Which do you teach when multiplying a decimal by 100/1000, etc., or dividing a decimal by 100/1000 etc.? Do I teach that numbers move or do I teach the decimal moves? What if they don’t understand numbers moving. Is it okay to teach students to move the decimal? They are very confused about numbers moving. They understand decimals moving.
Should I teach students to read 65.32 as sixty-five point thirty-two hundredths or stick to sixty-five and thirty-two hundredths? There are instances in real life in which students might come across stats that use “point” as in competitions such as beauty pagents, gymnastics, sport stats, etc. Should I clarify that there are some instances that they might come across reading a decimal as such? How do you teach them to tell the difference between when they should read “point” and when they should read the number using “and”.
(a) Please, please don’t move either. This is one of those magical quick tricks that looks so cute and efficient at first and leaves so many people confused later; it just is not worth it. More than half my college and universtiy level students (including, I am frightened by this, pre-engineering) make all sorts of errors with the moving decimals bit.
First, spend a little time multiplying decimals by 10 and 100 the hard way, writing rows of zeroes and counting decimals in the result. Not years, but a few examples a day for a few days. Also review whole numbers multiplied by 10, 100, etc.
Ask the student what pattern they see when multiplying a number by 10 — hopefully they will say something that shows they realize it has the same digits but all one place value larger. Review at this point tens place, hundreds place, etc. if needed, and 10 x 10 = 100, 10 x 100 = 1000, etc.
(Yes, this may be necessary; yesterday a grade 3 student given some challenge math about the metric system, meters and centimeters which is exactly the 10 and 100 problem; kid had not a clue because the teacher had omitted to teach multiplication first.)
OK, here’s the *logical* system: when we multiply by a number bigger than 1, our answer is bigger. Our system is based on tens, so multiplying by 10 makes one place bigger, by 100 two places bigger, and so on. Dividing by a number bigger than one makes the answer smaller; by ten, one place smaller, by 100 two places smaller, and so on. If you remember bigger and smaller, you can’t get mixed up on who is “moving” where, left or right (to this day I can’t tell you unless I do the problem and look at it first) and all that. You write enough zeros to make enough places larger or smaller (much simpler than the moving rule also).
(b) It is a really, really good thing to first learn decimals meaningfully as parts or fractions, eg 7.5 = seven and five tenths, 3.574 = three and five hundred seventy-four thousandths. Fine. Once this is learned, usually a few weeks to a month, we start to use the “point” verbalization as *shorthand*. I tell students to use this as a simple way to read off lists of numbers and write them and type them — a pure mechanical copying device. When you get to doing mathematical operations, remind the student again of the tenths place and hundredths place. Especially in multiplication, 1/10 x 1/10 = 1/100, and this explains *why* the decimal place rule in multiplication works.