Real life, mathematics, partial proportion and race horses

The following post brings together two recent events in my life into an attempt at a WCYDWT question for mathematics. It’s not a perfect fit for WCWYDT, but close.

What can you do with this?

The following is a photo of “Credit Muncher” just one of the race horses that has arisen out of my wife’s latest hobby, breeding race horses.

Portrait #1

She’s called “Credit Muncher” because I am somewhat worried about the potential for this hobby to consume vast amounts of money. I was, however, a little happy that we were breeding race horses, not racing them.

Racing a horse involves a continual outlay of money. First, there’s the expense of purchasing a yearling and then breaking it. At which stage you pause for a while before the horse is sent off to a trainer. This is when the real money starts being spent. Paying for someone to train the horse can cost upwards of $3,000 a month and the chances of winning are pretty slim. This has always seemed like a mug’s game to me. A good way to burn money. Thankfully, we were only breeding horses to sell to others.

That changed last night. My wife and mother-in-law went to the local thoroughbred sales. “Only to look”, said the wife. “I left my wallet at home by mistake”, was the cry on the day of the sales. So, I felt safe. Then last night, to my great surprise and chagrin, I find that both my wife and mother-in-law have purchased a yearling each. With the grand plan of breaking them, training them, and entering them in the Capricornia Sales race this time next year. The race has a total price purse of around $150,000 and all horses sold through a specific brand of sales is qualified (59 from this sale alone).

What questions spring to mind?

Improvements

As of yet, I haven’t seen the new horse. We’ve already spent some money for it to go to a professional for breaking. A video or photo of the specific horse would be an improvement. Perhaps a bit more context of horse racing as well.

The story could do with some work. I do, however, think that the pain in my voice as I explain the story is likely to be the secret ingredient to motivate the students.

Working in some more detail about the prize money (1st, 2nd, 3rd etc) and other potential races might help.

Of course, the big potential problem is that the topic is horse racing and I hear gambling can be a bit of a no go topic in schools.

There’s also the problem that this problem doesn’t leave a lot of room for exploration, or at least I don’t see it.

My questions

The proper WCYDWT is to leave it to the students to come up with the questions from the story/prompt.

This idea comes about from the fact that I have a driving question. How much is this going to cost us? And an extension, how much is this going to cost me as the months roll on?

The idea for this post came from the fact that one of the first mathematics classes I was in during EPL (embedded professional learning i.e. prac teaching) covered partial proportion. And the students just didn’t see the application. This class was one of those that contributed to an earlier post about the relevance of mathematics.

Partial proportion

The basic formula for partial proportion is

y = kx + c

In this case, y is the total cost of the horse. The total cost is partially proportional to the monthly cost of training plus the initial cost of purchasing and breaking the horse. Using some round about figures, that gives

y = $3000*x + $5000

Given there is about 6 months of training to occur before the sales race

y = $3000*6 + $5000
y = $23,000

Ouch!

If we race the horse for 12 months

y = $3000 * 12 + $5000
y = $41,000

2 years

y = $3000 * 24 + $5000
y = $77,000

A feeble first attempt at moving towards WCYDWT

Late last week I was thinking about how I could develop something approaching a WCYDWT lesson for mathematics. It is something I am going to have to do very soon now. As it happens, in looking for the WCYDWT link, I came across this Diigo group that I am going to have to return to.

The following is a first attempt. Actually, it’s the first example of me seeing something in my everyday life that I can connect to the curriculum and see some ideas for developing a lesson. Given that I am going to have to be developing lessons soon, I’m hoping to get into this practice more.

This type of thing may not connect directly with the strictures (if such exist) of WCYDWT. I guess I am using that as a useful label to encourage me to structure lessons that ask the students to generate the questions (which I am hopefully strongly guiding towards the curriculum) in the hope that it is more meaningful and interesting to them and consequently leads to better outcomes. The ultimate aim being to encourage them to see the relevance of mathematics.

A comparison of Household finances – The McGuffin

The Weekend Australian Magazine from last weekend had a “Trend Tracker” column on infographics (can’t find it online) which led with some infographics comparing Australian household finances from 1971 to those for 2011. The following table summarises the figures. In a lesson, I’d probably go with the graphics or some form of multimedia.

Figure 1971 2011
Average price of a home $21,000 $557,000
Average grocery bill $23 $250
Average household size 3.3 2.6
Average # of cars per dwelling 0.75 1.5
Average # of household appliances and gadgets 9 27
Average wage $84 $1250

This is one of the difficulties that I see with WCYWDT type problems, while I can see a number of questions that arise from this prompt, what will the students see? Of course, that is also one of the interesting aspects of this type of problem.

Within the Queensland syllabus, this seems to fit with “Chance and Data” and discussions of averages/means, but also with decimals, money and a few other places. Making these connections is one of the skills I need to develop further.

Some of the questions I can see (feel free to suggest more)

  • What does it mean to have 2.6 people in a household?
    The notion of averages etc.
  • Given the costs of houses, groceries etc and the average wage, are people better off or worse?
    Apart from the calculations, there are a range of further questions – not necessarily mathematical questions – about what “better off” means. i.e. do 27 gadgets make you better off than 9 etc.
  • What were the maximum and minimum values for these averages?
    Leading into more questions about what “average” actually means

An extension of this, somewhat fraught with peril, would be to get the students to provide data to do an in-class calculation of equivalent figures. Some possibilities might include

  • Real figures from home.
    i.e. bring in the grocery bill, Mum and Dad’s group certificate….obviously there are some major privacy issues arising from this approach.
  • Actually start with the students providing their figures.
    i.e. start the lesson with students in groups talking about how much they would like to earn, how much they think the would need to spend on groceries etc. Or perhaps ask them to provide the minimum, just right and maximum wages they’d like to earn (a Goldilocks approach). Get the class playing with those figures and then reveal the national figures.

An obvious extension to this would be to get access to the ABS raw data and see what other interesting data can be pulled from there, but also see if there are ways to get the students mining and manipulating that data.

Another option might be to get some average salary figures for different occupations (perhaps from the ABS) to give the students some idea of the range of salaries and then also to use those as data points to illustrate the concept of average. i.e. some occupations are above and some are below.

Which obviously leads into some of those survey results where everyone thinks they are average.