Unit 1. Measurement and shape

Transcription

1 Mathematical Literacy Unit 1 NQF LEVEL 3 Measurement and shape Generic Business Administratin

2 t Getting the meeting n 2 time Decrating the new ffice 3 kitchen Giving directins 1 Making table clths 4 and curtains MEASUREMENT AND SHAPE Buying urns 5 Assessment 8 Making 6 flded paper shelving patterns frm 7 Traditinal hme decratins UNIT 1 MEASUREMENT AND SHAPE 1.2

3 Overview Unit Standard has tw Specific Outcmes: SO 1 fcuses n measurement. SO 2 fcuses n shape. This unit uses a number f different cntexts t develp learners understanding f measurement and shape including: Reading infrmatin frm tables Knwing what is the apprpriate unit f measurement within a particular cntext Chsing the apprpriate measuring instrument fr a particular prblem Thinking abut the mst apprpriate way f measuring Thinking abut hw the cntext impacts upn the reasnableness f the measurement reading, calculatin r slutin. Cnverting between units f measurement Using estimatin techniques apprpriate t the cntext Calculating areas, perimeters and vlumes and hw cntexts impact n ne s apprach Develping mdels t describe situatins, t analyse them and t make predictins abut them Hw cntext can impact upn decisins abut what algrithms t use in calculatins Using the available technlgy t slve prblems in particular electrnic calculatrs Explaining the chice f algrithm and the prcedures used Calculating effectively, efficiently and crrectly Reading rad maps Understanding scale in sketches and maps Using scale bars and rati t calculate the actual size and distances. Symmetry and transfrmatin f shapes In additin t develping the mathematical skills f learners, this unit is als intended t give learners an pprtunity t develp an understanding f: Rad maps hw t read and interpret them and use them t calculate distances Giving directins including the drawing f simple maps Planning travel and meeting arrangements Calculating the requirements and csts f fitting a new ffice kitchen. The unit cnsists f eight activities f which ne is an Assessment. Mathematical literacy invlves using nes knwledge f shape, space, measurement, numbers and data t make sense f the wrld. It als invlves using ne s knwledge f particular cntexts t make sense f and increase ne s knwledge f shape, space, measurement, numbers and data. There are several key issues in measurement and shape, and the activities in this unit attempt t address them in ways that are relevant t business administratrs. Unit utcmes The fllwing Unit Standards, Specific Outcmes and Assessment Criteria are addressed by this unit: Measure, estimate and calculate physical quantities and explre, describe, represent, interpret and justify gemetrical relatinships in 2 & 3 dimensinal space relevant t life r wrkplace cntexts (US 14108). Estimate, measure and calculate physical quantities t slve prblems in practical situatins (SO1). Scales n measuring instruments are read crrectly (AC1). Quantities are estimated t a tlerance acceptable justified in the cntext f the need (AC2). The apprpriate instrument is chsen t measure a particular quantity (AC3). Quantities are measured t within the last step f the instrument. (AC4). Calculatins are carried ut crrectly (AC5). Symbls and units are used in accrdance with SI cnventins and as apprpriate t the given / specified situatin (AC6). Explre, analyse and critique, describe and represent, interpret and justify gemetrical relatinships and cnjectures t slve prblems in tw and three dimensinal gemetric situatins (SO2). Descriptins are based n a systematic analysis f the shapes and reflect the prperties f the shapes (AC1). Descriptins include quantitative infrmatin apprpriate t the situatin and need (AC2). Cnjectures, as apprpriate t the situatin, are based n well-planned investigatins f gemetrical prperties (AC3). Representatins f the prblems are cnsistent with and apprpriate t the prblem cntext. The prblems are represented cmprehensively and in mathematical terms (AC4). Results are achieved thrugh efficient and crrect analysis and the manipulatin f representatins (AC5). Prblem slving methds are presented clearly, lgically and in mathematical terms (AC6). Slutins are crrect and are interpreted and validated in terms f the cntext f the prblem (AC7). UNIT 1 MEASUREMENT AND SHAPE 1.3

