Jenny Houssart offers more ideas for an annus mathematicus
As 1999 is well under way, crystal-ball and tea-leaf gazers have already looked at what the year ahead might hold. If you are not feeling particularly clairvoyant, and buy your tea in bags, you may try looking into the number 1999 instead. Deciding if the number is prime can be a starting point - children can be encouraged to be systematic in their search for factors and to say when they don't need to test any more numbers.
Working out the 99-times table sounds a daunting task. But many older children laugh if you ask for the 100-times table. The secret lies in seeing how multiplying by 99 relates to multiplying by 100. The framework for teaching mathematics suggests that Year 6 pupils should be able to carry out calculations such as 13 x 99, by doing 13 x 100 then subtracting 13.
Examples for Year 4 and 5 pupils involve multiplying other numbers ending in 9 by similar methods. Thus 13 x 19 is suggested for year 5 and 13 x 9 for year 4. Multiplying by 99 even gets a mention in the "Laying the Foundations for Algebra" section.
So if your pupils can work out the 99 times table now, they may better understand algebra in the future.
* Is 1999 a prime number? How far do children have to go in testing for factors before they can be sure?
* Look for factors of 999. How can other three-digit numbers be tested for divisibility by 3 or 9?
* List the factors of 99. What can the children tell you about two-digit numbers that are multiples of 11? What about three-digit numbers that are multiples of 11?
* What are the factors of 9 and how many factors does it have? Which other numbers have an odd number of factors?
* What patterns can children see in the 9-times table? Can they use these patterns to check their answers when multiplying by 9.
* Ask the children to work out the 99-times table. Can they explain the method they use to multiply by 99? Can they begin to record what they do?
* Look for patterns in the 99-times table. In what ways is the 99-times table similar to the 9-times table?
Jenny Houssart is a research fellowat the Open University Centre for Maths