Comparing Without Touching: If A Is Longer Than B and B Is Longer Than C

This idea walks around your house all day. Surveyors and builders reason this way about distances too large to line up directly. This is worth learning because reasoning lets you know things you could not measure directly. Watch for it today, and when you spot it, tell someone what you noticed and how you knew. Ask yourself where else the same idea might be hiding, then go and look.

This is a good thing for a young mathematician to know. Sometimes you cannot put two objects side by side. If a table is longer than a chair, and the chair is longer than a book, then the table must be longer than the book, even though you never compared them directly.

This kind of reasoning works every time, and it lets you know things you did not measure. Careful thinking can reach conclusions your hands could not.

Try it with things too big to move. Is the couch longer than the door? Compare each to a piece of string, then compare the strings. Reasoning through a third object is how people measure things they cannot lift. Do it carefully rather than quickly, and thank God for a mind that can learn.