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Why do this problem?
, in line with the theme for this month, offers an 'action' to perform on a group of numbers which pupils can continue and explore. Or, you could think of the writing down of the 'description' of a sequence as an action performed on that sequence. It might particularly appeal to those pupils who enjoy number work
but who are perhaps not used to succeeding in this area.
Introduce the task by taking an example and work it through with the group/class of pupils, emphasising how careful we have to be with the simple act of counting.
Give them plenty of time to explore their own choice of numbers before bringing them together to share findings. Depending on the age and experience of the learners, you may like to give them a separate sheet of paper simply to note down anything they notice as they work. Encourage them not to rub out as they go along so they have a record of their thoughts, to some extent.
A whole-group discussion could focus on what they notice and what other questions they might have as a result of working on this task. Some children might be keen to try to explain their findings. Do encourage them in this, even if you are not sure of the reasons yourself. Admitting your possible uncertainty will spur them on!
Tell me about what you see happening.
What will you do now?
Can you make any predictions before you start the next one?
Change the rules so that only odd numbers are available, for example:
Rule 1 - The starting number must have just three different digits chosen from $1, 3, 5, 7$ Rule 2 - The starting number should have four digits, so thousands, hundreds, tens and ones.
For example, $3155$ or $1135$.
Some children might like to find out about 'Golomb sequences' which are related to this task.
Some pupils may need help in carefully counting the number of occurrences of each digit. It might, therefore, be useful for children to work in pairs so that someone else is always checking the counting.