Sums in a Square Grid

In this assessment, students investigate the sum of integers that are selected in a square grid of consecutive integers in a way that no two numbers are selected from either the same row or same column. Students begin the investigation by examining the 3 x 3 and the 4 x 4 grid, both with the starting number 1. Then, a closer look at the 3 x 3 grid (in Part B) and at the 4 x 4 grid (Part C) is concluded with discovering a general rule for the sum of the selected integers in the 3 x 3 and in the 4 x 4 grids. Finally, in Part D, to fully generalize the pattern, students examine the sum of selected integers in the k x k grid, with the starting number n.

Math Concepts: patterns sum sequence
MYP Related Concepts: change patterns
MYP Key Concepts: logic
MYP Global Context: Identities and Relationships
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