Transcript Creating tasks

Modelling
Tasks
Tasks
Lessons
Assessment
Reflecting
Modelling
Tasks
Tasks
Creating
Lessons
Assessment
Reflecting
Exploring
Session 1
Creating tasks
from real
situations
Tasks
Creating
Session 2
Creating tasks
from existing
resources
Classifying
Varying
Session 3
Workshop
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Develop your own resource
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Creating tasks
Try to look at the world through mathematical lenses!
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Objectives
In this sub-module you will consider how to:
• prepare new tasks from real situations
• rewrite/adapt existing text book exercises so that they
become modelling tasks
depending on the objectives you have for your lessons.
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Exploring
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Outcomes
• Tasks ready to be used in school
• Experience of developing tasks from a range of different
stimuli (for example, previous knowledge of modeling,
areas of personal interest, newspapers, web and other
media).
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Activity 1
Your group will be given a situation.
i working individually write your idea of a task on a sheet
stating your teaching objective
ii as a group discuss the different ideas
iii make a poster to present your ideas to other groups
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Situation 1: Used car for sale!
Used car for sale!
It is hard to believe but true – this announcement including
this picture was published in an Irish newspaper in 2003:
VW Golf, blue, year of construction
1985, driven only 65 km, only used in
first and reverse gear.
Original brakes. Original fuel and oil
Only 1 driver. Owner wishing to sell
due to employment lay-off.
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Situation 2: Bottled water
The data for bottled water consumption (in millions of
litres, 2003) for countries throughout the EU is shown
below:
Italy 11,325
Germany 10,230
France 8,507
Spain 5,316
Poland 1,833
Belgium 1,373
UK 1,355
Czech Republic 888
Portugal 845
Austria 816
Greece 627
Hungary 568
Slovak Republic 334
Netherlands 300
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Sweden 176
Slovenia 115
Ireland 102
Lithuania 94
Latvia 89
Denmark 88
Finland 83
Estonia 34
Cyprus n/a
Malta n/a
Luxembourg n/a
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Situation 3: Reading
A class of pupils aged 7 will
visit the nursery school to read
to a class of 5 year-olds.
Picture: Thanks to Mr. Absurd, published at Wikimedia Commons
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Situation 4: In the gym
The entrance to a school gym is
in the middle of its longer side.
From the entrance to one corner
the teacher has set out some
benches.
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Situation 5: Season ticket
In Budapest there is a 30-day student season ticket
available. This ticket is valid for 30 days including the day
of purchase.
Sylvia always buys this kind of ticket. Last year, she
bought the first one on the 5th of January.
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Situation 6: Giant foot
Picture: Copyright Richard Phillips 2001/2009 from Problem Pictures
www.problempictures.co.uk
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Situation 7: Flower garden
Claire can put a fence around
a little piece of the family
garden to make her own
flower garden.
Claire has three different
types of plant.
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Situation 8: Hotel
The picture shows a hotel in
Manchester, England.
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Presentation of results/discussion
Consider how different objectives influence the
development/presentation of tasks.
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Session 2
New tasks from old exercises
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Objectives
In this sub-module you will consider how to:
• prepare new tasks from real situations
• rewrite/adapt existing text book exercises so that they
become modelling tasks
depending on the objectives you have for your lessons
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Exploring
Creating
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Developing new tasks from old text book exercises
The next sequence of slides show pages from text books
from across Europe.
From each example try to develop a modelling task!
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From England:
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A possible solution.
Picture: Thanks to Mathiasspiontek, published at Wikimedia Commons
At a petrol station how far apart should the pumps be
placed to cater for cars that tow caravans?
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From Germany:
Despite intensive brushing after dinner
there is still one bacterium on one tooth.
This bacterium grows in a way that the
number of bacteria is doubled each hour.
a) How many bacteria will you find after 2,4,6,12 hours?
b) How many bacteria will there be if the person forgets all advice from his
dentist and brushes his teeth again after 24 hours?
c) Which function describes the growth of bacteria?
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A possible solution.
Brushing your teeth
Dentists recommend that you brush your
teeth after every meal to get rid of bacteria.
If someone didn‘t brush his teeth for 6, 12,
24, 48 hours, what would be the
consequences?
Develop a mathematical model that shows
how bacteria breed and how this can lead
to problems if you don‘t brush your teeth.
Task: © 2007 Cornelsen Verlag ScriptorMathematisches Modellieren
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From Hungary:
Erika has 7 books on one shelf and 11 books on the
other shelf. How many books does she have on both
shelves?
Taken out of Neményi-Oravecz: Matematika tankönyv 2. osztály, Nemzeti Tankönyvkiadó
Budapest, 1994
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A possible solution.
How many books might
there be on two shelves
each 1m long?
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From Cyprus:
At the cake shop
Monica and her mother went
to the cake shop. She saw
many sweet cakes there.
Strawberry cakes are placed
in trays. Each tray contains
10 fresh strawberry cakes.
How many cakes are there in
10 trays?
Complete the table.
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A possible solution.
How many cakes can a tray hold?
You will need to consider the size
of the cake and the size of the tray.
Can you find a relationship?
Picture: Thanks to Quadell, published at Wikimedia Commons
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Working with text books
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Workshop
An opportunity to develop
your own tasks with
colleagues
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Plenary discussion
Consider the process of developing tasks
- How would you summarise the process?
- What challenges does it provide for teachers?
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Main stages of the process of preparing tasks:
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Searching for, collecting and selecting material
Preparation of tasks (for chosen mathematical topic)
Providing possible (preferably more than one) ways of
solving the task.
Thinking over likely solutions and, if necessary,
adjusting the task.
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Exploring
Creating
Classifying
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Objectives
In this sub-module you will consider how to:
• prepare new tasks from real situations
• rewrite/adapt existing text book exercises so that they
become modelling tasks
depending on the objectives you have for your lessons
Tasks
33
Exploring
Creating
Classifying
Varying
Outcomes
• Tasks ready to be used in school
• Experience of developing tasks from a range of different
stimuli (for example, previous knowledge of modeling,
areas of personal interest, newspapers, web and other
media).
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