## Expanding Sponge

 Difficulty: Rating: GCSE Marks:

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?

## Inflating Mattress

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A new mattress arrives as a rolled up vacuum sealed cyclinder. The mattress is laid out flat as shown below, but air needs to be allowed into the packaging so it inflates to its final cuboid shape. As the mattress expands, the width and length won’t change, but the depth will increase significantly. The current depth is just 15% of the final depth of the mattress.

What is the difference in the finished volume of the mattress, and the volume of the cyclinder that was delivered?

Suggestions:
This question stretches the most able GCSE students. For those that don’t know where to start, it is always useful to remind them that marks are awarded for part of the final answer even if not completed. As no formulae are given for a question like this, the question works well to consolidate volume learning.  Students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

• Express the inflated volume as a percentage of the packed volume

## Home or Away Hoodie

 Difficulty: Rating: GCSE Marks:

## Low Energy Bulb Swap

 Difficulty: Rating: GCSE Marks:

## Maths Sign Sector

 Difficulty: Rating: GCSE Marks:

## Coffee Machine Sale

 Difficulty: Rating: GCSE Marks:

## Saucepan Discount

 Difficulty: Rating: GCSE Marks:

## Shopping Discounts

 Difficulty: Rating: GCSE Marks:

## Shoebox Distribution

 Difficulty: Rating: GCSE Marks:

## Distance Calculations

 Difficulty: Rating: GCSE Marks: