Measuring without a ruler
Maths · Early Years · The School
Put them side by side
Which pencil is longer? Hold them next to each other. Line up the ends so both start in the same place. That is the rule. Now you can see. This is the first kind of measuring. It works for length, so you can say longer or shorter. It works for weight, so you can say heavier or lighter. It works for cups, so you can say holds more or holds less.
Counting units
How long is the table? Lay cubes along it, end to end. Now count them. Fourteen cubes. That is measuring with a UNIT. Every cube must be the same size. There must be no gaps. If there are gaps, the number means nothing. Grown-ups use centimetres for this reason. Everyone agrees how big one is.
Heavier is not bigger
Hold a big empty box in one hand. Hold a small stone in the other. The small one is heavier. So size and weight are not the same thing. Balance scales settle it. The heavier side goes down. You can do the same with water. Fill and pour with cups. Which pot swallows more cups?
Lay cubes along the table edge. End to end, with no gaps. Fourteen cubes. Now measure it again with your hands. Five hand-spans. Both answers are right. The numbers are different because the UNITS are different. So you must always say which unit you used. Now get it wrong on purpose. Measure with a mix of big and small cubes. You might get eleven. You might get seventeen. From the very same table. That is why the units have to match.