I discovered these turtles online and decided to try assembling some myself. During this process, I created a straightforward math activity, which I named “Flip the Turtle”.

Challenge #1:

First, get two small baseboards. I found mine at Dollar General in a kit, but you can also find them at craft stores. Put the baseboards side by side and assemble one turtle. Once you’re done, try to “Flip the Turtle” onto the other baseboard.

These two turtles are considered “congruent” and demonstrate a symmetry. According to Wikipedia’s explanation today:

In mathematics, an isometry is a transformation that preserves a figure’s shape and size, such as a rotation or reflection. In two-dimensional or three-dimensional space, two geometric figures are congruent if they are connected by an isometry: either a rigid motion or a composition of a rigid motion and a reflection. They are equivalent up to a rigid motion if connected by a direct isometry. Learning these terms form a fundamental basis for acquiring math notation to make more complex analysis ( copying turtles ).

I read that and came up with Challenge #2:

There are 3 colors in each turtle. The second challenge is to map each of the colors in one turtle to a different color in the second turtle. For example, if I picked three new colors R-G-B, I need to make a new turtle mapping green to R, blue to G, and black to B.

Using the same colors R-G-B, how many different turtles can you make using this method of re-mapping colors ? See if you can write out the combinations on paper ( although it’s more fun to just try making as many different turtles as possible ).

Challenge #3:

I got this idea from chatting with ChatGPT: Total up the number of R-G-B colors needed all together to make all the unique turtles and how much it would cost if the R-G-B colors each cost x; and then how much it would cost if the R-G-B colors cost x, y and z.

Creating these “congruent” turtles was so enjoyable that I decided to iron them and save them for another time!