4 Business Administratin is a qualificatin that needs t help learners develp a set f general skills as well as the flexibility t apply these in a range f cntexts. In this unit we prvide learners with different cntexts mdeled n real wrkplace cntexts. We help learners t understand and think there way int each f the cntexts befre starting the activities. This unit develps the skills required t achieve the Assessment Criteria f Unit Standard Giving directins In this activity students read rad maps f a city and use the key t calculate distances. They draw up a set f directins which includes a simple map, they then think in general abut what they need t include when they give peple directins t get t a venue. Reading maps includes the skill f lking up a rad name in an alphabetical index, finding the crrect blck (cell) in the rws and clumns and understanding that a map is a styalised view frm abve. 2 Getting t the meeting n time This activity extends students map reading skills. Students are again asked t think abut directins and scale but nw als distance, speed, time. They are asked t think abut hw the time f day affects traffic flw and traveling time. They are asked t read aerplane timetables and t bk a flight. They are asked t schedule a meeting that best suit a persn wh has t fly in frm anther city and leave n the same day. Usually business administratrs will get smene else t find the mst cnvenient flight t bk, but it is useful fr them t have an understanding f what things limit the pssible suitable flights. 3 Decrating the new ffice kitchen In this activity we use the cntext f a new ffice kitchen t ask students t think abut calculating areas and perimeters f rectangular shapes. Learners are asked t wrk ut hw many wall and flr tiles f different sizes they will need t tile specific areas. They are als asked t calculate the csts f the different tiles. 4 Making table clths and curtains fr the new kitchen This activity uses extend bth the cntext f decrating a new ffice kitchen and the cncepts f area and perimeter. In this activity learners are asked t calculate hw much material and fringing they wuld need t make circular table clths and curtains fr a new ffice kitchen. They are asked t think abut hw the cntext impacts upn hw accurate their answers need t be and als hw they apply the cncepts f area and circumference. 5 Buying urns In this activity learners wrk with capacity and vlumes f cylindrical shapes. They use what they knw abut the area f a circle and see hw this relates t the vlume f cylinders. They als draw urns frm different views and use this t find ut infrmatin abut what it is the limits the least amunt f water that an urn can hld. They are asked t cnvert between different metric units f vlume and capacity. 6 Making shelving patterns frm flded paper One f the range statements in this unit standards states that learners shuld investigate symmetry and tessellatins in the cntext f artifacts and architecture. In this activity and the next activity we the cntext planning fr husing cnference. Students examine the patterns in traditinal paper shelving. Learners make their wn patterns by flding and cutting paper. They find ut mre abut reflected patterns. They then use what they knw t make paper chains and cards fr an ffice party. 7 Traditinal hme decratins In this activity the cntext f the husing cnference is extended. Students examine different kinds f traditinal external decratins n hmes. In this activity they fcus n hw patterns are made by placing a key element f the pattern in a variety f psitins. Learners explre the fllwing ways f changing the psitin f a shape: turning the shape (rtatin), flipping the shape (reflectin), sliding the shape (translatin). Learners analyse patterns using this language. They als make their wn patterns by making these mvements with shapes. 8 Assessment The assessment fcuses n students knwledge and skills arund pattern and design. In particular is assesses their ability t see the basic element in a design and hw this element has been mved (rtated, reflected r translated) t make up the pattern. It als assesses students ability t recgnise symmetry. UNIT 1 MEASUREMENT AND SHAPE 1.4

