Reasoning · Grade 3-2 Interpreting Graphs
Problem
The three drawn bars make 18, leaving 17.
If you know the whole (35) and part of it (18), the rest is just the whole minus the part — a subtraction a third grader does every day.
3.NBT.A.2Work BackwardsWriting Sam as Ruby gives twice Ruby plus Kai equals 13.
Replacing Sam with 'Ruby and 4 more' keeps everything in terms of just Ruby and Kai, so there are fewer mystery numbers to juggle.
3.OA.D.8Work BackwardsReplacing Sam with "Ruby and 4 more" keeps the total true while leaving only Ruby and Kai unknown.
Swapping a quantity for something exactly equal to it changes nothing about the equation, so the total still holds.
The total is the six readers added together, so writing one of them in terms of another simply regroups the same sum.
Kai is 0 or 1; 0 breaks Ruby, so Kai = 1.
'Fewest of all' means smaller than the smallest bar (2), so there are only two numbers to try — a quick guess-and-check settles it.
3.OA.D.8Guess And CheckThat gives Ruby 6 and Sam 10, with Kai fewest.
Checking that Kai's number really is the smallest of all six makes sure the 'fewest' clue is satisfied, not just the arithmetic.
3.NBT.A.2Guess And CheckFind the leftover total first, then let one clue ('4 more') shrink the puzzle — only Grade 3 add/subtract sense needed!