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Consecutive Digit Products (CDP’s)

Part I Carefully find the products of these multiplication exercises. (A)   41  × 3 (B)   576 × 6 (C)   11728 × 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 [...]

Seeing Double

Work these groups of problems to SEE-SEE a very strange-strange thing. When you are done, describe any patterns that you notice. (A)   532 +  252 =  _______      52 +  32 =  ______ 252 +  482 =  _______        22 +  52 =  ______ 482 +  762 =  _______        42 +  82 =  ______ 762 [...]

Trotter Dates

Naming numbers according to some property or characteristic that they possess is a legitimate — albeit egotistic — activity of some mathematicians. (See Keith Numbers for a simple and elegant example.) Another interesting name category that I have recently learned about is called “Niven Numbers”. These are merely numbers that are divisible by the sum [...]

Product Dates

[The following item appeared in the "From the File" section of The ARITHMETIC TEACHER, October 1983, p. 53. Later it was referenced in other NCTM publications.] Here is a novel activity that can be used with selected dates—for example, March 27, 1981—which might be introduced to the class in the following way: “Today is a [...]

Admirable Numbers

[NOTE: The information in this page is based on an article by J. M. Sachs. Admirable Numbers and Compatible Pairs. The ARITHMETIC TEACHER, October 1960. pp. 293-5] In two other articles we discussed the well known ideas of perfect, deficient and abundant numbers and amicable numbers. These categories are famous and often discussed in books [...]

Equal-Sum Groups

Problem Set I Separate each group of numbers into TWO smaller groups so that the sum of the numbers in each of the small groups is the same. NOTE: there may be more than one way to do a problem. If so, can you find the other ways? a)  {3, 7, 9, 13}        f)  [...]