Kakooma Polygon Shapes and Multiplication--Make Your Own

The 3rd through 6th graders were craving multiplication Kakooma after its introduction last week. Not only did we explore this new challenge but we did it with square, pentagonal, hexagonal, heptagonal, and octagonal patterns. We spent considerable time looking at the advantages of hexagonal tessellations vs. pentagons which do not tesselate. Bees have done the math and use hexagonal honeycombs because they hold the largest area of material (honey) as a ratio to the work to create the perimeter. They could have easily used equilateral triangles or squares which also tesselate but hold a small fraction of the area in relationship to its perimeter.

The 1-2nd graders were interested in exploring other shapes of Kakooma. We also learned about pentagrams and hexagrams (5 sided stars and 6 sided stars) and explored creating fractals of these shapes within larger similar shapes.

I gave the children many puzzles to solve but emphasized the importance of attempting the creation of Kakooma puzzles. The challenge is to make your puzzle non-obvious. The children were taught to introduce possible solutions that were common mistakes to make the puzzle more challenging. 

When creating their own Kakooma multiplication puzzles, they discovered that the solution cannot include prime factors. For example, if 6 was the final solution and the factors 2 and 3 were used to solve this puzzle, these prime factors would be impossible to solve in the main puzzle since you would need 1 and the number itself. Therefore, you would have duplicate solutions. 

Have fun creating your own Kakooma.