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Vn62.1 Multiplication 8/7 & 11/77

8/7 Robby has many times now seen Miriam on my lap receiving some
instruction in addition. Complaining of feeling left out, he has asked
for help in math. Robby said he needs help with addition of numbers
such as 9 plus 6 and 8 plus 7. I found him a set of flash cards for
practicing with. Robby looked through them, declared he knew them all,
and set them aside. Miriam picked up the box of cards and has reviewed
them once or twice. Robby also specifically asked for help with mul-
This afternoon he inquired how much is 24 times 42. Gretchen told
him the answer. I suggested Robby estimate the answer as 20 times 40
and showed him how to factor the product thus:

		20		2 x 10
	      x	40		4 x 10
				8 x 100	800

with Robby doing the intermediate products and the final multiplication.
I posed for him the problem of multiplying 20 times 400. Under the
previous work Robby wrote

		20		2 x 10
	      x	400		4 x 10
				8 x 100

After I inquired whether or not he had left out a zero, Robby made the
lower product 4 x 100, looked in puzzlement at his product of 10 times
100 being 100, changed it to a thousand and the result to 8000.

8/11 Miriam, aware that Robby is interested in learning multiplication,
is turning her attention to that. Today Miriam told me, “I know how to
do it, that other thing, not adding or take away. . . . 10 times 1 is like
10 ones.” I asked her how much is 2 times 4. Miriam answered ‘8.’

Bob How much is 3 times 6?
Miriam (after a long pause) 36.
Bob How did you compute that?
Miriam 12 plus 12 is 24 and 10 more is 34 plus 2 is 36.

Miriam then asked, “Is 20 times 20 equal to 60?”

Bob That’s a big number but not very close.
Miriam 40?
Bob That’s a lot closer, Miriam.
Miriam Is it 20?
Bob No. That’s not the way to get a good answer, Miriam. We’ll
talk about multiplication later.

Because Robby and Miriam spend more time with each other than with
anyone else and because they compete with each other for their mother’s
and my attention and approval, they both view each other’s activities
for comparative advantage.

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