Reading a Ruler IIIDate: 03/03/2005 at 23:19:37 From: Mary Subject: reading a ruler--instructions to explain to a child My daughter came home with a worksheet that had a ruler on it and it has letters on the ruler in which she is supposed to say the place (value) the letter represents on the ruler. Now it's been a while since I have done this. I am looking for simple, basic instructions to teach a child how to read a ruler. Of course I can instantly tell you where a 1/2 is; however, the rest is very vague to me. I somehow remember that we used to count the lines--where the line falls on the ruler is the top number of the fraction and how many lines in between 0 to 1 inch represents the bottom number (the whole). Is this correct? I like your examples on how to read a ruler. However, if you can just count where the line is and put that in the numerator and count how many lines make the whole and put that in the denominator that would be helpful to make it so that everyone truly understands how to read the ruler. Date: 03/04/2005 at 08:44:52 From: Doctor Ian Subject: Re: reading a ruler--instructions to explain to a child Hi Mary - It sounds like you've already read these items from our archive: Reading a Ruler http://mathforum.org/library/drmath/view/58333.html Reading a Ruler II http://mathforum.org/library/drmath/view/58439.html Is that correct? If not, you might want to take a look at them. In any case, let's look at an example. Suppose I'm measuring something that's something and 7/16 of an inch long. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ----------------------------------- xxxxxxxxxxxxxxxx In practice, I'd look at the 1/2 mark, and say "That's too big." So I'd look at the 1/4 mark, and say "That's too small." So now I know it's between 1/4 and 1/2, i.e., between 1/4 and 2/4, which is between 2/8 and 4/8. What's halfway between them? 3/8. So I look at 3/8, and say "That's too small." So now I know it's halfway between 3/8 and 1/2, i.e., between 3/8 and 4/8, which is between 6/16 and 8/16. What's halfway between them? 7/16. And that works. So I'm done. The whole system is based on successively breaking things into halves, so I just go with the flow. That is, you can imagine a ruler where the markings only go down to 1/2 an inch: | | | | | | | | | | | | | | ----------------------------------- 0 1/2 2/2 = 1 If we decide that's not fine enough, we double the denominators, | | | | | | | | | | | | | | ----------------------------------- 0 2/4 4/4 = 1 and that gives us room for more numerators: | | | | | | | | | | | | | | | | | | | | ----------------------------------- 0 1/4 2/4 3/4 4/4 And so on, through 8ths and 16ths and even 32nds, if we can make our markings finely enough. Of course, this is all but impossible to deal with unless you're pretty facile at converting between equivalent fractions with powers of 2 in the denominator, e.g., 1/2 = 2/4 = 4/8 = 8/16 = 16/32 That's the basic skill you need to make the system work. The idea of counting all the marks to figure out what the denominator should be would work in theory, but in practice it would be pretty slow. But with some practice, you could do something sort of equivalent but quicker. That is, you could start by identifying what size mark is next to the end of the thing you're measuring: | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ----------------------------------- xxxxxxxxxxxxx^ |_________ This is the size I want. Next, you could look at the 1/2 mark, and back up halfway to the 1/4 mark. If that's the right size, you can now just count quarters. If it's still too small, back up halfway to the 1/8 mark. If that's the right size (in the example above, it is), you can just count eighths. And so on. Note that when you're 'counting quarters' or 'counting eighths', you have to count any marks that are at least as large as the one you're using; but you can ignore any that are smaller. So that's pretty straightforward, but again it require at least a little facility with powers of 2 in the denominator. Is this helpful? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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