Problem
Since 1 cup = 8 fl oz, the start 11 cups 2 fl oz = 11 x 8 + 2 = 90 fl oz, and the end 13 cups 1 fl oz = 13 x 8 + 1 = 105 fl oz.
Using one unit (fluid ounces) makes the added amount easy to find.
3.MD.A.2Analyze The UnitsThe jug grew from 90 fl oz to 105 fl oz, so the 5 pours added 105 - 90 = 15 fl oz altogether.
The increase in the jug is exactly what the small cup added in total.
3.MD.A.2Work BackwardsAll 5 pours were equal full cups, so each cup holds 15 divided by 5 = 3 fl oz.
Sharing the 15 fl oz into 5 equal pours gives the size of one cup.
3.OA.A.3Analyze The UnitsThe capacity of one small cup is the total amount poured into the jug divided by 5.
The total poured in is the 5 cupfuls added together, and since each cupful was equal it forms 5 equal groups of one cup's worth.
The amount added is nothing more than the 5 separate pours combined, with no lemonade lost or gained in between.
Each pour filled the same small cup to the brim, so all 5 pours hold the same amount and stack up as 5 equal groups.
Since 5 equal groups of one cup make up the whole total, taking one group back means dividing that total by 5.
This only needs Grade 3 sense: find how much the jug grew, then split it into 5 equal cups!