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. Bowland Maths. Overview
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
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?
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!
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.
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.
Kate, Aminda and Amadej all had their 14th birthdays last
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?
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.
The 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].
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.
Smarties could be used to fill this room.
How many Smarties would you need to fill the room?
The Chancellor of the Exchequer wants to give all
pensioners an extra £10 per week.
How much will this cost a year?
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.
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?
Human chains are a form of protest in which demonstrators link their
arms in a show of solidarity. Not surprisingly, the organisers usually
report higher numbers than do the authorities.
Below are some notable chains and the numbers
claimed. Check each of the claims.
Do you believe them?
"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