Matchings_Teacher_Notes.docx

7/25/2019 Matchings_Teacher_Notes.docx

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Just For You Ltd: Teachers Notes

Resources needed for lesson: Paper and pen, modelling packs

(consisting of three grids of equal size (each individual grid should be

printed on dierent coloured paper) please see attached studenttemplate: one grid will represent the audience space one grid can be cut

up as the students wish to represent the !oor"level seating one grid can

be cut up as the students wish to represent the raked seating), graph

paper, #$tudents% &'cel orksheet (attached), access to &'cel $olver

*dd"+n

Lesson plan length: appro'imatel- . hour and a half to / hours

(Please note: it is created so that it can easil- be split into two . hour

lessons: the 0rst session would be up to the #graph work section and thesecond part from the #graph work section onwards)

Aimed at:* 1evel $tudents

Please note: 2he students% worksheets ma- be distributed at the start of

the lesson 2ell students however that -ou will work through the questions

as a class (2his is because -ou will be asking them some additional

questions throughout) 2he idea of having a students% worksheet for the

whole lesson however is so that it allows students to progress if the- 0nish

a certain activit- quickl-

Introduction

(appro'imatel- 3 minutes)

&ncourage the students to 0rst discuss what ma- go into the costs of

designing and building the audience area for the venue (ie cost of raw

materials, insurance costs, cost of hiring the venue, sta wages), and

what is meant b- pro0t and how this is calculated

4iscuss the bene0ts of modelling (ie planning what -ou are going to do)

and wh- this is important, eg if there are an- problems, the- can be

identi0ed now so that time and mone- is saved as much as possible

2he design of the audience area is simpli0ed for this pro5ect, but the idea

of it is to give the students an idea as to how we would run a pro5ect like

this in real life e are also, for similar reasons, onl- considering the cost

of the raked seating and !oor"level seating as a whole and the insurance

cost without considering sta wages etc


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Modelling

6uestion .:

(appro'imatel- .3"/7 minutes)

*sk the students to work in pairs or groups of 8, in order to think of the

best possible wa- to displa- their data and decide what the most logical

approach would be, to work out the dierent combinations 9ive a

modelling pack to each pairgroup of 8 &ncourage the students to use

their modelling packs to be able to visualise the audience area and

e'periment with the dierent combinations of seating choices possible b-

cutting up two of the grids (each one representing a dierent t-pe of seat)

into appropriate sizes (;or e'ample, the !oor"level seating needs to be of

size 73m'73m but there needs to be a 73m gap between each row, so

the- ma- choose to cut up the grid such that the !oor"level seating is of

size .m'73m instead)

*sk them to open up the $tudents% version of &'cel (attached) 2ell them

to onl- focus on the columns: #possibilit-, #!oor"level seating: amount

and #raked seating: amount for now, and input the combinations the-

have found (Please note: tell the students that the- can add moredelete

rows for the number of dierent possibilities as appropriate)

4iscuss the fact that there are man- dierent combinations which involve

0lling the whole capacit- of the room, therefore encourage them to use

their knowledge of formulas to work out the remaining values quickl-, b-

inputting them into the appropriate cells in &'cel

Please highlight the fact that the students are onl- 0nding the

combinations of raked seating and !oor"level seating which completely0lls the space

Please see attachment . to know what their table should look like so far

(Please note: this table has a few e'tra columns, of which answer question

/)

6uestion / and 8:

(appro'imatel- .7".3 minutes)


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&ncourage the students to now consider the rest of the table and think of

appropriate formulas to input into the worksheet to 0ll in these remaining

columns

Please see attachment . to know what their table should look like, as wellas the formulas the- should use

6uestion .? @ =, where .? is the number

of people per row on raked seating) 2he inequalit- is therefore:

6uestion 3:

(6uestion < and 3: appro'imatel- 3 minutes)

1ike in question


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#raph $or%

6uestion = and C:

(appro'imatel- .3 minutes)

+n order to plot the inequalities on the graph, students must think of the

inequalities as equations 2he- should think about where the equations

cross the '"a'is and -"a'is, so that their graphs are drawn as accuratel-

as possible 2he following tables could be used to assist calculations:

&onstraint '

; B 2otal Dalculations

7 E =8/'7 F .?'B @//7

B @.8=3

E 7 33 8/'; F .?'7 @//7 ; @?C=3

&onstraint (

; 2otalDalculation

E = ;@=

&onstraint )

B 2otalDalculation

E = B@=

&ncourage students to use graph paper to draw their constraints on a

graph *sk students to draw their lines be-ond the points the- have

plotted 2he- should use appropriate scales to use for their a'es

$tudents must then plot the points for the dierent combinations of raked

seating and !oor"level seating found earlier (ie in order to 0ll the whole

room) Bemind the students however that this was created without

)(F * '+R " ((,

2here is a ma'imum

capacit- of //7

people in the venue


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knowing the room capacit- (//7 people), therefore the- should onl- use

the points which meet this requirement

Please see attachment / to see what the graph should look like

6uestion G:

(appro'imatel- .7".3 minutes)

&'plain to the students that the optimal solutionis found in each corner

of the feasi-le region(or ver- near to it, taking into consideration the

fact that we can onl- have integer values)

&ncourage students to use a table to calculate the optimum solution at

each point

Please see attachment 8 for this table

Asing this table, the total pro0t, from the optimal solution is hence

H/8/777

Modelling the .ro-lem in /0cel

*sk students to now look at the #modelling the problem in &'cel sheet of

their &'cel workbook ;or this, all students must be able to access

#$olver 2his is available for free as an add"in in &'cel 2o 0nd this, for

IJce /7./, follow the following steps:

;ileIptions *dd"+ns $elect #$olver add"+nDlick #9o 2ickbo' for $olver add"in Dlick #ok

e can see in this worksheet that #$olver 0nds an appropriate solution to

the problem Ase attachment < to e'plain each part of the model and the

inequalities incorporated into #$olver to the students

*sk students to see how well this relates to the results the- calculated

earlier from their graphs +f there are dierences, discuss wh- this ma- be

(ie handwritten errors in graphs, onl- appro'imate solutions with graphs,errors in calculations)


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6uestion .7:

(appro'imatel- .7 minutes)

*sk the students to now use what the- have 5ust learnt about #1ol2er toanswer this question 2he answer to this question simpl- involves

changing the value in the #total capacit- of the venue bo' *sk students

to use the sheet in their workbook entitled #cop- of model . to show this

$tudents should see that, b- doing this, the number of people raked

seating and !oor"level seating should change, resulting in the total pro0t

changing

Please see attachment 3 to see this change

6uestion ..:

(appro'imatel- 3".7 minutes)

*gain, students should use their new knowledge of #$olver to answer this

question

;or this question, students need to think of an appropriate formula to use

in order to calculate the number of people in !oor"level seating, based on

the number of people in raked seating 2heir answer will then aect the

constraints which are inputted into $olver, and the cells which $olver is

allowed to change *sk students to use the sheet in their workbook

entitled #cop- of model / to show this

Please see attachment ? to see this change

Real3Life /0amples


&ncourage students to now read the e'ample given on their worksheet asto how linear programming can be used in real life *sk them if the- can

think of an- more e'amples where it could be used

/2aluation


*sk students to now individuall- think about the questions given on the

worksheet 2his will allow them to re!ect on the work the- have done

2here are no right or wrong answers this part is purel- the students% ownopinion

Matchings_Teacher_Notes.docx

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