You have a collection of buttons. Some are red circles, some are blue circles, some are red squares, and some are blue squares. If you sort by shape, how many groups do you get?
ATwo groups: red and blue
BTwo groups: circles and squares
CFour groups: red circles, blue circles, red squares, blue squares
DOne group: they are all buttons
Sorting by shape means grouping by shape only — ignoring color. All circles go in one group (both red and blue circles), and all squares go in another group. That gives exactly two groups. If you got four groups, you were sorting by both shape and color, which is a different sort. The attribute you choose determines the groups you get.
Question 2 Multiple Choice
A student sorts animals into groups: 'dogs, cats, fish, and birds.' Another student sorts the same animals into: 'pets and wild animals.' Which student sorted correctly?
AThe first student — they used more groups, so the sort is more detailed
BThe second student — they used fewer groups, which is simpler
CBoth sorted correctly — they used different attributes (species vs. domestication)
DNeither — animals cannot be sorted
Both are valid sorts based on different attributes. The first student sorted by species (type of animal). The second sorted by domestication status (pet vs. wild). A sort is correct if it consistently applies a clear rule. There is no single 'correct' sorting — the choice of attribute depends on what information you want.
Question 3 True / False
The same collection of objects can primarily be sorted in one correct way.
TTrue
FFalse
Answer: False
A collection can be sorted in as many ways as there are attributes to sort by. A set of buttons can be sorted by color, by shape, by size, by number of holes, or by material. Each sorting highlights different information about the same objects. Recognizing this multiplicity is part of logical thinking — the attribute you choose is a decision that shapes what you learn.
Question 4 Short Answer
Why does every sort need a clear, stated rule?
Think about your answer, then reveal below.
Model answer: A clear rule ensures consistency: every object is placed in a group based on the same criterion. Without a stated rule, you might switch criteria mid-sort (starting with color, then shifting to size) and end up with groups that do not make logical sense. A stated rule also makes the sort communicable — someone else can check your work, reproduce the sort, or sort new objects correctly. In logic, an unstated rule is untestable, and an untestable rule is not useful.
This connects to a core principle of logic: an argument or classification is only as strong as its stated criteria. In formal logic, you will eventually encounter the idea that a proposition must be clearly stated to be evaluated as true or false. Clear sorting rules are an early version of this same principle.