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To facilitate the ease of obtaining accurate results it would be useful to have calculators available for the children, particularly for the later extension ideas.
Children tackling this investigation will be:
It may be worth working through a few examples of the double-digit problem with the whole class so that the children get a feel for the procedure. Having done this, they are bound to start making their own predictions.
Before leaving them to investigate for themselves, it may be useful to talk about how they are going to record their results. This becomes particularly important when they come to tackle the three-digit extension suggested at the end. For those who reach this stage, a discussion about how to write down the six different triple-digit numbers systematically may prove valuable.
As usual, encourage children to talk to each other about their theories, helping them to express these clearly. Bring the class together as appropriate to share their findings and possible explanations.
The pupils themselves will come up with further variations to investigate so you can take on board their suggestions too.
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?