Description
The photograph shows a box containing jelly beans in an array. Looking closely, we see each compartment in this box contains six jelly beans of the same colour. They are arranged in two layers of three beans. There is a different flavour in each compartment.
Activities
- By looking closely at the photograph, determine the number of jelly beans in each compartment or cell of the box. Assuming the different colours denote different flavours, how many differently flavoured jelly beans are in this box?
- How could the repeated addition of 18 (that is, 18 + 18 + 18 +… ) be related to this picture?
- Record other ways of counting the number of jelly beans in the box.
- A systematic approach to looking at the number of flavours will help identify those that can be arranged in more than one way and those that cannot. How many differently sized rectangular boxes could be used to market small sample packs of 24 jelly beans each of a different flavour?
- One company claims to have 49 flavours of jelly beans. What kinds of rectangular boxes could they use? Show that another shaped box could also be used by the company.
- The number of jelly beans in each compartment, and how they are arranged, can be changed by the company as part of its marketing strategy. If the pack to be marketed by the company must contain equal numbers of exactly 10 flavours, what are the different ways of packing 200 jelly beans? Which of these packs would be the most marketable? Why do you think so?
- Suppose that a box in the shape of an equilateral triangle, with compartments in the shape of smaller equilateral triangles, is thought to be an attractive marketing proposition. Explore the numbers of flavours and the numbers of jelly beans in each compartment that could possibly be marketed in such a box. What generalisations can you make? Consider other boxes in the shape of regular polygons. Do your generalisations change or remain the same? Justify your response.
