Students complete a triangular array by inserting numbers into the top row and adding pairs of numbers for subsequent rows to achieve a final sum at the bottom. After discovering that the position of a number in the top row affects the final sum, they are challenged to find five different numbers that lead to a sum of 100 in the bottom row.

Students complete a triangular array by inserting numbers into the top row and adding pairs of numbers for subsequent rows to achieve a final sum at the bottom. After discovering that the position of a number in the top row affects the final sum, they are challenged to find five different numbers that lead to a sum of 100 in the bottom row. They then analyze the diagram algebraically to determine a formula for the final result in terms of the starting numbers. Next, they compare the coefficients in their formula to the corresponding row of Pascal’s triangle and use that pattern to predict and complete a larger array with a specified end sum. An overhead transparency, activity sheet, template for Pascal's Triangle, and solutions are included. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)