Parallels and Constant Difference

AVARAGE TIME: 1h / 1h and 30 minutes

The first exercises that we suggest, in accordance with the National Indications, are those concerning vertical, horizontal and parallel lines.


Using partial tables - where numbers appear only on two opposite sides - the students are asked to join all the numbers whose difference is zero.

The second task will be to join points with constant difference but different from zero; for example in the figure is represented the case with difference one. When the difference is no longer zero there are more ways to join the points, the objective is to obtain the configuration shown below.

At the end of the activity we suggest to propose to the class the sentence "if the difference is constant, with opposite sides, we obtain parallel lines".

Among the attachments there are ready-made grids of points divided according to the difficulty, corresponding to the distance between the points. It will be up to the teacher to choose the difficulty to propose, based on the year of the course and the level of the class.

We suggest for the first class to use the file parallele_tratteggiato.pdf, where the request will be that the students, without a line, follow the dotted line.


After becoming familiar with parallels, you can superimpose two constant difference compositions (one with reference to the vertical sides and one to the horizontal sides) to obtain a chessboard formed by parallelograms. After reflecting on the figures obtained, you can ask the class to color the checkered figure.




As a final task, we suggest that the children find some examples of parallel lines in the real world, as shown in the figure.



When the children have finished coloring their chessboards, they can be asked to put them side by side to obtain various configurations, like the one shown in the figure.