Matrix Cross Sum: Fill Every Empty Cell From Its Row and Column Totals

A Blank Grid Gives You No Starting Number, So the Cell You Commit First Forces All the Rest

Generate fresh 3×3 or 4×4 values and row/column sums. Any legal arrangement meeting the public sums is accepted; hints respect current entries and New set changes targets.

From Filling One Blank to Constructing a Whole Grid That Balances Both Ways (Grades 4-6)

Matrix Cross Sum starts from the missing-addend and multi-digit addition fourth graders already practice (4.OA.A.3, 4.NBT.B.4), where a single unknown part is recovered from a known total. Here there is no half-finished line to lean on: students construct several values at once so an entirely blank array balances down every column and across every row. Committing one cell and watching the targets force the others is a first taste of testing a value against an equation to see whether the whole system holds (6.EE.B.5)—exactly the move Grades 5 and 6 need before formal algebra.

Three Skills Practiced in Matrix Cross Sum

• finding missing addends from target totals
• treating row and column clues as connected equations
• cross-checking a value in two directions

Teacher and Parent Note

Start with the row or column containing the most known information. After entering a value, require the student to check both its row and column rather than finishing only one direction.