tasks modellingtasks lessonsassessment reflecting

Tasks

Modelling Tasks Lessons Assessment Reflecting

Creating

Tasks

Modelling Tasks Lessons Assessment Reflecting

Tasks

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Exploring Classifying Varying

Session 1Creating tasks from real situations

Session 2Creating tasks from existing resources

Session 3 Workshop

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Develop your own resource

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Try to look at the world through mathematical lenses!

Creating tasks

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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.

Objectives

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• 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).

Outcomes

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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

Activity 1

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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 waterThe data for bottled water consumption (in millions of litres, 2003) for countries throughout the EU is shown below:

Sweden 176Slovenia 115Ireland 102Lithuania 94Latvia 89Denmark 88Finland 83Estonia 34Cyprus n/aMalta n/aLuxembourg n/a

Italy 11,325Germany 10,230France 8,507Spain 5,316Poland 1,833Belgium 1,373UK 1,355Czech Republic 888Portugal 845Austria 816Greece 627Hungary 568Slovak Republic 334Netherlands 300

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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 Pictureswww.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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Consider how different objectives influence the development/presentation of tasks.

Presentation of results/discussion

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Session 2

New tasks from old exercises

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depending on the objectives you have for your lessons

Objectives

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The next sequence of slides show pages from text books from across Europe.

From each example try to develop a modelling task!

Developing new tasks from old text book exercises

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From England:

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A possible solution.

At a petrol station how far apart should the pumps be placed to cater for cars that tow caravans?

Picture: Thanks to Mathiasspiontek, published at Wikimedia Commons

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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.

From Germany:

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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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 TankönyvkiadóBudapest, 1994

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How many books might there be on two shelves each 1m long?

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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.

From Cyprus:

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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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An opportunity to develop your own tasks with colleagues

Workshop

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Consider the process of developing tasks

- How would you summarise the process?

- What challenges does it provide for teachers?

Plenary discussion

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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.

Main stages of the process of preparing tasks:

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depending on the objectives you have for your lessons

Objectives

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• 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).

Outcomes

tasks modellingtasks lessonsassessment reflecting

Documents

modelling tasks

new tasks

workshop slide

resource slide

school gym

kind of ticket

real situations session

existing resources session