**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.

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**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.

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.

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*(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*).

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?

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.

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.

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 ˝, ˝, 1˝, 2˝, 2˝.
Adjacent pairs of sides will add to 1,2,4,5and 3 )*