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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 3 Exploring Creating Classifying Varying Develop your own resource Tasks 4 Exploring Creating Classifying Varying Creating tasks Try to look at the world through mathematical lenses! Tasks 5 Exploring Creating Classifying Varying 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 6 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). Tasks 7 Exploring Creating Classifying Varying 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 Tasks 8 Exploring Creating Classifying Varying 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. Tasks 9 Exploring Creating Classifying Varying 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 Tasks 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 10 Exploring Creating Classifying Varying 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 Tasks 11 Exploring Creating Classifying Varying 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. Tasks 12 Exploring Creating Classifying Varying 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. Tasks 13 Exploring Creating Classifying Varying Situation 6: Giant foot Picture: Copyright Richard Phillips 2001/2009 from Problem Pictures www.problempictures.co.uk Tasks 14 Exploring Creating Classifying Varying 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. Tasks 15 Exploring Creating Classifying Varying Situation 8: Hotel The picture shows a hotel in Manchester, England. Tasks 16 Exploring Creating Classifying Varying Presentation of results/discussion Consider how different objectives influence the development/presentation of tasks. Tasks 17 Exploring Creating Classifying Varying Session 2 New tasks from old exercises Tasks 18 Exploring Creating Classifying Varying 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 19 Exploring Creating Classifying Varying 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! Tasks 20 Exploring Creating Classifying Varying From England: Tasks 21 Exploring Creating Classifying Varying 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? Tasks 22 Exploring Creating Classifying Varying 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? Tasks 23 Exploring Creating Classifying Varying 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 Tasks 24 Exploring Creating Classifying Varying 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 Tasks 25 Exploring Creating Classifying Varying A possible solution. How many books might there be on two shelves each 1m long? Tasks 26 Exploring Creating Classifying Varying 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. Tasks 27 Exploring Creating Classifying Varying 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 Tasks 28 Exploring Creating Classifying Varying Working with text books Tasks 29 Exploring Creating Classifying Varying Workshop An opportunity to develop your own tasks with colleagues Tasks 30 Exploring Creating Classifying Varying Plenary discussion Consider the process of developing tasks - How would you summarise the process? - What challenges does it provide for teachers? Tasks 31 Exploring Creating Classifying Varying Main stages of the process of preparing tasks: Tasks 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. 32 Exploring Creating Classifying Varying 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). Tasks 34