Thinking Mathematically

In the last few weeks I have asked several groups of teachers to indicate where 1 billion would go on this number line:

It has been really interesting to me that many have placed the 1 billion mark in a variety of areas and have had a variety of reasons why.  Many have attempted to use their understanding of place value digits  (there are 12 zeros in 1 trillion and only 9 zeros in 1 billion, so 1 billion should be 3/4 of the way toward a trillion) or their knowledge of prefixes to help (million, billion, trillion… so it must be 2/3 the way along the line). Others thought about how many billions are in a trillion asking themselves, “Is their one-hundred or one-thousand billions in a trillion?” Using this strategy, everyone picked a spot toward the left, but some much closer to zero than others.

Others did something interesting…

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