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Ideas for number investigations
By Sandra Norgate on Thursday, November 14, 2002 - 01:27 pm:

Here at Silverstone Infant School we are looking for some good ideas for problem solving and number investigations. We have 3 classes Reception,Year 1 and Year 2 with a total of 76 pupils. My maths co-ordinator is anxious to build up a resource base so that we can focus every week on an activity which will challenge the childrens' mathematical thinking. We should also like some simple questions which could be used in our daily maths lessons which will get them thinking! In two weeks time we are going to undertake the Numbers Day project which will form part of our Multiple Intelligences week!! Can any one help with some ideas, rsources etc. Many thanks Sandra Norgate Headteacher

By Liz on Thursday, November 14, 2002 - 04:53 pm:

Have you tried searching on the NRICH Prime site? If you click on "Library" on the lighthouse menu, you can use the Topic Tree to look for these sorts of problems. You may find that the Let Me Try are most suitable for KS1, but some of the Penta Problems will challenge the more able.
Investigations and number feature in the tree itself, but all our puzzles are designed to develop problem solving skills, so I am sure you'll find many more in the other curriculum areas too.
Good Luck...

By Andre Rzym on Thursday, November 14, 2002 - 05:37 pm:

There are many better qualified here to comment than me – firstly I’m not a teacher, and secondly I’m not sure what Y1,Y2 students are capable of. But I do have a few random thoughts (apologies if you’ve seen them before). I’d be curious as to whether the level is appropriate:

1) Polyhedrons: There is a truly beautiful book called “polyhedron models” by Magnus J Wenniger which describes dozens of polyhedra with photographs and drawings of the ‘bits’ you need to make them (e.g. for a cube you need 6 squares). What you could do is make some ‘templates’ for your children to cut the pieces out of coloured card, then they can assemble them. Note: (i) If you know a friendly engineer, get him to cut the templates out of thin steel/brass sheet for you so that they will last longer. (ii) Having built some models (tetrahedron, cube, etc) get the children to count the number of vertices, edges and faces, and see if they spot a connection between them

2) Palindromes. I’m not sure how interesting children might find these, but if you pick a number (e.g. 39) reverse the digits (93) add them up (132) and repeat, you eventually get a palindrome (reads the same in both directions). There is one exception! Can you find it?

3) Have a look at the excellent “mathematical puzzles and diversions” series of books by Martin Gardner. There is (if I remember correctly) some material that ought to be useful. For example in there (I think) are descriptions of flexagons (have a look here as well), chessboard problems etc. Plus some fun stuff on pentominoes etc. For the flexagons, I recommend using tillroll to make them. Try asking your local shopkeeper nicely for a few rolls. Decorate the triangles (asymmetrically) to show how they move on ‘flexing’.

4) It’s been a long time since I looked at this book (Cundy & Rollet, “Mathematical Models”), but there’s lots of good stuff in there. If I remember correctly, there’s some stuff on curve involutes and evolutes – it may sound dry but the shapes are pretty and you can make gear wheels with them – imagine making two, with pins through their centres - demonstrating that the teeth mesh together without slippage along the teeth. Lots of uses for these – clocks, gearboxes etc.

5) Magic squares. I’m sure you can find them on Nrich somewhere, as well as plenty of other source material.

6) This may be too hard, but are you familiar with the problems where letters stand for digits, and you have to find the mapping? I am thinking of something like CROSS + ROADS = DANGER [I think I made this up, but I hope you see what I mean]. You could make the problem easier by giving the children a start, telling them what digits a few letters correspond to. If you like this sort of thing, you can find more in Boris Kordemsky “The Moscow Puzzles”.

7) Number sequences. Build up a collection of number sequences. The child has to guess what comes next. E.g. arithmetic progressions, geometric progressions, Fibonacci numbers etc.

8) Pascals triangle. Arrange your entire class in an equilateral triangle facing you. You stand by one point and keep passing that person a ball. Each child has a coin. On receiving a ball he flips the coin. Heads he passes it back to the left, tails back to the right. Have some baskets at the back. At the end, gather the baskets and plot the numbers in each basket. You should get a bell-shaped curve.

9) Do your children understand what prime numbers are? If so, get them to lay out numbers 1..100 in a 10 by 10 grid (which they make) and use the sieve of Eratosthenes to strike out composite numbers and so find the primes below 100.

10) Get your children to make some Napiers bones, to illustrate their use as a multiplication tool (I think this is described on Nrich somewhere).

Andre