Problem
Average times count rebuilds a total: the two pairs come to 76 and 78, and all three to 114.
If a few people share equally, multiplying the share by how many people there are rebuilds the whole pile, which a sixth grader does whenever they undo an average.
6.SP.B.5Identify SubproblemsA pair whose average is 38 has 76 marbles between them.
An average is the total handed out in equal shares, so putting those equal shares back together rebuilds the total.
Multiplying the average by how many people share it undoes the dividing that made the average in the first place.
Taking the Emma-and-Sophia pair out of 114 leaves Olivia with 38.
Knowing the whole group and one part lets you take the part away to see the rest, just like spending some money and counting what is left.
4.OA.A.3Work BackwardsTaking the Sophia-and-Olivia pair out of 114 leaves Emma with 36.
The same take-away-the-known-part trick works from the other side, giving the person who was not in that pair.
4.OA.A.3Work BackwardsEmma and Sophia total 76, so removing Emma leaves Sophia with 40.
Once one member of a pair is known, the other is just the pair's total minus that member.
4.OA.A.3Work BackwardsAn average times how many things you have gives the total, and once you know totals you can subtract to find each piece.