Measuring without a ruler
Maths · Early Years · The School
Put them side by side
Which pencil is longer? Hold them next to each other with the ends level — that is the rule, both ends starting in the same place. Now you can see. Comparing directly is the first kind of measuring, and it works for length (longer/shorter), weight (heavier/lighter) and how much a cup holds (holds more/holds less).
Counting units
How long is the table? Lay cubes end to end along it and count: 14 cubes. That is measuring with a UNIT. The rule is that every cube must be the same size and there must be no gaps — otherwise the number means nothing. Grown-ups use centimetres for exactly this reason: everyone agrees how big one is.
Heavier is not bigger
Hold a big empty box in one hand and a small stone in the other. The small one is heavier! Size and weight are different things. Balance scales settle the argument: the heavier side goes down. Fill and pour with cups of water to compare capacity the same way — which container swallows more cups?
Lay cubes along the table edge, end to end with no gaps: 14 cubes. Now do it again with your hand-spans: 5 spans. Both are right, and the numbers are different because the UNITS are different — the answer only means something when you say which unit you used. Now try it wrongly on purpose: measure with a mix of big and small cubes and you might get 11 or 17 from the same table, which is why the units have to match.