# 293. Boxing Bounds

I thought this would make a nice little starter – address a few different topics, bit of problem solving, all over in 15 minutes. How wrong I was!

The Question: A company packs toys into boxes which measure 12cm by 8cm by 10cm (to the nearest centimetre). The boxes are packed into crates which measure 1m by 0.75m by 0.8m (to the nearest centimetre).
(a) Basic question – How many boxes fit into the crate?
(b) What is the maximum volume of a toy box?
(c) What is the minimum volume of the crate?

It was a simple question about fitting toy boxes into a shipping crate. It extended to looking at upper and lower bounds, then recalculating given this extra information. Simple? No chance!

Problem One
Not changing to the same units

Problem Two
Working out the two volumes and dividing to find the number of toys. When challenged on this, it took a while to get through to the basics of how many toys actually fit – mangled toys and split up boxes don’t sell well.

Problem Three
Maximising the arrangement of boxes – remainders mean empty space

Problem Four
Using the information from Problem Three to find the total number of toys

Problem Five
Working out the dimensions and volume of the empty space in the box

Problem Six
Trying to convert centimetres cubed into metres cubed. I don’t even know why they wanted too!

Problem Seven/Eight
What’s an upper/lower bound?

Problem Nine
What do you mean that the original answer changes when the box size alters?

Problem Ten
All those who weren’t paying attention when you went over Problem Two and don’t ‘get’ why the answer isn’t 625!

# 290. Alcoholic Percentages

The season of gratuitous excess is upon us and the reminders about safely consuming alcohol are popping up in supermarkets … usually next to the massive bottle of brandy, which are on special offer! We educators are counting the days to the holiday break.

But wait!

Keep your eyes peeled for all the alcohol awareness promotions. My local supermarket had information leaflets and these goodies:

Forget doing percentages about sale prices. How about working out the volume of alcohol in different beverages? Finding out how easy it could be to exceed the recommended intake? A bit of education of the effects of alcohol in a cross curricular lesson?

Now how much brandy soaked Christmas cake is equivalent to one unit of alcohol?