Bowland Maths

There are three new elements that need to be introduced to give the implemented curriculum the balance needed to develop effective performance in and with mathematics:• Non-routine problems • Substantial problems • Multiple connections

Overview

• When will the world’s oil reserves run out?• How much land would be needed to build a wind farm

to supply 25% of London’s electricity?• If the sea level rises by 50 cm, how many people will

be homeless in Bangladesh? London?• What will be the population of Europe in 2020?• An earthquake destroys Istanbul – how many people

are homeless, how much water, food and housing is needed, and how long will it take you to get it all there?

• What would it cost to give every pensioner another £10 per week?

• Can I afford to run a car?

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Overview

• Plausible Estimation (PE) underpins major decisions we make in our private and public lives. PE tasks show pupils just how powerful simple mathematics can be when making decisions about important topics.

• Plausible Estimation is also great for debunking spurious claims (‘we can grow all the biodiesel we need on set aside land’). Pupils will be able to see that the problems they are being asked to solve are the same problems faced by aid agencies, government planning agencies, and salesmen!

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Organisation and pedagogy

• ICT is not a requirement• Materials can be used as a block of lessons that will

take about 3-5 hours to complete, or as individual lesson plans that can be used as free standing ‘samplers’.

• There are also tasks called ‘sprinklers’ and ‘one liners’ that can be used as short 10-15 min free standing activities, in any lesson, and for homework.

• Your role is to launch lessons, manage group work and discussions, and to synthesise key mathematical ideas.

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Powerful ideas include

• Breaking large tasks into component parts;• Measurement accuracy depends on the purpose of

the measurement. If you use crude measures and the conclusions are not crystal clear, you have to do everything again, carefully!

• Solving problems in two (or more) different ways – if you get the same answer, you can be more confident than if you get just one answer;

• Calculating bounded estimates – make assumptions that are at the low end, and at the high end, and look at the difference. This will show you how sensitive the PE is to the assumptions that have been made.

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Heart Beat

Kate, Aminda and Amadej all had their 14th birthdays last

week.

Kate guesses she has had about 20 million heart beats,

so far. Aminda thinks that estimate is too low, but Amadej

thinks it is too high.

What do you think?

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Wealth

If Oprah converted her net worth to cents, she could

circle the Earth 128 times.

How wealthy is she?

Make up and answer other questions.

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Games On - VideoThe organizers of the 2012 London Olympics need your help! They want all the athletes to be present at the opening ceremony, in the centre of the athletics track.Can everyone fit in?

At the 2004 Olympic Games in Athens 11,000 people from 296 countries took part. Assume the same number take part in 2012.

The stadium has the dimensions shown on the diagram below [square sides are 10 metres].

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Stop Thief - Video

A bank manager says that an armed youth stole a bag containing £5000 in £1 coins and ran away. The insurance company are suspicious, and want you to investigate. Could the bank manager be lying?

Explain your reasoning carefully! Tell the insurers exactly what information you used, and what assumptions you made.

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Smartie Pants

Smarties could be used to fill this room.

How many Smarties would you need to fill the room?

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Bonus

The Chancellor of the Exchequer wants to give all pensioners an extra £10 per week.

How much will this cost a year?

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Simple Simon

Initial auditions with producers took place in April and May 2007, with callbacks in front of the judges in June. The number of applicants reached an all-time high with 200,000 people auditioning in the cities of London, Birmingham, Sheffield, Cardiff, Glasgow, Manchester and Belfast. Eight thousand people attended an open audition at Emirates Stadium (home of Arsenal F.C.), London, on 9 June 2007.

1) How long would these auditions have taken if they were all seen by the one panel of judges?2) How many judging panels do you think there were in the Emirates Stadium?

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Human Chains

Human chains are a form of protest in which demonstrators link their arms in a show of solidarity. Not surprisingly, the organisers usuallyreport higher numbers than do the authorities. Below are some notable chains and the numbers claimed. Check each of the claims. Do you believe them?

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Year Event Numbers Claimed Size of Chain

1997XII World Youth

Day, 1997 - Paris 400,000

A 36 km ring

around Paris

2004Hand-in-Hand Rally - Taiwan

1,000,000 by Authorities2,000,000 by Organisers

300 miles

2004 Israeli Chain 130,000 by Police

200,000 by Organizers90 kilometres

2004 Bangladesh 5,000,000 650 miles

Chain Gang – Baltic Protest

"Baltic Way" is the event which occurred on August 23, 1989 when

approximately two million people joined their hands to form a

human chain over 600 kilometre long across the three Baltic states

(Estonia, Latvia, Lithuania). This was organized to draw the world's

attention to the common historical fate which these three countries

suffered. It marked the 50 year anniversary since August 23, 1939

when Soviet Union and Germany divided spheres of interest in

Eastern Europe which led to 50 years of occupation for these three

states.

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