Reasoning · Grade 3-2 Weighing with Balances
Problem
In grams the readings are 4600 and 2900.
Using one unit (grams) everywhere makes the numbers easy to compare and subtract.
3.MD.A.2Identify SubproblemsThe two differ by one scale, so a scale is 1700 g.
Two loads that are alike except for one extra item differ by exactly that item's weight.
3.NBT.A.2Work BackwardsTwo loads that are alike except for one extra item differ by exactly that item's weight.
The shared part of the two loads weighs the same on both readings, so it cancels the moment you subtract one from the other.
Each reading is its items' weights added together, so what remains after the shared items cancel is the one extra item.
So one scale weighs 1700 g, that is 1 kg 700 g.
The 'extra' part of the heavier reading IS the scale we added.
2.OA.A.1Identify SubproblemsRemoving it from the second reading leaves three potatoes at 1200 g.
Working backwards: subtract the part we now know (the scale) to uncover the part we want (the potatoes).
3.NBT.A.2Work BackwardsShared among three, one potato is 400 g.
Equal sharing among 3 potatoes is division.
3.OA.B.6Identify SubproblemsWhen two weighings hold the same potatoes but one has an extra scale, the difference in the dials IS that scale's weight - subtract it off and you uncover the potatoes hiding underneath!