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Published 2011
There are, of course, many ways to organise children into groups. Unless the teacher has specific reasons for doing otherwise, a random mix method is best for this type of cooperative problem solving.
Random Mix by the Cards
Here is one way to achieve a random mix of pupils using a pack of ordinary playing cards. To form seven groups of four children, use all four card suits from one (Ace) to seven. Shuffle this pack and have each child choose a card. All the sevens form a group, all the sixes form a group and so on.
Introduction: This type of problem solving activity is well suited to developing and clarifying mathematical ideas that have already been introduced in other lessons. Therefore, in introducing the task to the class, the teacher can make links to previous work. If the mathematical vocabulary contained in the problem is of particular concern, then key terms should be revised.
Group work: The groups are formed and each child in a group is given one clue card. To maintain 'ownership' of the piece of information, the child may not physically give away the cluecard, but must be responsible for communicating the content to the group. Each pupil's role is now to work within his/her group to solve the puzzle, following the set of work rules. The teacher must also take care to follow these rules, and not take back responsibility for the task by interfering with the problemsolving processes or offering help before being asked by the whole group.
As always, it is advisable to have an extension question ready for a group that finishes before the others. It is also useful to have one or two 'extra' clues ready. These can be used to allow the inclusion of an extra group member, to give help to a group that is 'stuck', or to assist 'checking' when a group thinks it has finished the task.
Plenary  It is important for groups to report on their problemsolving processes as well as confirming the correctness of their end product. The teacher can use questions focus on particular issues and highlight points that have been observed during the session. For example:
A
PETER'S NUMBER
Peter's number is even.

B
PETER'S NUMBER
When you add the digits,
you get an odd number.

C
PETER'S NUMBER
Peter's number is a multiple of six.

D
PETER'S NUMBER
Peter's number is a multiple of four.

E
PETER'S NUMBER
One of the digits is NOT double the other digit.

F
PETER'S NUMBER
Peter's number is in the bottom half of the chart.

(More than one answer is possible until Clues E & F are incorporated)
Stick Figures
Each group needs a handful of sticks, all of the same length  such as matches, icecream or lolly sticks, or drinking straws. The aim is to arrange some of the sticks to make either a single shape or shapescombinations (depending on the level of complexity).
A
STICK FIGURE 3
There are three squares in the figure.

B
STICK FIGURE 3
The big square has an area four times larger than
each of the small squares.

C
STICK FIGURE 3
Eleven sticks are used to make afigure.

D
STICK FIGURE 3
One small square shares a side with the other
small square.

E
STICK FIGURE 3
The bottom half of the figure is a rectangle.

F
STICK FIGURE 3
Three sticks lie inside the large square.

Fractured Shapes
The clues in this type of problem are nonverbal. In the example below, the squares are cut up by the teacher and each member of a groupoffour is given three pieces marked with the same letter. The aim is for the group to make four complete squares.
Operations
Each group needs a set of digit cards (two or three copies of the digits 09) and a template of the algorithm, in this example a twocolumn sum
A
FIND THE SUM 1
All of the digits are even numbers.

B
FIND THE SUM 1
Adding the digits in the top number gives 10.

C
FIND THE SUM 1
The 'ones' digit in the first number is the same as the
'tens' digit in the answer.

D
FIND THE SUM 1
Both the digits in the second number gives 4.

E
FIND THE SUM 1
The difference between the digits in the answer is 2.

F
FIND THE SUM 1
Adding the digits in the second number gives 4.

A
MODEL VIEWS 2
8 cubes are used to build the model. 
B
MODEL VIEWS 2
The view from the top
looks like this.

C
MODEL VIEWS 2
The view from the front
looks like this.

D
MODEL VIEWS 2
The view from the right side
looks like this.

E
MODEL VIEWS 2
The view from one corner looks like this.

F
MODEL VIEWS 2
The view from one corner looks like this.

Burns, M. (1992) About Teaching Mathematics, Maths Solution Publications: California Erickson, T. (1989) Get It Together, EQUALS: University of California.
Gould, P. (1993) Cooperative Problem Solving in Mathematics, Mathematical Association of N.S.W. Australia. ISBN 0731013719 (Available through the Australian Association of Mathematics Teachers Catalogue code MAN466  http://www.aamt.edu.au/ )