Mathematical Studies and Applications: Mathematics, Business Studies

Transcription

1 POST-PRIMARY Mathematical Studies ad Applicatios: Mathematics, Busiess Studies Guidelies for Teachers of Studets with MILD Geeral Learig Disabilities

2 Cotets Itroductio 3 Approaches ad methodologies 4 Exemplars 20 Appedix 151

3 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Itroductio These guidelies are desiged to support teachers of studets with mild geeral learig disabilities who are accessig the juior cycle curriculum i the area of Mathematics. They are part of a suite of guidelies produced by the Natioal Coucil for Curriculum ad Assessmet with a focus o special educatioal eeds. Each set of guidelies correspods to a area of experiece of the Juior Cycle curriculum ad offers exemplars of good classroom practice i support of the kowledge ad skills associated with that area of experiece. These guidelies are is desiged to support the teacher of Mathematical Studies ad Applicatios for studets with special educatioal eeds, withi the cotext of a whole school pla. I additio to the guidelies preseted here, similar materials have bee prepared for teachers workig with studets accessig the Primary School Curriculum. Cotiuity ad progressio are importat features of the educatioal experiece of all studets, but they are particularly importat for studets with special educatioal eeds. Therefore, all the exemplars preseted here iclude a referece to opportuities for prior learig i the Primary School Curriculum. The exemplars have bee prepared to show how studets with mild geeral learig disabilities ca access the curriculum through differetiated approaches ad methodologies. It is hoped that these exemplars will eable teachers to provide further access to the other areas of the curriculum. A rage of assessmet strategies is idetified i order to esure that studets ca receive meaigful feedback ad experiece success i learig.

4 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Approaches ad methodologies I Approaches ad Methodologies idividual differeces are emphasised, ad potetial areas of difficulty ad implicatios for learig are outlied ad liked with suggestios for approaches ad methodologies for classroom use. Idividual differeces i talets, stregths, ad eeds All studets will beefit from a variety of teachig styles ad classroom activities. Studets with mild geeral learig disabilities will beefit particularly if the teacher is aware of their idividual talets, stregths, ad eeds before embarkig o a ew activity. Cosultatio ad/or ivolvemet i the Idividual Educatio Plaig process as well as teacher observatio will assist the teacher of Mathematical Studies ad Applicatios i orgaisig a appropriate learig programme for a studet with mild geeral learig disabilities. Such a approach will assist the teacher i selectig suitably differetiated methods for the class. If learig activities are to be made meaigful, relevat, ad achievable for all studets the it is the role of the teacher to fid ways to respod to that diversity by usig differetiated approaches ad methodologies. This ca be achieved by esurig that objectives are realistic for the studets settig short ad varied tasks esurig that the learig task is compatible with prior learig providig opportuities for iteractig ad workig with other studets i small groups allowig studets to sped more time o tasks orgaisig the learig task ito small stages esurig that the laguage used is pitched at the studets level of comprehesio ad does ot hider uderstadig the activity usig task aalysis i outliig the steps to be leared/completed i ay give task modellig task aalysis by talkig through the steps of a task as it is beig doe posig key questios to guide studets through the stages/processes, ad to assist i self-directio ad correctio

5 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY usig graphic symbols as remiders to assist studets uderstadig of the sequece/steps i ay give task/problem creatig a cogeial learig eviromet by usig cocrete ad, where possible, everyday materials, ad by displayig word lists, lamiated charts with pictures. It is importat to teach mathematical laguage actively to the studets with mild geeral learig disabilities ad to reiforce it o a daily basis, sice they may have geeral laguage difficulties. A mathematical dictioary of words, symbols, ad diagrams ca be kept by the teacher ad by the studets themselves ad ca be preseted as a wall chart display. Mathematical Laguage Mathematics should be see as a laguage with its ow vocabulary of both words ad symbols. May studets cofuse mathematical laguage with ordiary laguage. They say He s bigger tha me whe they mea older, or My table is loger tha his whe they mea wider. It is importat to teach this laguage actively to the studets ad to reiforce it o a daily basis. Studets will eed to be exposed to mathematical laguage ad have it reiforced at a receptive level i a variety of situatios before they will develop the ability to use it themselves. The vocabulary of mathematics, symbols, ad tools are used i particular circumstaces. I geeral the studet is ulikely to hear or read much mathematical laguage outside the classroom. The teacher, as the mediator betwee the studet ad the world of mathematics, eeds to examie the classroom use of mathematical laguage carefully. Is it cosistet, accurate, ad uambiguous? Will studets experiece the same use of laguage as they move from oe class to aother? Are studets able to use appropriate mathematical laguage precisely? Ca studets relate some mathematical laguage to real-world situatios? Such errors ca be avoided if a rage of differet examples is used to explai a cocept. For example, if a studet is taught that Figure 1 is a right-agled triagle ad promptly labels Figure 2 a left-agled triagle the presetatio of a rage of triagles i differet orietatios ca help correct the miscoceptio. Figure 1 Figure 2 Teachers eed to be aware of the dager of usig mathematical tricks ad short cuts. Certai phrases have become commo i the mathematics classroom, particularly i the areas of arithmetic ad algebra, but they ofte serve to coceal the cocept behid what is occurrig. Laguage that describes trasformatios i terms of the surface structure oly should be avoided, because it focuses attetio o the form rather tha the meaig which gives rise to the trasformatio. Examples of this would be: Take it over to the other side ad chage the sig. Cross multiply. Move the decimal poit over. Tur it upside dow ad multiply. Collect all the x s o oe side of the equatio. Always do to the top what you do to the bottom. To multiply by te add a ought. These descriptios tell someoe oly what to do, with the result that there is little impetus to examie them to see why they might be helpful. Cosistecy of approach is vital. It is importat that all teachig staff who are i cotact with the studet ad parets are aware of the termiology beig used. For example, where appropriate plaig has occurred the mathematics teacher ca use the laguage of measuremet (legth, perimeter, area, loger, shorter, etc.) while at the same time the Eglish teacher ca adopt reiforcemet activities that icorporate the same words ad the sciece ad/or woodwork teacher ca egage the studets i practical measurig activities. Parets ca also be ecouraged to use the words at home. Keepig parets iformed of the words beig used ad the importace of usig them frequetly will help the studet to use them i real cotexts.

6 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY The followig is a example of a ote that could be set to parets: This week s keywords i mathematics are: measure, size, legth, distace, uits, cetimetre, metre, kilometre, loger, shorter, how log? Please use them ofte ad ecourage your child to use them i appropriate situatios. Studets may have difficulties with mathematical symbols. Charts i the classroom showig the symbol, the word, a example, ad a diagram ca help to reiforce a correct iterpretatio of a symbol. Where possible a real-world lik to the symbol should also be icluded. Studets ca build up a dictioary of symbols as they progress through the course. Symbol Word Example Diagram Real-world itersectio A B={2,3} parallel X Y A road itersectio is where two roads cross each other. Trai tracks go o without ever meetig. Backgroud to the Juior Certificate Foudatio Level mathematics course These guidelies are writte i the cotext of the area of experiece Mathematical Studies ad Applicatios as outlied i the Juior Cycle Review (1999). The topics referred to i the exemplar material are draw from the foudatio level of the Juior Certificate mathematics course. Liks to the relevat primary school topics ad the correspodig statemets i the Juior Certificate School Programme are metioed. This sectio outlies the ratioale, aims, ad cotet of the foudatio level mathematics course. The foudatio level Juior Certificate mathematics course is desiged for studets who are ot ready for, or who are usuited to the ordiary level course. Studets may ot be ready to deal with some of the more abstract mathematical cocepts; they may be fidig the trasitio from primary to post-primary school particularly difficult; or they may have learig styles that are ot met by the traditioal approach at post-primary level. This challeges teachers to exted ad diversify their teachig styles. These studets still eed to lear mathematics to help them i everyday life (social mathematics), further study or traiig (vocatioal mathematics), or perhaps to ehace their thikig skills ad problem solvig skills. The foudatio level course is desiged to help the studet to costruct a clearer kowledge of basic mathematics develop improved skills i basic mathematics develop a awareess of the usefuless of mathematics feel she/he is makig progress through the itroductio of ew material egage i a rage of learig styles through, for example, the visual, spatial, ad umerical aspects of mathematics.

7 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY The particular target group may respod well to activities that improve studets self-cofidece (I ca do mathematics) The assessmet objectives, also stated i the syllabus, deal with mathematical kowledge, uderstadig, ad applicatio, ad with the studet s psychomotor skills ad the ability to commuicate what they are learig. improve studets cofidece i the subject (mathematics makes sese, mathematics is useful) support the acquisitio ad cosolidatio of fudametal skills embed mathematics i meaigful cotexts create opportuities for studets to experiece success create opportuities for studets to reflect o their ow experiece ad performace. The cotet of the Primary School Curriculum is take as the prerequisite for studets followig the foudatio level course. As will be see from the exemplars that follow, may of the primary strads have bee revised ad treated i greater depth. I this way there is a atural cotiuity from the primary curriculum to the post-primary curriculum. The specific aims of the foudatio level course, as stated i the syllabus, are that the course will provide studets with a uderstadig of the basic mathematical cocepts ad relatioships cofidece ad competece i basic skills the ability to solve simple problems the experiece of followig clear argumets ad of citig evidece to support their ow ideas a appreciatio of mathematics both as a ejoyable activity through which they experiece success, ad as a useful body of kowledge ad skills.

8 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Outlie of the course This table outlies the course cotet uder each topic. For more detail refer to the Juior Certificate Mathematics syllabus ad the Juior Certificate Guidelies for Teachers: Mathematics. These are accessible o Topic Cotet details Sets Number systems 1. Listig of elemets of a set. Membership of a set defied by a rule. Uiverse, subsets. Null set (empty set). Equality of sets. 2. Ve diagrams. 3. Set operatios: itersectio ad uio (for two sets oly), complemet. 4. Commutative property for itersectio ad uio. 1. The set N of atural umbers. Order (<, <, >, >). Idea of place value. Sets of multiples. Lowest commo multiple. The operatios of additio, subtractio, multiplicatio ad divisio i N where the aswer is i N. Meaig of a for a, N, = 0. Evaluatio of expressios cotaiig at most oe level of brackets. Examples: (4 1) x 3 3(14 5) (7 + 2) Estimatio leadig to approximate aswers. 2. The set Z of itegers. Positioal order o the umber lie. The operatio of additio i Z. 3. The set Q + of positive ratioal umbers. Fractios: emphasis o fractios havig 2, 3, 4, 7, 8, 16, 5, 10, 100 ad 1000 as deomiators. Equivalet fractios. The operatios of additio, subtractio ad multiplicatio i Q +. Estimatio leadig to approximate aswers. Fractios expressed as decimals; for computatios without a calculator, computatio for fractios with the above deomiators excludig 3, 7 ad 16. Decimals: place value. The operatios of additio, subtractio, multiplicatio ad divisio. Roudig off to ot more tha three decimal places. Estimatio leadig to approximate aswers. Percetage: fractio to percetage. Suitable fractios ad decimals expressed as percetages. Example: 32 ; 32% 100 Equivalece of fractios, decimals ad percetages. Example: 42 ; 0.42; 42% Squares ad square roots. 5. Commutative property. Priority of operatios.

