How to Factor Pyramid Math

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Pyramid math is a special technique used to teach basic addition skills through an illustration of 10 boxes stacked like a pyramid (four at the bottom, then three, then two, then one) and adding the numbers in adjacent boxes until reaching the top. The activity can be modified to use multiplication as well -- multiplying the numbers at the bottom until reaching the product at the top. Working backward (i.e., starting with the top number) provides the factors.

    Create a math pyramid by drawing a single row of four consecutive boxes adjacent to each other. Draw another three adjacent boxes directly on top of these--then another level with two boxes and finally one box on top of them all.

    Provide the final product in the top box. The number can't be prime or the product of two prime numbers or else the pyramid won't work. Similarly, the two factors of the product must share a common factor. For example, use the number 384.

    Factor the number in the top box into the row of two boxes below it. Remember that factors are numbers that can be multiplied together to make the number being factored.

    For example, 384 can be factored by 16 and 24.

    Factor the numbers in the row of two boxes into the three boxes below. The two numbers must have a common factor, which can be further broken apart in order to fill the pyramid.

    For example: 16 factors into 1 and 16, 2 and 8 or 4 and 4; 1 and 2 can't be factored further, so they are incorrect. Then, 24 factors into 1 and 24, 2 and 12, 3 and 8 and 4 and 6; 1, 2 and 3 can't be factored, so they are incorrect. Therefore, 16 and 24 share the common factor of 4, so the third row has 4, 4, 6.

    Factor the numbers in the three boxes of the second row into the four boxes at the bottom. Here, the number in the middle of the three boxes must have a factor common with each of the other factors (but not the same number with both of them). The end result will be the factors of the starting number.

    For example: 4 is factored into 1 and 4 or 2 and 2. Same with the second 4, and 6 is factored into 1 and 6 or 2 and 3. The last row can read either 1, 4, 1, 6 or 2, 2, 2, 3.


    • Since not all numbers factor in the way needed for pyramid math to work, when you create a pyramid math factoring problem, it may be best to begin at the top, filling in numbers in the four boxes, solving the problem through multiplication and then using the final number as the starting point for the factoring problem.


About the Author

Jess Kroll has been writing since 2005. He has contributed to "Hawaii Independent," "Honolulu Weekly" and "News Drops," as well as numerous websites. His prose, poetry and essays have been published in numerous journals and literary magazines. Kroll holds a Master of Fine Arts in writing from the University of San Francisco.

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