Grades 3–5 · Mathematics
How do rows and columns show multiplication?
A rectangular array is an arrangement with the same number of objects in every row and in every column. Rows run across the page; columns run down it. The regular alignment makes the group structure visible instead of leaving a scattered collection.
In the diagramAn array organizes equal rows3 rows · 4 counters in each rowRow 1Row 2Row 34 + 4 + 4 = 123 × 4 = 12 countersRows × counters per row gives the whole count.
The displayed array has three rows with four counters in each row. Each row contributes four, so the total is 4 + 4 + 4 = 12 counters. Multiplication records that repeated equal contribution as 3 × 4 = 12. Here the first factor is the number of rows, and the second is the number in each row.
The columns offer another view of the same collection: four columns each contain three counters. That gives 4 × 3 = 12 as well. The descriptions organize the objects differently, but no object is added or removed. An array therefore connects repeated addition, multiplication and the unchanged whole.
About this explanation
Starting knowledge: Count small collections and interpret repeated addition of equal amounts.
Sources
- Common Core State Standards Initiative — Grade 3: Multiplication with equal groups and arrays