Maths - Ages 11-16

Would this starter amaze your pupils? Choose a three digit number such as 856, multiply it by 1001 (allow low-ability pupils to use a calculator). Try this three more times. What do you find and can you explain why this is?

When you multiply any three digit number by 1001, the answer looks like the original three digit number repeated twice - 362 x 1001 = 362 362.

Go for a four digit number multiplied by 10001 - 4270 x 10001 = 4270 4270. Then ask pupils what they would have to multiply a five digit number by to make the answer look like it is the original number repeated twice (answer: 100 001).

Heidi Hartley is a teacher at Magical Mathematics and Enchanting English, a professional tuition centre in Stroud, Gloucestershire.