Which Word Does Not Belong: Four Defensible-Sounding Rules
Four students in a reasoning group defend different answers to the same item: 'Which word does not belong? hammer, saw, drill, ladder.'
Amara: 'Ladder, because the other three are tools you use to build something.'
Ben: 'Saw, because the other three make holes or drive things into wood.'
Chen: 'Drill, because it is the only one that needs electricity.'
Dara: 'Ladder, because the other three are tools you hold in your hand while you work.'
The teacher must mark one answer correct and explain the reasoning to the group. Two justifications point to the same word for different reasons, and one student's rule works only because of how a particular drill happens to be powered. The class has been taught to test a rule by checking whether it fits every remaining member of the set, not just two of them.
1. Evaluate each of the four justifications using the two-part test, and state which answer should be marked correct.
Read the worked answer
Amara (ladder). Rule: the other three are tools used to build. Check the remaining three: hammer, saw, drill all shape, cut, or fasten material. A ladder gives access; it does not work the material. The rule fits all three and picks out a category-level difference. Accept.
Ben (saw). Rule: the other three make holes or drive things. This fails immediately - a saw does neither, and a hammer drives rather than makes holes. The rule fits at most one of the three. Reject.
Chen (drill). Rule: the only electric item. True of a corded or battery drill, false of a hand drill or brace. The rule depends on which version of the object you picture, not on the category. Reject, even though the observation is accurate.
Dara (ladder). Rule: the other three are held in one hand. Fits hammer and drill; a saw is usually two-handed, and a ladder is not a hand tool at all. Same answer as Amara, slightly overstated reasoning. Accept with that caveat.
Mark ladder. Accept both Amara's and Dara's reasoning, and use the pair to show that one answer can be reached by more than one sound rule while a wrong answer can still be defended by a rule that only fits part of the set.
2. Explain why 'the drill is electric' is a trap and what it teaches about how these items should be worked.
Read the worked answer
It is a trap for two reasons. First, it is true of one version of the object and false of another, so it is not a property of the category - swap in a hand drill and the whole argument collapses. Second, it is genuinely clever, which is what makes it dangerous: it rewards noticing an incidental fact rather than comparing all four words on the same dimension.
What it teaches: reasoning items are built on features that survive a change of picture or example. If a proposed rule depends on a specific model, brand, size, or power source, it is not a rule the item can be testing. Give the group a two-question check to run on any rule:
- Does my rule fit every one of the three left over?
- Would it still work if the picture or the example changed?
The second question kills the electricity rule at once, and it also kills rules of the form 'the only one that is made of metal' or 'the only one that is red' when colour or material is incidental to the set.
3. Write one parallel set with a single defensible answer and one set that is deliberately ambiguous, and explain how you would handle the ambiguous set with the group.
Read the worked answer
Single defensible answer: 'hammer, wrench, ruler, screwdriver.' Ruler does not belong: the other three are used to turn or drive fasteners. The rule fits all three remaining words, and it survives any change of picture - any hammer, any wrench, any screwdriver still fits.
Deliberately ambiguous: 'apple, orange, tomato, peach.' Tomato can be defended as the only one not eaten as a fruit in everyday cooking, but it is botanically a fruit, so a second defensible rule produces the same word for a different reason; and a student who thinks of ketchup or salads may reach a different word entirely.
How to handle it: do not score it as right or wrong. Ask each student to state the rule first, then judge the rule, not the word. Ask which rule needs the least outside knowledge - the everyday-cooking rule beats the botanical one for this age group because it needs no specialist vocabulary. Then make the transferable point: when several rules are possible, prefer the one that uses the most obvious shared feature of the remaining items, because that is the difference the item was built to test.