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Inside the Beltway
Aug. 16, 2006
Math manipulatives to teach "carrying"
In addition to teaching my own, I tutor a
lot of neighborhood kids. Many have very little background for
doing math, but they all understand money. When you think about
it, money is a math manipulative we all use! Here is how to teach
"carrying" (trading, regrouping) with real money. Have on
hand several dimes and lots of pennies (later you'll add dollar
bills). Set on the table 2 boxes (or bowls, cups, or squares
drawn on paper), one for dimes, one for pennies. Set out several
objects. We usually used Beanie Babies, but you could use
anything. Put "prices" on each item. Until you add a box
for dollars, make all your prices under 50 cents. Give several of them
prices that end in 6, 7, 8, or 9. The student can "buy" any two
objects. He gathers the coins for each price, but when he puts
the money in the box, he cannot put more than 9 coins in any one
box. Suppose he had chosen a 29 cent and a 37 cent object.
He will have a total of 5 dimes and 16 pennies. He has to trade
10 pennies for a dime in order to put all the money in. Meanwhile
the teacher writes:
29
+
37
And as the student solves the
problem with the coins, the teacher writes the answer, saying, "This is
the way we will write the answer to 9 + 7. We write the 6 pennies
in the units place and to show we had to trade, we will write the 1
dime up here in the tens place." This is repeated until it seems
the student understands what is happening. This may or may not be
after one session. If the student's interest flags, tell him we
will do just one (or two or three more). Most things are bearable
if you know there is an end. Once that step is understood, the
teacher writes math problems and asks the student to solve them, using
the coins. Then the student solves written problems ("predict how
many coins will be in the boxes") and verifies them with the
coins. Finally, the student does the problems without resorting
to the coins. Obviously when you add the box for dollars you can
eventually get to problems in which you "carry" twice, that is, the
ones box gets full so you trade for a dime, then the dimes box gets
full so you trade ten dimes for a dollar.
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Aug. 16, 2006 - Untitled Comment
Thanks for the idea.
Heidi