By McCoy N.H.

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The two descriptions, one in terms of adding on and the other in terms of remainders, then describe the same thing. 1c More Remainders What is a reasonable meaning to give to the remainder on dividing –3 by –5? What about the remainder on dividing 2 by –5? Comment Numbers of the form –5n + 2 will have remainder 2 on dividing by –5, so the remainder on dividing by 5 and by –5 is the same, and more generally, the remainder on dividing by n and by –n is the same. 2a Fractionated What fraction of the first whole rectangle has been shaded in?

Make a note of where you are. Now imagine going forward 3 steps, then going backward 5 steps, then forward 4 steps, then backward 1 step. How many steps do you need to go (and in which direction) to get back to where you started? Comment A variant of this task was exploited by Bob Davis2 to introduce negative numbers and their arithmetic.

4) show that there are different ways of calculating tax and price, and care is needed to make sure that the correct calculation is being used. 9425 Chap 1 p1-25 21/2/05 2:33 pm Page 24 24 BLOCK 1 For each of these examples, the general expression reveals much more than the particular cases. Pedagogy of the Chapter The chapter, like most of the book, is structured around mathematical tasks. This provides one important reason that you should actually do the tasks yourself, rather than just thinking about them or imagining yourself doing them – that ‘doing’ is the only means by which you can experience the pedagogic ideas directly for yourself.