As a first approach, we suggest using unnumbered TALES tables - downloadable from the attachments section at the bottom of the page - with which the student can begin to analyze and explore the tool.
The only requirement will be to use the ruler to join pairs of points of their choice, even with different colors - obtaining results like those in the figures below.

 

This free activity is designed for students from grade two onwards, while in the other sections we will see activities suitable for grade one also.
As this is a free activity, each teacher can develop it according to their taste by adding any specific requirements. Here we present some suggestions, however we recommend that the students do more than one drawing.

A first idea could be to ask students if they recognize any particular properties within the drawn straight lines, such as vertical lines, horizontal lines, lines parallel to each other. These questions - appropriately formulated - can be asked even before the concepts such as verticality, horizontality and parallelism have been addressed by the class in an explicit way, just in view of a first approach.

FREE DRAWING WITH A SHAPE AT WILL

You simply ask - after students have made their own drawing - to color the shape among those obtained that they like best.

FREE DRAWING WITH AREA COMPARISON

Pupils are asked to identify and color - with pre-established colors - the largest figure and the smallest one among those obtained. This activity can be proposed even before the concept of area has been introduced, since the notions of large and small are intuitive: in fact, calculations are not required here but only a visual evaluation. To make this evaluation more precise - if you are uncertain about which of two figures is the largest, or the smallest - we suggest the method of dissection. One of the two figures is traced on another sheet (perhaps taking the vertices at the window) and cut out. We then cut the figure into several parts in order to try to make it fit the other: in this way it should be easier and more convincing to identify the largest figure, or the smallest one.

COLORING KNOWN POLYGONS

Pupils are asked to color - with predetermined colors - a triangle, a quadrilateral and a pentagon. In the configuration obtained, it is very likely that there are triangles, quadrialaterals and pentagons with neither horizontal nor vertical sides (such as those in the diagram): this makes the student to break away from the custom habit to which "a square is a square only if it has horizontal and vertical sides" and "a triangle has a horizontal base".

Among the downloadable files are the ready-made grids divided according to difficulty, corresponding to the distance between the points. It will then be up to the teacher to choose - depending on the context - the board to propose.