Gym Bag

Why do this problem?

This problem provides students with an opportunity to engage in mathematical modelling, using practical activity as a way of investigating a problem which focuses on nets.  Many students find it difficult to relate the net of a solid to its 3-D appearance or to mentally unpack a solid to visualise its net, and the modelling approach will help them with this, without getting bogged down in calculation.

This problem could be linked with the Design Technology curriculum, and used to support textiles work, particularly isses to do with seam allowance.

Possible approach

Equipment required:

• It would be really helpful to have a cylindrical drawstring bag available so students can see what the finished gym bag ought to look like.
• Lots of scrap paper, material and card
• Squared paper
• Rulers, compasses, scissors
• Sellotape and glue

Start by getting the class to measure some trainers to see how they compare with the dimensions given in the problem. The look at the drawstring bag, and see if they can work out what shapes you would need to cut out to make it.

The cylindrical part is a rectangle with length equal to the circumference of the base. 

Students should work out what the net is first, and see how it makes up into a cylindrical bag before considering the seam allowances required.  Scrap paper and sellotape would be ideal at this stage.

They will then need to think about the relative sizes of the rectangular section and the circular section.  How will they ensure that the length of the rectangle is the same as the circumference of the circular base?  How will they ensure that the finished article actually fits the trainers, if this is possible?  Squared paper would be useful at this stage.

Once they are ready to think about seam allowance, it might be better if they used fabric of some kind.  Working in groups would help at this stage, with each group using their own piece of fabric 100cm x 50cm.  This is an ideal opportunity to bring the Textiles teacher into the Maths classroom to provide expert advice.

Key questions

What shapes do you need for the gym bag?

How do you make sure the gym bag will be big enough for the trainers?

Is there a 'best' size for the gym bag?  What criteria might you use to judge?

Possible extension

If the piece of fabric 100cm by 50cm is big enough, what is the minimum sized piece of fabric which would do?
If it isn't big enough, how big a piece of fabric would be needed?

Possible support

For students who struggle to understand how the 3-D gym bag is related to the 2-D net, it helps to have a collection of cylindrical objects which they can take apart and put back together again.  
For students who struggle with working out if the fabric is big enough, practical activity will help them to decide.
Students who struggle with the seam allowance will need fabric to work with.