Australia Lesson Activities - Maths

THEME: Road Trains
SUBJECT AREA: Mathematics
TOPIC: Ratios / Comparison

2001 October 14, Sunday. Dorisvale Station, thirty-five kilometres from Pine Creek

Looking at the sheer weight of metal involved, and the speed at which road trains travel, it’s more surprising that they can usually stay on the roads, than it is that they sometimes come off. This particular driver had enough reason (if not an excuse) to lose control. In the past week he had driven thousands of kilometres between Kununurra, Darwin, and Katherine, sometimes stopping only to unload cattle, then moving on.

Road trains are found on roads throughout the Territory, and are one of the major hazards to other road users, along with cattle and kangaroos. They take a deceptively long time to overtake, and, one single lane roads, you need to completely clear the road to let them pass. Usually you’ll need to stop anyway, to wait for the dust cloud to clear.

Suggested learning activities: Look at the information below, which compares our support vehicle to the unfortunate road train, which blocked its path yesterday. Find the ratio for each comparison. By looking at the average ratio, find out, overall, how much ‘bigger’ the train is. Then compare the train to your family car.

Number of Wheels:
Train: 14 per trailer, 10 on engine
Canter: 6 total

Weight:
Train: 83 tonnes, plus 80x650kg beasts
Canter: 5 tonnes

Length:
Train: 40 metres
Canter: 7 metres

Cattle carrying Capacity:
Train: 80 head
Canter: 7 head

bel

THEME: ‘Cattle Ranching’
SUBJECT AREA: Maths
TOPIC: Money management - cattle mustering costs

Your job is to hire a crew to muster a large paddock (gather cattle from a large pasture). Not only is efficiency important, but you must complete the work in the most economical way possible. The paddock is 300 square kilometres, extremely rocky, and the cattle are scattered throughout. The options are to hire seven ringers (drovers) on horseback, or to hire a heli-mustering company using single pilot helicopters. Which do you think would be the most economical? Let’s take a look…

A ringer gets $100/day so a crew of nine would cost a station $900\day to employ. Cost of food for the crew, fuel for vehicles and assorted expenses can run an additional $100/day. Total: Cow camp costs: $1000\day. Due to the paddock’s size and rockiness, it will take approximately one week for the ringers to muster it. Total cost to complete the muster: $7000

To hire one helicopter to muster the paddock would cost a station $240/hour. This includes the use and maintenance of the helicopter and pilot’s fee of $60/hour. Helicopter fuel is another expense at $60/hour. Total: $300/hour. For a ten-hour day of work, one helicopter would cost $3000. Due to the quickness of travel and the ease with which a helicopter can move about the paddock, mustering time is considerably reduced as horses would have to negotiate the rough terrain, which would take longer to muster.

As a cattle station manager, which do you think would be the most efficient way to complete the mustering?

Suggested activities: Compare the costs of the mustering techniques, predicting the length of time each would take to muster the paddock. Analyse your costs for each and select the most efficient way to complete this job. (Hint: two helicopters mustered this pasture in five hours.) What would be the total costs involved and which is the most economical way to complete this job?

April

Interpreting Math Word Problems:

The Information:
Well, here we are at the Humbert River in the Gregory National Park. It is our second-to-last layover and we have two weeks left on the trip. Also, we will have a day of sponsorship filming as well. This leaves us with 11 riding days. The ride up to Darwin will be 590 kilometres from where we are now. It is necessary that we get to Darwin on time because if not, some members of the group will miss their flights, and lose a lot of money.

The Question:
How many kilometres do we need to average each day?

The Method:
We need to analyse the paragraph of info and find which bits are useful to us.

- There are 2 weeks left.
- There are 3 non-riding days.
- That leaves 11 riding days.
- We have 590 kilometres to travel.

Now that we have the information boiled down into little tid-bits, it is easy to look at the problem and figure out a solution.

590 kilometres divided by 11 days will give us the answer.

590/11=53.63

We must travel on average 53.63 kilometres a day!

Suggested activities

1. Use the method of boiling down information to show yourself what figures you need to work with in a math word problem.

2. Also, think up a word problem like this - about how much food you eat a year, how many miles you travel in car on the way to school, the distance each day on a trip you take, etc.

By,
Crister

THEME: Road to Lajamanu
SUBJECT: Maths

This unusual marker we came across 40 kms outside Lajamanu is known as a trig, or Trigonometry Point. They are built on the most prominent geological formation in the surrounding countryside so they can be seen from long distances. By sighting two or more Trig Points and taking a compass bearing allows surveyors to accurately determine their position on a map when plotting boundary lines of property, etc.

Note the two bisecting square sheets of iron on the top of the pole. This ensures that the full size will be seen from any angle. Lasers are also used with these trig points to accurately determine the distance the trig point is from your position.

For example:
The surveyor can see trig point A and Trig Point B from the homestead. From the map the surveyor knows that the distance between Trig A and Trig B is 12 kilometres. The angle between the compass bearings of A and B is 105 degrees. What is the distance from the homestead to Trig Point A?

Suggested actives:

Can you find any geological landmarks in your area? If so, does a map say the distance between them? Can you use trigonometry to find the distance from your house to one point?

By, Bushman John and his apprentice Crister

Download today's lesson activity (PDF)

Have you ever thought how something as benign as a rabbit could become such an ecological nightmare? Let’s take a look at how their patterns of development became such an environmental problem in the Australian Outback.

Rabbits live in underground burrows among dense vegetation, which also provides their food source. They are well protected from predators in these burrows as they can quickly hide.

A female rabbit may have up to five litters of five to seven offspring per year. Although the life span of a rabbit in the wild is not lengthy (maybe two to five years), she is able to reproduce by six months of age. (And, remember, this is only ONE rabbit!)

In a good year, with limited predators (dingoes, foxes, cats), rabbits may reproduce by the thousands. In the Tanami Desert region, with limited vegetation in a normal year, native species of herbivores, like the Bilby, will starve.

Suggested activities: How many offspring can one female rabbit have in her lifetime? Compute the number of rabbits born per year per female rabbit. Imagine the total number of offspring produced per year by a rabbit population if there are 100 rabbits living within a one square kilometre area. If the square kilometre can support only 100 rabbits, what will be the effect of a growing rabbit population on the surrounding area?

April

The bushfires here can be pretty frightening. As I write this, I can see one glowing in the night sky behind me, not too far from camp. In order to get my mind off it, I’ve come up with this little math problem for you to puzzle over:

Bushfires often start in one location and spread outward in a widening circle. The flames can spread with the wind at a speed of up to 50 kilometers per hour!

a) If the distance from the center of the fire to it edge is 200 meters, what circular area has the fire covered?
b) If the fire spreads out from the center as fast as possible (50 kph), how long will it take for the fire to cover a circular area of 100 kilometers?

2001 September 17. Monday. North of Ace Bore.

The heart of the fire we saw today was basically a bare piece of black and red ground. The action was at the edges of a circle surrounding this. The burning area itself was but a yard or two in width, and travelling gradually outward. I skipped through the ‘frontier’ of the burning, onto the blackened ground, and felt the heat of the sand – it was very similar to the temperature of the sand we had sat upon at billy tea break. This means the fire must be travelling quickly, to not have time to heat the ground as it passes across it.

Although a light but steady wind was present, it did little to blow the fire in any particular direction, so that the only things keeping it from burning outward in a geometric circle were fire-breaks such as the track we followed, and variation in the make up of the groundcover - especially underneath desert oaks, the tallest trees to be found in this area. At some points, the fire did manage to cross the track, as it is rarely used and very overgrown. Here we saw an hourglass shape as the burning ‘funneled’ through the gap.