9 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Applied arithmetic ad measure 1. Bills: shoppig; electricity, telephoe, gas, etc. Value added tax (VAT). Applicatios to meter readigs ad to fixed ad variable charges. Percetage profit: to calculate sellig price whe give the cost price ad the percetage profit or loss; to calculate the percetage profit or loss whe give the cost ad sellig prices. Percetage discout. Compoud iterest for ot more tha three years. Calculatig icome tax. 2. SI uits of legth (m), area (m 2 ), volume (m 3 ), mass (kg), ad time (s). Multiples ad submultiples. Twety-four hour clock, trasport timetables. Relatioship betwee average speed, distace ad time. 3. Calculatig distace from a map. Use of scales o drawigs. Statistics ad data hadlig 4. Perimeter. Area: square, rectagle, triagle. Volume of rectagular solids (i.e. solids with uiform rectagular cross-sectio). Legth of circumferece of circle = π. Legth of diameter Use of formulae for legth of circumferece of circle (2πr), for area of disc (i.e. area of regio eclosed by circle, πr 2 ). Use of formula for volume of cylider (πr 2 h). 1. Collectig ad recordig data. Tabulatig data. Drawig ad iterpretig pictograms, bar-charts, pie-charts (agles to be multiples of 30 ad 45 ). Drawig ad iterpretig tred graphs. Relatioships expressed by sketchig such graphs ad by tables of data; iterpretatio of such sketches ad tables. 2. Discrete array expressed as a frequecy table. Mea ad mode.

10 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Algebra 1. Formulae, idea of a ukow, idea of a variable (iformal treatmet). Evaluatio of expressios of forms such as ax + by ad a(x + y) where a, b, x, y N; evaluatio of quadratic expressios of the form x 2 + ax + b where a, b, x N. Examples: Fid the value of 3x + 7y ad of 6(x + y) for give values of x ad y. Fid the value of x 2 + 5x +7 whe x = Use of associative ad distributive properties to simplify expressios of forms such as: a(x ± b) + c(x ± d) x(x ± a) + b(x ± c) where a, b, c, d, x N. Examples: 3(x 2) + 2(x + 1) x(x + 1) + 2(x + 2) Relatios, fuctios ad graphs 3. Solutio of first degree equatios i oe variable where the solutio is a atural umber. Examples: Solve 3x + 4 = 19. Solve 4(x 1) = Couples. Use of arrow diagrams to illustrate relatios. Example: is greater tha 2. Plottig poits. Joiig poits to form a lie Drawig the graph of forms such as y = ax + b for a specified rage of values of x, where a, b N. Simple iterpretatio of the graph. Example: Draw the graph of y = 3x + 5 from x = 1 to x = 6.

11 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Geometry 1. Sythetic geometry: Prelimiary cocepts: The plae. Lie ab, lie segmet [ab], ab as the legth of the lie segmet [ab]. Agle; amig a agle with three letters. Straight agle. Agle measure; abc as the measure of abc. Acute, right ad obtuse agles. Parallel lies; perpedicular lies. Vertically opposite agles. Triagle (scalee, isosceles, equilateral), quadrilateral (covex), parallelogram, rectagle, square. Practical, ituitive approach, for example usig drawigs ad paper-foldig. For costructios, the use of compasses, set squares, protractor, ad straight-edge are allowed uless otherwise specified. Use of geometrical istrumets ruler, compasses, set squares ad protractor to measure the legth of a give lie segmet, the size of a give agle ad the perimeter of a give square or rectagle. Costructio: To costruct a lie segmet of give legth (ruler allowed). Costructio: To costruct a triagle (ruler allowed) whe give: the legths of three sides; the legths of two sides ad the measure of the icluded agle; the legth of a base ad the measures of the base agles. 11 Fact : A straight agle measures 180. (For iterpretatio of the word Fact see Guidelies for Teachers.) Fact : Vertically opposite agles are equal i measure. Fact : The measure of the three agles of a triagle sum to 180. Costructio: To costruct a right-agled triagle, give sufficiet data (ruler allowed). Fact (Theorem of Pythagoras): I a right-agled triagle, the square of the legth of the side opposite to the right agle is equal to the sum of the squares of the legths of the other two sides (verificatio by fidig the areas of the squares o the three sides or otherwise). Costructio: To costruct a rectagle of give measuremets (ruler allowed). Fact : A diagoal bisects the area of a rectagle (verificatio by papercuttig or otherwise). Costructio: To draw a lie through a poit parallel to a give lie. Costructio: To divide a lie segmet ito two or three equal parts. Costructio: To bisect a agle without usig a protractor. Meaig of distace from a poit to a lie.

12 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Geometry Meaig of base ad correspodig perpedicular height of a parallelogram. Fact : The area of a parallelogram = base x (correspodig) perpedicular height. 2. Trasformatio geometry: Cetral symmetry, axial symmetry. Use of istrumets to costruct the image (rectiliear figures oly) uder (i) axial symmetry ad (ii) cetral symmetry. 12

13 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Usig Calculators The use of calculators is a regular feature i the daily mathematics lesso i post-primary schools. Calculators are a ivaluable aid for all studets ad especially those with mild learig disabilities. Most importatly, calculators eable studets with mild geeral learig difficulties to achieve success i mathematics. For some of these studets memorisig umber bods ca be a problem. This ca be offset by usig a calculator, as log as the uderlyig operatios ad cocepts are uderstood by the studets. The overall aim i the use of calculators i the mathematics class is to eable studets to kow whe it is appropriate to use metal methods, writte methods, ad calculator methods, or a combiatio of these. A simple drill of Thik first, write, use the calculator, write, ad the compare the results agaist the origial estimate should be practised. Roudig off ad writig the estimate before usig the calculator ca esure that cogitive skills are beig developed ad will avoid mechaical use of the calculator. Ecouragig estimatio Through skillful questioig studets ca be ecouraged to use estimatio. Iterestig questios such as, Are 150 hours more or less tha a week? will ecourage a estimated aswer followed by calculator work. Eterig correctly Eterig the decimal poit eeds careful attetio, especially i relatio to moey problems, for example 20 is etered differetly to 20c, ad i tur to 2c. The fractio symbol b Usig the fractio symbol o the calculator a c ca make fractio calculatio achievable for studets Oce mastered, a problem like ca be aswered easily. Equivaleces ca be explored ad large fractios simplified. The teacher will eed to show this to the class ad to idividual studets. Studets workig i pairs or threes ca help each other. 13 The teacher will choose whether a scietific calculator or a simpler model will suit the studet. The latter usually has large keys ad is most effective i performig the four basic fuctios. However, i dealig with fractios the scietific models offer great relief from legthy ad complex algorithms. The calculator ca eable the studet to keep up with learig i the system of atural umbers, itegers, ratioal umbers, ad real umbers. The teacher will familiarise himelf/herself with the various brads of calculators beig used by the studets, ad assist them with mior differeces i operatig them. The followig are some approaches that teachers may fid useful. Pair ad small group work This ca be of great beefit whe studets are learig how to maipulate the calculator ad whe solvig problems. Iterpretig display correctly Pair work helps greatly with this. Questios like, What does 12.3 mea i a moey problem? How would 3 cets be represeted o the display? How would you key i twelve euro ad three cet? will stimulate a correct readig of the display. Studets should write their aswers o paper. I usig the memory butto a teacher ca judge the readiess of a studet for calculatios ivolvig more tha oe stage. For example, i calculatig the wall area of a room 250cm X 500cm X 300cm seems impossible for the studet with geeral learig difficulties, yet 2 X 3 X 5 whe stored to memory M+ (2 X 4 X 5 M+ ) ca be accessed by pressig Recall Memory. This is a algorithm that ca be practised ad used for larger umbers. Pair work is very useful i this cotext i developig cofidece ad i explorig methods.

14 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Checkig aswers The calculator offers the teacher ways of showig the studet how to check aswers usig iverse operatios, thus reiforcig the learig of basic operatios. For example, = 12 ca be checked by Idetifyig studets miscoceptios ad errors By observig the studet ad by egagig with him/her i calculator work the teacher ca ascertai at what stage i the problem-solvig process a misuderstadig may have occurred, ad ca deal with it rather tha gettig bogged dow i calculatio processes. If a error occurs as a result of operatig the calculator icorrectly, it ca be dealt with o a idividual, group, or class basis. Teachig strategies Whe plaig for teachig ad learig i the area of Mathematical Studies ad Applicatios a variety of teachig strategies eeds to be cosidered. These will respod to the particular challeges studets with mild geeral learig disabilities experiece i egagig fully with, for example, mathematical laguage, oral ad writte commuicatio, problem-solvig, ad the retetio of facts ad cocepts. The tables that follow list some of the potetial areas of difficulty, ad suggest appropriate strategies for classroom use. It is importat to remember that ot all studets with mild geeral learig difficulties face all of these challeges. Neither is it a exhaustive list. These are the most commoly foud potetial areas of difficulty. Usig ICT May computer programs ca be used at differet levels withi oe group or class. Useful software is available commercially ad ca be ivaluable i reiforcig cocepts, i assistig calculator usage i computatio, i providig problem solvig opportuities ad i makig mathematics fu ad ejoyable. Studets workig, usig ICT, i groups or pairs ofte make sigificatly greater progress tha those who work idividually, ad this should be bore i mid i classroom plaig. The orgaisatio of ICT facilities varies eormously from school to school, yet the opportuity for studets with mild geeral learig difficulties to avail frequetly of ICT i the developmet of their mathematical skills is highly recommeded. 14

15 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Addressig potetial areas of difficulty for studets with mild geeral learig disabilities s Potetial area of difficulty Short-term memory = Implicatios for learig Retetio of facts ad defiitios ca be a problem. + Possible strategies Ecourage the use of visual clues to aid memory, for example a verbal or writte defiitio of a isosceles triagle could be accompaied by a diagram with two sides ad two agles marked as equal. Ecourage studets to ivet rhymes, sogs or memoics to help them to recall facts ad practise estimatio skills, so that a calculator ca be used efficietly. Work o makig certai operatios automatic through usig fu games such as table-darts or fractio-decimal equivalece domioes. s Potetial area of difficulty Short attetio spa ad poor cocetratio = Implicatios for learig The studet fids it difficult to stay o a task, may rush the task, ad be easily distracted. + Possible strategies Provide shorter tasks with clear rewards for stayig o the task ad for completig it. For example, allow a studet to try a mathematical puzzle whe the task is completed. Use a variety of teachig methodologies; keep periods of istructio short ad to the poit, ad recap frequetly. Use teacher observatio efficietly ad ote achievemets, stregths, ad preferred learig styles i plaig future work. Ecourage studets to keep portfolios of work i which they record their mathematical achievemets. 15 s Potetial area of difficulty Uderstadig mathematical cocepts ad abstractios = Implicatios for learig The studet fids mathematics difficult ad has particular difficulty with certai abstract cocepts ecessary for algebra ad geometry. + Possible strategies Group discussio ca help the studet to liste to ad work with others. This is very useful whe itroducig a theme or cocept to promote a discussio with studets. I learig cocepts activities should be varied through the use of games, ICT, ad real-life problems relevat to the studet s experiece. Learig ca be made fu by usig fuy ames, silly scearios. or ulikely settigs. Ecourage co-operative learig activities, icludig pair-work ad small group exercises. Teach the topic i chuks rather tha as a sigle block.

16 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY s Potetial area of difficulty Spatial awareess = Implicatios for learig The studet may have difficulty orgaisig materials. She/he may display left/right cofusio whe recordig ad may ot recogise shapes if iverted or rotated. Topics such as geometry, applied arithmetic (area ad volume) ad graphig will be more challegig for this type of studet. + Possible strategies The studet should be give plety of work with three-dimesioal objects ad particular attetio should be paid to the laguage of spatial awareess. Ecourage the studet to make simple models (from cardboard or usig a dyamic geometry computer package) whe learig the properties of geometrical shapes. Whe discussig area or volume of a shape esure that the studet has access to a model of the relevat shape. Usig puzzles, tagrams, ad shape-makig kits i a fu way ca help the studet with this area of difficulty. Ecourage studets to be aware of their ow persoal space. Keep the patters of classroom orgaisatio cosistet. 16 s Potetial area of difficulty Applyig previously leared kowledge = Implicatios for learig The studet may fid it difficult to apply a skill or cocept already acquired i a differet settig, for example measurig i Geography, Sciece, or Home Ecoomics. + Possible strategies Revisit ad review previously leared kowledge regularly. Ecourage studets to revisit skills ad kowledge leared i a previous class, for example Yesterday we leared how to do a survey ad make a tally chart to show the results. Use a cross-curricular approach to the teachig of skills or cocepts that are commo to differet subjects, for example measurig agles i mathematics ad techical graphics or weighig i mathematics ad home ecoomics. Draw the studets attetio to what is happeig, for example This is just like the measurig we did last week. What did we use to measure our books? How did we place the ruler? Reiforce mathematical cocepts ecoutered i other areas of the curriculum ad ecourage the studet to make coectios, for example How did you fid the volume of somethig i sciece?

17 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY s Potetial area of difficulty Trasferrig of learig to real-life = Implicatios for learig The studet may ot use mathematics i real situatios. For example, she/he may ot use arithmetic whe buyig goods i a shop, may ot see the eed to measure whe cookig, or may ot recogise shapes i the eviromet. + Possible strategies Use real-life objects ad cois i appropriate situatios. Discuss with the studets how they sped moey. If possible, provide studets with opportuities to hadle real-life materials i real-life cotexts; for example, moey i a real shop or i the school shop. Esure that parets are aware of the importace of coutig ad hadlig moey or of measurig at home, for example sharig equally, weighig for cookig, or measurig whe doig DIY. s Potetial area of difficulty Visual sequecig + Possible strategies = Implicatios for learig The studet may ot be able to copy from the board or from a book ad may have difficulty with sequecig ad mirror writig. Teach the studet how to chuk iformatio ad how to check if it is correct; for example, copyig oly oe part of the sum at a time. Preset board work carefully, give clear istructios as to what the studet eeds to copy, ad use worksheets where appropriate. Use rhymes, sogs, memoics ad mid- maps to reiforce sequeces. Use visual cues. 17 s Potetial area of difficulty Cofusio with sigs ad symbols = Implicatios for learig The studet may ot read symbols ad may ask questios such as Is this a add sum? + Possible strategies Use charts to relate mathematical symbols to everyday symbols; for example, egg + chips, price, 20% off. Ecourage studets to verbalise what they are doig first; for example, lookig for ad idetifyig the symbol, or applyig the correct symbol if it is a writte problem. Ecourage studets to keep a symbol ad keyword dictioary.

18 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY s Potetial area of difficulty Laguage = Implicatios for learig The studet caot follow complex seteces or multiple meaigs ad may process oly part of the istructio. The studet fids it difficult to verbalise what she/he is doig i mathematics. The studet has difficulty i relatig the vocabulary of mathematics to real-life situatios. + Possible strategies Idetify specific mathematical terms ad esure that these are reiforced i differet settigs ad i other areas of experiece. Ecourage the studet to use relevat mathematical terms whe appropriate. Esure that the mathematical laguage used each week is commuicated clearly to studets ad their parets. Use a Key Word approach by displayig a wall chart of mathematical terms used each week, thus eablig the studet to build up a persoal mathematical dictioary. s Potetial area of difficulty Readig + Possible strategies = Implicatios for learig Readig difficulties ca prevet the studet from egagig with mathematics. He/she may be capable of completig the mathematical task but may become frustrated ad cofused by prited words. 18 Preset problems pictorially. Ask the studets to pick out the parts of the problem they ca read ad to focus o relevat iformatio. There is ofte a lot of redudat iformatio i a writte problem. Avoid presetig the studet with pages of textbook problems by givig modified worksheets (with diagrams) or verbally delivered istructios. s Potetial area of difficulty Followig istructios = Implicatios for learig The studet becomes cofused whe faced with more tha oe istructio at a time. + Possible strategies 00 Get the studet to repeat the istructio(s). Give short, clear istructios, ad use pictorial cues. Give verbal/writte hits. For example, use graph paper. What kid of problem is it? What do you eed to kow? What do you do ext? Preset clear guidace o how ad whe assistace will be give by the teacher/ other studets durig the lesso.

19 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY s Potetial area of difficulty Beig overwhelmed by the learig process = Implicatios for learig The studet becomes overwhelmed whe preseted with ew iformatio or skills ad cosequetly caot lear. + Possible strategies Adapt the materials give to a group. For example, have some compare the measure of agles usig a protractor while others use cut-out cards. Adapt teachig styles. For example, use more discussio at both the begiig ad ed of the lesso to help both teacher ad studet to uderstad how they are learig. Adapt the resposes required. The same activity ca ofte be doe with a group or class but some studets will aswer orally, some by usig symbolic represetatio, or some by usig a pictorial respose. Adapt the requiremets of the task. Oe group or idividual may oly have to do six of the questios, whereas aother may have to do te or more. Set persoal targets for the studets so that they do ot feel others are gettig less to do tha they are. 19

20 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplars These exemplars demostrate how certai strategies outlied i the previous sectio ca be used whe teachig a selectio of topics from the syllabus. These exemplars are ot iteded to cover the course or ay oe part of the course etirely. Teachers usig them are ecouraged to choose the learig outcomes, supportig activities, ad assessmet strategies that best suit the eeds of their studets. Some studets may oly achieve the first oe or two learig outcomes while others may achieve the full rage of outcomes. The importat factor is their iclusio i the experiece. The Juior Certificate Guidelies for Teachers: Mathematics cotais further exemplar material that ca be adapted to suit the eeds of a variety of studets. The guidelies also cotai useful refereces to mathematical resources ad websites. Structure of the exemplars Each of the exemplars is preceded by a outlie of the relevat sectios of the Primary School Curriculum, the Juior Certificate (foudatio/ordiary level) ad the Juior Certificate School Programme (JCSP). Some of the potetial difficulties experieced by studets with mild geeral learig disabilities that relate specifically to the area covered i the exemplar are outlied, ad suitable strategies are suggested. I additio, a approximate time scale, a list of resources, suggested outcomes, supportig activities, ad assessmet strategies for a lesso or series of lessos are provided. The exemplars are orgaised i the order i which the topics occur i the foudatio level mathematics syllabus. 20

21 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY No. Syllabus topic Exemplar Title Page 1 Mathematics Number systems Fractio attractio 22 2 Mathematics Applied arithmetic ad measure 3 Mathematics Applied arithmetic ad measure 4 Busiess Studies The Busiess of Livig Time What s the time 34 Walkig o the edge 45 Goig shoppig 54 Mathematics Applied Arithmetic ad Measure 5 Busiess Studies The Busiess of Livig Sources of icome ad iterpretig pay slips 63 6 Busiess Studies The Busiess of Livig Preparig Aalysed cash books 75 7 Busiess Studies Eterprise Statistics ad data hadlig 92 8 Mathematics Algebra Algebra activity Mathematics Relatios, fuctios ad graphs Plottig poits Mathematics Geometry What kid of triagle is it? Busiess Studies The Busiess of Livig Icome ad expediture Home Ecoomics Food Studies ad Culiary skills Desig ad make a pizza 139

22 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Syllabus topic: Mathematics: Number systems Fractio attractio Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Number Strad uit: Fractios Juior Certificate (Ordiary level) Number systems: The set Q of ratioal umbers. Decimals, fractios, percetages. Decimals ad fractios plotted o the umber lie. The operatios of additio, subtractio, multiplicatio ad divisio i Q. Juior Certificate School Programme Use of umber: Apply the kowledge ad skills ecessary to perform mathematical calculatios Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to te class periods. Potetial areas of difficulty > Short term memory > Uderstadig cocepts > Spatial awareess > Trasfer to real-life > Vocabulary/laguage difficulties 22 Strategies used i this exemplar Specific targetig of mathematical laguage Applyig fractios to real-life situatios Usig reiforcemet techiques Usig games to reiforce cocepts ad operatios Usig cocrete materials ad maipulatives Usig cross-curricular liks to home ecoomics, materials techology, ad sciece. Usig pair ad group work i specified tasks

23 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Resources Bars of chocolate, pizzas or cardboard/plastic models that ca be easily divided Card, paper, material that ca be folded, tor, ad cut Sets of fractio strips Sets of fractio domioes Strig/wool, post-it otes, ad scissors Kitche weighig scales Soft driks cotaiers All activities are based o studets workig i pairs or groups of three or four. Activity 1 ca be coducted as a whole class discussio, as the teacher chooses. There is commercially available software o Fractios which is useful for reiforcig studets uderstadig of fractio cocepts, such as Display it Yourself Series: Fractios ad Maths made Easy. Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. state where fractios are used i everyday life 1. Discuss where fractios occur i everyday life. 2. Sharig amog frieds 1. Studets draw a poster of a advertisemet or copy a recipe that shows the use of fractios i everyday situatios, ad give oral explaatios of the meaig of the fractios used i their posters split a variety of items ito differet fractios, usig fractio words ad terms appropriately 3. Foldig activities 2. Studets self-assess their work by askig questios such as: Was this sharig doe equally? What problems arose? 3. fold, tear, or cut a variety of items ito differet fractios, usig words ad terms appropriately. 3. Observe the studets discussig whether the foldig/tearig/ cuttig task bee accomplished ad what difficulties arose.

24 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Suggested outcomes Supportig activities Assessmet strategies 4. uderstad the cocept of fractios i terms of arragig them i order, ad as a way of describig how two thigs relate to each other 5. write fractios ad equivalet pairs of fractios 6. uderstad the eed for multiple ad LCM i additio list multiples 4. A series of group tasks usig real ad meaigful cotexts to explore fractio cocepts 5. Studets i pairs use couters to explore fractio relatioships 6. Discuss the eed for multiples, usig examples 4. Observe the studets egagig with tasks ad the extet to which they accomplish them. Ecourage self ad peer moitorig ad itervee whe ecessary. 5. Observe whether studets ca write fractios correctly o work-cards, usig umerator ad deomiator. 6. Observe whether the studets ca idetify the LCM 7. recogise equivalet fractios. 7. Play equivalet domioes games ad fractio bigo. explai the eed for LCM create lists of multiples ad select the lowest solve practical problems usig LCM Observe whether the studet matches equivalet fractios. Cross-curricular liks: These skills may be reiforced if similar cocepts i home ecoomics, materials techology, ad sciece are treated at the same time.

25 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Activity 1 Spot the fractio Usig appropriate visual aids, such as advertisemets ad labels, discuss where fractios occur i everyday life ad what expressios such as ½ price 1 3 extra free, add ¼ tsp of salt, half a metre, first half, half time, last quarter mea. Activity 2 Sharig with frieds The purpose of this activity is to give studets the opportuity to uderstad the cocept of simple fractios by sharig out items of various shapes amog various umbers of people. Studets experiece ad discuss sharig chocolate bars, pizzas, etc. with frieds. The activity ca be made simple (for example, sharig everythig betwee two people) or more complicated as appropriate. Resources Various bars of chocolate (A large 4x8 square bar of chocolate is a useful resource for this activity ad has eough squares to make a ice reward for everyoe at the ed of the lesso.) Note: A chocolate orage has 20 segmets ad so ca be used to demostrate the cocepts of halves, quarters, fifths, teths, ad twetieths. 25 A pizza ad pizza slicer Cardboard or plastic shapes that ca be used to represet bars of chocolate or pizzas whe it is ot possible or appropriate to use the real thig Laguage use Throughout the activity the teacher should liste to the laguage that the studets use to explai what they are doig. I additio to usig their ow words ad phrases studets should be ecouraged to uderstad ad use other appropriate keywords. Depedig o the actual activity, keywords may iclude share, split, slice, divide equally, how may pieces, what fractio, what is left, half, quarter, eighth, sixteeth. Skilled questioig by the teacher ca assist studets to move from the cocept of sharig or dividig to the cocept of fractio. Some sample sharig activities Studets may begi sharig usig the oe for you, oe for me method. Some studets may move o to workig out how may pieces there are, ad the how may each perso should get, without havig to deal the pieces out oe at a time. 1. A bar of chocolate has 6 squares, how would you (a) share it equally betwee 2 people? (b) share it equally betwee 3 people? 2. A bar of chocolate has 32 squares. How would you (a) share it equally betwee yourself ad a fried (2 people)? (b) share it equally betwee 4 people? (c) share it equally betwee 8 people? (d) share it equally betwee 16 people? (e) If you share it so that for every square you give a fried you get 3 squares, what fractio will your fried get ad what fractio will you get?

26 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics 3. Sharig a pizza amog frieds. Use a real pizza or cardboard or plastic segmets. (a) 4 frieds wat to share a pizza.what fractio does each get? Show the size of slice that each will get. (b) 8 frieds wat to share a pizza.what fractio does each get? Show the size of slice that each will get. (c) 6 frieds order a pizza. Eoi ad Fraces are very hugry ad wat two slices each. Ae, Breda, Carmel ad Des wat oly oe slice each. How may slices should the pizza be cut ito? Show how much (ad what fractio) each will get. (d) A pizza is sliced ito 8 equal pieces. Áie has oe quarter, Sue has oe half ad Séamus has what is left. Show how may slices each perso gets. Activity 3 Foldig activities The purpose of this activity is to give studets the opportuity to uderstad the cocept of simple fractios by foldig, tearig, or cuttig items of various shapes. Laguage use As explaied i the previous activity studets should be ecouraged to use ad uderstad appropriate words, icludig fold, half, quarter, eighth, what fractio of, five out of eight, legth by breadth, legthways, square. Some sample activities Paper foldig of differet shapes Foldig a rectagle ito quarters i differet ways: (a) Fold a rectagular (or square or circular) piece of material i half legthways ad cut alog fold. Do the same with the two pieces produced ad do the same agai. You should have 8 equal pieces of material. Measure the legth ad breadth of each piece of material. (b) Take a rectagular (or square or circular) piece of paper. Fold it i thirds (this may require some assistace), ad the i half. What fractio of the origial piece of paper is the folded piece? Ufold ad cout how may sectios have bee created. Colour i three of the sectios. What fractio of the paper is coloured? What fractio of the paper is ot coloured? Is there aother way of amig this fractio? (c) Similar coversatios ca be built aroud foldig shapes split ito differet fractios i differet ways. (d) Note that this paper-foldig method is useful whe teachig multiplicatio of fractios. For example (b) above demostrates that half of a third is a sixth. Cuttig sectios of material for a patchwork quilt. Take a piece of material measurig 32cm by 16cm. Fold material i half legthways ad cut alog the fold. Do the same with the two pieces produced ad do the same agai. You should have 8 squares of material. Measure the legth ad breadth of each piece of material (8cm by 8cm). By likig with the Home Ecoomics teacher it might be possible to make a patchwork quilt ad studets could see what fractio of the quilt is made up from their colour or patter of material.

27 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Activity 4: Group Activities (oe-two class periods) Measurig ad recordig fractios i differet cotexts Studets will work i groups, movig o the completio of oe task to the ext, but stayig util a task is completed. Co-operative learig is the key approach here. Task 1: How log is a piece of strig? Studets are required to measure ad label strig/wool legths as directed o task cards, for example 1 3m, ¼m, m, 2 5m, 3 10m, m, 1 10m, ½m, 1 3, ½m, 1 5m, etc. Studets place these o a wall-chart, appropriately labeled. They arrage the strigs i ascedig/descedig order, writig the list of fractios udereath. Pieces of the same legth are recorded i a sectio called equivalet fractios, for example ¼m = Calculators ca be used to simplify fractios ad to assist i explorig equivaleces. Task 2: The weight of kowledge Testig ad recordig equivaleces ad relatioships. Weigh schoolbooks usig kitche style scales. Record the weights o a wall chart, for example: Maths book : 400g A4 copy : 200g Write dow relatioships, for example a Maths copy weighs 200/400 or 1/2 the weight of a book. 27 This could be made ito a fu exercise as follows: Add all weights ad see how much you carry every day. If you were allowed leave your copies at home what fractio would that be of your bag s total weight? What fractio do your books make? Weigh the books you like. What fractio of the total are they? Record all these. Allow studets to record this iformatio i their Maths copies or record books. They will probably wat to do this ad brig it home to discuss it with their parets. Task 3: Thirsty work Comparig volume of soft drik bottles, cas, ad cartos. Usig 2l, 1.5l, 1l, 500ml, 330ml, 250ml ad 200ml bottles make out fractio relatioships (placig oe umber over the lie ad the other umber uder the lie). Ask the studets to cosider how may 500ml bottles would give the same amout as the 2l bottle? So, a 500ml bottle is a?/? of the 2000ml bottle? 500ml bottle = 500 = ml bottle Calculators should be used to check simplified fractios. Other bottles, cas ad cartos ca be dealt with similarly. This could be exteded to iclude prices ad value for moey. Prices could be compared also usig fractios.

28 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Activity 5 Workig with couters ad fillig work-cards Discuss with the studets that, for example, oe third meas dividig ito three parts. Ecourage them to talk through what they are doig. For example, Group 1 could use 12 couters/items ad complete cards such as 1 = 2 = = 1 = 2 = 3 = Based o16 ad 20 couters (ad other umbers) similar workcards ca be made out ad studets ca explore ad record equivaleces. Activity 6 Learig multiples Explai or discuss the eed for multiples, usig a simple example: 28 ¼ ¼ ¼ ½ ½ + = = 3 4 ¼ ¼ ¼ ¼ The studets list the multiples of 2 ad write them i their copies. This is repeated with the multiples of 4. They circle the lowest oe that is commo to both lists ad write: LCM = This ca be repeated for other pairs of umbers. Some studets might have a problem because they do ot kow their multiplicatio bods. The teacher ca work o that with those studets, or ecourage them to use a calculator i completig their lists. Whe learig multiples the studets list the multiples of various umbers.