5 14108 Measure, estimate, calculate physical quantities, explre, describe and represent, interpret, justify gemetrical relatinships in 2 & 3-dimensinal space relevant t the life r wrkplace f the cmm SO1 ACTIVITY Measure, estimate, and calculate physical quantities in practical situatins. AC1 Scales n the measuring instruments are read crrectly. ü ü ü SO2 AC2 Quantities are estimated t a tlerance justified in the cntext f the need. ü ü ü ü ü AC3 The apprpriate instrument is chsen t measure a particular quantity. ü ü ü AC4 Quantities are measured crrectly t within the least step f the instrument. AC5 Calculatins are carried ut crrectly. ü ü ü ü ü ü AC6 Symbls and units are used in accrdance with SI cnventins and as apprpriate t the situatin. Give pinins n the implicatins f the mdelled data fr the required purpse. AC1 AC2 AC3 AC4 AC5 AC6 AC7 Descriptins are based n a systematic analysis f the shapes and reflect the prperties f the shapes accurately, clearly and cmpletely. Descriptins include quantitative infrmatin apprpriate t the situatin and need. Cnjectures as apprpriate t the situatin, are based n well-planned investigatins f gemetrical prperties. Representatins f the prblems are cnsistent with and apprpriate t the prblem cntext. The prblems are represented cmprehensively and in mathematical terms. Results are achieved thrugh efficient and crrect analysis and manipulatin f representatins. Prblem-slving methds are presented clearly, lgically and in mathematical terms. Slutins are crrect and are interpreted and validated in terms f the cntext f the prblem. ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü UNIT 1 MEASUREMENT AND SHAPE 1.5

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7 1 Giving directins Assisting with travel arrangements is ften an imprtant part f business administratrs wrk. In this activity we ask learners t cnstruct directins frm the airprt. Giving directins always seems like an easy task, but fllwing directins is ften difficult. In this activity we hpe t give learners practice in writing ut directins and thinking abut hw t give gd written directins. ABOUT THIS ACTIVITY Learners are asked t read rad maps. This includes finding streets in the index (which gives practice in negtiating ne s way arund an alphabetical listing), and understanding hw the index states n what page and in which cell t find the street. Then learners need t find the crrect cell n the crrect page. Wrking with rad maps gives learners practice in using a grid and the assciated language. Learners are then asked several questins abut the maps befre being asked t draw a simple map and prvide directins. Reading maps entails interpreting a view frm abve with particular stylised cnventins. This activity prepares learners t meet the fllwing utcmes f Unit Standard 14108: SO 1: Measure, estimate and calculate physical quantities in practical situatins: AC 1, 2, 3, 5, 6 SO 2: Explre, describe and represent, interpret and justify gemetrical relatinships: AC 2, 3, 4, 5, 6 MANAGING THIS ACTIVITY The maps and infrmatin that learners need are prvided n the handut. Hwever, it wuld be better fr them t lk up the infrmatin in a map bk as this entails finding the pages in the index and mving frm ne page t anther. In the apprpriate answers we prvide further guidance abut what the key learning issues are and hw t assist learners with these. 1.1 The keyplan is n page 1 f the handut, page ii f the map bk. (a) The airprt is n page 19 f the map bk. Learners can find this n the keyplan. (b) Mwbray is n pages 15 and 16 f the map bk. Learners can find this n the keyplan. 1.2 It is usually easier t lk up the rad in the index at the back f the bk. The index tells yu in what cell yu will find the rad fr which yu are lking. Check that learners knw hw t use an alphabetical listing. Sme learners may knw t lk up smething by its first letter but nt cnsidering finding their way arund the listing by lking at the secnd and third letters f the wrd. In this example the R s appear n pages 80 t 82. It is quicker t scan the list fr R than t start reading frm the beginning f the list n page 80. (a) The index tells yu t find Rseberry Rad n page 16 and in cell number CD 31 f the grid. This is in the tp left hand crner f the grid n page 31. Check that learners knw the language f grids and understand what cells, rws and clumns mean in the cntext f a grid. Like many wrds they have different meanings in ther cntexts. Learners may think abut the nn-mathematical meanings when they hear the wrds. Check als that learners understand the cnventin f rad map bks which give the page number in bld fllwed by the cell number. Yu may want t ask learners t check whether this is the same r different in ther radmap bks and t find the place where the cnventin is explained in a particular map bk. 1.3 In this questin we ask learners t fcus n describing the part f the rute n the freeway, which includes thinking abut the distances befre reaching key landmarks, and imprtant rad signs and rad names. (a) Yu turn nt the N2. (b) The legend is n the tp left hand crner f page 11 in the map bk and page 1 f the handut. (c) 1 cm is 2 kilmetres. Many learners may find it easier t measure 1 cm n the scale bar and t see that this shws 2 km than t wrk with the rati written in figures. UNIT 1 MEASUREMENT AND SHAPE 1.7

