I'm reading The Poisonwood Bible for my book club and I just realized we meet this Sunday, not next Sunday, so I'm freaking out about how much I have to read. I like to show Parker my progress in the book and how much I have left.
I got to page 200 this morning. The whole book is 543 pages. Part of our conversation about this was:
M: If the book were 500 pages, then what would halfway be?
P: 2 and a half.
M: 2 and a half pages?! I'm
P: No... 2 hundred and 50 pages.
M: How did you do that?
P: I thought of 2 and a half and then my brain made it larger.
I think that what Parker is doing here (although this is all largely subconscious) is using hundreds as a unit. He has done half of 5 many times and/or could do it quickly in his head. So half of 5 hundred is 2-and-a-half hundreds.
This illustrates one of the most important aspects of our number system. "500" is both "five-hundred ones" and "five hundreds." In fact, "500" goes by many names, including "fifty tens" and "one hundred and forty tens."
Being able to see "500 ones" as "5 hundreds " plays an important role in understanding many of the algorithms for adding, subtracting, multiplying, and dividing multidigit numbers traditionally taught in math class. Consider the multiplication algorithm often taught in school:
Look at the third step, where the "4" is multiplied by the "1". That's not really a "1" it's "1 ten" and that's why we write the answer where we do (shifted over one to the left). Because 1 ten times 4 ones is 4 tens. Similarly, in the next step the 3 in the answer is really 3 hundreds because it's 3 tens times 1 ten.
By using units the algorithm allows us to use math facts about small numbers to solve problems about large numbers. The problem with the use of this algorithm in school is that it's often taught before children really understand these units and it is often taught in a way that hides what is going on (it's taught as a series of steps instead of through sense-making based on the underlying number properties).
Post a Comment!!
Reply to my tweet or Facebook post, or comment below.