29 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Workig i pairs or groups of three the studets ca complete the followig lists. Calculators ca be used Multiples of 2 = 2,, 6, 8,,,,,, 20,,, Multiples of 3 = 3,, 6,, 12,,, 21,, 27,,, Multiples of 4 = 4, 8,,, 20,,, 32,,. Multiples of 5 =,, 15, 20,, 30,,,, 50. Multiples of 6 =, 12,,, 30,, 42,, 54, 60. Multiples of 7 = 7,,, 28, 35, 42,,,, 70. Multiples of 8 =, 16,,, 40,,, 64,,. Multiples of 9 =,,,, 45, 54, 63,,, 90. Still i pairs, studets take turs highlightig/pickig out the lowest commo multiple (LCM) i two rows, completig workcards such as the followig : 29 Write the LCM of the followig umbers LCM of 2 ad 3 is LCM of 2, 3 ad 4 is LCM of 5 ad 7 is LCM of 8 ad 6 is

30 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Activity 7 Fractio games Resources Each studet playig the game eeds a set of fractioal parts. Each set of cards should be marked with a differet iitial (A, B, C, etc.) so that the sets ca be re-formed at the ed of the game. The game ca be played by betwee two ad four studets. 1. Cut from light-weight cardboard five rectagular sectios measurig 24cm by 6cm. 2. Mark oe strip as a uit measure Mark the other four strips ito fractioal parts as show below. Cut alog the lies, mark each piece with the same iitial, ad place the pieces ito a evelope for storage. ½ ¼ ¼ ¼ The fractioal pieces ca be made more robust by lamiatig them. 5. A umber of differet games are possible usig these fractioal pieces. Two games are described below. A. Make oe! 1. Each player is give a evelope of fractioal parts as described above. Each player retais his/her uit strip as a measure. All players empty the rest of their pieces ito a commo pile ad the pieces are mixed up. 2. Each player i tur draws a piece from the pile util all the pieces are goe. 3. Each player the assembles his/her pieces to make as may uit strips as possible. 4. The first player to costruct three uit strips (or whole) is the wier. B. Make half! 1. The game begis as above, but a time limit of three miutes is set. 2. The player who ca make the greatest umber of strips equivalet to a half is the wier. Other activities As a iitial itroductio to dealig with fractioal parts, studets ca be ecouraged to solve real-life problems based o splittig a pizza or a bar of chocolate ito various fractioal parts. Paper foldig activities such as those outlied i the Primary School Curriculum: Mathematics Teacher Guidelies are also useful.

31 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Pizza Problem Joe cooked a large pepperoi pizza for his frieds. He has a quarter of the pizza himself. Mary ad A share aother quarter betwee them. Pat, Seá, ad Kare share the rest betwee them. Draw a picture of the pizza ad show the size of the slice that each perso ate. More theoretical games such as that outlied here ca provide reiforcemet of the cocepts leared. Additioal variety could be provided by costructig five circular regios, which are marked ad divided ito the same set of fractioal parts as the rectagular strips show above. It is importat that studets see a variety of fractioal values represeted i a variety of ways. 31 More games: Equivalet fractio domioes Resources Sets of domioes ca be purchased from good educatioal suppliers. Alteratively, a set of domioes ca be made from cardboard. This game is based o a set of equivalet fractio domioes. Percetage ad decimal versios of domioes are also commercially available. Basic rules This is a game for two to four players. All of the domioes are placed face dow i the cetre of the table. Studets draw the same umber of tiles each ad spare tiles are left to oe side. Players take turs i playig a tile. (Usually, whoever has the highest double goes first.) Domioes are played at either ed of the row of tiles by matchig the adjacet halves of the tiles usig equivalet fractios (matches with). Doubles (domioes with the same fractio o both halves) are usually placed at right agles to the other domioes. The wier is the player who gets rid of all of his/her domioes first.

32 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics A sample game 32 Note: Studets will eed to uderstad the cocept of equivalet fractios before playig this game. Oce the basic rules of domioes are uderstood the group of studets teds to act as a self-checkig mechaism, ad the teacher is usually oly called o to judge a play if the group caot agree.

33 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 1: Mathematics Yet more fu! Fractio bigo Resources A set of bigo cards such as the oe show below ca be made o sheets ad photocopied before beig cut out idividually. Alteratively, they ca be produced as lamiated sheets ad studets ca mark them with soluble markers. The crosses ca the be erased before the ext game is played. 1. Studets are give various grids of fractios as bigo cards. Oe such grid is show below. 2. The teacher writes oe fractio at a time o the board. The teacher will eed to choose suitable fractios based o the rage of fractios appearig o the bigo cards. A call-out card could be produced as a guide. 3. Studets put a cross o ay fractios o their bigo card equivalet to the oe called out. 4. The first studet to mark off a full row or colum o his/her card is the wier ad gets to act as caller for the ext game. Cards are collected ad redistributed for subsequet games. 5. Whe someoe wis the game the marked bigo cards ca also be swapped i pairs, ad studets ca check each other s work based o the list of fractios o the board. Studets who are havig difficulty with the activity may eed to egage i further work to assist their uderstadig of equivalet fractios. 33

34 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Syllabus topic: Mathematics: Applied arithmetic ad measure What s the time Primary School Curriculum (5th ad 6th classes) Strad: Measures Strad uit: Time Juior Certificate (Ordiary level) Applied arithmetic ad measure: Twety-four hour clock, trasport timetables Juior Certificate School Programme Time, Speed ad Scale: Demostrate ad apply a uderstadig of time, speed ad scale Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to fourtee lass periods. Potetial areas of difficulty > Short term memory > Procedures > Uderstadig cocepts > Spatial awareess > Applicatio of previously leared kowledge > Trasfer to real-life > Cofusio with sigs ad symbols 34 Strategies used i this exemplar Group discussio activity drawig out the laguage of time, why we eed to keep track of time, etc. The use of storytellig Usig visual represetatios of time (for example poster, clock, timelie) Situatig mathematics i real-life cotexts Usig cocrete materials Usig studets persoal experieces (for example timelie, TV guide) Ecouragig studets to use relevat mathematical laguage Usig appropriate ICT resources Resources A large poster of a clock (12-hour ad 24-hour) with movable hads A variety of clocks (both aalogue ad digital), caledars, trasport timetables (relevat to the geographical area of the studet), TV ad radio schedules Provicial bus timetables (available at /bus) Trai timetables (foud at TV listigs (accessed through The Irish Times olie at The mathematics teacher ca lik with the home ecoomics teacher to ecourage the use of time i a practical situatio, for example cookig ad bakig, while time is beig taught i the mathematics class.

35 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. egage i discussio about the importace of keepig track of time 2. use words related to time appropriately 1. Questio ad aswer sessio about time 2. Studets take part i the Time for a story 3. Timetable ad timelie activity ad 24-hour clocks activity: Air Traffic Cotrol 1 ad 2 1. Teacher otes studets resposes 2. As studets take part i the Time for a story, (see Activity 2 page 36) the teacher ca assess the studets ability to complete a storylie at the various levels of the activity ad their ability to use the keywords appropriately. 3. apply a basic kowledge of time to their everyday activities 4. chage time betwee a 12- hour clock ad a 24-hour clock 5. work out the differece betwee two give times 6. use a trasport timetable accurately, for example work out the trai to catch i order to be o time for a meetig. 5. Followig a TV guide 6. Catch that trai! 3. Observe studets draw a persoal 12-hour timelie markig what they did o a particular day. 4. The persoal timelie activity may be repeated usig a 24-hour clock. Teacher records whether studets ca successfully record their activities usig the 24-hour clock, ad otes where difficulties arise Note what method the studet is usig: estimatio, basic coutig techique, subtractio. Studets who ca use a variety of methods may be able to check their aswer more successfully. 6. Role play: oe studet phoes to iquire about trai times ad aother studet is the iformatio service. Ca studets commuicate their query ad their reply accurately? Cross-curricular liks: Skills ca be reiforced if similar cocepts i other subjects, for example timig a cake i the ove i home ecoomics, are treated at the same time.

36 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Activity 1 Studets provide aswers i respose to the teacher s questios: How would we kow a day/moth/year has passed if we did ot have a clock (su/moo/seasos)? Why do we eed to keep track of time? How do we keep track of time? Do some people s jobs deped o time? How do we measure time? What words relate to time? Activity 2 Time for a story Resources Prepared cards Studets take turs to add a lie to a story about time. Each lie of the story starts from where the previous perso fiished ad metios a time iterval ad a fiishig time. Cards such as those show ca be distributed to studets iitially to help suggest a story lie. The challege to studets is to liste to the perso speakig ad kow whe it is the right time to read out their lie. Sample cards for Time for a story I got up at 8 o clock ad spet 15 miutes gettig washed ad dressed. I was ready at 8.15am 36 At 8.15am I started breakfast. This took me 30 miutes. I fiished breakfast at 8.45am At 8.45am I left the house. It took me 10 miutes to walk to school. I got to school at 8.55am I got to school at 8.55am ad classes started at 9am. I had classes for 2 hours ad the had a break at 11am At the 11am break I met my frieds for 15 miutes ad the wet back to class at 11.15am

37 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Further activities As studets experiece success with this activity a ew set of cards ca be distributed with oe piece of iformatio omitted that the studet must supply, for example the fiishig time. This activity ca progress with studets ivetig their ow stories ad times. At this stage the use of certai keywords ca be ecouraged by distributig cards cotaiig a word that studets must iclude i their story lie. Such keywords may iclude time, secods, miutes, hours, days, moths, years, clock, timetable, o time, late, early, a.m., p.m. Activity 3 Complete your persoal timelie Timetables Studets examie a copy of their school timetables ad ask ad aswer questios. For example, What time do we have our morig break? For how log, does the break last? What time do we have Eglish o Modays? This activity ca be exteded by usig a variety of timetables. 37 Resources A simple timelie Cards showig actio words or pictures Glue Studets are give a blak timelie ad a rage of cards with pictures or actio words o them. Studets stick the cards at a appropriate place alog the timelie. Whe the timelie is completed, studets discuss i pairs the reasos why they placed each card at a particular poit o the timelie. The activity as preseted uses words rather tha pictures. Time for sleepig? What time do you ormally sped i bed asleep? Cut out the card with the word sleepig o it ad place it o the timelie at a time whe you would ormally be asleep. Do the same for each of the other cards.

