Applying Maths to solve problems in the real world…

Expanding Sponge

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GCSE Text:
A sponge is supplied in a vacuum sealed pack. The thickness of the sponge will expand when it is released from the packet. The sponge thickness currently measures 12mm and on the label it says that the packed thickness is one fifth of the final sponge thickness.

a) What will be the final thickness of the sponge when it is released from the packet?

b) The label also says that the product weight has been reduced by 40% by supplying the product vacuum sealed. If it weighs 24g whilst sealed, how many grams of plastic packaging have been saved per sponge by provided it vacuum sealed?

Suggestions:
Whilst the first question is accessible to all, many students struggle with the numbers on the second question. Discussions normally flow surrounding the percentage that we have or have lost, and of course the sponge is a constant so it’s only the plastic weight that is being affected by the reduced size.

This works well as a consolidation for reverse percentage learning, and students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

Before vacuum packing was introduced, a trade box could hold only 30 sponges. How many can it hold now that it contains vacuum packed sponges instead?

What other benefits are associated with vacuum packing the sponges?