Undercover Sum: Deduce Every Hidden Cell From Row and Column Totals
Some cells sit face-up while others stay hidden, and every row and column carries a target total. You tap a masked cell, work out its value from what the line still owes, and confirm it against the crossing total.
The Hard Part Isn't the Subtraction — It's Knowing Which Hidden Cell to Solve First
Give students a partly-revealed grid and many freeze: with several cells still masked, subtracting the shown numbers from a total leaves more than one blank and no single answer. The detective move is to scan for the one row or column that hides exactly a single cell. Suppose a row shows 4 and 9 against a target of 20 — that line still owes 20 − 4 − 9 = 7, so its last cell can only be 7. The instant you place that 7, it stops being a clue you are missing and becomes a clue you now hold: the column running through it, with a total of 21 and a revealed 6, is suddenly down to one blank and forces 21 − 7 − 6 = 8. Each solved cell collapses the next line to a single unknown, so the grid unravels as an ordered chain of deductions instead of a wall of simultaneous guesses.
From One Missing Addend to a Chain of Missing Addends: Grade 5-6
A single line — target minus the revealed parts — is exactly the missing-addend equation x + p = q from 6.EE.B.7, and Undercover Sum strings those equations together so each solved unknown feeds the next. Students rely on multi-digit addition and subtraction fluency from 5.NBT.B.5 to keep every subtotal exact, because one slip early in the chain topples every deduction that depends on it. Naming each masked cell as its own unknown draws on the variable-and-expression reasoning of 6.EE.B.6, and the habit of always attacking the most-constrained line first is the same order-of-attack instinct that later powers systems of equations.
Three Skills Practiced in Undercover Sum
- subtracting known parts from a target total
- combining horizontal and vertical clues
- eliminating candidates through cross-checks
Teacher and Parent Note
Have the student write the known subtotal and remaining difference beside each line. After finding a hidden value, require a second check in the perpendicular direction.