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By Max D Larsen; James L Fejfar

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Extra resources for Essentials of elementary school mathematics

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In particuJar, this says that if a, b, c, d E A and if a = b and c = d, then a • c b * d. " the operation is said to be well defined. The last word to be stressed is of. " introduced by David Page of the Illi­ nois Arithmetic Project and described in "Number Lines, Functions, and Fun­ damental Topics" is especially useful in helping children understand this concept. 40 3 I Binary Operations For * to be a binary operation on A , a * b must be an element of A . Hence for every a , b E A , a * b E A .

Define EB on Q by a (b) h a (c) e _ a+e h + d" EB d- With Q as in (a), define 0 on Q by h With Q as in (a), define a - b 3 if m is divisible by 4, is divisible by 3, if otherwise. 6m n = �n o e d = ae bd . * on Q by * e - d = ad + be --- bd U sing the operations as defined below, compute the terms in (a)-(x). (i) (ii) (iii) (iv) a O b = a - b for all a , b E /. a # b = a + b + l for all a, b E /. a EB b = a + b - a b for all a, b E /. a · b = 2ab for all a, b E £, where E is the set of even integers.

For any set A , A U A = A. For any two sets A and B, A � B if and only if A U B = B. ) Children do not think about sets as abstractly as introduced here. How­ ever the concept of set, although not verbalized, is essential to the develop­ ment of understanding of many concepts, such as number, addition, and so on. One strategy for developing some familiarity with the concept of set is to use pieces of yarn and the large, thin attribute blocks. ) Putting a piece of yarn around the red blocks defines the set of red blocks without excessive verbalization.

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