38 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Workig at school Watchig TV Sleepig Meetig frieds Eatig luch 5am 9am 1pm 5pm 9pm Whe you are fiished, talk to the perso beside you about why you placed each card at that time o the timelie. 38 Assessmet strategy 2: Persoal timelie Studets make a timelie i words ad pictures to represet their day. This ca be doe iitially usig the 12- hour clock. This activity ca be used to assess the studet s ability to sequece evets ad to estimate how log certai activities ca take. Studets, i pairs, ca the be ecouraged to ask each other questios based o their timelie. For example: At what time did you play sport? How log did you sped doig your homework? Did you sped more time watchig TV or playig sport? Woke up, got ready, walked to school School starts Break met my frieds Luch walked home, ate luch Back to school Walked home got a book i the library Did my homework Played sport Watched TV Bed 8am 9am 10am 11am 12 oo 1pm 2pm 3pm 4pm 5pm 6pm 7pm 8pm 9pm

39 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Activity 4 Air-Traffic Cotrol 1 Note: This activity as preseted is quite complicated. It may be more appropriate to choose a smaller selectio of flights to begi with. Warig! Warig! Due to a computer error some iformatio has bee lost or mixed up. All air-traffic cotrollers are advised to check the departure ad arrival times carefully ad to put the plaes i order as follows: 1. Cut out each of the flight iformatio sheets below. 2. Arrage the strips ito the correct order based o the times give. 3. Eter the flight umbers from EI 152 to EI 178 goig up i eve umbers. DUBLIN TO LONDON HEATHROW, JANUARY Flight No. Depart Arrive Flight No. Depart Arrive 08:55 10:10 14:05 15:20 39 Flight No. Depart Arrive Flight No. Depart Arrive 13:00 14:15 15:30 16:50 Flight No. Depart Arrive Flight No. Depart Arrive 12:00 13:15 17:35 18:55 Flight No. Depart Arrive Flight No. Depart Arrive 20:05 21:15 19:15 20:25 Flight No. Depart Arrive Flight No. Depart Arrive 18:35 19:50 10:20 11:40 Flight No. Depart Arrive Flight No. Depart Arrive 07:50 09:10 16:30 17:50 Flight No. Depart Arrive Flight No. Depart Arrive 19:55 21:05 EI :50 08:05

40 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Activity 4a Air-Traffic Cotrol 2 Well doe! You have maaged to sort the flights ito the correct order. Ufortuately, we have discovered aother error i the computer system. All times must ow be etered i 12-hour clock format. Your ext task is as follows: Chage all of the times show from the 24-hour clock to the 12-hour clock. Do t forget to use AM or PM. Fill your aswers ito the table below. Flight No. Depart (24-hour) Depart (12-hour) Arrive (24-hour) Arrive (12-hour) EI : am 08: am EI :50 09:10 EI :55 10:10 EI :20 11:40 40 EI :00 13:15 EI :00 14:15 EI :05 15:20 EI :30 16:50 EI :30 17:50 EI :35 18:55 EI :35 19:50 EI :15 20:25 EI :55 21:05 EI :05 21:15

41 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Vocabulary Air-traffic cotroller Flight No. Depart Arrive 24-hour clock a perso who orgaises the departure ad arrival of plaes the flight umber used to tell which plae is which the time that a plae takes off from a airport the time that a plae lads at a airport time based o 24 hours startig with 00:00 (midight) Discussio topic Why is the 24-hour clock used i airports ad o may timetables? 41

42 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Activity 5 TV Times Note: This activity as preseted is quite complicated. It may be more appropriate to choose a smaller selectio of programmes to begi with. Part of the TV schedule for RTE 1 o Moday, 08 Jauary 2001 TIME PROGRAMME 13:00 13:25 ONE O CLOCK NEWS AND WEATHER. CINNLINTE NUACHTA 13:25 13:55 HOME IMPROVEMENT 13:55 14:25 NEIGHBOURS 14:25 14:55 DOCTORS 14:55 15:25 THE BILL 15:25 15:30 NEWS SUMMARY AND WEATHER 15:30 16:50 OPEN HOUSE. NEWS SUMMARY 16:50 17:20 SHORTLAND STREET 17:20 17:30 NUACHT 17:30 18:00 NEIGHBOURS 18:00 18:01 THE ANGELUS 18:01 19:00 SIX-ONE NEWS AND WEATHER 19:00 19:30 NATIONWIDE 19:30 20:00 WILDLIFE ON ONE 20:00 20:30 NO FRONTIERS 20:30 21:00 EAR TO THE GROUND 21:00 21:35 NINE O CLOCK NEWS AND WEATHER 21:35 22:35 REBEL HEART 22:35 23:35 IRELAND OVERSEAS 23:35 23:40 NEWS SUMMARY AND WEATHER. AN EVENING PRAYER 23:40 01:40 ACCIDENT 01:40 02:05 GRACE UNDER FIRE 42

43 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Look carefully at the TV listigs show ad the aswer the followig questios: 1. At what time does the Oe o clock News begi? Give your aswer i the 24-hour clock ad also i the 12-hour clock format. 2. How log does Wildlife o Oe last? 3. How log does Shortlad Street last? 4. Which programme is loger, Grace Uder Fire or Doctors? 5. I wat to record Neighbours o video. How much space do I eed o my videotape? Give your aswer i miutes. 6. I wet to sleep at 9.40 p.m., but I set the alarm for the start of Grace Uder Fire. How much sleep did I get? 7. I watch a programme o RTE 2 that eds at 7.40 p.m. The I switch over to Wildlife o Oe. How much of Wildlife o Oe have I missed? 43

44 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 2: Mathematics Activity 6 Catch that Trai Note: Begi with very simple timetables ad the gradually itroduce more complicated examples. Usig a worksheet such as below, studets become familiar with a rage of differet timetables ad ca aswer questios such as those suggested. I additio, studets ca make up their ow scearios based o a particular timetable. Studets ca also be ecouraged to access timetables o the worldwide web. Here is a extract from the timetable for trais ruig from Dubli to Cork. Use the iformatio give i the table to aswer the questios which follow. Trai A B C D E F Dubli, Heusto 05: 25 08: 30 10: 50 13: 20 17: 10 19: 15 Newbridge 19: 41 Kildare 09: 00 19: 50 Portarligto 14: 02 20: 07 Portlaoise 06: 16 09: 25 14: 14 20: 19 Ballybrophy 09: 41 20: 35 Templemore 09: 55 14: 40 20: 48 Thurles 06: 51 10: 09 12: 11 14: 54 21: 03 Limerick Jct. 07: 13 10: 31 12: 33 15: 16 18: 49 21: 25 Charleville 07: 33 10: 53 12: 53 15: 37 21: 46 Mallow 07: 50 11: 21 13: 11 15: 54 19: 23 22: 03 Cork 08: 19 11: 49 13: 39 16: 22 19: 51 22: At what time does the earliest trai leave Dubli? 2. Which trai makes the most stops? 3. Which trai makes the least umber of stops? 4. At what time does trai D leave Thurles? 5. How log does trai A take to travel from Dubli to Cork? 6. I arrive i Dubli to catch the 08:30 trai to Portlaoise but it is cacelled due to a problem o the lie. How log will I have to wait for the ext trai to Portlaoise? 7. If I live i Portarligto, which is the earliest trai I ca get to Cork? 8. If I live i Kildare, which is the earliest trai I ca get to Cork? 9. I eed to be i Cork before 8 p.m.. What is the latest trai I ca catch from Dubli to get there just i time? 10. I wat to travel from Thurles to Cork to meet a fried who lives fiftee miutes away from the trai statio. What is the latest trai I ca catch to meet my fried at 2pm?

45 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Syllabus topic: Mathematics: Applied arithmetic ad measure Walkig o the edge Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Measures Strad uit: Legth Juior Certificate (Ordiary level) Applied arithmetic ad measure: SI uit f legth (m) Juior Certificate School Programme Perimeter, area ad volume. Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to fourtee class periods. Potetial areas of difficulty > Short-term memory > Uderstadig cocepts > Spatial awareess > Cofusio with sigs ad symbols > Laguage 45 Strategies used i this exemplar Frequet practice with the cocept of perimeter through a variety of differet activities The use of cross-curricular approaches Access to models of relevat shapes Practisig of estimatio skills Measurig familiar real-life objects Ecouragig studets to use relevat mathematical laguage Usig worksheets with pictorial clues Pair work ad group work. Resources Various tools for measurig legth, such as small rulers, metre sticks, tape measures, strigs of various colours, a trudle wheel

46 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. egage i discussio about the purpose of measurig legth 2. measure legth usig appropriate measurig tools 3. use strig ad a cetimetre ruler to calculate distace from a simple map 1. Studets egage i a structured discussio o the purposes ad methods of measurig legth. 2. Studets measure a rage of legths relevat to their experiece. 3. Map measurig exercise. 4. Classroom measuremets 5. Usig cut-out shapes 1. Oe studet from each group reports three poits from the discussio back to the class. 2. Each studet challeges aother studet to estimate, measure, ad record a legth i the classroom. Studets have a rage of measurig tools to choose from. 3. How well do the studet s measuremets compare to the accurate measuremets? 4. use a cetimetre ruler to measure straight lies 5. use a cetimetre ruler to measure the edges of a variety of mathematical shapes (square, rectagle, triagle) 6. uderstad the cocept of perimeter, for example the distace you travel whe walkig aroud a shape 7. fid the perimeter of various shapes draw o squared paper by coutig the uits aroud the edges 8. Calculate perimeter from represetatioal diagrams. 6. Floor exercises 7. Measurig the perimeter of shapes o squared paper. 8. Calculatig ad recordig accurately. 4. Studets measure colour-coded strigs of various legths ad complete a table. I pair-work: oe draws a lie of a certai legth ad the other first guesses the legth ad the measures it. A correct guess gets 2 poits ad a correct measuremet gets 1 poit. Colour of strig Red Blue Legth of strig 5. Studets assess their ow accuracy. 6. Ca the studet explai perimeter? Ca the studet also work it out by addig the legths of the sides of the shape? Peer assessmet is itrisic i this activity. 46 Use the worksheet o page 53 to assess the studet s uderstadig of calculatig the perimeter of various shapes. 7. Teacher observes studets accuracy. 8. Teacher observes studets accuracy i calculatio ad recordig. Cross-curricular liks: These skills ca be reiforced if similar cocepts i geography (maps) ad PE (measurig distace jumped or throw ad perimeter of pitch or court) are treated at the same time.