If a fire began in an evenly vegetated area, where there was no road to distort it, and burned out a circle, we could calculate the area which would be burnt after a given amount of time, by observing how fast the fire travels, and using the formula for the area of a circle: πR2, where R is the radius, or half of the distance across the circle.
If a fire circle with a diameter of eighteen metres travelled at six metres per minute in every direction, work out the following:

* The area of the initial burnt section
* How large the circumference – distance around the fire - would be.
* The diameter of the fire circle after five minutes burning.
* The area of the circle after five, fifteen, and thirty minutes burning.
* How long would it take for the fire to cover one square kilometre.

Missions and Math

How much water do you use in a day? Think about your showers, drinking, food preparation, and even what your dog drinks! Can you imagine getting all the water you would need for six months?! That’s a lot of water!

The missionaries out here in the centre of Australia would have to get all the water they would need from the rain! They used rain catchments to get the water and a whole bunch of big tanks to hold it!

We can use so simple multiplication to find out how much water they would need to collect. First we need some givens, or facts that we can work off of.

Givens:
The average person needs about 4 litres of water a day to wash, drink and cook with.
The mission, while still using the rain catchments, had about 20 people in all using the supply.
The dry season would last about 6 months a year on average (Sometimes it would be more, and sometimes less, but we will go with 6 months as an average).

The Math:
The amount of water a person uses in 6 months can be found by multiplying first by 7 (the number of days in week), then by 4 (4 weeks in a month), then by 6 (6 months in the dry season).

4 x 7 x 4 x 6 = 672

A person would use 672 litres in 6 months! That’s crazy!

How many litres would 20 people use in 6 months?

672 x 20 = 13, 440

20 people would use 13, 440 litres in 6 months! Wow!

With this number in their mind, the missionaries could find out what quantity of water their water tanks would hold.

As the mission got bigger and swelled with an overwhelming amount of people, they had to put in a pipeline from a spring about 8 kilometres away!

Suggested activities:

If you and a about 15 other mates, or friends were going to go and set up a community in the middle of nowhere, could you find out how much water you would need to have available?
Think about how long at a time that it wouldn’t rain for.
How much water would you use in a day?
Also, would you ever wash up?…

By,
Crister

Check out the latest statistics from the Datasheet

"Allright, you men, gather up on the road for the day's instructions."
The sun was breaking over the horizon and Josh, as the day's team
leader, was gatherng us prior to our departure. for the day's ride.
"First order of the day is to set your watches back one half hour.
Yesterday we came into the Northern Territory so we're in a new time
zone today.

Crister spoke up, "Why didn't we do this last night, Josh, when we had
more time?" Josh smiled, "Because I would've had to get up a half hour
EARLIER!"

The Northern Territory is on Central Standard Time, which is plus 9 1⁄2
hours from GMT. This is half an hour behind the eastern states,1 1⁄2
hours ahead of Western Australia, and the same as South Australia. Confused?
Don't forget to throw in Daylight Savings Time! It doesn't apply to the
Northern Territory, so from November to March, the eastern states are 1
1⁄2 hours ahead of Northern Territory time, and South Australia is one
hour ahead.

Suggested activities: Examine a time zone map of your country.
- Determine how many time zones are established What determines the size or area of each time zone? Does Daylight Savings Time occur in each area and, if not, what affect does this have as you travel between time zones?
- Select another country around the world and compute the time difference
between the two countries, i.e., if you live in Alice Springs, NT, what time/day is it in Chicago, Illinois, US? (Don't forget to figure in the International Date Line!)

April

Check out the latest statistics on the Datasheet

Check out the latest statistics from the Datasheet

Sunday, 2001, August 26. On the Plenty 'Highway', fifty kilometres east
of Jervois Station.

Despite what might seem to be an advantage in a largely barren
ecosystem, a small creature's survival in the desert can be more
difficult than that of a large animal. Although they do not have the
need for great amounts of water, they require water more often, both
because their bodies do not have the capability to store it, and
because they lose a greater percentage through the skin (or other body
covering). Termites must keep humidity levels inside their mounds and
underground work areas very high to prevent desiccation.

Imagine an 80 kilogram person shrinking to the size of a termite - 8
milligrams. That person would have 200 times more surface area compared
to their volume. Having that much less protected flesh would mean that
they would be losing 200 times as much moisture in the same level of
humidity.

