Why do this problem?
is a fun activity that involves addition as well as spacial awareness. It allows pupils to extend their knowledge of both in an accessible environment.
I have used this activity with whole classes and small groups of children. I prepared the grid sheets for them and asked them to get four multilink each, three of one colour and one of a different colour. (Here
is a $100$ square that you can print off.)
It was good to see the invented methods the children used to record their results. Some used loads of different coloured crayons and drew them on the sheet. Others created little pictures or diagrams and the sums that went with them.
There are a few rather surprising things that occur and it is good for the children to find out why. It shows a lot about children's number awareness with numbers going up and down in tens, and up and down in units. When they had finished with the head in one square they compared their results with others who had started somewhere different.
Finally I gave them the option of numbering the $100$ square in a different manner. I do recommend this as a very interesting thing to do. There are lots of possibilities and they result in all kinds of answers when the same rules apply as they had at the start.
Tell me about this worm you've got.
What's the largest total you've seen so far?
Tell me about your recording.
Using different sizes of worms and/or different sizes of field and then compare. One child once came up with the idea of allowing the worms to bend upwards so that you had two or more parts over the same number. So we'd see something like this:
So it had its head on $64$ and three parts all on $63$: $64 + 63 + 63 + 63 = 253$
For more extension work
What is the effect of numbering the $100$ square in a different way. Examine the $4x4$ square in the middle. Which way of numbering gets the largest/smallest numbers in this central square?
Consider other shapes to the field and new ways of numbering the smaller areas inside. eg. a hexagonal/octagonal field.
Some support is sometimes necessary for some pupils and separating the two elements out may help. So we make all the different shapes of worms with cubes first and then consider where the head will go.