Something New to TryAuthor(s): Arnold F. TorranceSource: The Arithmetic Teacher, Vol. 5, No. 2 (MARCH 1958), p. 103Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41162186 .

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March, 1958 103

Something New to Try Many youngsters who have asked me if

there was any way of making long division palatable have discovered in this method an end to their former frustration and often surprisingly enough after a short trial period find they can endure and even like long division.

I recommend that teachers and students who try this technique do at least a dozen problems alternately with the traditional method before they discard the new opera- tion because it is new and therefore suspect

Sample 1

Key 144 1- 12) 1728 2- 24 12

4- 48 52 8- 96 48

Check- 120 48 48

Sample 2

Key Dbls. 256 1- 179) 45824 2- 358 358

4- 716 1002 8 - 1432 895

Check- 1790 1074 1074

First the divisor is doubled three times, with (1) being placed next to the divisor, (2) placed next to the first doubling, (4) next to the 2nd doubling, and (8) next to the last doubling; meaning respectively 1, 2, 4, and 8 times the divisor.

To test for 3 times the divisor we add the doublings opposite the key numbers for 1 and 2; to test for 5 times the divisor we add the doublings opposite the key numbers 1 and 4; for trial (6) use keys 2 and 4; for trial (7) use the sum of keys 1, 2 and 4 or 1 from 8; for trial of 9 times the divisor use the doublings opposite 1 and 8.

We check the results of our doublings by adding the doublings opposite the key numbers 2 and 8 which should give us ten times the original divisor; if it does not, we must do our doubling again.

We now proceed easily with our long division in the usual way with the aid of so many known and accurate key trial divisors, eliminating guesswork. No multiplication tables are necessary beyond the two's table, quite a boon to the youngster who does not know his tables and to the teacher who has the double complication and frustration of trying to teach long division to students not knowing their tables. Most youngsters learned the two's table before other mathe- matical obstacles had caused them to give up in the arithmetic field as being a field too difficult for their intellects. This method of long division may well salvage the self respect of many of these students enabling them to go on in the field of mathematics.

Contributed by Arnold F. Torrance Garden City, N. Y.

Dress up Your Graphs The teaching unit on graphing in junior

high school grades is sometimes a source of great inspiration to me.

If I am to teach the vertical bar, the broken line, the circle, or the pictograph type, I always try to use some clever ideas in different ways to attract interest and atten- tion to the title of the graph as well as the information it contains.

The following is a list of things I suggest that students try out and they do it with great success.

1. Always use color. Coloring pencils, water colors, or crayons for printing titles, numbers, drawing or sketching symbols.

2. Use geometric patterns to fill in verti- cal bars or horizontal bars or to draw sym- bols in pictographs (triangular, circular, rectangular).

3. Use common symbols to show certain ideas . . . clouds, sun, rain, snow, hail for

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