Comparing decimals worksheets

The pairs are built for the two wrong rules children actually use. One says a longer decimal is bigger, so 4.45 beats 4.5 because 45 beats 5; the other, learned later, says a shorter one is bigger because tenths are bigger than hundredths, so 4.5 beats 4.55. On this sheet the longer number is bigger about half the time and smaller the other half, so neither rule gets a child through the page — only lining the points up does.

The equal pairs are there because trailing zeros are where a lot of decimal trouble starts: 3.40 is 3.4, and a child who marks it bigger is reading the digits as a whole number. Every value keeps the places it was drawn with — 3.40 stays 3.40 on the page — because that is the form the question is about. A tenths sheet in the builder has none of these pairs, since every number on it has one place.

The answers were worked out when the problems were, so the key is the same page with the answers drawn in rather than a second attempt at the same questions — there is no way for the two to disagree. The number in the footer is the seed the sheet was built from: it is printed so that the identical sheet can be had again next week, rather than one that merely looks like it.

This page is one sheet out of a family that can print thousands, and the settings behind it — how many problems, how big the numbers get, how they are laid out, whether there is room to work — are all switches. The builder link at the top of the page carries this sheet’s own settings, so the bench opens on exactly the sheet here rather than on a blank one.

The configuration travels in the address bar rather than on a server, so the link can be bookmarked or sent to somebody as it stands — and what they open is this sheet, down to the seed, rather than another one like it.

Not in the games, which drill facts rather than number sense.