to be able to find the volume of a cone, cylinder and sphere using the formulae and to be able to find the density of objects.
students working at a B/A grade who are familiar with using the formulae for the volume of cylinders, cones and spheres.
: about 45 minutes.
 A set of digital weighing scales
 Around 5 items of fruit and / or vegetables. Good ones to use are apples, pears, plums, grapes, carrots, bananas, tomatoes, oranges and any other fruit and veg which is edible without cooking.
 A large jug that has volume markings on the side and is about half full of water up to a marking that is relatively easy to count on from.
This is an excellent lesson to tick that pesky ‘promotes a healthy lifestyle’ box on some of the more detailed lesson observation sheets! Obviously the real idea behind this activity is to give students a kinaesthetic way to investigate density and for more able students to brush up on their knowledge of volume of solids.
Students enter the room to find a classic youtube starter of one of the annoying orange clips (if you really don’t want to show one of these then there are lots of other youtube videos such as ‘The good food song’ by the kids animation series or the sesame street healthy food song) to really set the atmosphere.
Then students get into groups of around four or five students and each group has a selection of fruit and vegetables in addition to the all important challenge card in an envelope, their jug of water and a set of digital weighing scales. The challenge is simple – using the equipment in front of you put the fruit and vegetables into order of most dense down to least dense. At this point it is worth simply letting the groups have a 5 minute discussion on just how they plan to do this. The always useful textbooks at the side of the room can provide them with valuable reference material such as ‘what exactly is density?’. Then at the end of the 5 minutes groups feed back on how their ideas. During the 5 minutes any really stuck groups can be prompted with questions such as ‘what will happen if I put this tomato into the water and what will it show me?’.
A spot of whole class discussion is now in order. A few of the students may well know Archimedes principle that ‘for a submersed object the volume of displaced fluid is the volume of the object’ from Science. If not then an impromptu circle time story about the crown of gold would be appropriate here. In addition students need to know how to change the displaced volume of ml into cm 3 .
The groups then use the jug of water to find the water displaced and thus the volume of each item of fruit and veg. At this point they will discover that most of the items float and they will need to find ways of fully submerging the item without displacing more water – i.e. sticking their whole hand in to keep it held down wont work! They then weigh each item and work out it’s density, placing the objects in order of most dense to least dense. Groups that finish before others can start the philosophical discussion of the relationship between denseness and tastiness and ensure that the key points from the lesson are recorded in their books.
Allow around ten minutes at the end of the lesson to wrap things up, clean up all of the spilt water, look at the maths behind the methods used and have the import discussion of how accurate their results are, especially depending on how they kept their item submerged. If you are not using the fruit and veg to follow this up (see next lesson) then now is a fine time for students to try out their theories and eat the items!
Students could create a display of their findings or they could follow up the lesson with further work on this topic, possibly looking at past exam questions.