Measuring with a scale

In your book, Maths Mela (Chapter 6), you measure things with a scale: a box, an eraser, a pencil, a comb. Put one end of the thing at the 0 mark and read the mark where the other end reaches. If a pencil starts at 0 and ends at 9, it is 9 cm long. The gap between two marks next to each other is 1 cm.

Some things are very small. Is a grain of wheat more or less than 1 cm? It is less than 1 cm; it would fit inside one gap on the scale. A small ant is also less than 1 cm. An eraser and a rajma seed are longer than 1 cm.

Ashwin's scale is broken. It does not start at 0 any more! Can he still measure? Yes. He puts one end of a paper at a mark, say 8, and sees the other end reaches 14. The length is the number of 1 cm gaps from 8 to 14. Count them: 8 to 9, 9 to 10, 10 to 11, 11 to 12, 12 to 13, 13 to 14. That is 6 gaps, so the paper is 6 cm long. A quick way: 14 − 8 = 6.

Another paper goes from 12 to 16 on the broken scale. 16 − 12 = 4, so it is 4 cm long. Always take away the starting mark from the end mark. Do not just read the end mark.