8 (d) It is useful t be able t tell peple hw far they shuld expect t travel befre lking ut fr a key landmark. An example f this is given in questin belw. (e) They can travel abut rughly 10 km t 12 km n the N2 befre turning ff. If they had lcal knwledge f Cape Twn they wuld be lking fr the Raapenberg Rad / Mwbray / Pinelands ff ramp. 1.4 Yu may want t talk with learners abut checking that when they give directins they are certain that the signbard explains a rad r ff-ramp in the way in which they think it des. This is particularly imprtant when giving directins t peple wh d nt knw the area and are nt able t translate between what the signbard says and what the directins may state e.g. Wynberg ff ramp frm M3 is marked as Travat Link. This may make sme sense t sme peple frm Cape Twn but nt necessarily t smene frm Phalabrwa. (a) Smetimes rad signs will use ne name and smetimes they will use anther. Travellers need t be reassured that they are n the crrect rad. Fr example, if they think they turned nt the N2 but a signbard suddenly appears that mentins Settlers Way, are they still n the crrect rad? (b) The N2 in this particular sectin is als called Settlers Way. (c) The M52 is knwn as Raapenberg Rad in that sectin. (d) Yu turn left int Klipfntein Rad. If yu turn right the rad is called Durban Rad. (e) Yu can find ut that this rad is called Durban Rad n page 15 f the map bk. This is shwn n the left hand side brder f page It will be easier fr learners t describe the rute verbally than t write it dwn. Describing it t a friend helps t clarify ne s thughts. The pairs shuld assist each ther t imprve their directins. 1.6 Here is ne ptential rute descriptin: Lk fr the N2 t Cape Twn rad signs and ff-ramp n the Airprt Apprach Rad. This sectin f the N2 is called Settlers Way. Yu will drive alng the N2 fr abut 10 km 12 km. During this time yu will pass (amngst ther things): infrmal settlements, the Heideveld, Mdderdam Rad (M10) ff-ramp, the Vanguard Drive ff-ramp (M7) the Jan Smuts (M17) and Bunga Avenue ff-ramps as well as a sewerage plant n the left and cling twers n the right. After abut 10 km lk fr the Raapenberg Rad / Mwbray ff-ramp t the left. Turn left int Raapenburg Rad at the rbts. Cntinue alng Raapenberg Rad until yu get t the next set f traffic lights. Turn right int Klipfntein Rad (it culd still be called Durban Rad at this pint). Turn left int the secnd rad yu cme t and cntinue fr 2 blcks. Yu will find N.13, Muntain View Bed and Breakfast n yur right hand side. Ask learners t read their directins t each ther. The class shuld chse the clearest and simplest directins. Discuss the principle f mre is less in this srt f situatin it is ften easier t fllw simple directins than directins that give t much detail. Learners maps shuld indicate whether they are drawn t scale r nt. 1.7 It is useful t have the telephne number f the place f accmmdatin in case they get lst. Then they can phne and ask fr further directins. They may als be delayed and need t tell peple when t expect them. This questin is nly included as a practical task learners will need t be given a fax number t use. 1.8 Learners may be able t give gd directins but find it hard t generalize abut what the key features f gd directins/ maps are. Often it is mre difficult fr learners t wrk frm the general t the specific than it is fr them t wrk frm the specific t the general. Yu may like t start by asking learners t give directins t smewhere nearby e.g. the clsest statin. After listening t several examples ask learners what the key features f gd directins are: they shuld talk abut landmarks and ways f estimating distances, fr example a certain number f blcks (if walking), side streets r buildings r hw far in kilmetres r apprximately hw lng it will take t get there. Signbards are excellent landmarks. UNIT 1 MEASUREMENT AND SHAPE 1.8