47 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Activity 1 Let s talk about legth Rules for group discussio The establishmet of a umber of rules for small group discussio ca assist the smooth ruig of structured discussio i the classroom. Ideally, the teacher ad studets ca draw up the list of rules together. The rules should be simple, easy to uderstad, ad be preseted as positive behaviours to be ecouraged rather tha egative behaviours to be avoided. Some suggestios are icluded here, but teachers ad studets may iclude differet rules that are relevat to their situatios. Rules for group discussio 1. Liste to each perso as he/she is talkig. 2. Ivolve each perso i the group. 3. Wait util a perso is fiished before you speak. 4. Ask questios if you do ot uderstad. 5. Make your poit clearly. 6. Respect differet poits of view. 47 Structured Discussio The teacher iitiates a structured discussio about the purposes ad methods of measurig legth. Some possible questios to iitiate the discussio might iclude: How far do you travel from home to school? Does ayoe come by car? Have you ever checked the distace o the display o the dashboard? I live ext door to aother teacher i the school so it is the same distace from both of our houses to the school.we both drive to school, ad I oticed the other day that it shows a loger distace o my dashboard display for the jourey tha o hers. Why might that be? (I take a differet route, have to drop my childre off o the way, etc.) Has ayoe decorated a room i their house recetly? Was ay legth measured for that? Why? (the height of the room to see if a piece of furiture would fit i, the legth ad width of room to see how much carpet was eeded, the width of the widow for curtais, etc.) How were the legths measured? (measurig tape, ruler, roughly comparig to the legth of the arm, etc.) The farmer up the road from me is buildig a ew fece aroud his field. He was woderig how to fid out how much wire he will eed. Has ayoe got ay ideas? (usig a measurig tape; walkig aroud the field, coutig how may steps it takes, ad the measurig the legth of his step; if the field is rectagular, walkig aroud oly half of the field; etc.) Some discussio o the meaig ad use of the followig keywords may arise as a result of the discussio: legth, width, height, distace, perimeter, how far? earer, farther, measure, ruler, measurig tape, millimetre, cetimetre, metre, kilometre.

48 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics The studets are the give work cards that iclude a variety of activities ad are ivited to write o the card why ad how legth is measured i each situatio. Suitable activities iclude: buyig shoes, buyig trousers, buyig a evelope to post a caledar to a fried, puttig up a shelf i your room, markig lies o a soccer pitch, checkig the height of a teis et, gettig a ribbo to go across a door for a opeig ceremoy, makig a wall hagig, fidig out the distace betwee two tows o a map, fidig out the distace from the school to the earest shop/library/sports cetre/bus stop, etc. Studets iitially work i pairs ad discuss what to write o the card. After the cards are completed, studets form small groups ad discuss what they wrote o their cards. The teacher circulates ad remids groups of the rules of discussio whe ecessary. As described i the first assessmet strategy, oe studet voluteers to report three geeral poits about the use of legth to the class. Activity 2 Measurig legths Persoal legths Studets work i threes to measure various persoal legths (oe to measure, oe to be measured, ad oe to check the measuremets). Studets record their ow measuremets o a card such as the oe below. Teachers may decide to chage the persoal legths metioed below depedig o the studets ivolved, particularly if the studets have physical disabilities. 48 The card could be chaged to show pictorial clues for the legths to be measured. Studets may fid it iterestig to ote the followig approximate ratios: Legth from figer to figer with arms outstretched: Height = 1:1 a b Legth of head: width of head = 1.6:1 (see a:b i diagram) More details of the ratios of the body ca be foud i Juior Certificate Guidelies for Teachers: Mathematics (page 31). Studets estimate ad the measure legths i the classroom icludig the legth of the desk, the width of the desk, the legth aroud the edge of the desk, the dimesios of blackboard/door/widow.

49 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Studets ca work i pairs. Skills ivolved iclude How to estimate the legth ad compare it to some kow legth (for example, a metre stick, the legth of a figer) Selectig the appropriate measurig tool for the task (a ruler, a measurig tape, a strig, a metre stick, a trudle wheel) The accurate use of the measurig tool (where the scale starts, what to do if the legth is ot a exact amout of uits) Selectig the appropriate uit of measuremet (mm, cm, m, km) ad fidig this uit o the measurig device Keepig track of measuremets, for example whe usig a ruler to measure a log distace the studet eeds to keep a record of the ruig total. (Name) Measuremets Had-spa: cm 49 Legth from figer to figer with arms outstretched: cm Legth of head from top to chi: cm Width of head from ear to ear: cm Height: cm Legth of foot: cm

50 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Activity 3 How far is it? Use a piece of strig or a strip of paper to fid the distace from oe poit to aother ad measure the strig or paper usig a cetimetre ruler. Fill i the table below ad aswer the questios. A D C B From To Distace (cm) From To A B B C A C C D A D D A Distace (cm) If I go from A to B to C, how far have I travelled all together? 2. How far is it from C to A to B? 3. What is the distace from D to A to C? Extesio activity A sample map is icluded below. (Note: It may be too detailed for use with may studets ad a simpler oe could be foud to replace it.) A local map would be of most iterest to the studets. Studets ca use strig ad a cetimetre ruler to aswer questios such as those below. These skills ca be reiforced if similar cocepts i geography are taught at the same time. 1. If you travel alog the N24 from Clomel to Carrick-o-Suir how may cetimetres would you travel o the map? 2. Which is the loger distace o the map: from Fethard to Cashel alog the R692 or from Fethard to Killeaule alog the R689? 3. A crow flies i a straight lie from Calla to Niemilehouse. I drive alog the R698 road from Calla to Niemilehouse. What distace o the map did each of us travel? Who travelled the shorter distace?

51 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Activity 4 Classroom Measuremets Studets idetify various straight lies i the classroom ad, workig i groups, measure them i cetimeters, for example width/legth of a copy; legth of pecil/pe; height of teacher s marker etc. Guidace may be provided to esure that the legths beig measured are small eough for the studets to maage. Activity 5 A rage of coloured, cut-out shapes is provided with kow measuremets. Studets measure, record ad compare their aswers to the accurate oes. For ease of measuremet shapes should iitially have legths of whole uits oly. Activity 6 Taped lies are laid o the floor i the shape of squares, rectagles ad triagles. Studets walk aroud the lies with a trudle wheel ad measure the total distace walked. Other studets measeure each side with a tape measure ad/or metre stick ad add the legths of the sides. Studets compare the results of the two methods. 51 Activity 7 A rage of differet rectagular shapes is draw o squared paper. Studets cout aroud the edge (as if they were walkig it) to get the perimeter of each shape.

52 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Activity 8 Fidig the perimeter: walkig the lie A farmer wats to measure the perimeter of a field o his farm. He kows the legth of each edge of his field. Help him to fid the total distace as he walks aroud. Start at A ad follow the arrows, writig dow the distace as you walk. A 10m 8m 8m 52 10m Distace walked: 10m Perimeter = m

53 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 3: Mathematics Now fid the perimeter of the fields below i the same way m 11m 2m 4m 4m 4m 5m 2m 6m 6m 5m 3 4 6m 3m 3m 4m 3m 53 5m 7m 4m 5 3m 6 6m 2m 2m 2m 2m 4m 4m 4m 5m 2m 2m 2m 2m 2m 4m

54 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Syllabus topic: Busiess Studies: The Busiess of Livig Mathematics: Applied Arithmetic ad Measure Goig shoppig Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Number Strad uit: percetages Strad: Measures Strad uit: Moey Juior Certificate (Ordiary level) Applied Arithmetic ad Measure: Bills. Profit ad Loss. Percetage profit. Percetage discout. Busiess Studies: The Busiess of Livig: Budgetig Juior Certificate School Programme Mathematical Educatio: Use of calculator Apply the kowledge ad skills eeded to maage moey i daily life. Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to six class periods, depedig o the progress of the studets. Potetial areas of difficulty > Difficulties i uderstadig mathematical operatios, such as additio, subtractio, multiplicatio, percetages > Limited vocabulary, creatig difficulty with terms like discout, total, subtotal > Limited sight vocabulary, creatig difficulty with the ames of grocery items ad acroyms such as V.A.T. > Short attetio spa ad lack of cocetratio ad applicatio > Poor motor skills, creatig difficulty with usig calculators > Followig istructios 54 Strategies used i this exemplar Laguage developmet through listeig, talkig, discussio, copyig, writig, readig for choice, etc. Reiforcemet techiques, usig graded extesio ad developmet of tasks Usig real materials, for example ewspaper advertisemets (full page spreads of special offers), receipts from local shops, calculators (icludig large-keyed oes) as used i some hardware shops. Pair work ad role playig Usig studets persoal experiece Visual aids, such as the OHP/data projector ad wall charts ICT Resources Newspaper advertisemets, shop receipts, special offer otices Calculators, icludig large-key oes Packagig of grocery items; stickers for pricig Paper ad markers for studets wall charts Some good software is available that allows studets to use a calculator o scree, for example Edmark Calculator collectio, Maths Made Easy

55 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. egage i discussio o the uses of moey 1. Moey Talks activity (p 56) 2. Pair work o weekly sped together with developig coi skills 1. Observe studets talkig about ad/or illustratig four poits about the uses of moey. 2. Studets assess their ow estimatig accuracy by compariso with actual costs. 2. be aware of appropriate uses of moey i their ow lives ad of the value of moey 3. Class discussio o persoal expediture o a particular day 4. Role play of power cut i local shop Pairs assess each other o coi skills 3. Observe studets makig a list ad calculatig the cost. 4. Observe studets, i role, make lists ad calculatig the cost of their lists. 3. list items of persoal expediture 5. The class/group talks about goig out ad what it costs 5. Observe studets participatio i class/group work. 4. list typical items of daily grocery expediture 5. list typical items for a eveig s etertaimet, ad calculate the total cost 6. calculate multiples of uit prices usig multiply fuctio o calculator. 6. Studets pla a class outig to the ciema 7. Sales, discouts ad calculator work. - Oe works o estimate, the other o cost, ad thay compare them. - Studets list items ad prices, the totals. - Discuss ay problems with estimatig or big differeces betwee the estimate ad the full cost. 6. Observe studets participatio ad ivolvemet i activity. Note studets ability to use calculator correctly. 7. Observe studets i pairs makig their ow sales posters ad labels. 55

