Romania

The Pythagorean Theorem – multiple approaches

The Pythagorean Theorem is nothing new for seventh graders. This content is taken up again, after having been studied last year at an intuitive level. In conclusion, going through this lesson has been a challenge to arouse their curiosity and keep them motivated in the given context. For this we used the Europeana scenario mentioned above, for a group of 23 students, age range: 13-14 years. Thus, this lesson combined multiple approaches, depending on the learning style of each pupil: visual, auditory, kinaesthetic.

Technology-based learning

The lesson started with a refresher on the right triangle. To start we used the video How many ways are there to prove . Starting from this, I discovered with the students, inductively, the connection between the sum of the squares of the catheters and the square of the hypotenuse.     

       In order to support students with kinesthetic learning styles, and not only, we proposed a practical activity to highlight this connection. They cut out the squares formed on the outside of a right-angled triangle and noticed that the two surfaces of the squares, which have each side as a cathetus, coincide with the surface of the square with a side equal to the length of the hypotenuse.

      We have pointed out that this theorem was known since the time of the Egyptians, who built right angles to the pyramids by working with the famous 3-4-5 triangle. They had a long rope, which had a knot to delimit lengths of 3, 4 and 5 units. They knew that this triangle had a right angle. 

      We proposed to the students to infer, frontally, the relationship between the lengths of the legs and the hypotenuse from their previous knowledge. They used triangles like this, applied the cathetus theorem to both cathects and noticed that adding the two relations together gives the Pythagorean theorem. 

       To emphasise the importance of this theorem and its applicability, we suggested other online resources to students, such as 118 approaches to proving the theorem  or Europeana resources:

Demonstration puzzle for pythagoras’ theorem. 

    To fix the knowledge, we proposed solving two problems in pairs. At the end of the task, we had a discussion on the solutions proposed by the students. For the next meeting, I challenged them to search the Europeana collections for online resources that refer to the Pythagorean Theorem. These resources will be uploaded to the Google Classroom platform so that they are visible to each student.

Proof of the Pythagorean Theorem

Pythagorean Theorem – online and offline

  The main learning outcomes that we have obtained from the implementation of this learning scenario are :

– Adapting the lesson content to each learning style of the students, so that they are cognitively and emotionally involved in the learning process;

– Increasing students’ motivation, following the use of technology in some parts of the mathematics lesson;

 At the end of the activity, the students were very pleased with the proposed activities, stressing that they would like most of the mathematics lessons to contain modern learning elements and methods.


       The European resources were adapted to the specific needs of the class of pupils and the length of the lesson, i.e. 50 minutes. We did not use all the resources of the learning scenario we implemented, but we used other Europeanana resources than those suggested. My opinion is that the use of the digital heritage of arts and science in classroom activities offers new opportunities for teachers and students to make mathematics more attractive and enjoyable among students.

Did you find this story of implementation interesting? Why don’t you read about the related learning scenario? Pythagorean Theorem (EN-CUR-373) created by Diego Tich

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Public Domain Mark 1.0: the featured image used to illustrate this article has been found on Europeana and has been provided by the Slovenská národná galéria.

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