Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.) It is seen as a possible follow-on from Plants.
In "Plants" we had three children sharing $10$ plants in the three overlapping circles.
This particular challenge is about extending that, so that we consider four and then maybe five children in a similar way.
In considering these larger numbers we have to examine a different arrangement of the circles (possibly changed into slightly different shapes).
You will need to draw these four (first of all) areas in such a way that there is a section for each of the sharing situations. In the case of plants there were seven sections - allowing for each child to have an overlapping part with each and all of the other children.
Once you have drawn an arrangement for four areas I suggest that you start with allocating $4, 5, 6, 7$ to the areas.
As before, where can a certain number of plants go? I suggest you start with a number like $19$ for the total number plants.
Find all the answers that satisfy the requirements of having $4, 5, 6, 7$ shared in the different regions using $19$ plants.
Want to go still further? Then go to More Plant Spaces.