This open problem provides an excellent opportunity to consolidate coin value
 
recognition and utilise addition skills. The level of difficulty is easily
 
manipulated by specifying which coins should be considered. For example, the
 
youngest children might only work with coins with a value of 1, 2 and 5 pence
 
(or whatever the relevant currency). Perhaps a better approach is to allow
 
individual children to select which coins they want to work with. This allows
 
each child to set the level of difficulty to suit themselves.
 
<p>
 
One advantage of a problem that has many solutions is that it is possible for the teacher to discuss the problem fully with the class and have them find a few solutions together before they go off and work on their own. This helps to ensure that each child adequately understands the task and will be successful at least a basic level. A discussion point that is likely to arise is whether the order of coins makes a difference. For example, Is 1+1+2+2+2 considered to be the same solution as 1+2+1+2+2?
 
<p>
 
Providing real, toy or paper coins will encourage the children to pursue more combinations than they might otherwise have the patience to record. As the children are working, take the opportunity to chat with individuals and groups about what they are discovering and gently encourage them to organise their solutions in such a way that it becomes easier to check for repetitions and compare their findings with others. This will encourage some children to use a more systematic approach and maximise the chance that all possible solutions will be found.
 
<p>
 
A whole class discussion will make a valuable closure to this activity. If the children have managed the problem quite well and found many solutions, one way to manage the closing discussion would be to set up a framework for displaying the solutions systematically and guide the children to contribute solutions to the display.<br>
 
For example:
 
<p>
 
<table>
 
<tr>
 
<td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td>
 
</tr><tr>
 
<td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>2</td>
 
</tr><tr>
 
<td>1</td> <td>1</td> <td>1</td> <td>2</td> <td>2</td>
 
</tr><tr>
 
<td>1</td> <td>1</td> <td>2</td> <td>2</td> <td>2</td>
 
</tr><tr>
 
<td>1</td> <td>2</td> <td>2</td> <td>2</td> <td>2</td>
 
</tr>
 
</table>
 
and so on.
 
<p>
 
This requires the children to search through their recorded solutions and
 
look for particular characteristics and make comparisons. Patterns will
 
become more obvious to the children and missing solutions can be identified.
 
<p>
 
If the children have been quite random in their approach to finding solutions
 
and have not found very many, consider returning to the problem a few days
 
later for another try. Begin by complementing them on their previous efforts
 
and encourage them to find even more answers. Discuss ways to build patterns
 
as they search and work through an example like the one above. Perhaps the
 
class could be divided into teams to see which group can find the most
 
solutions.
 

 

 
<p>