Suggested learning activities: using these figures, work out how much
water loss your own pet, or the average pet dog (10kg) or cat (3kg) or
bird (100g), might have compared to a human. Find the average weights
of different animals; and try this with them. How much less water per
kilogram might an elephant need, under the same conditions?

bel

Check out the latest statistics from the Datasheet

AVERAGES + PERCENTAGES

Here are some statistics from the general update:

The Great Artesian Basin lies beneath 200 000 people and one fifth of the country.

There are about 4700 bores throughout the basin, 850 of which are uncontrolled.
34 000 kilometres of bore drains are exposed. 5 700 mega litres flow these from bores each year

It is estimated that around ninety-five per cent of open channel water is lost through a combination of evaporation, seepage, and breakouts

Suggested learning activities:
- Calculate the average number of litres lost per person (living over the basin) each year.
- Calculate the average number of litres lost per kilometre of exposed bore drain each year.
- Calculate how many litres of water are lost to evaporation, seepage and breakouts in the exposed bore drains each year.
- Calculate the percentage of bores that are uncontrolled.

jason

Check out the latest statistics from the Datasheet and Series

Check out the latest statistics from the Datasheet

2001 August 19. Sunday. Mount Isa.

Greg and Margaret, our hosts here in the outskirts of Mount Isa, have a small property which they have kindly allowed us to share with their chickens, dogs, goats, and two dromedaries. If you can stand the smell long enough to get close to them, the dromedaries are intriguing creatures. Here are some of the fascinating statistics I have discovered regarding these animals:

1. A 12% loss of body weight through dehydration is enough to kill a human being. A camel is able to lose 40% of its body weight before suffering dehydration.
2. In the years between 1860 and 1907, an estimated 12 000 camels were imported into Australia.
3. Dromedaries have a slow metabolic rate, due to their sixty-metre long intestine. Men’s intestines are around seven metres long.
4. The body temperature of a camel can fluctuate between 34 and 41 degrees Celsius. In humans, sickness and death result from just two or three degrees of variation in temperature.
5. Gestation lasts between 12½ and 14 months, compared to 9 months for human beings.
6. Camels can calve every two or three years up until the age of twenty, compared to every one or two years for humans until the approximate age of fifty.
7. During the early expeditions, each camel would carry up to 600 kilograms of water and supplies on its back. They would walk with these supplies for an average of 40 kilometres per day.
8. The Australian outback is inhabited by around 100 000 wild camels.
9. A camel can survive without water while working hard in the sun for over a week. A man will suffer terribly after just one full day.

There are many comparisons here between humans and camels. See if you can work out the ratios of the different comparisons. If the average camel weighs two hundred and fifty kilograms, and carries six hundred kilograms on its back, what would be the equivalent of how much you would carry based on your own weight? How far do you think you could walk in a hot dry desert carrying that weight?

bel

Find out the latest statistics from the Datasheet

Check out the latest statistics from the Datasheet

Find out the latest statistics from the Datasheet

Here is a math question that can help the group. The support vehicle has given the group the ability to see more difficult terrain before fuel and water stops, however. The support vehicle does have its limitations as well. Could you help us decide whether we can make it from Croydon to Julia Springs with theses few givens in hand?

The ride from Croydon to Julia Springs is 375 kilometers. There are no fill-up stations for water or fuel between these two points. The truck holds 320 liters of fuel and gets an average of 14 kilometers per liter.

The truck also holds 250 liters of water and the group uses, as an average, about .95 liters a kilometer. The group averages 80 kilometers a day.
Here are your questions.

1) Does the group have enough fuel to make it from Croydon to Julia Springs? If there is extra how many kilometers can the group go off coarse and still get to Julia Springs?
2) Does the group have enough water, considering their current minimum intake of water per kilometer, to make it to Julia Springs? If not, how would the group need to cut down their water consumption in kilometers and could they afford to get lost and back track at all?

