Reasoning · Grade 6-1 Deductive Logic (2)
Problem
Split on whether one person is tallest.
Lining people up left-to-right by height is something a first grader does on the playground, and once the blanks are drawn, 'tallest' and 'shortest' stop being words to juggle in your head and become positions you can point at.
1.MD.A.1Draw A DiagramAssuming he is tallest gives a contradiction.
Comparing just two people at a time -- Noah against Sam -- is all it takes to switch clue 2 on, and knowing that only one person can hold first place is the same everyday fact a kindergartener uses when only one child can be the line leader.
K.MD.A.2Eliminate PossibilitiesSupposing Noah is the tallest leads to a contradiction, so that whole branch can be thrown away.
One clue that the supposition makes false is enough to kill it, however plausible the rest of the branch looked.
The clues chain together into one line-up, so following the supposition far enough forces two clues into direct conflict.
Assuming he is shortest lets the clues fix the order.
With three blanks and two of them filled, the last person has nowhere else to go -- that is just counting places, and it saves you from thinking there is still a choice to make.
1.MD.A.1Draw A DiagramThat order satisfies all three clues.
Reading a clue backwards -- checking that the order you built obeys it -- uses the same comparing-by-position skill as building the order did, so a young solver can verify their own work.
1.MD.A.1Make A Systematic ListFive of the six orders die, so one remains.
Six orders is a short enough list that a fourth grader can write them all out, so the case argument can be double-checked by plain brute force rather than trusted on faith.
1.MD.A.1Make A Systematic ListWhen a clue says 'either this or that', try both -- the one that makes you say two opposite things at once is wrong, and then check that the other one really fits every clue.