Triangular and Square Numbers for Kindergarteners

Whenever I visit Revolutionary or Civil War battlegrounds, I always marvel at how ammunition was stored. Cannonballs were stacked in triangles of spheres and it was referred to as cannonballing. 

This amazing sequence of numbers where we start with 1 and add 2, 3 + 3, 6 + 4, 10 + 5, etc. The first 10 numbers in this sequence is 1, 3, 6, 10, 15, 21, 28, 36, 45, and 55. We see these numbers come up all the time.

I hot glued the first 8 layers of these numbers with tennis balls to have them feel how these numbers look and grow. We built triangular pyramids and even rhomboidal pyramids. We studied the equilateral triangles and discussed the differences between this pyramid and the great pyramids of Giza which were rectangular bases.

The attached pdf has pictorial representations of these numbers and prompted the children to count to the first several triangular and square numbers. Answers are provided as well. They key learning objective for me was to get them to adopt alternative approaches to counting by ones each time. For example, if they know the third triangular number is 6 and they see that the next triangualr number adds 4 to the bottom row, they can just add 4 to 6 to get 10. Then add 5 to get 15 and so on. 

With the square numbers, take the previous square and add an L row and column to build the next square. I gave them blank graph paper so they can create their own pictorials of these numbers.

Have fun exploring the pdf this week. Also, I would love for them to create their own triangular numbers. They can use the graph paper I supplied, or use manipulatives such as golf balls, marshmallows, etc. If they are too large to bring to class, take a picture.