Isometric graph paper and 3D pictures

Translated from this post by Jane Kats.

At our math festivals and during Mousematics lessons we actively use isometric graph paper, aka “triangular grid paper”.  Sheets with a triangular grid can be downloaded on our site here in the free downloads section, next to symmetric butterflies and a big color-in Christmas tree.

We use this paper in a variety of ways.  For example, to draw diagrams of structures we build using pattern blocks – this is a great fit because these consist of hexagons, equilateral triangles, rhombuses, and trapezoids with 60 degree angles.

Triangular grids are also very useful for teaching children to draw their constructions in 3D.  With younger kids, we draw the pictures ourselves and have them build the structure based on the diagram.  Starting in grades 2-3, students are perfectly ready to draw their own constructions.

It is easy to build a structure out of 2 pieces, and we start with these as a warmup.


We then increase the number of pieces to 4.


Building based on three projections is much harder.


We also discovered that it is easiest to learn to draw your constructions using these rectangular blocks that have convenient dimensions, 1x3x7 cm.  It is much easier than drawing pieces that are constantly blocking each other.

You can also play domino run with these blocks if you have sufficiently many pieces. 


We have also used isometric graph paper to draw “continue the pattern” designs, and for many children this assignment is much more challenging than the equivalent on a regular, square grid.

How do you use standard and isometric graph paper in your classes?


About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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