This problem is suitable for children who can count to 12 through to those
 
who can carry out mental addition. A useful way to begin this problem with a
 
large group of young children is to sit them all in a circle and roll two
 
extra-large dice in the middle. Ask a child to give the total and to explain
 
how they got the answer. Write the answer on a chart or chalkboard. Ask the
 
children to suggest what other totals might occur when the dice are rolled
 
again. Record their predictions. Roll the dice again and ask the children to
 
see if the total is on the list of predictions. (Perhaps you could ask if
 
there's a way to find the totals without actually rolling the dice).</P>
 

 
<P>Break the children into pairs or threes and give each group two
 
dice. Explain that the task is to find all the answers that can be made by
 
adding (or counting) all the dots on the dice. Suggest that it would be
 
helpful to keep a record of the totals they find. </P>
 

 
<P>When a group thinks it has found all the totals ask them to think about
 
how they can be sure their list is complete.</P>
 

 
<P>An extension for this activity is for children to record the number
 
relations that they find, place them into groups or sequences and look for
 
patterns.</P>
 

 
<P>For example:</P>
 
<P>1 + 1 = 2</P>
 
<P>1 + 2 = 3</P>
 
<P>1 + 3 = 4</P>
 
<P>1 + 4 = 5 and so on.</P>
 

 
<P>OR</P>
 
<P>1 + 1 = 2</P>
 
<P>2 + 2 = 4</P>
 
<P>3 + 3 = 6</P>
 
<P>4 + 4 = 8 and so on</P>
 

 
<P>More able children would benefit from further analysis of a full set of recorded possibilities. Perhaps these could be written into a table. Discussion about similarities and differences between the additions could take place (e.g. Is 2 + 3 = 5 the same as 3 + 2 = 5?). Ask the children to consider the question "When you roll the two dice are you more likely to get a total of 7 or a total of 2?".</P>
 

 
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