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How full is choc-full?

By David Shaw, 12 May 2016

Do some maths and end up with some tasty rocky road!

Safety: Use clean hands and equipment. You don’t need to use peanuts. If you’re making this for someone with a peanut allergy, use more snakes instead of peanuts.

You will need

• A small dish, about 2 cups in size
• Baking paper
• Butter or spray oil
• 2 cups of marshmallows
• ½ cup of peanuts
• ½ cup of snake lollies, cut into small pieces
• Scissors or a sharp knife
• 400 g of dark chocolate
• Microwave container or saucepan

Line a dish with baking paper.

What to do

1. Grease the small dish with butter or spray oil.
2. Line the dish with baking paper.
3. Put the marshmallows into the dish, so they reach the top. Is the dish really full?
4. Mix the peanuts and snake pieces in a bowl, and then pour them into the dish. Shake the dish so they get into all the cracks. Is the dish really full?
   

   Is this dish full?

5. Break the chocolate up, and very gently melt it on the stove or in a microwave. When it’s melted, pour it into the dish. Gently stir the contents of the dish to let the chocolate fill all the gaps. Is the dish full now?
6. Put the tray into the fridge and let it set for a few hours. Then cut the rocky road into small pieces and enjoy!

What’s happening?

Add the snakes and peanuts.

Is a dish full of marshmallows really full? This yummy recipe shows that there’s still heaps of space in a ‘full’ dish.

Mathematicians and scientists need to know how tightly packed things are. The number they use to measure this is known as the packing density. Packing density measures the proportion of the container that’s actually filled with stuff, rather than gaps. Solid rock has a packing density of 1 because it has no gaps. Lightly packed peanuts might have a packing density of ½, meaning 1 cup would contain ½ cup of solid peanut, and ½ cup of air.

Mix in the chocolate – is it full now?

Packing density depends on the shapes you’re packing and how they are arranged, but it doesn’t really depend on the size of the shapes – which means that peanuts pack about as well as rice bubbles. There are more gaps between the rice bubbles, but the gaps between the peanuts are much larger.

One way to increase packing density is to use a mixture of different sized objects. The smaller peanuts help fill the gaps between the bigger marshmallows. Of course in this recipe, there’s still plenty of space for the chocolate!

If you’re after more maths activities for kids, subscribe to Double Helix magazine!