1. friend or freak? a brief curriculum on multiplication Willem Uittenbogaard

2. theorem 1 stop learning the algorithms no standard procedures no columnwise arithmetic agree or disagree

3. stop learning the algorithms we can do it by: calculating by heart clever calculating sensible use of a calculator

4. also suitable for +, x and : multiplication as an example for each of the other operations it’s the same story

5. all multiplications are freaks! a list: 37 × 249 53 × 187 13 × 619 approach?

6. with a calculator or a algorithm? children, often……. are trying use a not understood algorithm type something on a calculator are even calculating table products with a calculator figure out between products with a calculator

7. friend or freak? another list: 17 × 237 10 × 237 83 × 346 100 × 346 1000 × 129

8. are there any friends? yes, 10 ×, 100 × and 1000 × how do you do that? by moving the zeroes the money context can help does it always work? → friends of 10

9. friend or freak? another list: 17 × 239…………freak 10 × 169…………friend of 10 27 × 153…………freak 20 × 60…………...? 40 × 70…………...?

10. are there any new friends? yes, 20 x 60 and 40 x 70 how do you do that? 20 x 60 = 2 x 600 = 1200 use the money context. you can do 2 x 6 plus two zeroes. does it always work? → tables with zeroes

11. friend or freak again a list: 27 x 473…………..freak 100 x 73…………..friend of 10 30 x 80……………tables with zeroes 9 x 34………………? 11 x 27……………..? 101 x 27……………?

12. can we make new friends? may be 9 × 34 and 11 × 27 how can we do it? 9 × and 11 × are both close to 10 × 9 × is one time less and 11 × one time more: 340 – 34 and 270 + 27 and you can do them with your head → almost friends of 10

13. first we have to practice! do I recognize them all? 100 × 69 11 × 54 37 × 83 50 × 90 have a good look at the numbers and then choose your strategy improve the knowledge of tables and maintain it!

14. friend or freak? again a list: 24 × 25……………? 12 × 35……………? 14 × 55……………?

15. no friend, or …? you can make 12 rows of 50 and then again another 6 rows of 100, then it becomes a friend of 10. does it always work? because of the 24, that is even and the five. → halve and double

16. a nice couple of friends 10 x 37 9 x 47 11 x 67 200 x 60 16 x 35 1001 x 123 → a nice couple

17. theorem 2 I think all children can learn this! not as a trick, but with insight and applicable! agree or disagree

18. are there any more friends? what do you think of: 10 x 10 11 x 11 13 x 13 ………. 20 x 20 worth a research; try to memorize → squared numbers are friends too!

19. and what about these ones? 5 x 5 15 x 15 25 x 25 35 x 35 …… 75 x 75 … not as an algorithm, but as a subject of research look for the patterns, find the rules, understand them and use them. →”best” friends

20. one has more friends than the other again a list: 24 x 12,5 = 12 x 25 = 6 x 50 = 300 125 x 840 = 250 x 420 = 500 x 210 = 1000 x 105 = 105.000 3 x 210 = 9 x 70 = 630 54 x 56 = 50 x 60 + 4 x 6; is it correct? always? → far friends?

21. what do we do with this freak? can we do something about: 7 x 234 yes we can: 7 x 200……..tables with zeroes 7 x 30 ……...tables with zeroes 7 x 4 ……….table and then add: 1400 + 210 + 28 not columnwise, but in your head: 1610 + 28 = 1638 (no algorithm for +) → freak becomes friend

22. and the rest of the freaks? 23 x 347……..? with a calculator! and take enough time to do it! so always give lists with problems! how to do it? →calculator becomes friend!

23. theorem 3 the more friends you have, the easier it is! we do not need standard procedures or columnwise arithmetic agree or disagree

24. finally a lot of attention for knowledge of tables! strategies with their own names practice with lists of problems not bear, but attached to a suitable context let the children do their reasoning! no escape in algorithms sensible use of the calculator

25. why like this? because of my experience in working with grade 5 pupils of River East Elementary School in Manhattan, NY thanks to the children and Peter Markovitz, their teacher with warmth I remember their eagerness and enthousiasm to find out something new, week after week

26. for who? áll children in the primary schools everyone in his own way: with more or less friends at the end you only have friends: the calculator can easily become a good friend each cell phone has a calculator

27. et voilà a brief curriculum multiplication in 15 minutes