9 Sme imprtant features f gd directins are: T mentin imprtant landmarks (clearly marked buildings r institutins whse structure makes their functin bvius, like msques and churches and schls, as well as sign bards and turn ffs) that the persn will pass n the way, what places r features they can lk ut fr befre cming t an ff-ramp, an upcming street int which they must turn etc. Indicate hw far they shuld cntinue n a particular rad e.g. a certain number f kilmetres, a particular amunt f time, hw many blcks r turn ffs r side streets they will pass. This helps peple fllwing the directins t knw that fr a while they can relax and nt be n the lkut fr the next turning. It is imprtant t let peple knw if this is apprximate e.g. yu will g past streets and Y amngst ther streets, yu will travel fr abut N km, r whether the infrmatin is exact i.e. yu will nly crss ver 3 streets, r the fllwing 2 intersectins, r it is exactly 9 km. Give them all the streets that they will need t turn int and whether they need t turn left r right. UNIT 1 MEASUREMENT AND SHAPE 1.9

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11 1 Giving directins Ms Mdishane is cming fr a jb interview at yur cmpany. She is flying frm Durban t Cape Twn and will be staying at the Muntain View Bed and Breakfast. Yu have been asked t draw a map and send her written directins frm the Cape Twn Internatinal Airprt t the place she will be staying. Yu need t use a rad map t find the best rute frm the airprt t the Muntain View Bed and Breakfast. The handut prvides sample pages frm a Cape Twn rad map. Hwever, it wuld be better if yu culd bring a real map bk int class t lk up the infrmatin. The address fr the Muntain View Bed and Breakfast is: 13 A Rseberry Rad Mwbray Phne: Find the keyplan t the map pages n the handut On what page will yu find the airprt? On what page will yu find Mwbray? 1.2 Nw that yu knw n what page Mwbray is, yu need t find Rseberry Rad n that page Use the index t the map bk supplied t determine the page number and cell number in which Rseberry Rad can be fund. 1.3 Getting frm the airprt t Mwbray: What is the first rad yu wuld turn int when yu leave the Airprt Apprach Rad? Lk back at the keyplan. Where n the page d yu find the legend? cm n the map crrespnds t what distance in reality? Why is it useful t be able t knw distances when giving directins? Hw far alng the N2 d yu need t travel befre turning ff it? 1.4 Landmarks are imprtant in giving directins. Street names and rad signs are a type f landmark that is very useful when giving directins. But there are als ther imprtant landmarks. Sme f these are marked n rad maps but thers are nt. It is als imprtant t check what the rad signs say as they smetimes explain things in unexpected ways Smetimes rads change names at sme pint. Why is it imprtant t give peple all the names f the rad? In the sectin f the N2 that yu need t describe fr this rute, it is als knwn by anther name. What is that name? What is the rad name fr the M52 in the sectin f the map yu will be describing? What is the name f the rad yu turn int at the end f the M52? This rad has ne name if yu turn left and anther name if yu turn right. Give bth names On what page in the map bk will yu find the secnd name f the rad yu mentined abve in questin 1.4.4? 1.5 Tell a partner hw yu wuld get frm the airprt t Muntain View Ldge. Listen t his/ her directins and use it t imprve yurs. 1.6 Nw write dwn the directins and draw a map. 1.7 Why is it useful t put the telephne number f the Bed and Breakfast n the directins? Fax the map and directins t Ms Mdishane. 1.8 Write a list f the key pints yu need t keep in mind when yu give smene directins. WORKSHEET 1 UNIT 1 MEASUREMENT AND SHAPE 1.11

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