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APPLICATIONS OF THE FILM IN MATHEMATICS
hands. Mary counts the tens — 10, 20, 30, 40, 50, and Tom goes on counting — 51, 52 ... 62.
Just as Tom finishes, 10 ones group themselves together into a ten group and jump near the other tens. Mary says, "6 tens and 2 ones are the same as 5 tens and 12 ones."
Picture stage: Show 3 tens and eight ones in one row, and 2 tens and 4 ones in a row just underneath. Each ten is represented only be a group of ones. Draw a line to enclose 10 of the ones, then have them move into the bottom row to form a new ten. We now have 6 tens and 2 ones.
Symbol stage: In the picture stage, "tens" are represented by groups of dots or lines. Now we substitute figures and words. Thus, we have "3 tens and 8 ones" in the top row, and "2 tens and 4 ones" just underneath. The plus sign appears at the left of the bottom row, and a line is drawn under the row. Then, in synchronization with the narrator's voices it is shown that: (1) 8 ones and 4 ones are 12 ones; (2) 3 tens, and 2 tens are 5 tens; (3) 5 tens and 12 ones are the same as 6 tens and 2 ones.
Starting again where we had the symbols and words on the screen, the narrator's voice says, "3 tens and 8 ones, that's 38," and the number 38 replaces words and symbols. "Two tens and four ones, that's 24," and 24 replaces words. Line is drawn under 24, and plus sign appears at the left of 24.
Narrator adds the numbers: "8 ones and 4 ones, that's 12 ones. But let's make 1 new ten from 12 ones and add it with the other tens." As he says this a small 1 in a circle appears above 3. "12 is a ten and 2 ones. We'll write the 2 which means 2 ones here." Voice adds the tens: "1 new ten and 3 tens are 4 and 2 more tens are 6." Each number named vibrates as the voice mentions it.
In a similar manner, a film would objectify the "borrowing" in subtraction. The terminology here is unfortunate. The film might clarify the idea for pupils greatly to show that in
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