From: Gail (for Teacher2Teacher Service)
Date: Dec 01, 2007 at 05:42:39
Subject: Re: Scale drawing

Hi Janet, 

Thanks for being such a great resource to your grandson. My class is working
with proportions right now, and one of the topics we are working on is scale,
so this is a great time for you to ask this question.

Think of it this way: every half inch of a drawing is worth 10 feet in
real life. That means every inch of the drawing is worth 20 feet in real
life, and every quarter of an inch in the drawing is worth 5 feet in real
life. Do you see where I got those from? I just doubled both amounts, and
then halved both amounts.

You have 3.5 feet to think about, and you know that amount is smaller than 5
feet, so you know the number of inches has to be smaller than a quarter of an
inch.

Let's try halving both numbers again: 1/8 in : 2.5 feet

2.5 feet is too small, but now we know the answer is larger than 1/8 inch,
but smaller than 1/4 inch.  This gives us an idea where the answer is.

Now we can find an equivalent ratio for 1/2 in : 10 ft. How about dividing
both numbers by 10, so that you know how many inches are associated with 1
foot?  That would be 1/20 in : 1 ft.  Since you have 3.5 ft, now you can
multiply both numbers by 3.5 to find out how many inches are associated
with 3.5 feet. 1/20 x 3.5 is 0.05 x 3.5, or 0.175 in. And if you write that
as a fraction, you get 175/1000 in, which simplifies to 7/40 (a little
smaller than 1/5). Remember our estimate? 7/40 is smaller than 1/4, but
larger than 1/8, so we can feel comfortable that we are correct.

I think the key with these problems is to get students to think about the
relationships between the two amounts first, and to do what we did, to
write a few equivalent ratios to get a range the answer falls in.

I hope this helps.  :-)  

-Gail, for the T2T service

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