Square and Oblong Numbers and Pyramids

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After exploring rectangles created from candy last week, we moved on to looking at tennis ball squares of 1, 4,9,16,25,36,49,64,and 81. We developed several strategies for counting by 2s, 3s, 4s, 5s, 6s, 7s, 8s, and 9s. Then the children stacked these squares sequentially to form a square pyramid and explored its properties.

We introduced a new concept of oblong numbers. These are formed by rectangles of 1x2,2x3,3x4,4x5,5x6,6x7,7x8,8x9,9x10 and so on. The first nine oblong numbers are 2,6,12,20,30,42,56,72, and 90. They formed these numbers by creating an oblong pyramid with a base of 9x10 and building on that. They made conjectures about what the pyramid would look like when it got to the top. Some said one tennis ball like the square pyramid and some thought it would be a 1x2 rectangle; of course, it was the latter.

They carved out an inverted oblong pyramid out of the top to form a solid that looked like a stadium. We also used a keystone approach to building a tunnel under our oblong pyramid. I was even surprised by the results. Several classes made four tunnels run through the pyramid.

The challenge for the week is for them to practice creating rectangles of the squares and oblong numbers they generated. The attached pdf will allow them to write down the dimensions of each of these rectangles, record the number, draw the rectangle, and for the more advanced student, add the numbers to determine how many tennis balls would be needed to create a pyramid of a certain base.

For example, a square pyramid with a base of 9x9 would require 285 balls and an oblong pyramid with a base of 9x10 would require 330 tennis balls.

They were also challenged to compare square and oblong numbers. They might see that the difference is always the amount of the smallest dimension. For example comparing the square and oblong number of 1 and 2, 4 and 6, 9 and 12, 16 and 20 we see the difference of 1, 2, 3, and 4, respectively, and so on.

Finally, they were challenged to build pyramids with materials that they had in their house like Legos, sugar cubes, etc. They may want to bring them in next week, but were encouraged to take a picture if transporting the pyramid proved cumbersome.

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