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Modelling

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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.

You will have considered how pupils can use:

graph plotters

spreadsheets

dynamic geometry software

to assist with mathematical modelling.

Outcomes

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

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

Race

Fencing

Garage door

Cooling cup

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

Race

Fencing

Cooling cup

Garage door

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

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

…..?

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

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?

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

…..?

length

width

length

width

length

width

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

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!

Garage door

How do garage doors work?

rod pivots

fixed point slides up and down

for example, consider

different positions of the pivoting rod

Different lengths of garage door

…. ?

Mathematical problem

Real-world problem

Real solution

Mathematical solution

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?

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

Objectives

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

You will have considered how pupils can use:

graph plotters

spreadsheets

dynamic geometry software

to assist with mathematical modelling.

Outcomes

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:

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