How to Do a Diamond Problem in Math

By Amy Harris; Updated April 24, 2017
Multiplication and addition are used to solve diamond problems.

Diamond problems in math facilitate the development of skills that will be used in algebra. A diamond problem features a diamond divided into four cells, two of which contain numbers and two of which are left empty for you to fill in. Different cells may be empty depending upon the level of difficulty.

Structure and Objective

In basic diamond math problems, the left and right cells contain the given numbers, and the object is to fill in the top and bottom cells with new numbers. The top cell is meant to contain the product of the numbers on the left and right, and the bottom cell is intended for their sum. Thus you multiply the numbers in the left and right cells and insert the result into the top cell, then add the numbers in the left and right cells and insert that result into the bottom cell. In advanced problems, the top and bottom cells are filled and the left and right cells are empty. In this case, you find two numbers that, when multiplied by each other produce the top number and when added, produce the bottom number; insert them into the left and right cells.

About the Author

Based in western New York, Amy Harris began writing for Demand Media and Great Lakes Brewing News in 2010. Harris holds a Bachelor of Science in Mathematics from Penn State University; she taught high school math for several years and has also worked in the field of instructional design.