UPDATE I tried printing a few of these last week and the fit is way off. Feel free to tinker with them and share updates. I'm not sure when I will get a chance to revisit these. Sorry.
I designed these fraction prisms for the MakerBot Academy Math Manipulative Challenge. #makerbotacademymath
I call them Euclidean Shards because
A. They look like shards and
B. I got the idea from the Euclidean Algorithm, which calculates for the highest common factor
These shards aim to teach students fraction addition and subtraction, and the relationships between fractions. All the while utilizing all three dimensions that a 3D printer allows.
My goal was also to create objects that are beautiful and eye-catching by design.
The concept is (somewhat) simple:
Each prism side is a fraction of a foot. On one shard/prism you will have three sides which are all consecutively half the length of the longer side. The base isosceles triangle on the flat base of the prism has one side which is the shortest length of the prism, and two which are the shorter length of the prism.
For example, the 1/3 shard will have a side that is a 1/3 feet, 1/6 feet, and 1/12 feet. Then the base isosceles will have a side that is a 1/12 feet and two sides which are 1/6 feet.
Example of usage:
Take the picture shown in the gallery of a 1/7 side of a shard laid down next to a 1/4 side of a shard. A student can then solve for 1/7 + 1/4 by trial and error or by using the shards to confirm their answer. In this case 11 of the 1/28 sides will line up perfectly and show that 1/7 + 1/4 = 11/28.
In this example, 28 can be a hard least common denominator to arrive at if one is unfamiliar with fractions, but now it becomes more intuitive because 1/28 is on the same shard as the 1/7.
In addition to teaching fractions these shards can aid in teaching measurements because they are all fractions of a foot/12 inches.
The shards are stackable and the design files include a case.
For the full set please print the following quantities of shards and case parts.
1/2 Shard - 2x
1/3 Shard - 4x
1/4 Shard - 4x
1/5 Shard - 4x
1/7 Shard - 4x
1/9 Shard - 4x
Case Insert 1 - 1x
Case Insert 2 - 1x
Case Lid - 1x
Case Base - 1x
When assembling the case please keep in mind which side is up for the inserts as they can (but should not) go in upside down.