Fractional Triangles also encourages children to explore the part-whole relationship but goes beyond halves to include finding quarters, thirds, sixths and ninths. Bryony's Triangle is a wonderful example of a rich task that brings together development of the part-whole concept and reasoning. (Incidentally, it is worth using thin card for this activity.)
Although all these tasks use paper as the medium, of course it is important that children have experience of a range of resources. How would they halve a lump of playdough? How would they halve a weight?
And how often do we vary the 'whole'? Is it always 'one'? What about sharing two pizzas between three? In the NRICH task Chocolate, the 'whole' is one, two or three bars of chocolate. Learners have to make a decision about the best table to stand at if the chocolate on it is shared between everyone at that table. Encouraging children to record their ideas themselves helps us 'see' their thinking and assess what they are doing.