Packing Pencils

I want a new pencil case for my 15 coloured pencils. I don't want one that will take up too much room in my bag, but it does need to be big enough for my pencils.

Alison thinks I should get the blue triangular one. Charlie thinks I should get the green cylindrical one. Steve prefers the red hexagonal one.

I like them all, so I'm going to get the one which takes all 15 pencils comfortably, but takes up the least room in my bag.

When I measured them I discovered that they were all 20cm long, with a maximum width of 4cm. They are all prisms and their cross-sections are an equilateral triangle, a circle and a regular hexagon respectively.

Try making three 'pencil cases' out of card, to see which would be the best fit.

• How many pieces of card do you need for each?
• What shape would they be, and how many of each shape do you need?
• What lengths do you already know, what might you need to find out? Is there a simple practical way to find any missing information, or could you calculate any missing lengths?

Cut out the three nets then stick them together with sellotape to make the 'pencil cases', leaving an opening of some kind. Looking at them, do you have any sense which would be best? Which appears to have most space inside, which least? Which will take up most room in my bag, which least?

Find 15 pencils and see how they stack in the 'pencil cases'. Which is best now?