Imagine there are some aliens on another planet, called Octies, who have four fingers on each hand — so eight all together. Because they have eight fingers, they like to count in 8s. They have a different way of writing down numbers. They start the same as us: 1, 2, 3, 4, 5, 6, 7 … but then something very different happens.
For them, the next number after 7 is called ‘one-zero’. They write it like this: 10. After one-zero they count on in this way: one-one, one-two, one-three and so on. Here are their numbers written down: 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21 …
As you can see, after one-seven, Octies go to two-zero and two-one.
Thinking and teaching mathematically can sometimes seem very black or white. Answers are usually right, or wrong and thinking creatively can seem a challenge. The above challenge, taken from Andrew Day‘s “The Numberverse – How numbers are bursting out of everything and just want to have fun” shows how a little playfulness and manipulation of numbers and number rules can get the brain cells thinking a little differently. In fact, Day wants to make pupils feel ‘stuck’ and to get children comfortable with this feeling – a necessity to give them confidence in working their way out of problems.
The book has its roots firmly based in philosophy, with some activities very well suited for p4c sessions – which is an interesting notion, as not many educators will have thought to incorporate numeric thinking into their philosophical sessions. For example, here is another activity idea from the book:
- Show the image of a chess board…
- ..and ask how many square there are. Get pupils to explain how exactly they got to that number.
- Find out if anyone has a different answer.
- In pairs, get children to think of another answer to the question, how many squares are there?
Day offers great ideas of extending this, initially simple, idea into some philosophical and mathematical thinking that can get pupils to see alternatives to their original answer. From the original answer usually given (64), you should end up with over 200 as an answer (we won’t share the exact figure here. See page 133!!!). Such activities, like this one, can help develop pupils resilience – one of the key facets advocated within the book.
We love this book. Not only does it give educators activities which you can pick up and run with, but it also is a catalyst to get children to think beyond the mathematical boundaries which they have been taught and grown accustomed to. There are activities within the book for children getting to grips with early number concepts, through to activities which have no upper-age limit. What is key, for each exercise (and teaching generally), is the questioning and considered timing to extend thinking further.
We actually suggest that you buy this book to keep a paper copy, although the Kindle version is also available priced £14.24* here via Amazon.
The Numberverse – How numbers are bursting out of everything and just want to have fun, by Andrew Day is published by Crown House Publishing Limited, with an RRP of £14.99* (Hardcover) and is available by following the Amazon link below.
Image Source: Chessboard | Book Link: Amazon.