1 / 39

Modelling

Modelling. Tasks. Reflecting. Lessons. Assessment. Lessons. Modelling. Tasks. Reflecting. Lessons. Assessment. Lessons. ICT. Objectives. In this sub-module you will consider how ICT can be used as a tool to assist with mathematical modelling.

myra
Download Presentation

Modelling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modelling Tasks Reflecting Lessons Assessment Lessons

  2. Modelling Tasks Reflecting Lessons Assessment Lessons ICT

  3. Objectives In this sub-module you will consider how ICT can be used as a tool to assist with mathematical modelling.

  4. You will have considered how pupils can use: graph plotters spreadsheets dynamic geometry software to assist with mathematical modelling. Outcomes

  5. Use your Teacher dairy to: Identify the ways in which you currently use technology in your teaching Consider how you think technology might be used by your students when mathematical modelling Identify any professional development needs you may have regarding using technology. Teacher diaries

  6. Key ways in which technology can be used as a tool when modelling: exploring many situations quickly (for example, carrying out iterations, looking at lots of configurations of spatial situations) exploring how functions might be used to model data varying parameters of a situation (altering assumptions on which a model is based) Technology as a tool

  7. Race Four modelling problems Fencing Garage door Cooling cup

  8. Work on one of the modelling problems: try to think about how groups of students of different ages/ abilities might approach the problem(for example, younger students may avoid an algebraic approach by carrying out calculations in a methodical way) consider how you think technology could be used by your students when working on the problem if possible, use technology to assist you. Activity 1

  9. Race Four modelling problems Fencing Cooling cup Garage door

  10. Race In a school playground there are two trees: one is small and one is large. There is also a straight fence. A group of pupils organise a race: each pupil starts at the small tree, then has to touch the fence before running to the large tree to complete the race. Where is the best place for a pupil to touch the fence? This task was inspired by the following paper: Petit S. (2006): Le tilleul et le marronier. Bulletin de l’APMEP n°466 p. 597

  11. Simplifying assumptions: both trees lie on a straight line parallel to the fence pupils run at the same speed throughout the race (therefore we need to find the shortest distance that pupils run) it takes no additional time for pupils to touch the fence and change direction of running …..?

  12. for example, consider the trees are not at the same distance from the fence pupils run each leg of the race at a different speed (for example, they run to the fence twice as quickly as away from it) …. ? Mathematical problem Real-world problem Real solution Mathematical solution … developing the model ….

  13. Fencing You have 10 metres of fencing and need to fence your pet rabbits in a run. You can use two existing walls in a corner of a garden to form two sides of the run. What arrangement will give the rabbits the maximum area in which to exercise?

  14. Simplifying assumptions: the walls are very long the walls meet at right angles the sides of the fence are parallel to the walls – making the rabbit run rectangular …..?

  15. An alternative approach using spreadsheets – possibly leading to an algebraic approach length width

  16. length width

  17. length width

  18. for example, consider that there is only one wall the walls are not at right angles …. ? Mathematical problem Real-world problem Real solution Mathematical solution … developing the model ….

  19. Garage door How close to an “up-and-over” garage door can you park a car? This is an important issue for architects to consider when they design a house – they may need to save space!

  20. Garage door How do garage doors work? rod pivots fixed point slides up and down

  21. for example, consider different positions of the pivoting rod Different lengths of garage door …. ? Mathematical problem Real-world problem Real solution Mathematical solution … developing the model ….

  22. Cooling cup How can you mathematically model the temperature of a cup of tea as it cools? Does the model work for other situations? For example, can detectives use this to calculate when a murder took place by taking the temperature of the corpse?

  23. In this case it is useful to consider the validity of the model perhaps explore this with other liquids as they cool …. ? Mathematical problem Real-world problem Real solution Mathematical solution … developing the model ….

  24. Objectives In this sub-module you will consider how ICT can be used as a tool to assist with mathematical modelling.

  25. You will have considered how pupils can use: graph plotters spreadsheets dynamic geometry software to assist with mathematical modelling. Outcomes

  26. exploring many situations quickly (for example, carrying out iterations, looking at lots of configurations of spatial situations) exploring how functions might be used to model data varying parameters of a situation (altering assumptions on which a model is based) Technology as a tool Key ways in which technology can be used as a tool when modelling:

  27. Use your Teacher dairy to: Reflect on what you have learnt when doing this sub-module Identify ways in which you think you could now develop lessons in which students could use technology as a tool to assist them with mathematical modelling. Teacher diaries

More Related