Magic Numbers!

This is a quick way to demonstrate some ‘mathemagical’ powers – it also serves a useful purpose in that it will give children an entertaining opportunity to make use of investigative/problem solving skills.

You show the children a set of ‘raffle tickets’ each of which features a small identification number and a main four-digit ‘raffle’ number. Ask a child to pick a ticket at random, to show it to the rest of the class and to tell you only the small identification number.

As soon as you hear the number you can write the main four-digit number on the board. You can repeat this as many times and as quickly as you wish – much to the children’s surprise!

Here’s how it works:

The pdf file attachment contains a series of 36‘raffle tickets’. The numbers on the tickets are not random, however, but are related to the smaller identification numbers. As soon as you hear the number simply add 11; this gives you the first two digits of the ‘raffle’ number. Next, add these two digits together to generate the third digit (ignore the 10’s in totals greater than 10). Finally, add the second and third digits together (again, dropping any 10’s) to obtain the last digit.

For example:

Child says “21”

• you add 11 and write 32...
• add the 3+2 to get 32 5...
• add the 2+5 to get 32 5 7

or,

Child says “67”

• you add 11 and write 78...
• add the 7+8 to get 78 5 (ignoring the ten in 15)
• add the 8+5 to get 78 5 3 (ignoring the ten in 13)

Finally, as a problem-solving activity, let the children work in a group to look through all of the ‘raffle tickets’.

• Do they see any patterns in the numbers?
• Can they work out what is happening?
• Some numbers are missing from the set of tickets, can the children determine what four-digit number would be generated by the missing ones, what would 11, 14 or 24 produce?

Note: the system for generating numbers need not stop at four digits. If the pattern is continued, the numbers generally appear random, until a 0 is generated in which case the numbers hiccough.

  8  –  1909090...

44  –  5505050...

13  –  24606060...

25  –  3695493257303030...

64  –  7527965167303030...

19  –  303369549325729101010.... 

However, some numbers hiccough more quickly than others! You could challenge your children to see if they can find out which numbers start to repeat the 0x0x0 pattern quickly.
 

Here's a thumbnail image of the whole pdf (instructions and set of raffle tickets).

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