More, fewer, or the same — Mathematics, 4–6 years
Two groups can be compared by matching their objects. A group has more when some objects are left without a partner; it has fewer when it runs out first.
Comparing groups
To compare two groups, pair one object from the first group with one from the second. If every object gets a partner, the groups are equal. If one group has objects left over, that group has more, and the other has fewer.
Why matching beats looking
A spread-out group can look bigger than a close group, even when both contain the same number. Matching removes the effect of spacing and size. This solves a real problem: deciding fairly who has more, without trusting only what our eyes seem to see.
Which plate has more?
Plate A has three crackers. Plate B has five crackers, spread farther apart. Put one cracker from A beside one from B: make three pairs. Two crackers on B have no partner. Therefore B has more, A has fewer, and the difference is two crackers.
The longer row
It is easy to say that the longer-looking row has more, especially when its objects are spread out. That is reasonable: in everyday life, a larger-looking pile often does contain more. But spacing can trick us. Push the objects into pairs, and compare partners instead of the length of the row.
Fair shares
Comparison helps when two people want to know who has more pieces, cards, or building blocks. Put the objects side by side or pair them one at a time. If one person still has pieces without a partner, the shares are not equal yet.
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