A Simple Number Generating Device;

the Paper Roller

Many of you will have struggled to create dice or number spinners so that you children can play number games. Here is a much more simple way of generating numbers, simpler to make than a dice and easer to use than a spinner. It was developed in a Teachers’ workshop in Pelimatalawa in Sri Lanka. I am sure it may have been used before but in many years of teaching I have never encountered it. It is such a good idea that it needs to be more widely known. Do you remember “Owzat”? We used to play it for hours with the two metal octagonal prisms, used as rolling dice to create the runs and wickets taken in a game of cricket. I believe the game has made something of a comeback during the Cricket World Cup. When we lost the metal rollers we marked dots on six sided pencils but it was difficult to mark the thin sides.

The paper Roller is based on the same idea. Take a strip of paper or thin card about 10cm long and 2cm wide or you can if you like just cut a strip from A4 paper. Fold it in half three times to create eighths. Open and roll up along the folds so that each fold is in the same direction.

Now overlap two of the parts and glue to create a hexagonal prism. You may have to pinch the folds to make it approximately regular. Mark numbers on each face and you have a simple Number Roller.

Here children in a school in Sri Lanka are using a pair of number rollers to play a simple addition game. The sum of the numbers is calculated and then checked off on the number grid.

Variations

The great thing about the paper roller is that

· it is simple enough for even young children to make their own rollers,

· it is cheap and you can put what ever you like on the faces,

· you can squash it flat and keep it in an exercise book until you need it again

· you can make it really large for demonstration purposes,

· and you can vary the number of faces.

Varying the Number of faces

How about a five sided roller? Just overlap three of the parts instead of two and glue. Now if you put the numbers on the outside and roll two numbers come on top and one is hidden underneath. So children roll and call out the sum (or difference or product) of the pair. There are only 5 and they will quickly learn them and they then can go on to play with a different roller marked with different numbers which reinforces other number pairings. Or you can write the numbers INSIDE the roller and use it as a 5 number generator.

(A Puzzle: What numbers can be put on the roller so that the numbers on adjacent faces when added give the numbers from 1 to 5? See below for an answer).

Are the Rollers Fair?

Most number generators such as dice or spinners are meant to be fair and have an equal probability that each number will be shown. The Number Rollers described above will have a bias built in and this makes them useful when investigating probability. Can children predict which number will come most often and why? How do we test to find out how big an influence the extra weight due to the double thickness on some sides has?

Designing Fair Rollers

To make the roller fair the paper or card on each face of the roller should be of equal thickness. One way to do this is to have a double thickness everywhere. Take a longer strip and fold it into sixteenths. Then roll it up to form an octagonal prism with a complete overlap. Glue all faces inside and write numbers on each face.

Activity with Octagonal Rollers

If you number two rollers with the digits from 2 to 9 then when both are rolled they will generate all the product pairs except those involving 1.This provides excellent practice at the basic tables. Below are a couple of sample activities from the many hundred that can be based on the rollers.

Product Game Two players only one octagonal Roller

Each player rolls the Octagonal Roller to generate three numbers. These can be placed any where in the multiplication grid shown here. The winner is the player who can create the largest answer with their three numbers.

Factor Game Two players Two rollers

Each player uses the two rollers twice to generate a pair of two digit numbers. Find the highest common factor of these two numbers. This is your score. See who can get the highest total score after three rounds

(Puzzle Answer;

Put these numbers on the five sides of the roller ½, ½, 1½, 2½, 2½. Adjacent pairs of sides will add to 1,2,4,5and 3 )