Problem Teachers' Notes Hint Solution

Split the class into five groups and give each group one of the pictures from this sheet. (It may be useful to have multiple copies of each picture, depending on the number of children in a group.)

To begin with, allow time for everyone individually to work out the total number of fingers, including thumbs, on their picture. Then encourage them to discuss their methods amongst the whole group. You could suggest that each group makes a poster which explains all the different ways of counting that they have used.

Rotate the pictures so that each group now has a new picture. Once again, ask them to work out the total number of fingers, then to share methods again. If new ways of working out the answer have been used, these could be added to the poster.

Once all the pictures have been seen by every group, you can bring the whole class together. They could display their posters and everyone could have time to look at the other groups' posters. Then, ask them to comment on what they have done and seen. Were there some methods that lots of people used? Why do they think that is? Were there some methods that they wouldn't have thought of? Did any of them change the way they worked out the total number of fingers for different pictures? Why?

It may be that questions arise that can be followed through to a greater depth or you could use the alien context at the foot of the problem to challenge the children to find the totals with some of the aliens' hands.

Tell me what you think.

How did you work out the total?

Do you agree with what s/he said?

Why?

Can you tell others about that?

In addition to considering Alien hands, this activity could be extended further into the aliens counting in different bases according to the number of fingers they have on a hand.

Some pupils may benefit from having some paper cut-outs of hands.