Hope we all make it to Julia Springs safely.
Mike “Mick” Roney

Also, check out the LATEST STATISTICS on the Datasheet & Series

Check out the latest statistics on the Datasheet

Check up on the latest statistics on the Datasheet, and the Series

Check out our lat/long position, distance traveled, temperature averages and other useful information on the Datasheet

Did you have cereal for breakfast this morning, or yesterday, or the day before…? Was it a big bowl or a small bowl? Did you use different amounts of milk for the different amounts of cereal? You bet you did!

Normal Amount of Cereal :(=) +/- 1cup of milk
Double Amount of Cereal : +/- 2 cups of milk

Those are called ratios. Ratios are used in all parts of your everyday life. Cooking is a perfect example of the use of ratios. With your cereal it does not really matter if you use too much milk, or too little. In baking, frying, or whenever a chemical reaction takes place, the amount you put of one substance compared to another is very, very important.

One of our staples or main foods is a certain kind of bread called Damper. Damper is made with flour, water, salt and beer. Beer is the substitute for yeast (the alcohol is burned off). What amount of flour you put in is a direct relation to how much salt, water and beer is included. The relationships of the ingredients in our damper bread are as follows.

4 cups of flour: 1 beer can: 3 teaspoons of salt: 2 cups of water (added slowly during the whole process)

But what if you wanted to make more? How about we double it (x2)!

4(x2): 1(x2): 3(x2): 2(x2)
8 cups of flour: 2 beer cans: 6 teaspoons of salt: 4 cups of water

Now we know the new ratios simply by multiplying each amount by 2!

Our group usually uses 6 cups of flour to make enough damper for the ten of us. That means that we multiplied the original 4 cups of flour by 1 and a half (x1.5). So now we must multiply the rest of the original amounts by 1.5.

4(x1.5): 1(x1.5): 3(x1.5): 2(x1.5)
6 cups of flour: 1.5 beer cans: 4.5 teaspoons of salt: 3 cups of water

Now you try to find out how much other ingredients will be needed if 12 cups of flour were used. Hint: What multiplied by 4 equals 12?

Next time you and a friend or parents are cooking, you can find out the different ratios used in all the ingredients!

Ratios are you in many different ways that just cooking too: Painting, building, sports…etc! Can you think of any?

By, Crister, who is now very hungry for damper after writing this!

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Check out the latest on the -
Datasheet

Check out the latest on the -
Datasheet (our location/miles covered etc)
Series (Number of flats/wipeouts etc)

One joke we had while resting on the side of a sandy section on day 1 was to have a contest to see who would have the most crashes… flats… broken spokes… B.O.B. flats…etc. And so, now we have the X360 series, an accumulation of mishaps and funny things that happen along the trail. As the trip progresses more categories will come into place. There will be averages, maximums, totals and much more as the numbers build up! So far Mike is in the lead with 6 crashes, beating out all others in all other categories! Well-done Mike! I myself hope to pass him in whatever category possible (even if I have to make one up)! So, put your sport caps on, because here comes the all-new X360 series!

Download the current DATASHEET.

By, Crister

Yesterday, while putting on my new bicycle computer at the mouth of the Starke River I learned of a very handy conversion.
The bike computer measures:
Current speed.
Average Speed.
Maximum speed.
Time spent riding.
Distance ridden.

Here in Australia they use kilometers instead of miles to measure distance. I’m from America, so I’m used-to miles. All of the maps we are using use kilometers, so I changed a setting on my bike computer to work in kilometers rather than miles.
I’m not used to kilometers and I find myself converting kilometers into miles while I ride, so I can better understand the distances being talked about. Here’s how I do it:

When converting miles to kilometers you can multiply your miles by the number, 1.6. Here’s an example:

5 mi????= km????
5 x 1.6 = 8
5mi = 8km

When converting kilometers to miles, which is what I usually do, you can multiply by .6. Here’s an example:

5km???? = mi????
5 x .6 = 3
5km = 3mi

Now, when you do your own traveling all around the world you will be able to convert the different measuring systems into what is best for you!

>> Download today's DATASHEET.

By, Crister