56 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Activity 1 Moey talks Keywords Keywords that may arise durig the discussio iclude moey, otes, cois, euro, cet, shoppig, bill, charge, chage, cheque, credit card, laser card, loyalty card, save, bak, accout, Post Office, credit card, holiday, bus fares, trai fares, sigle, retur, studet rate, pocket moey, tax, VAT, restaurat, tip, value for moey, sale, discout, profit, loss. Pairs Some sets of cards ca be produced with keywords ad their meaigs. Ideally, the meaigs ca come from the studets uderstadig of the words as a result of classroom discussio. Some sample cards are show below. I twos or threes, studets play a matchig memory game by puttig the cards ito a words pile ad a meaigs pile, turig all of the cards upside-dow, mixig them aroud (withi their piles), ad takig it i turs to tur over oe from aywhere i each pile. If they pick a word ad its correct meaig they keep the pair ad get aother tur. Otherwise, they place the cards back i their origial positios ad the ext perso has a go. The studet who collects the most pairs is the wier of the game. 56 Sample cards for Pairs game Words pile Cois Notes Value for moey Discout Meaigs pile Moey that is made from metal Moey that is made from paper It s worth what you pay for it The price is cheaper tha usual

57 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Activity 2A Studets are preseted with a card, each card showig differet amouts of moey i euro ad cet. I pairs studets discuss how they would sped their moey over the course of a week. This ca be followed up by a class discussio o what sort of thigs it is appropriate to sped moey o, value for moey, savig etc. Activity 2B You owe me Studets work i pairs. The aim of this activity is for oe studet to ask for a certai amout of moey ad for aother studet to try to make it up i the least amout of cois possible. The teacher ca write a list of possible amouts o the board or studets ca make up amouts themselves. Studets ca complete the secod ad third rows of a table such as the oe below for assessmet purposes. (The table is show fully completed.) 57 You owe me: 50 cet 30 cet 1 euro 15 cet 5 euro 23 cet 4 euro 61 cet List of cois received 50c 10c, 20c 1, 5c, 10c 2, 2, 1, 20c, 2c, 1c 2, 2, 50c, 10c, 1c Least umber of cois possible

58 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Activity 3 How do you sped your moey? I a class discussio studets are ivited to braistorm all aspects of persoal expediture i a typical day. The teacher writes them o the OHP, with the costs supplied by the studets. Studets select ad list three/four items, with prices, bought o a typical day, selectig them from the OHP. Studets calculate the total cost. Use Work-card 1 for studets who are ot sure about layout. Use calculators. What chage would you get from? Extesio activity Studets could brig i shop receipts to check real costs. A wall chart of shop special offers could be used ad the total cost of two/three items calculated. Activity 4 Makig out bills. Make up a story about a power cut i a local shop. A calculator has to be used to work out bills. 58 Boxes ad packagig of commo products ca be used, alog with price stickers based o real till receipts or advertisig charts from ewspapers. Studets role play customers ad shopkeepers, workig i pairs/threes. Oe studet ca write out a list of messages with a estimate of prices ad a estimate of the total, the secod calculates the real cost, ad the third, (a store detective perhaps) checks the bill. The umber of items ca be varied to suit studets capabilities. Work-card 2 ca provide practice, if ecessary. Note: Studets could brig i shop receipts to check real costs. Activity 5 Eveig etertaimet The class/groups talk about goig out, what it costs, where they like to go, what they ca afford, hidde costs, etc. List three items with costs ad roud up or roud dow. Calculate total estimate. List the items with real prices, rememberig to use decimal poits. Calculate the total usig a calculator. Compare ad discuss results. Workcard 2 may be used as a template for this activity.

59 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Activity 6 Trip to ciema Studets pla a class outig to the ciema. They calculate how may tickets are eeded. If the bus costs 80c each, how much would be paid i all for the bus? The teacher buys treats for class members. How may Tarz bars would be eeded ad how much each do they cost? Estimate ad the calculate usig the multiply fuctio o the calculator. A effective assessmet of this learig outcome would be to pla a real class/group outig, do all the estimates ad calculatios, go o the outig, ad see if the estimates ad calculatios were right. A trip to the local pizza parlour would be just as useful. Activity 7 59 Iitiate a class discussio recallig percetages, discouts i sales (20%, 50% off) ad supermarket or shop posters of % discouts. Sale time! Usig a calculator to work out % discouts of 10%, 20%, 50%. Aims: To eable each studet to build o previous kowledge of percetages, for example 50% of 1 = 50c, 25% of 1 = 25c = 0.25, 15% of 1 = use a calculator to get a % of a umber. calculate a % discout. The teacher istructs studets to use a calculator to get 15% of 60 as follows: Key i.15 x 60 = ANS. Key i 60 - ANS = Discout price. Studet tasks: Make out SALE labels for items of clothig. Make out a SALE poster for four/five special offers Use Work-card 3 as a example, if ecessary.

60 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Workcard 1 2 c Crisps. Sweets. What chage would you have from 21? Total. Crisps. Bar. What chage would you have from 22? 60 Fizzy drik. Total. Milk. Juice. Bread. What chage would you have from 25? Tea Bags. Total.

61 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Workcard 2 Write these prices to the earest c Write dow the total estimate. (Add the figures i the boxes.) 2 Usig the calculator, add the real prices. 2

62 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 4: Mathematics Workcard 3 PRICES SLASHED! Not to be missed! Up to 50% off all Stock! Ruers were 370 Now oly % discout? 62

63 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Syllabus topic: Sources of icome ad iterpretig payslips Icome ad payslips Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Measures Strad uit: Moey Strad: Data Strad uit: Represetig ad iterpretig data Juior Certificate (Ordiary level) Sectio Oe - The Busiess of Livig, Budgetig: Expediture. Juior Certificate School Programme Busiess Studies Persoal Fiace: Maage persoal fiaces i the areas of icome, expediture ad budgetig Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to five/six class periods. The time scale ca be adjusted accordig to the teacher s assessmet of class/studet achievemet of targeted outcomes. Potetial areas of difficulty > Poor vocabulary (failure to uderstad termiology such as gross, et, deductios, etc.) > Delayed laguage developmet (failure to uderstad acroyms such as PAYE, PRSI) > Poor uderstadig of cocepts > Spatial awareess (iability to iterpret pie charts ad figures uder differet headigs i payslips) > Trasferrig learig to real-life situatios (such as idetifyig sources of icome beyod studet s experiece) 63 Strategies used i this exemplar Laguage developmet (busiess terms such as gross, et, PAYE, etc.) The use of reiforcemet techiques The use of cocrete materials Role playig as employer ad employee Pair work Class discussio The use of studets persoal experiece The use of visual material o the OHP ad wallcharts Case studies/examples Itroductio to the jobs sectios of ewspapers Resources Play/Moopoly moey Pes, paper, etc. for studets to draw wall charts Jobs sectios from ewspapers Acetate for the OHP or lamiated wall charts (which ca be writte upo several times), showig a pie chart with slices labeled PAYE, PRSI, ad Net Icome

64 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. describe ways i which people get moey 2. uderstad the words: job/ employmet, wages/ earigs/ icome, uemploymet beefit 3. ame differet sources of icome 1. Braistormig ad discussio 2. Keyword approach 3. Groupwork usig characters from TV soap. 4. Agoy aut role play 5. Discussio usig examples 6. Discussio followed by examples. Calculator work i pairs. 1. Observe studets describig three ways i which people ca get moey. 2. Observe studets completig Worksheet A, matchig forms of icome to their sources. 3. Observe studets workig i groups to draw wall charts showig the possible sources of icome for each of the people idetified. 4. uderstad why people get social welfare paymets 5. discuss the differet words describig uemploymet beefit, ad other fiacial supports such as Disability Allowace, Old Age Pesio, etc. 6. uderstad part-time work ad apply differet methods of paymet 4. Observe studets completig Worksheet B to idetify the reasos why people receive Social Welfare paymets. 5. Observe studets completig Worksheet C, matchig photocopies of beefit books to words ad pictures. 6. Observe studets participatio i discussio ad calculator work. 64

65 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Suggested outcomes Supportig activities Assessmet strategies 7. Apply a hourly rate of paymet use calculators to work out a weekly wage for thirty-five hours work discuss why some people ear more per hour tha others 7. The teacher offers to pay studets a hourly rate for every hour i school today. Usig calculators, the studets calculate how much they are etitled to ear. Studets work i pairs, usig calculators, to work out a weekly wage for thirty-five hours work. 7. Observe studets completig Worksheet D, i pairs, to calculate the weekly wage for give scearios about hourly rates of paymet. Observe studets suggested aswers to the fial questio i Worksheet D, leadig to a geeral discussio about how much people ca ear i differet jobs. 8. Apply a piece rate of paymet 8. The teacher offers to pay studets a set rate for every page they have used i their copybooks (piece rate). Usig calculators, the studets calculate how much they are etitled to ear. 8. Observe studets completig Worksheet E, i pairs, to calculate the weekly wage for give scearios about piece rate paymet. 65 use calculators to work out a weekly wage for a perso beig paid by piecework Studets work, usig calculators, work i pairs to calculate a weekly wage beig paid to a perso for piece work. 9. Uderstad the cocept of overtime 9. The teacher iitiates a geeral discussio about the cocept of workig more hours tha usual i a week. For example, i a school settig studets may be ivolved i sport or other extra-curricular activity. Itroduce the cocepts of overtime paymet ad double time. 9. observe studets completig worksheet F, i pairs, to calculate the overtime rates ad paymets for a give sceario.

66 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Worksheet A People get moey for differet reasos Draw a lie to joi a ewspaper advertisemet with oe of the words o the bottom of the page. Do the same for each of the other advertisemets too. Perso wated to serve behid deli. Great Aut Maud has died ad left all her moey to her family. If you are oe of them, you have bee left by her. Cogratulatios! You have wo 2100 i our raffle! Newsflash! The Old Age Pesio has goe up to 2166 per week. Happy Birthday! Here is 225 for you to sped o yourself. Teacher wated for very ice class of studets. 220 per hour. 66 Employmet Wiigs Work Iheritace Social Welfare Preset Note: This exercise could be exteded by usig a page from the Job Sectio of a curret ewspaper. A class discussio could take place about the differet types of job that a perso ca get, the differet rates of paymet that they may ear, ad so o.

67 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Activity 1 Studets are ivited to braistorm o all the ways people ca get moey (work, wiigs, presets etc.) Activity 2 Write key words o board or place chart with them o the wall. