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FILM AND EDUCATION
grouping must be indicated by drawing boxes or lines. The pictures may be placed on the board or pupils may be supplied with mimeographed materials.
As each box is made to enclose a group of 3 dots, this is explained as subtracting "a three". From 15 dots a three can be subtracted five times.
Symbol stage: In this stage symbols with which pupils are familiar are used to represent the successive subtractions of equal groups; then the new symbolism of division is presented as a way of indicating the result of the successive subtractions which have taken place. The explanation may be somewhat as follows:
We can show with numbers what we did each time we took away 3 dots and put them in a box. First we had 15 dots. We took away 3. There were 12 dots left. We took 3 away from 12; this left 9 dots; we took 3 away from 9 dots; this left 6; again we took 3 away from 6; this left 3; then we took away the last 3. In the subtractions we've made, we see that we subtracted 3 five times, so we know we separated 15 into five 3's.
We have another way besides the subtraction way to show how many 3's there are in 15. We call the other way the division way. We write 15 to mean the 15 dots we had in the big group. We place a frame part way around 15 like this: | 15. This frame tells us to divide the 15 up into smaller groups. When we write a 3 outside the frame this way, 3 15, it tells us to divide the 15 up into groups of 3 each. When we find out by subtracting, by drawing boxes, or by dividing things that there are five 3's in 15, we show this by writing 5
5 above the frame this way: 3 I 15.
The teacher may now return to the division activities
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