Question posted on LivingMathForum: My 10 year old just can't seem to grasp that concept for the past few years.  This is so frustrating for him (and for me).  I've tried so many ways to illustrate rounding by 10s, 100s, 1000s using pictures, words, rulers, diagrams - with no success.  Please - any concrete ways I can help my otherwise excellent math student get this? 

Suggestions:
Money seems the obvious choice to me. How about rounding when you go grocery shopping, and see how close you come to the total?

What happens if you round off all the cents without rounding to the nearest dollar? (You'll end up short at the cash register).

What happens if you round to the nearest dollar (You should be very close)

Why are you not exact? (Because it's highly unlikely you'll have an equal amount of things you buy that will round up as down, and the amounts rounded
differ)

One thing I noticed because I did so much rounding in my career was that I would develop a sense about which way the rounding was going. So if I ran across a .50, I'd round up or down depending on what I noticed the trend to be up to that point.

If you have Excel, experimenting with the rounding functions in it can produce the same results. If you have a column of figures you want to round, you can put a formula in the next cell over that will either round using the standard convention, round up or round down. You can experiment with these options to see what happens.

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How about using scales? We use a triple-beam balance to weigh all sorts of treasures and it is easy to "see" how to round using it. Even a bathroom scale could get across the idea....

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Try having him write the 2 choices for the rounding answer below the number

Round 68 to the nearest 10

     68
60       70

Then he circles the one that is closest to the #

If he is rounding 2,341 to the nearest hundred he would write

         2,341

2,300            2,400

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Or, what about using number lines? He would *see* 60 and 70 in their respective places, and *see* which one is closest to 68. He can even count up & down the number line to confirm his "hypothesis".

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Ideas for Learning Rounding from the Living Math Forum