123

CDP's

789

Part I

     Carefully find the products of these multiplication exercises.

	(A)   41	   (B)   576		(C)   11728
	      3		  6		         2


     Did you notice something interesting about your answers?

     If you did your work correctly, you should have noticed that the digits in each product were "in order". That is rather interesting, don't you think?

     When the digits appear "in order" like that, we say they are

consecutive digits.


     Here are some more problems. Each one has a "consecutive digit product (CDP)".

(1) 81 7 (6) 18 13
(2) 263 3 (7) 335 7
(3) 57 8 (8) 64 54
(4) 23 15 (9) 219 31
(5) 27 21 (10) 167 34

tt(8/4/82)


Teacher's Note: This and the following three activity pages were written before calculators were commonly accepted for use in the classroom. Hence, you should take this into consideration when using this material.

The fundamental purpose behind this seeming "drill & kill" sort of activity is actually the opposite. Namely, once you have multiplied the numbers, you should have, if done correctly, a surprise awaiting you: a product with some interesting aspect, in this case consecutive digits of one form or another. In this way, a reward of sorts is provided while at the same time practicing the old fashioned (or, if you prefer, time honored) skill of multiplying whole numbers. And not to be overlooked is the encouragement of the habit of examining one's answer to see if it is reasonable; in this activity the focussing on the answer is merely to see if it meets the criteria of the lesson. But in general the habit of "looking back" is one that is not well established in the minds of many and needs to be promoted more.

tt(6/5/98)


531

CDP's

246

Part II

     Here are some more problems that have "consecutive digit products". But this time there is a difference. What is it?

	(A)   48	    (B)   727		(C)   18107
	      9		   9		         3


     Of course, you see that the digits are still in order, but this time their order is reversed!

     Try the following exercises to see yet another type of answer.

	(D)   27	    (E)  617		(F)   3251
	      5	          4		        3


     In those problems the digits are either odd or even, while at the same time they are still consecutive.

     Now, all the problems below use these ideas. But, which is which?

(1) 107 3 (6) 443 17
(2) 181 3 (7) 149 58
(3) 51 15 (8) 89 86
(4) 679 8 (9) 149 29
(5) 1193 3 (10) 59 23
tt(8/4/82)

579

CDP's

864

Part III

     Here are twenty more problems. Most of them have products of consecutive digits; but some of them do not! Can you find those that do not have CDP's?

(1) 617 2 (11) 73 12
(2) 47 21 (12) 197 45
(3) 36 12 (13) 823 12
(4) 128 27 (14) 2932 8
(5) 65 19 (15) 2659 13
(6) 93 73 (16) 953 57
(7) 76 31 (17) 178 43
(8) 97 56 (18) 733 32
(9) 298 29 (19) 557 8
(10) 24 19 (20) 138 331
tt(8/4/82)

2002

CDP's

5757

Part IV

     This lesson presents several new ideas. Two of them are: number palindromes and number tautonyms.

     Perform the multiplications to see these interesting types of products--and others--come out.

     In all of them, however, the idea of consecutive digits is still there.

(1) 3261 14 (11) 945 143
(2) 333 37 (12) 3717 143
(3) 353 91 (13) 2354 273
(4) 8182 8 (14) 902 273
(5) 407 333 (15) 3435 33
(6) 6105 87 (16) 2277 243
(7) 3737 66 (17) 537 418
(8) 9731 66 (18) 20134 33
(9) 443 223 (19) 20219 6
(10) 2442 263 (20) 50471 3
tt(8/7/82)

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