How to Factor Pyramid Math

Small student making pyramid with blocks
••• Comstock Images/Stockbyte/Getty Images

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.

Related Articles

How to Factor Expressions in Algebra
What Is Factoring in Math?
How to Compare LCD & LCM in Fifth Grade Math
How to Factor Monomials
How to Solve a Math Factor Puzzle
How to Factor Polynomials With 4 Terms
How to Factor Binomial Cubes
How to Find the Product of Fractions
How to Find the Greatest Common Factor of Two Numbers
How to Find All The Factors of a Number Quickly and...
Tricks to Factoring Trinomials
How to Write Polynomial Functions When Given Zeros
How to Factorise in Math
How to Calculate a Coprime
How to Do Multiplying & Factoring Polynomials
How to Write a Repeating Decimal As a Fraction
How to Write the Prime Factorization in Exponent Form
Math Activities for Teaching Factors
How to Find the Geometric Sequence
Tricks for Factoring Quadratic Equations