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Math Extension Real World Problems
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Plan an event . . . Plan the itinerary and costs for a class excursion or camp. Plan the menu and other entertainment activities for our end of year class party, including food quantities, costing, time, and job allocations. Plan the layout and costs for an area of the school grounds which is to be landscaped or turned into a playground area (take into account any budgetary and space constraints) Plan a roster for a round-robin competition – could be handball games at lunch times
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Design Design your dream bedroom and work out what would it cost to fit it out with all the things you'd love to have. Make sure you get real costings from shops such as Bunnings, IKEA, Masters etc. Use shopping catalogues for ideas, pictures and prices. Design a school (perhaps on the same site and for the same number of students as your school). Design a bus timetable for your suburb that takes into account how long it takes to get from one end of the route to the other, which places to visit, and when more/fewer buses are needed. Design a sports centre.
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Property Developer You are to design a four-room house. It can have as many storeys as you like, but every room must have a room underneath it or be on the ground. There are costs for building the house: each square metre of roof costs $3000 to tile, and each square metre of outside wall costs $1000 to paint. Design some houses and work out how much they cost to build. To limit the scope of the problem, assume every room is a cube of the same size. Then you can make models of the houses using blocks. How many different houses can you design? Which is the most expensive house to build and which is the cheapest? Extension problem: What if you had a five-room or six-room house?
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FERMI Questions Fermi questions ask for an estimate of something. Often they are very open-ended questions which may initially seem impossible to answer. By making some sensible assumptions and estimates, however, we may be able to come up with a moderately good approximation of the real answer quite quickly. They are named for Enrico Fermi, an Italian physicist, who liked to ask these kinds of questions.
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FERMI Example How far could I walk in a month?
If I walk for 8 hours each day (and the rest of the time is spent eating and sleeping!) at 3 km/hr (this is a moderate walking pace for students on flat ground), then I can walk 24 km in a day. To make calculations easier, let's round this to 25km per day. So every 4 days I walk 100km. A month has 30 days (or so), and thus I can walk about 750 km in a month. How far is this? A map could be used to show that it is about the distance from Melbourne to Adelaide.
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FERMI example How many students could fit in our classroom?
Lay out some string to make a square metre (a square 1m along each side), and then see how many students can stand comfortably inside this area. I can imagine about 9 students fitting inside. A school classroom might be about 10m × 10m, which makes 100 square metres all together. If each square metre can hold 9 students then there is room for 900 students in the classroom. How does this compare with how many students are in the school?
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FERMI example If all the people in Australia held hands, how long would they stretch? There are about 20 million people in Australia, but some are big and some are small, so we probably need to use an "in between" estimate for arm span. I will use 1m for the average arm span, because we only want an estimate. This means that our 20,000,000 people could stretch for 20,000,000 metres. Since there are 1000 metres in a kilometre, all the Australians could stretch for 20,000 kilometres. 20,000km is hard to visualise. Since it is about 4000km from Brisbane to Perth, if all the people in Australia held hands they could make 5 lines from Brisbane to Perth.
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FERMI questions How many people could you fit into the classroom? How many soccer balls?
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FERMI QUESTIONS How old are you if you area million seconds old? A million hours old? A million days old?
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FERMI QUESTIONS Could you fit $1,000,000 worth of $1 coins in your classroom? What about a billion dollars worth of $1 coins?
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FERMI QUESTIONS How much money is spent in the school tuck-shop each day? In a week? Over the year?
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FERMI QUESTIONS If all the people in Australia joined hands and stretched themselves out in a straight line, how long would it reach?
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How long would it take to count to a million?
FERMI QUESTIONS How long would it take to count to a million?
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FERMI QUESTIONS If all the people in the world moved to Victoria, how crowded would it be?
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FERMI QUESTIONS How many cups of water are there in a bath tub? What about in an Olympic pool?
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How many grains of rice are in a 10kg bag?
FERMI QUESTIONS How many grains of rice are in a 10kg bag?
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How many children are needed to have a mass the same as an elephant?
FERMI QUESTIONS How many children are needed to have a mass the same as an elephant?
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FERMI QUESTIONS How many packets are needed to measure a single line of M&Ms to a distance of 100m?
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How long would it take to drive to the moon (if you could!)?
FERMI QUESTIONS How long would it take to drive to the moon (if you could!)?
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FERMI QUESTIONS What is the total mass in kilograms of all the students in your school?
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What is the weight of garbage thrown away by each family every year?
FERMI QUESTIONS What is the weight of garbage thrown away by each family every year?
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FERMI QUESTIONS If you had a stack of $2 coins as tall as Mt Kosciusko, what would it be worth? Could you fit all the coins in your bedroom?
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FERMI QUESTIONS How far could you walk in one year?
Research some stories of people that have walked around Australia?
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FERMI QUESTIONS How much water does your household use each week? Can you answer this without using a water bill?
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How many blades of grass on a school oval?
FERMI QUESTIONS How many blades of grass on a school oval?
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Spend exactly $1,000,000 using things for sale in the newspaper
FERMI QUESTIONS Spend exactly $1,000,000 using things for sale in the newspaper
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How much paper is used at our school each week?
FERMI QUESTIONS How much paper is used at our school each week?
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How many beats will your heart make in a lifetime?
FERMI QUESTIONS How many beats will your heart make in a lifetime?
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FERMI QUESTIONS How many bricks are there in one wall of the classroom? The whole school?
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FERMI QUESTIONS How many books are read by children in our school/class in one year? About how many pages is that?
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What distance will a ball point pen write?
FERMI QUESTIONS What distance will a ball point pen write?
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Come up with your own FERMI question.
FERMI QUESTIONS Come up with your own FERMI question.
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