Problem
Draw the 80 tangerines as one bar and cut it in four; box A takes one part, 20.
A fifth grader can split a bar of 80 into 4 equal groups of 20 and see that one group is box A.
5.NF.B.6Draw A DiagramAfter box A, the leftover part of the bar is the other 3 of the 4 parts, which is 3/4 of the whole. In tangerines that is 80 minus 20.
Taking away the 1/4 piece leaves 3 pieces, so the rest is easy to count as 60 tangerines.
5.NF.B.6Identify SubproblemsBox B takes two thirds of the remaining 60, not of the original 80, so it takes 40.
The word 'of the rest' tells us to start counting again from the leftover pile, so the bar for 2/3 is the 60-pile, giving 40.
5.NF.B.4Draw A DiagramBox B takes two thirds of the 60 that were left, not two thirds of the original 80.
The problem says two thirds of the rest, so the whole being cut up at this step is the leftover pile and not the pile we started with.
A fraction always names a share of some particular whole, so the same fraction of a different whole is a different amount.
Two thirds means cutting the whole into three equal parts and taking two, and those parts are only as big as the whole they were cut from.
That leaves 60 - 40 = 20, which is the unused third of the remainder.
Once box B is filled, only the unused third of the leftover pile remains, which is 20 tangerines.
5.NF.B.6Identify SubproblemsWhen a problem says 'of the rest,' start counting again from what is left, not from the original whole.