Wednesday, 30 December 2015

Quibans 3 - Environmental impact of meat

Here is Quibans 3, with an excerpt from an article by George Monbiot.  The hyperlinks are those in the original article - it shouldn't be necessary to follow these links in class.
Warning: your festive meal could be more damaging than a long-haul flight
A kilogramme of beef protein reared on a British hill farm can generate the equivalent of 643kg of carbon dioxide. A kilogramme of lamb protein produced in the same place can generate 749kg. One kilo of protein from either source, in other words, causes more greenhouse gas emissions than a passenger flying from London to New York.
A paper published a few days ago suggests that switching from meat to green vegetables would be environmentally damaging. Per calorie, growing lettuces produces more greenhouse gases than rearing pork. But all this establishes is that lettuces are low in calories. You would need to eat 15kg of lettuce in order to meet your daily energy requirement, which might be reasonable if you were a 200kg rabbit. As another study remarks, “20 servings of vegetables have less greenhouse gas emissions than one serving of beef”.
As the world’s people adopt the western diet, a paper in the Climatic Change journal estimates, the methane and nitrous oxide produced by farming could rise to the equivalent of 13bn tonnes of carbon dioxide a year by 2070. This is more than all human activities combined can safely produce without exceeding 2C of global warming. Climate breakdown looks inevitable – unless we all change our diets.
All sorts of questions jump out here:
  • How much lettuce would an ordinary size rabbit eat per day?
  • Does a human need more or less lettuce than a rabbit, proportionate to its size?
  • In the final paragraph, how much meat is he assuming will be eaten per person per year on average?  Is that reasonable?
How much does a rabbit weigh?  Is a kilogram reasonable?  The same as a bag of flour?  15/200 = 0.075kg per day, which is 75g for a 1kg rabbit.  Is scaling in this way reasonable?  If the rabbit weighs 2kg then it would need 150g of lettuce.

How much does an adult human weigh in kg?  I genuinely don't know.
1kg is about 2.2 pounds.  1 stone is 14 pounds, so 1 stone is just over 6kg.  A 12 stone adult would therefore weigh over 12 x 6kg = 72kg.  The rabbit can weigh nearly three times that, so it needs less food.

13 billion tonnes is 13 000 billion kg.  Dividing by 650kg (using the figures from the first paragraph) you get 20 billion kg of meat protein.  There are about 7 billion people on the planet, so that is about 3kg per person per year.

Link to the article:


Quibans 2 - Games Consoles

Here is Quibans 2:

This news story from the Daily Telegraph contains some figures that at the least require some interpretation and might actually be contradictory.

How much does your gaming habit add to your energy bill?
Britain's love of gaming is costing us dearly, after the cost of energy required to power our favourite consoles has rocketed in the past 30 years.
Today's hi-tech machines cost around four times as much money to run as the humble platforms of yesteryear, including the Sega Mega Drive, Super Nintendo and Nintendo 64, according to research from British Gas.
Today, one pound's worth of electricity will power your Xbox One for around 22 hours, at an average cost of £43 a year, while Sony's PlayStation 4 is considerably cheaper at £35 per annum at 25 hours of play.
At the opposite end of the scale, £1 would have generated 49 hours of Sega Mega Drive game play, at an annual cost of £11. The Nintendo 64 matched the yearly price with 48 hours of play, while the Super Nintendo eked out 48 hours of play per pound, at an annual cost of £12.
It takes around 47 hours of gameplay to complete Fallout 4 on Xbox One, at a cost of around £1.69, whereas 97.5 hours of playing The Witcher 3: Wild Hunt on PlayStation 4 will cost you £3.86, the data found.
World of Warcraft is better value, costing £31.66 for 1180 hours of play on your desktop PC.
 The first thing that springs to mind here is to wonder:
  • Do people play for longer nowadays than they used to on older machines?
Let's use the numbers.  

Number of hours per £1
Annual cost
Number of hours per year
Xbox One
22
£43
946
PlayStation 4
25
£35
875
Sega Mega Drive
49
£11
539
Super Nintendo
48
£12
576

So this appears to be telling us that users of an Xbox One will play for longer (on average) than owners of a PlayStation 4, and that they both play considerably longer than people used to on the older consoles.
On average that is over 2 and a half hours per day.

The penultimate paragraph I quoted above doesn't seem to fit with the rest of the information.
If the Xbox One lasts for 22 hours for each £1 of electricity then 47 hours of gameplay should cost about 47/22 = 2.1, which is about £2.10, not the £1.69 in the article.  Does this mean they messed up the figures?  Or that some games require more energy than others?  Or something else?  [37 hours (rather than 47 hours) does fit - perhaps it was a typo?]

The PlayStation 4 figures give us 97.5/25 = 3.9, which is £3.90 and this does fits with the £3.86 in the article (allowing for rounding errors).

The final sentence leads to another question:

  • What is the energy-efficiency of a PC?
1180/31.66 = 37, so you get 37 hours per £1 on a PC (playing World of Warcraft).

Link to the article:

Wednesday, 23 December 2015

Quibans 1 - Black Friday

Here is Quibans 1.
I projected this:
"Amazon said that at 9.10pm, Black Friday 2015 became its biggest sales day ever in the UK with more than six million items ordered."
Carry out some calculations to help you decide how many items were ordered in the whole day.
Why might your answer be an under-estimate?
Why might your answer be an over-estimate?

Save this part until after they have answered the earlier questions:
"The UK version of the website sold more than 7.4m items while other retailers had problems with web sales due to huge demand."
What do you think now?

A follow-up question might be: 
On average, how many items did they sell per second on Black Friday?

If you assume items are bought at the same rate throughout the day and use exactly 6,000,000 as the number of items sold by exactly 9.10pm then you get about 6.8 million items sold across the day.

Does this mean that more people shopped later in the evening?  Or was the "more than six million items" really 6.5 million?  (Making the assumption that if it were over 6.5 million then "nearly 7 million items" would have been used.)  In this case you get 7.37 million items over the whole day, which rounds to 7.4m.

Links to the stories from which the quotes are taken:
http://www.manchestereveningnews.co.uk/whats-on/shopping/web-retailers-break-records-black-10517322
http://www.bbc.co.uk/news/uk-34952739


Tuesday, 22 December 2015

What are Quibans?

Quibans are Questions Inspired By A News Story.

Students who are studying the post-16 course referred to as 'Core Maths' need to be able to solve problems and to sift through data as they use mathematics.  One good source of material for this is the media, with the opportunity either to comment on the way mathematics has been used or to work out some things based on a news article or other source.

This blog will include links to the news story (or other material), excerpts from it (as relevant) and then some questions that could be asked.  The questions will not be exhaustive or definitive and it might well be appropriate to ask students to come up with their own questions (and then to answer them).

Quibans 71: I’d walk a million miles for one of your goals

Apparently (thanks to Scott for the heads-up), Scottish football fans sing “I’d walk a million miles for one of your goals”.  [ Link ]   ...