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Hospitality

NQFLEVEL

4Unit 3

Measurement

Mathematical Literacy

Mathematical Literacy — Hospitality nqf level 4

UNIT 3 — MEASUREMENT �

Activity6

Furnishing a room

Activity1

Where are you

Activity2

Getti

ng to

the conference on tim

e

Activity4

Wor

king with scale

Activity9 O

rgan

isi

ng a teleconference

Activity5

Hair colouring

Activity8

Wall

papering a room

Activity3 M

aking sense of plans

MeasUreMent

• Using scales• Maps• Calculating distances• time Zones

• estimating quantities

• spatial orientation• Physical modelling

Activity5

settin

g ou

t cha

irs in a conference room

Activity10

assessment


UNIT 3 — MEASUREMENT 3

Overview

Unit standard 9016 has two specific Outcomes: o sO 1 focuses on measurement. o sO 2 focuses on shape.

this unit uses a number of different contexts to develop students’ understanding of measurement and shape, including:• thinking about the most appropriate way of

measuring in a particular context.• thinking about how the context impacts

upon the reasonableness of the measurement reading, calculation or solution.

• Using estimation techniques appropriate to the context.

• Knowing what is the appropriate unit of measurement within a particular context.

• reading information from tables.• Converting between units of measurement.• Calculating areas and perimeters and how

contexts impact on one’s answers.• How context can impact upon decisions about

what algorithms to use in calculations. • Developing models to describe situations, to

analyse them and to make predictions about them.

• Using the available technology, in particular electronic calculators, to solve problems.

• Calculating effectively, efficiently and correctly. • explaining the choice of algorithm and the

procedures used.• Understanding scale in sketches and maps• Using ratio to calculate the actual size and

distances.

In addition to developing the mathematical skills of students, this unit is also intended to give students an opportunity to develop an understanding of:• road maps – how to read and interpret them

and use them to calculate distances.• Planning travel and meeting arrangements.• Interpreting floor plans.• arranging furniture in rooms.

the unit consists of ten activities of which one is an assessment activity.

Mathematical literacy involves using one’s knowledge of shape, space, measurement, numbers and data to make sense of the world. It also involves using one’s knowledge of particular contexts to make sense of and increase one’s knowledge of shape, space, measurement, numbers and data. there are several key issues in measurement and shape, and the activities in this unit attempt to address them in ways that are relevant to hospitality.

the following Unit standards, specific Outcomes and assessment Criteria are addressed by this unit:

represent, analyse and calculate shape and motion in 2- and 3-dimensional space in different contexts (Us 9016).

• estimate, measure and calculate physical quantities in practical situations relevant to the adult (sO1).

o scales on measuring instruments are read correctly (aC1).

o Quantities are estimated to a tolerance justified in the context of the need (aC2).

o the appropriate instrument is chosen to measure a particular quantity (aC3).

o Quantities are measured to within the last step of the instrument (aC4).

o appropriate formulae are selected and used (aC5).o Calculations are carried out correctly and the least

steps of the instruments used are taken into account when reporting the final values (aC6).

o symbols and units are used in accordance with sI conventions and as appropriate to the situation (aC7).

• explore, analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems in two and three dimensional geometric situations (sO2).

o Descriptions are based on a systematic analysis of the shapes and reflect the properties of the shapes accurately, clearly and completely (aC1).

o Descriptions include quantitative information appropriate to the situation and need (aC2).

o 3-dimensional objects are represented by top, front, and side views (aC3).

o Different views are correctly assimilated to describe 3-dimensional objects (aC4).

o available and appropriate technology is used in producing and analyzing representations (aC5).

o relations of distance and positions between objects are analysed from different views (aC6).

o Conjectures, as appropriate to the situation, are based on well-planned investigations of geometrical properties (aC7).

o representations of the problems are consistent with and appropriate to the problem context. the problems are represented comprehensively and in mathematical terms (aC8).

o results are achieved through efficient and correct analysis and the manipulation of representations (aC9).

o Problem solving methods are presented clearly, logically and in mathematical terms (aC10).

o reflections on the chosen problem solving strategy reveal strengths and weaknesses of the strategy (aC11).

o alternative strategies to obtain the solution are identified and compared in terms of appropriateness and effectiveness (aC12).

Unit outcomes

Activity6

Furnishing a room

Activity9 O

rgan

isi

ng a teleconference

Activity10

assessment



this unit develops the skills required to achieve the assessment Criteria of Unit standard 9016.

Activity 1 – Where are you?In this activity the learners consider the need to have different scales for maps of south africa. they analyse the appropriateness of a map with a particular scale for a situation. this activity could be developed into a project.

Activity 2 – Getting to the conference on timethis activity uses the context of getting delegates to a conference to engage the learners in measuring, calculating and estimating. they will be using maps to calculate distances and travelling times between towns and using flight schedules to make decisions about travel arrangements. Learners are asked to analyse different travel options and to justify their choice of solution to the problem.

Activity 3 – Finding your way around the conference centreIn this activity, the learners engage with a floor plan of a conference centre. the centre has four levels. In order to develop the spatial orientation skills of the learners, they are asked to do various tasks relating the floor plans to the actual building. they identify features on the plans and work out routes to get from one venue to another. they also consider numbering systems for the rooms of the conference centre.

Activity 4 – Working with scalesIn this activity the learners work with ratios in the form of scale drawings. they convert feet and inches into the appropriate sI units. they calculate actual areas using formulae and conversion scales. they will check these calculations against known areas and work out the percentage difference between their calculated area and the given area.

Activity 5 – Setting out chairs in the conference roomIn this activity learners will be looking at the arrangement of furniture in a conference facility. they will be looking at the bird’s eye view of the chairs and tables and determining which arrangement will suit the situation. they will be using two different skills in order to do this. they will be modeling the situation physically and they will also be using formulae to calculate the number of chairs and tables that can be fitted into a room. they will critique each method.

Activity 6 - Furnishing a bedroomthis activity follows on from activity 5 and the learners will once again use physical modeling to find solutions. In this activity the learners will be furnishing a bedroom. they will be making scale drawing of the furniture and the room. they will be costing the various options and will be determining the best ratio of furniture arrangement for optimum profit.

Activity 7 – Carpeting a roomIn this activity the learners consider how to carpet a room. the learners explore the notion that the amount of carpeting is not determined by the area of the floor of a room. this is because carpeting is sold in rolls which have a fixed width. Learners are therefore encouraged to determine the amount of carpeting by once again modeling the situation physically. they will also calculate the percentage wastage for each situation.

Activity 8 – Wallpapering a roomthis activity follows on from activity 7 but uses wallpapering a room as the context. Once again learners are led through a process so that they can conclude that the amount of wallpaper needed cannot be determined by the area of the walls of a room. Wallpaper is also sold in rolls with a fixed width. In this activity the learners read values off tables rather than physical modelling.

Activity 9 – Organising a teleconferencethis activity focuses on international time zones. Learners have to read off an information table, work with world maps and do calculations in order to facilitate an international teleconference. they will also be looking up information in the telkom phone book.

Activity 10 – Assessment. Should we use this lodge?this is an assessment activity. It incorporates the skills learnt in the previous activities. In this activity learners have to work with scale and make accurate scale drawings of rooms. they use top views of furniture to assess how many delegates can be accommodated in a room. they will verify their findings by calculating the number of delegates using formulae. the learners will also work out their own coordinate system to number seating places.



9016 Represent, analyse and calculate shape and motion in 2-and 3-dimensional space in different contexts

Whe

re a

re y

ou?

Get

ting

to th

e co

nfer

ence

Mak

ing

sens

e of

the

plan

s

Wor

king

with

sca

les

sett

ing

out c

hairs

in a

con

fere

nce

room

Furn

ishi

ng a

bed

room

Carp

etin

g a

room

Wal

lpap

erin

g a

room

Org

anis

ing

a te

leco

nfer

ence

asse

ssm

ent a

ctiv

ity. s

houl

d w

e us

e th

e lo

dge?

aCtIVItY 1 2 3 4 5 6 7 8 9 10

sO1 Measure, estimate, and calculate physical quantities in practical situations relevant to the adult.

aC1 scales on the measuring instruments are read correctly.

aC2 Quantities are estimated to a tolerance justified in the context of the need.

aC3 the appropriate instrument is chosen to measure a particular quantity

aC4 Quantities are measured correctly to within the least step of the instrument.

aC5 appropriate formulae are selected and used.

aC6 Calculations are carried out correctly and the least steps of instruments used are taken into account when reporting final values.

aC7 symbols and units are used in accordance with sI conventions and as appropriate to the situation.

sO2 explore, analyse & critique, describe & represent, interpret and justify geometrical relationships.

aC1 Descriptions are based on a systematic analysis of the shapes and reflect the properties of the shapes accurately, clearly and completely.

aC2 Descriptions include quantitative information appropriate to the situation and need.

aC3 3-dimensional objects are represented by top, front and side views.

aC4 Different views are correctly assimilated to describe 3-dimensional objects

aC5 available and appropriate technology is used in producing and analysing representations.

aC6 relations of distance and positions between objects are analysed from different views.

aC7 Conjectures as appropriate to the situation, are based on well-planned investigations of geometrical properties.

aC8 representations of the problems are consistent with and appropriate to the problem context. the problems are represented comprehensively and in mathematical terms.

aC9 results are achieved through efficient and correct analysis and manipulation of representations.

aC10 Problem-solving methods are presented clearly, logically and in mathematical terms.

aC11 reflections on the chosen problem solving strategy reveal strengths and weaknesses of the strategy.

aC12 alternative strategies to obtain the solution are identified and compared in terms of appropriateness and effectiveness.



Activity 1 – Where are you?

ABOUT THIS ACTIVITYthis activity highlights the need to have different scales for maps. the learners will explore the advantages and disadvantages of the different scales i.e. what information the map gives you and what information is lacking. they will also give directions using maps.

this activity is aligned with unit standard 9016 and addresses aC 1,2,3,4,6,7,8,9,10,11 of sO2.

MANAGING THIS ACTIVITYLearners will need the worksheet from this activity and the maps on the handout for this activity. the last question can be done in groups as a project.

1.1 this map tells you that the place you are looking for is in Kwa-Zulu natal which is in south africa which in turn is in africa. It also shows you that Kwa-Zulu natal is on the east side of south africa. It does not show/indicate in which town or city the place you are looking for is found nor does it give any indication of how you can get there. It also does not show you the main cities or any routes so you have no idea as to what mode of transport you could possibly use.

1.2 this map is a more detailed map of south africa. From this map you can see that the place you are looking for is inland and near the Lesotho border. However, it does not even tell you that the country you are bordering is Lesotho. It shows you that there are nine different provinces. It does not give you any detail of possible routes or which town/city you will be near.

1.3 this map zooms in on Kwa-Zulu natal and gives you an idea of the nearest towns. It doesn’t, however, give any indication which are the bigger towns and cities or which towns/cities have airports. It does not give any indication of the terrain i.e. if there are mountains nearby or not. It still does not give you any idea of the possible routes you could take. You have lost the bigger picture of where Kwa-Zulu natal is in relation to the rest of south africa

1.4 this map gives the most useful information in terms of getting to the cottages. It gives a sense of the size of the towns. It indicates that Durban and Johannesburg are the main centres. It shows that you can get to the cottages by road and gives the numbers of the roads. It indicates that the n3 is the main road from Durban to Johannesburg. It does not, however, give you any idea of the terrain of the country or the condition of the roads.

1.5 Map 5 does not give you any information at all as to how to get to the resort. It does not give you any indication where it is in south africa. It is localised and only shows you how to get to the various venues in the resort. It is useful only once you have arrived at the resort.

