Reasoning · Grade 3-1 Setting Up the Equation
Problem
Name them w, x, y, z from smallest and write the four conditions.
Giving each number an in-order name turns four word clues into four tidy equations I can attack one by one.
3.OA.D.8Identify SubproblemsTaking 70 from 206 gives y = 136.
The 'all but the greatest' total already contains the least-pair total, so taking it away leaves just y.
3.NBT.A.2Work BackwardsThe total of all but the greatest already contains the least pair's total, so taking that away leaves the second-greatest on its own.
The three smaller numbers are the least pair together with the second-greatest, with nothing missing and nothing counted twice.
With the whole and one part known, subtracting hands back the other part, because taking away undoes putting together.
594 less 136 gives z = 458.
Once y is known, the greatest pops out of its pairing with the second-greatest.
3.NBT.A.2Work Backwards487 less 458 gives w = 29.
Knowing the greatest unlocks the least through their shared sum of 487.
3.NBT.A.2Work Backwards70 less 29 gives x = 41: 29, 41, 136, 458.
The last clue fills in the only number left, and the values land in the order their names promised.
3.NBT.A.2Work BackwardsPull the clues apart one subtraction at a time and each hidden number falls right out - just Grade 3 adding and subtracting!