Crossing the Bridge

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Crossing the Bridge

• Four friends must all cross a bridge in 17
  minutes.
• They start on the same side of the bridge.
• A maximum of two people can cross at any time.
• It is night and they have just one torch.
• People that cross the bridge must carry the
  torch.
• Each person walks at a different speed.
• A pair must walk together at the rate of the
  slowest
• Rachel - takes 1 minute to cross
• Adam - takes 2 minutes to cross
• Jenny - takes 5 minutes to cross
• Harry - takes 10 minutes to cross
• How can they all cross in 17 minutes?

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Crossing Bridges

• Jennifer Piggott
• 2007
• www.nrich.maths.org

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Outline

• NRICH
• Philosophy
• Content
• Some maths
• Reflections on crossing bridges

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The Yonghy Bonghy-Bò

• On the Coast of CoromandelWhere the early
  pumpkins blow,In the middle of the woodsLived
  the Yonghy-Bonghy-Bò.Two old chairs, and half a
  candle,--One old jug without a handle,--These
  were all his worldly goodsIn the middle of the
  woods,These were all the worldly goods,Of the
  Yonghy-Bonghy-Bò,Of the Yonghy-Bonghy-Bò.

By Edward Lear
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(No Transcript)
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Enrichment

• Content
• Posing and solving problems and tackling rich
  tasks.
• Teaching
• Creating an atmosphere of sharing, critical
  evaluation and difference. Modelling what it is
  to be mathematical.
• Pupils who
• Are creative and imaginative, are comfortable
  with feeling uncomfortable.. Work within a
  community.
• Longer term effects
• Confident independent learners who can apply
  knowledge beyond the classroom.

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Make 37
Four bags contain a large number of 1s, 3s, 5s
and 7s.
Pick any four numbers from the bags so that their
total is 16.
Pick any ten numbers from the bags so that their
total is 37.
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Good Problems

• Are very much about and for individuals
• Initial impact
• Have particular content outcomes

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Crossing Bridges
NRICH
Teacher

• A model
• Rationale
• Assessing need
• Testing
• Optimising input
• Building
• Supporting not leading
• Crossing
• Keeping a watchful eye

Learner
NRICH
Teacher
Learner
Teacher
NRICH
Learner
Learner
NRICH
Teacher
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www.nrich.math.org

• Four main aspects to the site
• Monthly magazine
• Archive
• Maths finder
• Mapping documents
• Articles and games
• Packages
• Ask NRICH
• Thesaurus
• Plus the Newsletter and other publications.

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(No Transcript)
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Rich Tasks

• accessible,
• intriguing,
• challenging,
• low threshold - high ceiling,
• contexts for problem posing,
• offer potential for elegant or efficient
  solutions,
• broaden mathematical content knowledge and
  skills,
• encourage creativity and imaginative application
  of knowledge,
• reveal patterns or lead to generalisations or
  unexpected results,
• reveal underlying principles,
• enable learners to make connections,
• encourage collaboration and discussion,
• develop confident and independent critical
  thinkers.

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Rich Contexts

• have time to explore starting points and
  alternative routes,
• encourage dialogue and interactions,
• Include modelling and metacognition,
• Make use of props and cues, not hints and clues,
• involve a community or practice,
• develop and use appropriate language,
• allow sharing,
• encourage creative, independent thinkers,
• value different approaches,
• use critical evaluation of effective and
  efficient methods,
• develop learners confidence in being
  mathematical,
• support the application of knowledge beyond the
  classroom,
• are appropriate to everyone.

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What bridges to build?

• For pupils
• Safety ? Challenge
• Dependence ? Independence
• Wary of the new ? Exploration
• Solitude ? Communication
• For teachers
• Keeping control ? Letting go
• Cautious ? Trusting
• Talking ? Listening
• Leading ? Supporting

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Basket Case

• A woman goes into a supermarket and buys four
  items. Using a calculator she multiplies the cost
  (in pounds) instead of adding them.
• At the checkout she says, "So that's 7.11" and
  the checkout man, correctly adding the items,
  agrees.
• What were the prices of the four items?

www.nrich.maths.org May 2005
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Finding out more

• Go to www.nrich.maths.org
• Search for- Crossing Bridges
• Email- Jennifer Piggott jsp38_at_cam.ac.uk

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Keep Your Distance

• There are four points on a flat surface
• How many ways can you arrange those four points
  so that the distance between any two of then can
  be only one of two lengths?
• Example

www.nrich.maths.org Sep 2005
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Concrete wheel
100 mph
100 miles
nrich.maths.org May 2006
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Smith and Jones
Mr Smith and Ms Jones are two maths teachers, who
meet up one day. Mr Smith lives in a house with a
number between 13 and 1300. He informs Ms Jones
of this fact, and challenges Ms Jones to work out
the number by asking closed questions. Ms Jones
asks if the number is bigger than 500. Mr Smith
answers, but he lies. Ms Jones asks if the
number is a perfect square. Mr Smith answers, but
he lies. Ms Jones asks if the number is a
perfect cube. Mr Smith answers and (feeling a
little guilty) tells the truth for once. Ms
Jones says she knows that the number is one of
two possibilities, and if Mr Smith just tells her
whether the second digit is 1, then she'll know
the answer. Mr Smith tells her and Ms Jones
says what she thinks the number is. She is, of
course, wrong. What is the number of Mr Smith's
house?
http//nrich.maths.org/public/viewer.php?obj_id21
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