2.1 On map.

2.2 take the n3 from Johannesburg twards Durban. Continue past Harrismith on the n3 and exit at Bergville toll Plaza. turn left towards Ladysmith. turn right onto the Winterton r600 which will cross back over the freeway and go past the spionkop Dam to Winterton. Go through Winterton, pass Cathedral Peak and continue till you get to Berghaven.

2.3 take the n3 towards Johannesburg. If it is daytime turn left to Loskop and continue until you meet the r600. turn left and continue until you reach Berghaven.

2.4 If it is night time you need to bypass the Loskop turnoff and take the next turnoff which is the Winterton offramp. turn left onto the r74 and continue until you meet the r600. turn left onto the r600 and continue past Cathedral Peak till you reach Berghaven.

3 no solution needed





Activity 1 — Where are you?An important aspect of the hospitality industry is advertising. When advertising your restaurant, conference centre, hotel etc it is essential to give potential clients very clear directions as how to get to you. Your directions need to have different levels of information. Look at the handout for this activity.• For overseas visitors, you need to establish that you are in South Africa (see map 1).• Then you need to say which province you are in (see map 2).• Next, you must indicate which town/city you are in or which town/city you are closest to

(see map 3).• You need to give directions to your business (see map 4).• In some cases where your business has various buildings or is part of a bigger complex eg. a game

reserve, you will even need to give them a localised map (see map 5 ).

Each map is giving your client a different piece of information.

1 Answer the following questions using the maps in the handout.

1.1 What information does map 1 give you and what information does it not give you?





2 Answer the following question using map 4 of the handout.

2.1 It is important to give directions as to how to get to your business. Read through the directions to the self-catering cottages which go with map 4 and trace the route on the map.

2.2 The directions that you used in question 2.1 say that this route is “a little longer”. Write down direction for an alternative route from Johannesburg and mark it on the map using a different colour to the one used in question 2.1.

2.3 Write down two alternative routes to get to the cottages from Durban. Why do you need two different routes?

3 Find a resort/hotel/conference centre in the area that you live in and put together a collection of maps that give you the same levels of detail as the ones in this activity.

worksheet 1

Directions:

From JHB take the N3 to Harrismith

Route 1 — Harrismith via Sterkfontein DamThis route is a little longer but more scenic. Take Bloemfontein turn off for 3 km then left to QwaQwa — after 11 km turn left onto the R74 to Bergville past the Sterkfontein Dam [60 km] — through Bergville to Winterton [20 km]. In Winterton turn right on the R600 to the Central Berg, travel 26 km to arrive at Berghaven.





handout 1

Map 1

Map 2 Map 3

Map 4 Map 5



Activity 2 — Getting to the conference on time

ABOUT THIS ACTIVITYthis activity uses the context of getting delegates to a conference to engage the learners in measuring, calculating and estimating. they will be using maps to calculate distances and travelling times between towns and using flight schedules to make decisions about travel arrangements. Learners are asked to analyse different travel options and to justify their choice of solution to the problem.

this activity is aligned with unit standard 9016 and addresses aC 5,6 of sO1 and aC 2,5,6,8,9,10,11,12 of sO2.

MANAGING THIS ACTIVITYLearners will need the worksheet and handout for this activity. they will also need a calculator. Learners will be expected to support their answers with calculations. there is scope for discussion of answers so this activity could be done in pairs.

1.1 Bloemfontein

1.2 He would leave Bloemfontein on the n5 going north. at Winburg he would turn right and continue on the n5 through Bethlehem to Harrismith.

1.3 about 305km

1.4time =

distancespeed

therefore time taken to get to Harrismith ≈305100

≈ 3 hours

2.1 Flight sa1081; flight sa314/sa1019; flight sa322/sa1007 and flight sa324/sa1081. Flight sa1081 as it is a direct flight.

2.2

Flight number advantages Disadvantages

Flight sa1081 • Direct flight so spends the least time travelling.

• Leaves early so he gets to conference centre early and could possibly get some work done there.

• Leaves early so he misses out on a morning’s work in Cape town.

• He has to be at the airport at 5am.

Flight sa314/sa1019

• Leaves at a reasonable time so he only needs to get to the airport at about 7am.

• He will get to the conference centre well before sunset.

• It is not a direct flight, so he will have to change planes in Johannesburg.

• He spends a lot more time travelling compared to the direct flight.

Flight sa322/sa1007

• Leaves at a reasonable time so he only needs to get to the airport at about 8:40.

• He will have some time before he flies off to do some work.

• He will get to the conference centre before dark.


• He spends the most time travelling with this option.

Flight sa324/sa1081

• Leaves at a reasonable time so he only needs to get to the airport at about 9:10.

• He will have more time than the previous flight to do some work before he leaves.

• He will spend less time than the previous two flight travelling as he will spend less time between connecting flights.

• He will get to the conference centre before dark.


• He spends a lot more time travelling compared to the direct flight.

For this exercise, flight sa1081 has been chosen.


UNIT 3 — MEASUREMENT 1�

2.3 05:00

2.4 07:35

2.5 It will take him about an hour to get his luggage, sort out his hired car and navigate his way out of Bloemfontein. It is about a three hour drive to Harrismith and then about half an hour to find the conference centre. He will arrive at the centre approximately 4½ hours after he lands in Bloemfontein. this means he arrives at approximately 12:00.

2.6 the conference ends at 12:00 which means that if he leaves within half an hour of finishing , he should get to Bloemfontein at about 16:00. the flights available to him are flights sa1086; sa1012/sa367; sa1014/sa375. the best option is possibly the nonstop flight sa1086. this leaves at 17:55 which means that he has to be at the airport at the latest 16:55 at the latest.

2.7

Itinerary for Mr Mtembu

Monday (day before the conference starts)

arrives at Cape town International airport 05:00

Flight sa1081 leaves 06:00

arrives Bloemfontein 07:35

arrives Conference Centre ≈ 12:00 (4½ hours travel time)

Friday (day conference ends)

Leaves Conference Centre ≈ 12:30

arrives at Bloemfontein airport 16:55

Flight sa1086 leaves 17:55

arrives Cape town International airport 19:25 3.1 about 186 km

3.2

time = distancespeed

therefore time taken to get to Harrismith ≈186100

≈ 2 hours

3.3 First option to get to the conference: Flying to Bloemfontein and then driving to Harrismith.

Best flight would be flight 8481, which leaves at 08:50 and gets to Bloemfontein at 10:20. It is a direct flight and takes 1½ hours. From question 2 we know that it will take about 4½ hours to get to the conference so all in all it will take about 6 hours traveling time.

second option to get to the conference : Flying to Pietermaritzburg and then driving to Harrismith.

Best flight would be flight sa400/sa8036, which leaves Pe at 6:30 and arrives in Pieremaritzburg at 11:20. this flight goes to Johannesburg first and then on to Pietermaritzburg and takes 3hours and 50 minutes. Driving time to Harrismith from Pietermaritzburg is an hour less than from Bloemfontein so it will take about 3½ hours. therefore in total it will take about 7 hours.

she should fly to Bloemfontein en route to the conference.

3.4 First option coming home: Flying from Bloemfontein.

she should get to Bloemfontein at about 16:00. this means that she will be too late to catch a plane that night. she will have to overnight in Bloemfontein and then catch the first flight out on saturday morning. the first flight will be flight sa1026/sa413 which goes via Johannesburg. she will get to Pe at 12:30.

second option coming home: Flying from Pietermaritzburg.

she should get to Bloemfontein at about 15:00. she has two options here. If she hurries she can catch the sa8039/sa405 flight at 15:45 which means an overnight stop in Johannesburg and she gets home at 11:00 on saturday or she can spend the night in Pietermaritzburg and catch flight sa8035/sa419 which leaves at 10:15 and goes via Johannesberg. she will then only get home at 17:05.

she should fly from Pietermaritzburg en route home if she wants to get home an hour and a half earlier.



Activity 2 — Getting to the conference on timeYou are working at a big conference centre, which is situated on the banks of the sterkfontein Dam. the closest town to the centre is Harrismith in the Free state. there is a conference starting on tuesday at 8am and ending at 12am on Friday.

Part of organising a conference is making sure that the delegates arrive at the conference on time. You need to organise travel arrangements for Mr Mtembu from Cape town and Dr scholtz from Port elizabeth. they want to fly if possible.

1.1 Find Harrismith on the map. Which is the closest airport to which Mr Mtembu can fly?

1.2 Describe the route that he must take from that city to get to Harrismith. Use road numbers to help you.

1.3 Use the numbers alongside the route and calculate approximately how many kilometers Mr Mtembu will have to drive in order to get to Harrismith.

1.4 approximately how long will it take him to get to Harrismith if Mr Mtembu drives at an average speed of 100km/h?

2 You now need to look at flights from Cape town for Mr Mtembu. Points to consider include: he is a busy man so would like to spend as little time as possible travelling, he does not like to drive in the dark so when you book the flight you need to consider how long he will take to drive to Harrismith. at this time of the year, sunset is at 7pm.

2.1 Using the flight tables on the handout, determine four flights which could be options for Mr Mtembu.

2.2 Discuss the advantages and disadvantages of each flight and then decide which flight you feel would be the best option for him. Use this flight to answer the rest of the questions.

2.3 at what time must he be at Cape town International airport?

2.4 at what time does he land in Bloemfontein?

2.5 estimate at what time he will reach the conference centre. Discuss how you made your estimation.

2.6 repeat the process for his return trip.

2.7 Write up an itinerary for Mr Mtembu’s travel arrangements, giving the times that he must be at the airport, flight times and numbers, and approximate times for car travel.

3 Dr scholtz is coming from Port elizabeth. she can fly to either Bloemfontein or to

Pietermaritzburg and then drive to Harrismith.

3.1 How many kilometres is it from Pietermaritsburg to Harrismith?

3.2 approximately how long will it take her to get to Harrismith if Dr scholtz drives at an average speed of 100km/h?

3.3 Using the flight schedules on the handout, determine which would be the better option for Dr scholtz: to fly to Bloemfontein and then drive to Harrismith or to fly to Pietermaritzburg and then drive to Harrismith. Justify your choice by showing your calculations for the various options.

3.4 Do the same for her trip home.

worksheet 2



handout 2.1



For domestic flights all passengers must be at the airport at least 1 hour before take–off.

Flight times from Cape town to Bloemfontein

Frequency Depart arrive Flight number stop/via

X67 0600 0735 sa1081 nOnstOP

7 0830 1005 sa1091 nOnstOP

6 1230 1405 sa1093 nOnstOP

7 1245 1420 sa1087 nOnstOP

X67 1535 1710 sa1085 nOnstOP

7 1655 1630 sa1095 nOnstOP

X67 1805 1940 sa1083 nOnstOP

7 0600 1130 sa302/sa1021 JnB

X67 0800 1240 sa314/sa1019 JnB

X7 0940 1425 sa322/sa1007 JnB

X67 1010 1425 sa324/ sa1007 JnB

X-except DLY- daily 1-Mon 2-tues 3-Wed 4-thurs 5- Fri 6-sat 7-sun

Flight times from Bloemfontein to Cape town


X67 0810 0950 sa1082 nOnstOP

7 1035 1215 sa1092 nOnstOP

6 1435 1615 sa1094 nOnstOP

7 1450 1630 sa1088 nOnstOP

X67 1555 1735 sa1005 nOnstOP

X67 1755 1925 sa1086 nOnstOP

7 1915 2050 sa1096 nOnstOP

X7 1250 1910 sa1008/sa357 JnB

DLY 1640 2110 sa1012/sa367 JnB

X67 1810 2310 sa1014/sa375 JnB


Flight times from Port elizabeth to Bloemfontein


234 0850 1020 sa8481 nOnstOP

X67 0815 1240 sa404/sa1019 JnB

X7 0815 1425 sa404/sa1007 JnB

6 1000 1405 sa681/sa1093 CPt

7 1000 1420 sa681/sa1087 CPt

X67 1130 1530 sa410/sa1005 JnB

DLY 1130 1615 sa410/sa1009 JnB

X67 1230 1735 sa412/sa1013 JnB

7 1300 1735 sa316/sa1023 JnB

X67 1310 1710 sa663/sa1085 CPt


handout 2.1



handout 2.1

Flight times from Bloemfontein to Port elizabeth


234 1050 1225 sa8486 nOnstOP

X67 0610 1100 sa1016/sa405 JHB

X67 0750 1200 sa1002/sa411 JnB

X67 0810 1240 sa1082/sa662 CPt

6 0830 1230 sa1026/sa413 JnB

DLY 0940 1715 sa1004/sa419 JnB

7 1035 1420 sa1092/sa682 CPt

7 1200 1705 sa1022/sa419 JnB

67 1350 1840 sa1020/sa421 JnB

7 1450 1840 sa1088/sa684 CPt

6 1450 1935 sa1008/sa481 JnB

DLY 1640 1100 + 1♣ sa1012/sa405 JnB

X-except DLY- daily 1-Mon 2-tues 3-Wed 4-thurs 5- Fri 6-sat 7-sun ♣ this means that passengers will have to spend the night in Johannesburg.

Flight times from Port elizabeth to Pietermaritzburg


X67 0630 1120 sa400/sa8036 JnB

7 0755 1520 sa464/ sa8038 JnB

X7 0815 1520 sa404/ sa8038 JnB

X67 1230 1710 sa412/ sa8040 JnB

7 1300 1840 sa416/ sa8046 JnB


Flight times from Pietermaritzburg to Port elizabeth


X67 0625 1100 sa8031/sa405 JnB

6 1015 1705 sa8035/ sa419 JnB

X67 1145 1605 sa8037/ sa417 JnB

X6 1145 1715 sa8037/ sa419 JnB

DLY 1545 1100 + 1♣ sa8039/ sa405 JnB

X-except DLY- daily 1-Mon 2-tues 3-Wed 4-thurs 5- Fri 6-sat 7-sun ♣ this means that passengers will have to spend the night in Johannesburg.



Activity 3 — Finding your way around the conference centre

ABOUT THIS ACTIVITYIn this activity the learners will be analysing the floor plans of a conference centre. they will be identifying various features on the floor plans and working out routes. they will be visualising how the four floors of the building fit onto one another.

this activity is aligned with unit standard 9016 and addresses aC 1,2,3,6,9 of sO2.

MANAGING THIS ACTIVITYLearners will need the worksheet and the floor plans for the centre, which are found in the handout for this activity. Learners might need some guidance in interpreting floor plans to get them started. some answers will be drawn onto the handout itself.

1.1 the first floor numbering starts with 1, the second floor with 2 and the third with 3. the basement does not have a specific number to indicate its position. Perhaps it should have had a zero. this could be a point for discussion.

1.2 a lift.

1.3 there are lifts going to every floor. there is a ramp leading up to the entrance.

1.4.1 they are interleading. room 122a appears to have a counter top on two sides of the room. 1.4.2 room 122a could be where the delegates book into the centre. this reception room then leads into room

122 which would be the office for the reception area.

1.5

staircase Where it is going

at entrance From the outside into the foyer or the other way round

100L From the foyer to the outside or the other way round

100a Down to the basement and up to the second floor

100B Down to the basement and up to the second floor

100C Down to the basement and up to the second floor 2.1 solution on handout.

2.2 the third floor.

2.3 the basement.

2.4 the first floor.

2.5 answers could include: the basement is below ground level and will therefore not have a view; the reception area and the dining room are found on the first floor which means that this floor is busy and possibly noisy, therefore there are the fewest bedrooms on this floor (however, there need to be at least some bedrooms on this floor to accommodate physically challenged delegates); the third floor offers the best view.

2.6.1 the first room on the left as one comes out of the lift is numbered 201. the numbers then go up consecutively as one goes down the corridor. there are three corridors: one going away from the lift, one going behind the lift and one going off to the right from the lift. the numbers follow from the corridor straight ahead down the corridor to the right and then down the corridor behind the lift. the numbers end with 227. the numbers jump from 216 to 219 due to the open spaces on the second floor.

2.6.2 the numbers on the third floor follow the same basic layout as the second floor. However, after 321 the numbers jump to 350, 351, 352 and 353, then return to the normal numbering again and end with 327.

2.6.3 an advantage of having the numbering following the same sequence on both floors is that the number of the room indicates the position of the room. One can thus deduce that 301 and 201 will be in the same position but on different floors. the jump in numbering on the third floor is necessary for the last 6 bedrooms to co-incide with the numbering on the second floor.

2.6.4 One has to follow the numbers down the passage without having any sense of where one’s room will be.

2.6.5 It would enable one to get an idea of where the room would be i.e. Whether the room was at the top of the corridor or at the bottom of the corridor. It also enables one to know if one’s room is on the left hand side of the passage or the right hand side.


UNIT 3 — MEASUREMENT �0

2.6.6 a suggested numbering would be to have a letter to indicate which corridor one’s room was in eg. 2a2 would indicate that the room was on the second floor and was the second room in corridor a. an advantage of this numbering would be that the corridors could be labelled in the same way for every floor. this means that even in the basement one would label the conference room with a letter to indicate which corridor one must go down in order to find it.

3.1 the dining room.

3.2 It will give the dining room a feeling of spaciousness. It will make the corridor on the second floor much lighter and also give it a feeling of spaciousness.

3.3 at the entrance foyer.

3.4 One gets one’s first impression of the centre as one enters the foyer and having that open area gives the foyer a sense of spaciousness and lightness.

4.1 solution on handout.

4.2 Walk to the lift from room 16. take the lift to the third floor. as you get out of the lift turn right and then immediately right again (a U-turn). Continue down the passage till you get to your room at the end of the passage on the left hand side.

4.3 First route: use the stairwell at the far end of the room and go up the stairs to the third floor. Walk down the passage until you come to the hallway where you will find the lift. turn left and go to the end of the passage and your room will be on the left hand side.

second route: go out the entrance of the room, turn first left and then first left again and take the stairs to the third floor. at the top of the stairs turn left and your room will be at the end of the corridor on the left hand side.

4.4 the second route is the shorter.

5.1 there are three exits from this room.

First route: go out the entrance of the room, down the passage, turn first left, first left again and go up the stairs. there is an exit right at the stairs on the left hand side which will take you outside the building.

second route: use the exit on the right of the entrance which will take you outside into a courtyard. Use the stairs to get you to ground level.

third route: use the stairwell at the far end of the room to get you to the first floor. there is an exit to the outside at that point.

5.2 the basement is below the ground. In order to get light into the room, the soil has been dug out and retainer walls have been put in. this means that one can now put in a window which will look out onto the retainer wall. the symbol represents the retaining wall and the window.

5.2.1 23 delegates.

5.2.2 It shows that the room is tiered.

5.2.3 no solution provided. a suitable solution would refer to easy access for the wheelchair; not blocking up entrances and exits; and the comfort of the person in the wheelchair.

5.2.4 no solution proveded.



Activity 3 — Finding your way around the conference centrethe conference centre that you work at overlooks the sterkfontein Dam and has four floors. the plan for each floor is found on the handout for this activity. the centre has 48 bedrooms, all with a bathroom en suite, as well as a number of conference venues.

1 the entrance to the centre is found on the first floor. On the floor plan this is labelled 100M. the entrance leads into a foyer and a reception area. rooms 110 and 108 are the dining room and kitchen area respectively. answer the following questions using the floor plans.

1.1 Look at the numbering of the different floors. How can you tell which floor you are looking at by the numbers of the rooms?

1.2 What is the feature labelled 100H in the foyer?

1.3 Identify two features which make this centre accessible to people in wheelchairs.

1.4 Find rooms 122a and 122.

1.4.1 What do you notice about these two rooms?

1.4.2 What do you think these rooms would be used for? Justify your answer.

1.5 Colour in all 5 staircases on the first floor. Write the number of each staircase, where applicable, and explain where each staircase is going.

2 establish what a bedroom with a bathroom en suite looks like on the floor plan and then answer the following questions.

2.1 Circle all 48 bedrooms on the floor plans on the handout.

2.2 Which floor has the most bedrooms?

2.3 Which floor has no bedrooms?

2.4 Which floor has the fewest bedrooms?

2.5 Why do you think the bedrooms are arranged like this?

2.6 Look at the numbers of the bedrooms on floors 2 and 3.

2.6.1 Using the lift as your reference point, describe how the rooms are numbered on the second floor.

2.6.2 Compare this to the numbering on floor 3. What is the same and what is different?

2.6.3 Using your answers from 2.6.2, discuss why you think there are these similarities and differences.

2.6.4 What disadvantage is there to numbering the rooms in this way?

2.6.5 What would be the advantage in numbering the rooms alternately i.e. all the odd numbers on one side of the corridor and all the even numbers on the other side?

2.6.6 suggest another way to number the rooms. Discuss the advantages of your way.

3.1 there is an area next to room 216 which is labelled “open to below”. If you looked down into this area, what would you be looking at?

3.2 Why do you think they have this open area?

3.3 there is a smaller open area next to rooms 220 and 221. If you looked down into this area what would you be looking at?

3.4 Why do you think they have included this open area?

worksheet 3


UNIT 3 — MEASUREMENT ��

4 there are 6 conference venues numbered 5, 16, 214, 215, 216 and 353.

4.1 Find these on the floor plan and colour them in using a different colour to the one you used previously.

4.2 Describe, in detail, the shortest route that a delegate could take to get from the conference room 16 in the basement to his/her bedroom numbered 323. Mark it on your floor plan.

4.3 If the lift were out of order, describe two alternative routes for the delegate. Use a different stairwell each time. Mark these routes on your map – use a different colour for each route.

4.4 Which of your two routes is the shorter?

5 the floor below the first floor is the basement and is below ground level.

5.1 How many exits are there from room 16? Describe the various escape routes from this room if there was a fire. remember that in the event of a fire, one cannot use the lift.

5.2 the symbol in figure 1 (below) is found only in the basement floor plan. What do you think it represents?

5.3 room 5, in the basement, is a specialised teleconference facility and has a fixed arrangement of chairs. the plan of the layout is found on the handout.

5.3.1 How many delegates can it seat?

5.3.2 What do you think the symbol, which the arrow is pointing to, in figure 2 (below) tells you about the room?

5.3.3 Where would a suitable place be for a person in a wheelchair? Mark it on the floor plan. Justify your answer.

5.3.4 Work out a numbering plan for the seats. Label these seats on the handout. explain why you have numbered them in this way.

Figure 1 Figure 2

worksheet 3



`

Basement

First Floor

handout 3.1



Second Floor

handout 3.1

Third Floor



handout 3.1



Activity 4 — Working with scales

ABOUT THIS ACTIVITYthis activity focuses on the scale of the floor plans used in the previous activity. the floor plans are from the United states of america which means that the dimensions are given in feet. Learners are ask to convert these to appropriate sI units and then to calculate the scale used in the drawing of the floor plans. Learners are also asked to calculate percentage difference as a way of making comparisons. they will practise finding dimensions of rooms using scale.

this activity is aligned with unit standard 9016 and addresses aC 1,2,3,4,5,6,7 of sO1 and aC 1,2,3,4,9,10,11 of sO2.

MANAGING THIS ACTIVITYLearners will need the worksheet for this activity and the handout from activity 3. they will also need a ruler and a calculator. the solutions to the first question may differ from learner to learner as it will depend on how each learner has measured the dimensions of the room. the scale is standardised from question 2 onwards, which means that the learners’ answers should be more uniform. However, once again the learners are measuring off the floor plan so answers may differ slightly. the solutions below have been determined using a particular copy of the floor plans. the size of the floor plans might have altered in the printing process so some measurements will not be compatible. However, the scale of the map should not alter as it is a ratio and the actual dimensions of the rooms should thus be comparable. answers given here, therefore, are merely to show the process and should not be seen as the only possible answers.

1.1 number of inches in 28ft = 28 × 12 = 336” therefore no. of cm = 336 × 2,54 =853,44cm therefore no. of m ≈ 8,53m

1.2 3cm

1.3 3cm : 8,53m

1.4 3 : 853 ≈ 1 : 284 ≈ 1 : 300

1.5 Width of room in cm = 1,5cm therefore actual width in cm = 1,5 × 300 = 450cm therefore the width of the room = 4,5m

1.6 area of room = length × width = 8,53 × 4,5 = 38,25m2

1.7 area = 448 × 0,093 = 41,66m²

1.8 It is less than the brochure area.

1.9 Difference = 41,66 – 38,25 = 3,41m²

1.10 % difference =3.4141.66

× 100 ≈ 8%

1.11 error creeps in with measuring and rounding off. For our purposes 8% is not too much of a problem. However, engineers, builders and architects would think differently.

2.1 to 2.6

room Length in m Width in m area in m²

5 0,035 × 300 = 10,5m 0,031 × 300 = 9,3m 10,5 × 9,3 = 97,65m²

16 0,055 × 300 = 16,5m 0,035 × 300 = 10,5m 16,5 × 10,5 =173,25 m²

214 0,016 × 300 = 4,8m 0,016 × 300 = 4,8m 4,8 × 4,8 = 23,04m²

215 0,030 × 300 = 9m 0,015 × 300 = 4,5m 9 × 4,5 = 40,5m²

353 0,028 × 300 = 8,4m 0,016× 300 = 4,8m 8,4 × 4,8 = 40,32m²

note that 215 and 353 have a similar area, even though their shape is different.

3.1.1 Length = 0,015 × 300 = 4,5m Width = 0,015 × 300 = 4,5m ∴ area = 4,5 × 4,5 = 20,25m²

3.1.2 Length = 0,007 × 300 = 2,1m Width = 0,005 × 300 = 1,5m



∴ area of bathroom = 2,1 × 1,5 = 3,15m²3.1.3 area of the bedroom = 20,25 - 3,15 = 17,1m²

3.1.4

% taken up by bathroom =3.1520.25

× 100 ≈ 16%

3.2.1 the lift shaft juts into room 227.

3.2.2 the area of the bedroom is the same as 226 but one must subtract the area of the lift shaft. Length = 0,006 × 300 = 1,8m Width = 0,003 × 300 = 0,9m ∴ area of lift shaft = 1,8 × 0,9 = 1,62m² ∴ area of 227 = 17,1 – 1,62 = 15,48m²

3.2.3 Difference = 1,62m² which is the area of the lift shaft.

3.2.4

% difference =1.6217.1

× 100 ≈ 9,5%

this means that room 227 is 9,5 % smaller than the standard bedroom.

3.3.1 total area is the same as the standard bedroom = 20,25m²

Length of bathroom = 0,008 × 300 = 2,4m Width = 0,007 × 300 = 2,1m ∴ area of bathroom = 2,4 × 2,1 = 5,04m² ∴ area of bedroom = 20,25 – 5,04 = 15,21m²

3.3.2 Difference in area = 17,1 – 15,21 = 1,89m²

3.3.3

% difference =1.8917.1

× 100 ≈ 11%

this means that room 311 is 11% smaller than the standard bedroom room.



Activity 4 — Working with scalesIn the previous activity you worked with the floor plans of the conference centre. an important aspect of working with floor plans is to make sure that you know what scale has been used in the drawing up of the plans. this conference centre was built as a replica of a centre in the United states of america and the plans are therefore in feet and inches.

1 Determining the scale of the floor plan. You will need the following conversions to establish the scale of the plans.

1 inch (“) 2,54cm

1 foot (ft) 12 inches

1 ft 0,093m²

the length of the room numbered 216 on the floor plan is given as 28ft.1.1 Using the conversion table, convert this to metres.

1.2 Measure the length of the room in centimetres.

1.3 Hence set up a ratio _____cm : _____m which relates the length on the floor plan to the actual length of the room.

1.4 Using the appropriate conversions, reduce the ratio to _____: ______ in its simplest form (round off to the nearest 50).

1.5 the ratio in question 1.4 is the scale of the floor plans. Use this scale to find the width of the room.

1.6 Hence, calculate the area.

1.7 In the brochure for the centre, it states that the area is 448 ft². Check the accuracy of your scale by converting the area given in the brochure to m².

1.8 Comment on the accuracy of your calculated area.

1.9 Calculate the difference, if any, between the quoted area and the area you calculated.

1.10 One way of evaluating the significance of this difference is to calculate the percentage difference. Use the formula below to calculate the percentage difference of the areas.

% difference =Difference in areasarea in brochure

× 100

1.11 now comment on the accuracy of your calculation.

2 For the rest of this activity, use the scale 1:300. Calculate the area of the following conference rooms. note the following: One calculates

areas of conference rooms in order to determine how many delegates can be seated comfortably in the room. therefore when calculating the areas below calculate the “clear meeting area”. this means the area that you actually have to work in. to do this you need to measure the shortest distances that form the room’s length and width.

2.1 room 5

2.2 room 16

2.3 room 214

2.4 room 215

2.5 room 353

3 Finding the area of the bedrooms.

3.1 the standard bedroom:

3.1.1 Find the total area of the bedroom and en suite bathroom for room 226.

3.1.2 Find the area of the bathroom.

worksheet 4



3.1.3 Hence find the area of the bedroom.

3.1.4 What percentage of the total area does the bathroom take up?

3.2 Bedroom 227:

3.2.1 Why is the area of 227 smaller than that of 226?

3.2.2 Calculate the area of the bedroom only of 227.

3.2.3 Calculate the difference in area between 226 and 227.

3.2.4 Find the percentage difference in area of 227 and 226. Use the formula from 1.10 to help you.

3.3 Bedroom 311:

3.3.1 Calculate the area of the bedroom only of 311.

3.3.2 Calculate the difference in area between 311 and 226.

3.3.3 Find the percentage difference in area of 311 and 226.

worksheet 4



Activity 5 — Setting out chairs in the conference room

ABOUT THIS ACTIVITYFurniture in a conference venue can be arranged in different ways in order to facilitate different types of meetings. this activity looks at seven different ways of arranging chairs and tables in a conference venue. the learners will be using two different skills to determine the number of delegates that can be seated in a venue using a particular arrangement of furniture. Firstly, they will use given formulae to calculate the number of delegates that can be seated using a particular arrangement of furniture and secondly, they will model the situation physically using scale drawings. they will make a comparison of the two methods.

this activity is aligned with unit standard 9016 and addresses aC 1,2,3,4,5,6,7 of sO1 and aC 1,2,3,4,5,6,7,8,9,10,11,12 of sO2.

MANAGING THIS ACTIVITYthe learners will need the worksheet for this activity as well as the handouts for this activity. they will also need a calculator, a ruler and a pencil. It might be useful to have a discussion about the different arrangements of furniture shown on the handout and the types of meetings that might require a particular arrangement.

1.1 Classroom style room 16: number of rows. Usable space = 16,5m – 2,6m – 0,9 = 13m no. of rows = 13m ÷ (0,45 + 0,9) = 9,62 rounded down = 9 rows.

(the need for rounding down could be discussed at this point.) number of chairs in each row. Usable room width = 10,5m – 1,575m (15% of 10,5m) = 8,93m no. of tables per row = 8,93m ÷ 1,8m (table length) = 4,96 tables therefore the number of chairs = 4 × 3 = 12 chairs therefore the number of chairs in the room = 9 rows × 12 chairs = 108 chairs.

room 353: number of rows. Usable space = 8,4m – 2,4m – 0,9m= 5,1m no. of rows = 5,1m ÷ (0,45 + 0,9) = 3,7rows rounded down = 3 rows. number of chairs in each row. Usable room width = 4,8m – 0,72m (15% of 4,8m) = 4,08m no. of tables per row = 4,08m ÷ 1,8m (table length) = 2,26 tables rounded down = 2 tables therefore the number of chairs = 2 × 3 = 6 chairs therefore the number of chairs in the room = 3 rows × 6 chairs = 18 chairs.

Lecture/theatre style room 16: number of rows. Usable space = 16,5m – 2,6m – 0,9 = 13m no. of rows = 13m ÷ (0,5 + 0,6) = 9,63 rows rounded down = 9 rows. number of chairs in each row. Usable room width = 10,5m – 1,575m (15% of 10,5m) = 8,93m no. of chairs per row = 8,93m ÷ 0,45m (chair width) = 19,8 chairs rounded down = 19 chairs therefore the number of chairs in the room = 9 rows × 19 chairs = 171 chairs.

room 353: number of rows. Usable space = 8,4m – 2,4m – 0,9m = 5,1m no. of rows = 5,1m ÷ (0,5 + 0,6) = 4,6 rows



rounded down = 4 rows. number of chairs in each row. Usable room width = 4,8m – 0,72m (15% of 4,8m) = 4,08m no. of chairs per row = 4,08m ÷ 0,45m (chair width) = 9,06 chairs rounded down = 9 chairs therefore the number of chairs = 4 × 9 = 36 chairs. Banquet style room 16: no. of tables fitting into length of room = 16,5m ÷ 3m = 5,5 tables rounded down = 5 tables no. of tables fitting into width of room =10,5m ÷ 3m = 3,5 tables rounded down = 3 tables therefore the total no. of tables = 5 × 3 = 15 tables therefore the total no. of chairs = 15 × 8 = 120 chairs.

room 353: no. of tables fitting into length of room = 8,4m ÷ 3m = 2,8 tables rounded down = 2 tables no. of tables fitting into width of room = 4,8m ÷ 3m = 1,6 tables rounded down = 1 table therefore the total no. of tables = 2 × 1 = 2 tables therefore the total no. of chairs = 2 × 8 = 16 chairs.

1.2 Classroom style

room 16: area of room = 173m². For 300 people the area of the room needs to be 1,6 × 300 = 480m². this means that room 16 can

accommodate groups of less than 300 people. each person will need 1,8m² of space. therefore the maximum number of people that can be accommodated in the room = 173m² ÷ 1,8m² = 96,1 people. rounded down, this means that room16 can accommodate a maximum of 96 people.


accommodate groups of less than 60 people. each person will need 2m² of space. therefore the maximum number of people that can be accommodated in the room = 40m² ÷ 2m² = 20 people.

room 353: area of room = 40m². although the dimensions of this room differ from those of room 215, the area is the same. the calculation

will be the same as the above calculation. Lecture/theatre style


accommodate groups of less than 300 people. each person will need 1m² of space. therefore the maximum number of people that can be accommodated in the room = 173m² ÷ 1m² = 173 people.

room 215: area of room = 40m². For 60 people the area of the room needs to be 1 × 60 = 60m². this means that room 215 can accommodate

groups of less than 60 people. each person will need 1,2m² of space. therefore the maximum number of people that can be accommodated in the room = 40m² ÷ 1.2m² = 33,3 people. rounded down, this means that room16 can accommodate a maximum of 33 people.

room 353: Calculation will be the same as the one above.

Banquet (round table) style room 16: Maximum number of people = 173 ÷ 1,25m² = 114,4 people. rounded down, this means that the

room can accommodate a maximum number of 114 people.

rooms 215 and 353: Maximum number of people = 40 ÷ 1,25m² = 32 people.

Mathematical Literacy — Hospitality NQF LEVEL 4


Hollow square style

Room16: Maximum number of people = 173 ÷ 2,8m² = 61,78 people. Rounded down, this means that the room can accommodate a maximum number of 61 people.

Room 215 and 353: Maximum number of people = 40 ÷ 2,8m² = 14 people.

1.3 The difference between the two calculations is not signifi cant in most cases. The only case where there was a marked difference was for the classroom style for room 16. The fi rst formula gave a much higher number of people. This difference could be due to the room being much longer than it is wide. Formulae I takes this into account and works with these dimensions whereas formulae II does not. The areas of rooms 215 and 353 are the same but their dimensions differ. This would explain why for formulae I, the estimated number of chairs differs for each room whereas for formulae II the number of chairs is the same for each room.

2.1 The diagrams below are all drawn using a different scale to the scale used in the activity.

2.2



2.3

2.4

2.5 The values determined from the drawings and the calculated values are similar. This says that both methods are valid. One advantage of the physical modeling is that you can get a sense of what the room will look like with a particular type of arrangement.



Activity 5 — Setting out chairs in the conference roomDifferent clients have different needs with respect to how they wish to use the conference rooms at the conference venue. these needs almost always impact on how they want the chairs and/or tables arranged. the handout shows a range of different furniture arrangements that clients often ask for. Most conference venues develop a table such as the one below that shows how many people can be accommodated in each of the conference rooms so that when a client asks they can simply look it up as opposed to having to go to the conference venue and try it out first.

room Dimensions area Ceiling CL L/t Ban HB tc/Bd Hs

5 10,5m × 9,3m 98m² 2,6m -- -- -- -- 23 --

16 16,5m × 10,5m 173m2 2,6m --

214 4,5m × 4,8m 23m2 2,2m -- -- -- -- 10 --

215 9m × 4,5m 40m2 2,4m --

216 9m × 4,5m 40m2 2,4m --

353 8,4m × 4,8m 40m2 2,4m --

Key CL: ClassroomL/t: Lecture/theatreBan: BanquetHB: Herringbonetc/Bd: teleconference/BoardroomHs: Hollow square

there are at least two ways in which conference facilities complete the table. either they use a formula or they actually set out the furniture and count the number of chairs.

1 Using formulae1.1 refer to the formulae labelled “Formulae I” on the handout and use these to determine

the number of people that can be accommodated in rooms 16 and 353 using the following seating arrangements:• Classroom style• Lecture/theatre style• Banquet (round table) style

1.2 refer to the formulae labelled “Formulae II” on the handout and use these to determine the number of people that can be accommodated in rooms 16, 215 and 353 using the following seating arrangements:• Classroom style• Lecture/theatre style• Banquet (round table) style• Hollow square

1.3 Discuss any differences that arise from using the two different formulae.

2 Using physical modelling scale models can help us both to determine solutions and to verify solutions that we

determine by means of other methods. the handout has a number of 1 : 50 scale drawings of the different items of furniture and

their different arrangements.

worksheet 5



2.1 Verify the number of people that can be seated in a banquet style arrangement in room 16 by:• drawing a 1 : 50 scale drawing of room 16, and• copying and cutting out sufficient scale drawings of the round banquet table and

sticking these onto the scale drawing of room 16.

2.2 Verify the number of people that can be seated in a classroom style arrangement in room 215 by:• drawing a 1 : 50 scale drawing of room 215, and• copying and cutting out sufficient scale drawings of the table and chairs and sticking

these onto the scale drawing of room 215.

2.3 Verify the number of people that can be seated in a lecture style arrangement in room 353 by:• Drawing a 1 : 50 scale drawing of room 353, and• Copying and cutting out sufficient scale drawings of the chairs and sticking these onto

the scale drawing of room 353.

2.4 Determine the number of people that can be seated in a herringbone lecture style arrangement in rooms 16 by:• Drawing 1 : 50 scale drawings of rooms 16 and• Copying and cutting out sufficient scale drawings of the herringbone table and chairs

arrangements and sticking these onto the scale drawings of the rooms.

2.5 Discuss any differences you may have found between the calculated values for each room and the actual number of chairs and/or tables that you were able to fit into each room by means of the scale drawings. What does this say about the merits of each of the methods?

worksheet 5



Different furniture arrangements for conference rooms

HANDOUT 5.1

Classroom Lecture/Theatre

Banquet I Banquet II

Herringbone Boardroom/Hollow Square

U-Shape



FORMULAE I

the formulae below are based on formulae published on the following website: http://www.pcma.org/templates/Conferon/charts/Ch7_2.htm

For the purpose of this activity we will assume that the tables and chairs used have the following dimensions (as these change so the formulae will have to be adjusted):

Conference table: rectangular: 180cm × 45cm × 76cm round: 152cm diameter × 76cm; seats 8 people

Chairs: 50cm (front to back) × 45cm (side to side)

Calculating the capacity of function rooms:

Classroom-style setupstep 1: Determine the number of rows that can be accommodated:nOte: For the tables we are using, the ideal gap between the tables is 90cm.• take the clear room length (determined in the previous activity and provided in the table at the

start of the activity) and subtract the space between the screen and the front row (the minimum distance should be the height of the room, though more is desirable) and the space between the back wall and back row (minimum of 90cm).

• Divide by the distance allocated to each row measured from the front of the table to the front of the next table.

• round the resulting number down to the nearest row.

eXaMPLe: 9m (length of room 215) – 2,4m (room height) – 0,9m (distance from back wall) = 5,7m (usable room length); 5,7 ÷ 1,35m = 4,22; rounded down = 4 rows.

step 2: Determine the number of chairs that can be placed in each row:• take the clear room width (determined in the previous activity and provided in the table at the

start of the activity) and subtract space for aisles (normally about 15%).• Divide by the length of the tables being used.• round the resulting number down to the nearest number of tables.• Multiply by the number of chairs that can be placed at each table.

eXaMPLe: 4,5m (width of room 215) – 70cm (15% of 4,5) = 3,8m (usable room width); 3,8 ÷ 1,8 = 2,11; rounded down = 2 tables → 6 chairs per row

step 3: Determine the number of chairs in the room:• Multiply the number of rows by the number of chairs in each row.

eXaMPLe: 4 rows × 6 chairs per row = 24 chairs.

Lecture-style setupstep 1: Determine the number of rows that can be accommodated:nOte: For the chairs we are using, the ideal gap between the chairs is 60cm.• take the clear room length (determined in the previous activity and provided in the table at the

start of the activity) and subtract the space between the screen and the front row (the minimum distance should be the height of the room, though more is desirable) and the space between the back wall and back row (minimum of 90cm).

• Divide by the distance allocated to each row measured from the front of the chair to the front of the next chair.


handout 5.2



eXaMPLe: 9m (length of room 215) – 2,4m (room height) – 0,9m (distance from back wall) = 5,7m (usable room length); 5,7 ÷ 1,1m = 5,18; rounded down = 5 rows.

step 2: Determine the number of chairs that can be placed in each row:• take the clear room width (determined in the previous activity and provided in the table at the

start of the activity) and subtract space for aisles (normally about 15%).• Divide by the width of the chairs being used.• round the resulting number down to the nearest number of chairs.

eXaMPLe: 4,5m (width of room 215) – 70cm (15% of 4,5) = 3,8m (usable room width); 3,8 ÷ 0,45 = 8,4; rounded down = 8 chairs per row.

step 3: Determine the number of chairs in the room:• Multiply the number of rows by the number of chairs in each row.


Banquet-style setup (round tables)It is customary to leave a gap of 75cm all around a table with a diameter of 152cm. this allows both enough space for the chairs and for people, including waiters, to move between the chairs.

step 1: Determine the number of tables that can be accommodated:• take the clear room length (determined in the previous activity and provided in the table at the

start of the activity) and divide by the diameter of the table plus 1,5m. round the result down to the nearest table.

• take the clear room width (determined in the previous activity and provided in the table at the start of the activity) and divide by the diameter of the table plus 1,5m. round the result down to the nearest table.

• Multiply the two numbers together to determine the number of tables.

step 2: Determine the number of chairs in the room:• Multiply the number of tables by the number of chairs at each table.

eXaMPLe: 9m (length of room 215) ÷ 3m = 3 tables; 4,5m (width of room 215) ÷ 3m =1,5; rounded down = 1 table; ∴ 3 tables with 8 chairs per table = 24 chairs.

handout 5.2



FORMULAE II

The formulae below are based on formulae published on the following website: http://www.pcma.org/templates/Conferon/charts/Ch7_2.htm

To determine how large a room should be for a given group of people and a given setup, multiply the number of people by the values below:

Classroom style:• 2m² per person for groups of less than 60 people• 1,8m² per person for groups of 60 to 300 people• 1,6m² per person for groups of more than 300 people

Theatre style:• 1,2m² per person for groups of less than 60 people• 1m² per person for groups of 60 to 300 people• 0,9m² per person for groups of more than 300 people

Banquet style:• 1,25m² per person

Boardroom or hollow square style:• 2,8m² per person

U-shape style:• 3,25m² per person

1 : 50 SCALE DRAWINGS OF FURNITURE

HANDOUT 5.3



Activity 6—Furnishing the bedroom

ABOUT THIS ACTIVITYIn this activity, learners will consider different furniture arrangements in the bedrooms of the conference centre. Theywill be drawing scale models of each room and its furniture and will model the various options physically. They will be costing the various options and determining the best ratio of furniture arrangement for optimum profi t.

This activity is aligned with unit standard 9016 and addresses AC 1,2,3,4,5,6,7 of SO1 and AC 1,2,3,4,6,7,8,9,10,11,12 of SO 2.

MANAGING THIS ACTIVITYLearners will need the worksheet and handout for this activity as well as the fl oor plans for the centre which are found on handout 3. They will also need coloured paper, a ruler and a pair of scissors.

1.1 No solution needed.1.2 No solution needed.1.3 Double

1.4.1 King (extra) 1.4.2 Queen (extra)

1.5 Double (203cm) Twin (190cm) Single (190cm)



Some suggested arguments could be:• It would be better to have two single beds as they take up the least amount of space which makes the

room feel more spacious. • It would be better to have two double beds because this would mean that the room could accommodate

four people as opposed to only two.• Two double beds take up a lot of space which leaves very little space in which to arrange the other

furniture that is needed in the room.

2 Possible responses to question 2:

KING

QUEEN



DOUBLE ROOM – DOUBLE BED

DOUBLE ROOM – TWIN BED



DOUBLE ROOM – SINGLE BED

Each learner will have a different opinion as to how to furnish the rooms. The following are some suggested arguments:

One receives more money for two people sharing a room than for a one-person occupancy of a room. Adouble occupancy room has a rate of 2 × R395 = R790 per room whereas a single occupancy room has a rate of R695. Therefore most rooms should have a double occupancy capacity, either in the form of one double bed or two single beds. Two single beds in a room is a more practical option for a conference bedroom as delegates might be prepared to share a room with another delegate but would not like to share a bed.

Two double beds in a room make the room crowded and it is not always practical for four conference delegates to share two double beds. Four single bed in a room might be a better option. King-size bed surcharge is R125 per day. Many delegates will not be prepared to pay so much extra so rooms with king-size beds should be limited.



Activity 6—Furnishing the bedroomsIn addition to knowing how to put out the furniture in the conference rooms, it is important to plan the furnishing of the guest/bed rooms.

The guest/bed rooms of a conference facility should have, at a minimum,:• Either one large bed or two single/twin beds to allow for delegates to share a room.• A wardrobe into which the delegate can place his/her clothes. • A writing table and chair(s) at which the delegate can sit and write notes etc.• A dresser and chair (although the chair used at the writing table can also be used at the dresser).• At least one comfortable chair (sofa) that can be used while watching television. The sofa could

also be a sleeper type couch that can be folded out to accommodate minors sharing a room with their parents.

When furnishing a room, you can either go to a furniture supplier and/or study their catalogue to determine the sizes of the furniture items, or you can refer to the “industry standards” for furniture. Some industry standard dimensions for the furniture we are interested in are supplied in the handout.

1 Choosing the bed(s) The sketch alongside is a scale drawing of room 226

with a bed and two bedside tables in one possible position in the room.

1.1 Draw a 1 : 50 scale drawing of room 226.

1.2 Draw on coloured paper and cut out one or more (as needed below) 1 : 50 scale models of each of the beds described in the handout.

1.3 Determine the largest possible bed that can be used in the position on the diagram alongside.

1.4 Determine the best position in the room for the following:

1.4.1 A king-size bed, both regular (203cm long) and extra length (215cm long), with a bedside table on each side.

1.4.2 A queen-size bed, both regular (203cm long) and extra length (215cm long), with a bedside table on each side.

1.5 In the case of a bedroom with two beds decide, with reasons, whether or not it is better to use two double, two twin, or two single beds. Each bed should have at least one bedside table.

2 Placing the remaining furniture into the rooms

2.1 Draw on coloured paper and cut out enough 1 : 50 scale models of the furniture needed to complete the questions that follow:

2.2 Place a minimum of two wardrobes into each room.

2.3 Place at least one three-drawer dresser and a chair (desk) into each room (you can of course choose to place a six-drawer dresser if you prefer). If you do use a six-drawer dresser in the rooms with one bed, you need only use one wardrobe in those rooms.

2.4 Decide on the most appropriate size writing table for the room. There should be at least two chairs (desk) per writing table although one of these can be shared with the dresser.

2.5 If there is space, try to put a sofa or a sofa and coffee table into each room – you should decide on the size of the sofa (using the values supplied on the handout). It would be ideal if this sofa could fold out as a sleeper couch.

WORKSHEET 6



3 For each of the different furniture arrangements that you have developed in question 2, make a list of the things that you think are good (i.e. advantages of the choices that you have made) as well as list of those things that you are not as happy about (i.e. the disadvantages of the choices that you have made).

4 In light of the work that you have done in the activity so far, draw a 1 : 50 scale drawing of room 227 and determine the most appropriate way to furnish this room.

5 as this activity has evolved you have designed the following room arrangements: type a: One king-size bed type B: One queen-size bed type C: two double beds type D: two twin beds type e: two single beds

now consider the following tariffs charged by a hotel group in south africa:• single occupancy: r695 per person per day (bed and breakfast).• Double (or greater) occupancy: r395 per person per day (bed and breakfast) – this

applies to two people sharing a room with one bed and up to four people sharing a room with two beds.

• King-size bed surcharge: r125 per day.

Motivate a ratio of rooms with two beds to rooms with one bed and in each case determine the number of each of these rooms to be furnished in the ways that you are proposing.

refer to the hotel floor plan and decide, with reasons, how you will furnish each of the rooms according to the ratio you have determined.

worksheet 6



Some standard furniture dimensions (note the heights have been omitted):

Beds: Single: 90cm × 190cm Twin: 100cm × 190cm; 100cm × 203cm; and 100cm × 215cm

Double: 138cm × 190cm; and 138cm × 203cmQueen: 152cm × 203cm; and 152cm × 215cmKing: 195cm × 203cm; and 195cm × 215cm

Tables:Bedside: 38cm × 48cmCoffee (rectangular): 45cm to 60cm × 90cm to 152cm* Coffee (round): 90cm to 110cm diameterWriting table: 92cm to 102 cm × 50cm to 60cm*

* Note: rectangular tables are typically manufactured with the ratios shown below

Chairs:Desk chair: width varies from 40cm to 45cm at the back and about 48cm at the

front; chairs with armrests can be as wide as 54cm from the outside of the armrest to the outside of the armrest

depth is typically 40cm to 45cmLounge/sofa: width typically varies from 142cm to 152cm – determined as follows:

60cm per person plus 10cm to 15cm for each armrest, with a full size sofa typically being 230cm wide

depth typically varies from 46cm to 56cm

Wardrobes and dressers: Three-drawer dresser: 85cm × 45cm Six-drawer dresser: 165cm × 45cm

Wardrobe: 90cm × 60cm

HANDOUT 6

50cm56cm60cm70cm80cm90cm

110cm

122cm

140cm

152cm

180cm

180cm to 300cm



Activity 7—Carpeting a room

ABOUT THIS ACTIVITYIn this activity the learners will explore different ways of carpeting a room. They will analyse the difference between mathematical solutions and practical solutions to the problems they will encounter in the process. They will draw sketches and do calculations.

This activity is aligned with unit standard 9016 and addresses AC 1,2,3,4,5,6,7 of SO1 and AC 1,2,3,4,7,8,9,10,11,12 of SO2.

MANAGING THIS ACTIVITYLearners will need the worksheet for this activity and the fl oor plans of the convention centre found on the handout from activity 3. Learners should be made aware that carpeting is sold in rolls and has a standard width. They also need to be aware that carpets are woven in a particular way and so cannot just be joined in an ad hock manner.

1.1.1 Solution 1 used 12m and solution 2 used 11,2m.

1.1.2 Solution 1: The amount of carpet left over = 3 × 2,5 = 7,5m².

Solution 2: The amount of carpet left over = 2,2 × 2 = 4,4m².

1.1.3 Solution 1: % waste = 7.540.5

×100 ≈ 18,5%

Solution 2: % waste = 4.440.5

×100 ≈ 11%

1.2 There is a larger carpeted area that has no joins in it. Solution 2 has a join right in the middle of the room.

2.1 17,1m² (from activity 3)

2.2 No, it cannot be used as the length of the piece that needs to be carpeted is 2,4m and the length of the left-over carpet is 2.1m.

2.3 2 × 2.4 = 4,8m

Amount of extra carpet remaining = (3 × 0,3) + (1 × 2,4) = 3,3m²

2.4 No, laying the carpet the other way would require you to purchase 6m of carpeting, as the piece that remains uncovered is 3m long. This is more than the original way which only had a piece of only 2,4m long uncovered.

3.1 Some of these solutions have already been calculated in activity 3.

Room Length Width Area

16 0,055 × 300 = 16,5m 0,035 × 300 = 10,5m 16,5 × 10,5 =173,25 m²

22 0,031 × 300 = 9,3m0,021 × 300 = 6,3

0,020 × 300 = 6m0,005 × 300 = 1,5m

(9,3 × 6) + (6,3 × 1,5)= 62,25m²

214 0,016 × 300 = 4,8m 0,016 × 300 = 4,8m 4,8 × 4,8 = 23,04m²

353 0,028 × 300 = 8,4m 0,016 × 300 = 4,8m 8,4 × 4,8 = 40,32m²

12 0,024 × 300 = 7,2m0,015 × 300 = 4,5m

0,014 × 300 = 4,2m0,013 × 300 = 3,9m

(7,2 × 4,2) + (4,5 × 3,9)=47,79 m²

4,5m

4,5m

2,4m

3,0m



3.2 The solution diagram for room 22 has been drawn.

3.3 Worked solution for room 22: Area of carpeting needed = 2 × 4m × 9,3m

= 74,4m² Area of fl oor to be carpeted = 62,25 m² Area of carpet not used = 12,15 m²

Therefore percentage left over = 12.1562.25

× 100 = 19,5%

Room 16: Area of carpeting needed = 3 × 4m × 16.5m

= 198 m² Area of carpet not used = 24,75m²

Therefore percentage left over = 24.75173.25

× 100 = 14,3%

Room 214: Percentage wasted = 67,7%

Room 353:Percentage wasted = 42,8%

Room 12:Percentage wasted = 35,6%

4.1 The biggest wastage seemed to occur with the square room with the smallest dimensions. This occurred because the length of the room was greater than 4m, which is the width of the roll of carpet. The other small room, namely the bedroom, has a more awkward shape to carpet but you can use off-cuts to do so which resulted in less wastage.

4m



Activity 7—Carpeting a roomIn this unit we have been interested in the use of measurement and how it applies to the hospitality trade. Measurement is part of a larger topic, namely geometry, which is the study of space and shape. One of the topics that we associate with geometry is area i.e. calculating the area of different shapes.In this activity we will explore how the problem we are solving can impact on how we can use a formula such as the formula for the area of a rectangle: area = l × b.

Although it is probably fair to say that not everybody who works in the hospitality trade will do the calculations that we work with in this activity, the purpose of the activity is to make the point that formulae sometimes need to be adapted for a particular situation.

We begin this activity with an extended illustration – you will be expected to perform calculations based on this illustration.

Consider room 216 in the conference facility. It is 9,0m long by 4,5m wide. We can calculate the area of room 216 to be:

Area = 9m × 4,5m = 40,5m²

This would suggest that we need to buy 40,5m2 of carpeting to carpet the room. Since carpeting is sold in rolls that are 4m wide, it may at fi rst seem reasonable to calculate the length of carpeting to buy as follows:

Because Area = l x b

It follows that l = Areab

l = 40,5m²4m

l = 10,125m

If, however, you bought exactly 10,125m of carpet you’d be in quite some trouble. To illustrate this let us consider how we would cover the fl oor with a 10,125m length of carpet.

APROACH 1 (cutting up the excess)In this approach you could lay out the carpet as shown below. It would be too long for the room and not wide enough. Because of our calculations we know that the excess piece should be able to cover the part of the room not yet covered. This could be done in at least the two different ways shown below.

WORKSHEET 7

4,5m

9,0m

Room 216

4,5m

9,0m

Room 216



Before going into why such an approach would not be used in practice, we need to recognize that the left hand solution gives rise to an additional problem. Carpet is woven in a specifi c direction and pieces that are laid next to each other need to lie in the same direction to ensure that the colour looks the same and that any patterns in the carpet are maintained (the arrows show the direction of the weave). In this solution the carpet does not all lie in the same direction.

The “mathematical” solutions shown in the diagrams are just that: mathematical solutions. They“work” mathematically but would not be used in practice for the following reasons:• It is almost impossible to cut carpet as accurately as would be required for this solution and some

of the pieces are simply too small to work with.• There would be too many joints in the carpet – with each joint taking time to make and also being

a weak spot in the carpet.• In practice, people who install carpets always allow for some extra carpet in case the walls of the

room are not completely straight.

WORKSHEET 7

B

A

B

A A

A

B

B

C

C

D

D

E

E

F

F

G

G

H

H



APPROACH 2 (anticipating some extra)In practice, the people who install the carpets may choose one of the two solutions that follow. Thesemethods reduce the number of joints and allow for some extra carpet incase the wall are not straight etc. In the sketches below 1cm represents 1m.

1 The amount of left over carpet Refer to the two sketches above and answer the following questions:

1.1 For each solution determine the following:

1.1.1 The length of carpet which was used.

1.1.2 The amount of carpet left over (in meters squared).

1.1.3 The amount of carpet that is left over as a percentage of the amount of carpet needed.

1.2 Not only does solution 2 reduce the amount of unused/left-over carpet but the two pieces (labelled A and B) are wider and hence more substantial, making them easier to work with. Under what circumstances would solution 1 nonetheless be considered a good solution?

WORKSHEET 7

A B C

A

B

C

A

A

B

B

Solution 1 Solution 2



2 Revisiting room 226 A scale drawing of room 226 is printed

alongside.

2.1 Calculate the area of the bedroom (excluding the en-suite bathroom) – you have done this calculation before in a previous activity.

2.2 If a piece of carpet with length 4,5m is bought and placed in the room as shown in the second sketch, will the area of the carpet that must be cut off for the bathroom be enough to cover the remaining part of the room? If yes, can it be used as a single piece and/or can the direction of the carpet weave be maintained? How much extra carpet will remain ?

2.3 How long should the length of carpet be so that the missing piece can be cut as one piece from the off-cut? How much extra carpet remains with this solution?

2.4 Is it possible to use less extra carpet by laying the carpet in a different direction? Justify your answer by showing your working.

3 Some other rooms Answer the questions that follow for each of the following rooms:

• 16• 22• 214• 353• 12

3.1 What area of carpet is needed to cover the fl oor?

3.2 Draw a sketch diagram to show how the carpet should be laid to reduce the amount of left-over carpet as much as possible.

3.3 Determine the amount of carpet that is left over as a percentage of the amount of carpet needed.

4 Refl ection4.1 Can you establish any relationship between the shape and dimensions of a room and the

amount of carpet that will be left over after carpeting the room? Discuss.

WORKSHEET 7

4,5m

4,5m

2,4m

3,0m

4,5m

4,5m

2,4m

3,0m



Activity 8 — Wallpapering a room

ABOUT THIS ACTIVITYIn this activity the learners will explore wallpapering a wall. they will look at two methods of calculating the amount of wallpaper needed for the job. the first method uses the area of the wall and the area of the wallpaper. the second method uses a table of values which has been developed by wallpaper manufacturers to estimate the amount of wallpaper needed.

this activity is aligned with unit standard 9016 and addresses aC 5,6,7 of sO1 and aC 1,2,3,4,7,8,9,10,11,12 of sO2.

MANAGING THIS ACTIVITYLearners will need the worksheet from this activity and the floor plans for the conference centre found on the handout from activity 3. this activity once again emphasizes that as with carpeting one cannot use the area of a room to estimate the amount of wallpaper required to wallpaper a room.

1.1.1 surface area of door recess = (2 × 2,08m × 0,09m) + (0,9m × 0,09m) = 0,4554m²

there are two doors so the total surface area = 2 × 0.4554 ≈ 0,91m²

surface area of window recess = (2 × 1,2m × 0,09m) + (2 × 2,5m × 0,09m)

= 0,666m²

1.1.2 surface area of the door = 2,08m × 0,9m = 1,872m²

1.1.3 surface area of the window = 2,5m × 1,2m = 3m²

1.1.4 surface area of wall = 4,5m × 2,2m = 9,9m²

If you look at the diagram carefully, you can see that you need four of these measurements. although the walls change to make the bathroom, essentially you are still wallpapering a square room. therefore total surface area for the walls is

4 × 9,9m² = 39,6m²

1.2 total surface area to be covered = (39,6 + 0,91 + 0,666) – (2 × 1,872) – 3 ≈ 31,43m²

1.3 number of rolls needed = 31.435.2

= 6,04 rolls. You need 7 rolls.

1.4 the measurement that is given for the wallpaper is not taking the shape of the room into account. the area of 5,2m² can be obtained from any number of combinations of dimensions.

2.1 Perimeter of room 226 = 4 × 4,5 = 18m

Height of room falls into the first band, therefore 9 rolls are needed. there is no actual value for a perimeter of 18m but it is wiser to take too much rather than too little, so it is better to take 9 rolls.

2.2 there is a difference of two rolls. the table takes into account the shape of the room and specifically the perimeter. a roll of wallpaper has a specific width and it is important to calculate how many widths will fit into the perimeter of the room. the first method does not take this into account at all.

2.3 area of wall to be wallpapered = 31, 43m²

area of wallpaper needed = 9 rolls × 10,5m × 0,52m

= 47,25m²

Difference in areas = 47,25 – 31,43

= 15,82m²

% difference = 15.8231.43

× 100

= 50,3%

3.1 to 3.4 room Perimeter number of rolls Comments

214 19,2m 9 -

215 27m 12 -

353 26,4m 12 -

16 54m 24 Used the fact that 27m used 12 rolls and then doubled it.



4 area measurements can be used in contexts such as painting a wall. a spread rate is quoted on a tin of paint i.e. the manufacturer estimates how many litres of paint you will need to paint 1m². In this context, the length and width of the room is irrelevant and one merely needs to work out the total surface area to be painted. Wallpapering, carpeting, tiling, etc. all require one to take into consideration the dimensions of the room. all these items are sold in standardised widths and so there will inevitably be some wastage. One cannot, therefore, realistically use the area of a room to estimate the amount of material needed. the length and width of the room are far more important in these contexts.



Activity 8 — Wallpapering a room

In the previous activity we explored how the formula for area alone is not particularly useful in helping us to calculate how much carpet we need to buy to carpet a room. the same is true for wallpaper, as we will show in this activity.

1 revisiting room 226 one more time. a scale drawing of room 226 is drawn

alongside. It is further given that:• the height of the room is 2,2m;• the two doors are exactly the same

size and 2,08m tall;• the window is 1,2m high; and• the wall recess around each door

and window is 0,09m as shown in the diagram below.

1.1 taking the above into account calculate the following:

1.1.1 the surface area of the recess around each window and door to be wallpapered

1.1.2 the surface area of each door.

1.1.3 the surface area of the window.

1.1.4 the surface area of each wall.

1.2 Hence, determine the total surface area in room 226 to be covered in wallpaper

1.3 If a typical roll of wallpaper covers 5,2m2, determine how many rolls of wallpaper are needed to cover the walls of the room.

1.4 Discuss why the answer you have developed in 1.3 is unlikely to work out in reality.

worksheet 8

4,5m

4,5m

2,1m

3,0m

2,5m

0,9m

0,09m

0,09m

4,5m

4,5m

2,1m

3,0m

2,5m

0,9m

0,09m

0,09m



2 Using a table of values to determine the amount of wallpaper needed to wallpaper a room.

Wallpaper is sold in standard rolls (10,5m × 0,52m). Most wallpaper manufacturers have developed a table of values such as the one below to help people decide how many rolls of wallpaper to buy for a given project.

InstrUCtIOns FOr UsInG taBLe:• Measure the perimeter of the room, including around chimneys and other protrusions.• Measure the height of the wall to be wallpapered.• Unless there are very large windows or other areas which will not be wallpapered,

ignore these when measuring the perimeter and height.• Use the table to determine the number of rolls that are recommended and always buy a

few extra rolls if the wallpaper you are using has a very large print on it.

number of rolls of wallpaper required

Perimeter of the room

9m 10m 12m 13m 14m 15m 16m 17m 19m 21m 22m 23m 24m 26m 27m 28m 30m

Heig

ht o

f the

room

2.15 - 2.30m 4 5 5 6 6 7 7 8 9 9 10 10 11 12 12 13 132.30 - 2.45m 5 5 6 6 7 7 8 8 9 10 10 11 11 12 13 13 142.45 - 2.60m 5 5 6 7 7 8 9 9 10 11 12 12 13 14 14 15 152.60 - 2.75m 5 5 6 7 7 8 9 9 10 11 12 12 16 14 14 15 152.75 - 2.90m 6 6 7 7 8 9 9 10 11 12 12 13 14 14 15 15 162.90 - 3.05m 6 6 7 8 8 9 10 10 12 12 13 14 14 15 16 16 173.05 - 3.20m 6 7 8 8 9 10 10 11 13 13 14 15 16 16 17 18 19

2.1 By determining the appropriate dimensions, use the table above to decide on the number of rolls of wallpaper needed for room 226.

2.2 Compare the answer you developed in 1.3 with the answer developed in 2.1. Is there a large discrepancy? Discuss reasons for this.

2.3 Using your answers to 1.2 and 2.1, calculate the percentage wastage of wallpaper. 3 Use the chart to determine the number of rolls needed to wall paper the following rooms

in the conference centre/hotel – where the table cannot be used directly, describe how you used the table to assist you:

3.1 214

3.2 215

3.3 353

3.4 16

4 Discuss how the context impacts on how we use equations such as area = l × b.

worksheet 8



Activity 9 — Organising a teleconference

ABOUT THIS ACTIVITYthis activity focuses on international telecommunication. Learners will work with international time zones and calculate the best time(s) to have a teleconference with people from all over the world. they will use a world map and an information table in order to determine the times in other cities. they will also look up information in the telkom Phone Book.

this activity is aligned with unit standard 9016 and addresses aC 5,7 of sO1 and aC 8,9,10,11 of sO2.

MANAGING THIS ACTIVITYLearners will need the worksheet for this activity. there should also be a few telephone directories available for the students to look up information. It might be helpful to have a globe of the world and a torch available to use in anexplanation of time zones.

1.1 It is a service provided by telkom whereby a number of people can be connected simultaneously by telephone.

1.2 10116

1.3 One must take into account international time zones.

1.4 Yes. south africa has only one time zone, so it is the same time everywhere in south africa.

1.5 no. south africa and australia have different time zones so times will differ.

1.6.1 all places on earth do not experience night and day at the same time. the earth rotates on it own axis which means that at any one time some places will be facing the sun and be experiencing day, while others will be facing away from the sun and be experiencing night. In between the places that are experiencing midday and midnight, are places experiencing all the other times of the day and night. the world therefore has been divided into zones. these zones lie in a north-south direction (see map) and people in each zone have their watches set to the same time. all zones are set with reference to the Z zone. this is the zone that runs through the town of Greenwich in england.

1.6.2 australia has three time zones.

1.6.3 australia is a very large country from east to west. sydney will experience sunrise long before Perth so the country needs to have more then one time zone.

1.7.1 10:00 or 10am

1.7.2 5:00 or 5am

1.7.3 16:00 or 4pm

1.7.4 23:00 or 11pm the night before.

2.1.1 City Country Zone

London england Z

sydney australia K

Perth australia H

nairobi Kenya C

Washington Usa r

2.1.2 Place Times

south africa 8:00 10:00 12:00 14:00 16:00 17:00

London 6:00 8:00 10:00 12:00 14:00 13:00

sydney 16:00 18:00 20:00 22:00 24:00 1:00

Perth 14:00 16:00 18:00 20:00 22:00 23:00

nairobi 9:00 11:00 13:00 15:00 17:00 18:00

Washington 1:00 3:00 5:00 7:00 9:00 10:00



2.2 the only time that seems to be suitable is when it is 14:00 or 2pm in sa. although not all the participants are at work, at least it is a time when they would all possibly be awake. that latest time is 10pm and the earliest is 7am.

2.3 & 2.4 City SA time Time in that country Dialling code

Kinshasa 9:00 till 17:00 8:00 till 4:00 need to dial 0903#

new York 15:00 till 17:00 8:00 till 10:00 091212,646

san Francisco 17:00 till 20:00although this is outside sa work hours, it suits

the san Francisco client.

7:00 till 10:00 091415,650

Cairo 8:00 till 17:00 8:00 till 17:00 09202



Activity 9 — Organising a teleconference

some of the delegates at the conference need to speak to various international experts and ask you to organise a teleconference for them.

the following people need to be included in the discussion:• Mr smith from London• Prof. Lee from sydney• Ms thomas from Perth• Prof. Kenyata from nairobi• Dr argent from Washington

1.1 What is meant by the term “ teleconference”?

1.2 Use the telkom Phone Book to find the number you could dial in order to set up a teleconference or to find out more information about a teleconference.

1.3 What is an important factor that you need to take into account when you are organising an international teleconference?

1.4 Will the time in all parts of south africa be the same i.e. if it is 3:30pm in Cape town, will it be 3:30pm in Durban? explain your answer.

1.5 Will the time in south africa and australia be the same i.e. if it is 3:30pm in Cape town, will it be 3:30pm in Perth? explain your answer.

1.6 Look at the map below and answer the questions that follow.

1.6.1 Why do we have time zones?

1.6.2 From the map one can see that south africa has one time zone. How many time zones does australia have?

1.6.3 Why do you think australia has more than one time zone?

1.7 the countries that are in the Z zone are said to have universal time. the time in all the other zones is calculated from this time. If it is 8:00 in england, what will the time be in the countries listed below? Use the table on the map to help you.

1.7.1 south africa

1.7.2 argentinia

1.7.3 Western australia

worksheet 9



1.7.4 alaska

2.1 When setting up your teleconference you will need to take time zones into consideration. the first step is to determine in which countries the participants live.

2.1.1 Find each city on the map in the handout and write down in which country and in which time zone each city is located.

2.1.2 the teleconference must be at a time that suits all participants. However, this does not necessarily mean that all participants will be at work at that time. they might have to get up very early or stay up late at night. the following table relates the time in south africa to the time in other countries for an 8 hour work day. Copy the table and fill in the missing values.

Place Times

south africa 8:00 10:00 12:00 14:00 16:00 17:00

London

sydney

Perth

nairobi

Washington

2.2 Using the table above, find a possible south african time which would be suitable for everyone to have a teleconference. try to make it a time when the people in the other countries will be at work. Justify why you chose that particular time.

2.3 Determine the possible south african times between 8am and 5pm in which you could phone people in the following places listed below. try to make them times when the people in the other countries will be at work. If this is not possible, justify the time you have chosen.

2.3.1 Kinshasa

2.3.2 new York

2.3.3 san Francisco

2.3.4 Cairo.

2.4 Use the telekom Phone Book to determine the code that you would need to dial for each of the cities in 2.3.

worksheet 9



Activity 10 —Assessment activity:Should we use the lodge?

ABOUT THIS ACTIVITYThis is an assessment activity. It incorporates the skills learnt in the previous activities. In this activity learners have to work with scale and make accurate scale drawings of rooms. They use top views of furniture to assess how many delegates can be accommodated in a room. They will verify their fi ndings by calculating the number of delegates using formulae. The learners will also work out their own co-ordinate system to number seating places.

This activity is aligned with unit standard 9016 and addresses AC 1,2,3,4,5,6,7 of SO1 and AC 1,2,3,6,7,8,9,10,11 of SO2.

MANAGING THIS ACTIVITYLearners will need the worksheet and handout for this activity. The handout for this activity is similar to the handout for activity 5. They will also need a ruler, pencil and a pair of scissors. Coloured paper may be useful. Remind the learners to add space around the furniture arrangements before they fi t them into their scale drawings of the rooms.

1.1 No solution supplied.1.2 No solution supplied.1.3 No. The dimensions of the conference room are bigger than the meeting/dining area, yet in the fl oor plan the

conference room is much smaller. 1.41.4.1 Area of meeting/dining area = 12m × 5,5m = 66m²1.4.2 Area of conference room = 17m × 7,5m = 127,5m²1.51.5.1 No solution.1.5.2 No solution.2.1.1 8 × 7 = 56 people2.1.2 10 × 3 × 3 = 90 people, therefore the classroom arrangement can accommodate more people.2.1.3 Learners must add a circle of radius 3cm around the round table arrangement in order to give the footprint

of the space needed. Six tables can fi t into the room so the room can seat 6 × 8 = 48 people. The dining room can accommodate fewer delegates. The diagram below is drawn using a smaller scale.



2.1.4 Learners must box the table in order to give the footprint of the space needed. Six tables can fi t into the room so the room can seat 6 × 8 = 48 people. The number of delegates that can be fi tted in is the same.

2.1.5 Answers will vary for this question. Some suggested options are:

• Fifty people could easily be accommodated. You would only need one sitting for meals and the conference room is more fl exible i.e. you can change the seating arrangement depending on the requirements.

• Ninety people could be accommodated. You would need to have two sittings for meals. The conference room arrangement would be classroom style. However, you could always use both the conference room and the dining room as meeting places.

2.2.1 Classroom arrangement for conference room.

Formula I: Usable room length = 17m – 2,4m – 0,9m = 13,7m

Number of rows = 13,7m ÷ 1,35m = 10,14

Rounded down = 10 rows

Usable room width = 7,5m – 1,125m = 6,375m

Number of tables = 6,375 ÷ 1,8m = 3,5

Therefore rounded down = 3 tables

Number of chairs per row = 3 × 3 = 9

Therefore number of chairs = 10 × 9 = 90 chairs.

Formula II: Area of the room = 127,5m²

For 60 people you require 120m² of space, therefore one would try using the next category of 1,8m² per person.

Number of chairs = 127.51.8

= 70,8. Therefore number of chairs will be 70.

2.2.2 Banquet (round table) arrangement in the dining area.

Formula I: Number of tables in length = 12m ÷ 3m = 4 tables

Number of tables in width = 5,5m ÷ 3m = 1,8 tables

Rounded down = 1 table

Number of chairs in the room = 4 × 1 × 8 = 32 chairs.

Formula II: Number of chairs = 661.25

= 52,8 chairs. Rounded down = 52 chairs.

2.3 No solution supplied. The co-ordinate system used must have some kind of reasoning behind it. No solution supplied. Answer must have a valid reason.



Activity 10 — Assessment activity: Should we use the lodge?

You have been sent the floor plan of a small conference centre via the internet (see handout) and need to assess its suitability.

1.1 Find the entrance in the picture (marked a) on the floor plan and mark it with an a.

1.2 Find the outside kitchen door in the picture (marked B) on the floor plan and mark it with a B.

1.3 Do you think that the floor plan is drawn to scale? Give a reason for your answer.

1.4 Calculate the area of the following rooms:

1.4.1 the meeting/dining area

1.4.2 the conference room

1.5 Using a scale of 1:50, draw a scale drawing of the following rooms:

1.5.1 the meeting/dining area

1.5.2 the conference room

2.1 the handout for this activity is similar to the one you used in activity 5. remember to add the space needed around the furniture arrangements to the scale drawing.

2.1.1 Using the scale drawing of your conference room and the appropriate scale drawing on the handout, arrange as many chairs and tables as you can to give a herringbone arrangement. Once you are satisfied with your arrangement, stick the chairs and tables onto your scale drawing. How many delegates can you accommodate in this room with this arrangement of tables and chairs?

2.1.2 redo question 2.1.1, but this time arrange the chairs and tables in a classroom arrangement. How many delegates can you accommodate? Which arrangement could accommodate more people?

2.1.3 Using the scale drawing of your meeting/dining area and the scale drawing on your handout, arrange as many chairs and tables as you can to give a banquet (round table) arrangement. Once you are satisfied with your arrangement, stick the chairs and tables onto your scale drawing. How many delegates can you accommodate? Can the dining room accommodate more or fewer delegates than the conference room?

2.1.4 redo question 2.1.3, but this time use the banquet I arrangement. Can you fit more or fewer delegates into the dining room with this arrangement?

2.1.5 Use the information gained from the calculations you made and estimate the number of delegates you think could be accommodated at this centre. Discuss how you came to that number and suggest ways in which you could increase that number.

2.2.1 Verify your answer to 2.1.2 by using formulae I and formulae II on the handout. the height of the room is 2,4m. Which formulae gave the number of delegates that was closest to your answer in 2.1.2?

2.2.2 Verify your answer to 2.1.3 by using formulae I and formulae II on the handout. Which formula gave the number of delegates that was closest to your answer in 2.1.3?

2.3 You want to seat each delegate in a particular seat. Determine a co-ordinate system for each of the arrangements that you have drawn and fill it in on your diagrams. explain how your co-ordinate systems work.

2.4 If you had a delegate who was in a wheelchair, mark a suitable place or places on your four diagrams where he/she would be most comfortable. explain why you chose those particular seats.

worksheet 10



Different furniture arrangements for conference rooms

Classroom Lecture theatre

Banquet I Banquet II

Herringbone Boardroom/Hollow square

U-shape

HANDOUT 10.1



FOrMULae I

the formulae below are based on formulae published on the following website: http://www.pcma.org/templates/Conferon/charts/Ch7_2.htm

For the purpose of this activity we will assume that the tables and chairs used have the following dimensions (as these change so the formulae will have to be adjusted):

Conference table: rectangular: 180cm × 45cm × 76cm

round: 152cm diameter × 76cm seats; 8 people

Chairs: 50cm (front to back) × 45cm (side to side)

Calculating the capacity of function rooms:

Classroom-style setupstep 1: Determine the number of rows that can be accommodated:

nOte: For the tables we are using, the ideal gap between the tables is 90cm.

• take the clear room length (determined in the previous activity and provided in the table at the start of the activity) and subtract the space between the screen and the front row (the minimum distance should be the height of the room, though more is desirable) and the space between the back wall and back row (minimum of 90cm).

• Divide by the distance allocated to each row measured from the front of the table to the front of the next table.


eXaMPLe: 9m (length of room 215) – 2,4m (room height) – 0,9m (distance from back wall = 5,7m (usable room length); 5,7 ÷ 1,35m = 4,22; rounded down = 4 rows.

step 2: Determine the number of chairs that can be placed in each row:

• take the clear room width (determined in the previous activity and provided in the table at the start of the activity) and subtract space for aisles (normally about 15%).

• Divide by the length of the tables being used.

• round the resulting number down to the nearest number of tables.

• Multiply by the number of chairs that can be placed at each table.

eXaMPLe: 4,5m (width of room 215) – 70cm (15% of 4,5) = 3,8m (usable room width); 3,8 ÷ 1,8 = 2,11; rounded down = 2 tables → 6 chairs per row.

step 3: Determine the number of chairs in the room:

• Multiply the number of rows by the number of chairs in each row.


handout 10.2



Banquet-style setup (round tables)It is customary to leave a gap of 75cm all around a table with a diameter of 152cm. this allows both enough space for the chairs and for people, including waiters, to move between the chairs.

step 1: Determine the number of tables that can be accommodated

• take the clear room length (determined in the previous activity and provided in the table at the start of the activity) and divide by the diameter of the table plus 1,5m. round the result down to the nearest table.

• take the clear room width (determined in the previous activity and provided in the table at the start of the activity) and divide by the diameter of the table plus 1,5m. round the result down to the nearest table.

• Multiply the two numbers together to determine the number of tables.

step 2: Determine the number of chairs in the room:

• Multiply the number of tables by the number of chairs at each table.

eXaMPLe: 9m (length of room 215) ÷ 3m = 3 tables. 4,5m (width of room 215) ÷ 3m = 1,5; rounded down = 1 table, ∴ 3 tables with 8 chairs per table = 24 chairs.

FORMULAE IIthe formulae below are based on formulae published on the following website: http://www.pcma.org/templates/Conferon/charts/Ch7_2.htm

to determine how large a room should be for a given group of people and a given setup, multiply the number of people by the values below:

Classroom style:

• 2m² per person for groups of less than 60 people

• 1,8m² per person for groups of 60 to 300 people

• 1,6m² per person for groups of more than 300 people

theatre style:

• 1,2m² per person for groups of less than 60 people

• 1m² per person for groups of 60 to 300 people

• 0,9m² per person for groups of more than 300 people

Banquet style:• 1,25m² per person

Boardroom or Hollow square style:• 2,8m² per person

U-shape style:3,25m² per person

handout 10.2



HANDOUT 10.3





handout 10.4

AB

unit 3 measurement - brombacherbrombacher.co.za/.../downloads/2011/06/l4-unit-3-measurement.pdf ·...

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