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By Harold Fletcher, C. Plumpton, Arnold A. Howell

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The role of the teacher is a vital one. Every opportunity must be taken for discussion and in providing rich and varied concrete experiences from which abstraction and discovery can take place. Though some parts of the day are often more specifically devoted to mathematics it is important to remember that at all times situations arise for developing mathematical ideas and vocabulary. , there are many opportunities for mathematics to develop unobtrusively. In the remainder of the chapter suggestions are given for some of the more directed activities which are designed to give greater understanding of number and other relationships.

X = {* | x £ U and x is even}. Y — {y\y € U and y is a multiple of three}. Note. There are several other ways of expressing the results. 2. P = {1,3, 5, 7, 9}. Q = {5,10}. ^ = {2,4,6,8,10}. Q' = {1,2,3,4,6,7,8,9}. PDQ = {5}. P U ß = {1,3, 5, 7, 9, 10}. (Pr\QY = {1,2, 3, 4, 6, 7, 8, 9,10}. (PU G ) ' = {2,4,6,8}. ) 4. C 35 THE LANGUAGE OF SETS Shaded region is Au(BnC) (AKJB) 36 MATHEMATICS WITH UNDERSTANDING - BOOK 1 4. ) (AuC) Shaded region is (AuB)n(AuC) 5. (A\JB)Ci(AUC) = {18, 24, 36, 48}. CHAPTER 3 RELATIONS AND SORTING A SET of four boys, Edward, Fred, George and Harry were asked to say which drinks they liked out of the following list: Coffee, Lemonade, Milk, Tea and Water.

RELATIONS AND SORTING 41 A. The domain = {a, b) and the range = {x, y, z}. ) Mapping Alice, Brenda and Charles respectively own a doll, ball and a bat. Let A = (Alice, Brenda, Charles} and B = {Doll, Ball, Bat}. The Cartesian Product, AXB = {(Alice, Doll), (Alice, Ball), (Alice, Bat), (Brenda, Doll), (Brenda, Ball), (Brenda, Bat), (Charles, Doll), (Charles, Ball), (Charles, Bat)}. Consider the relation, R, where R = {(x, y) : x ζ A, y € B and x owns y}. It may be represented diagramatically thus : "Owns" Every member of the first set has one and only one image.

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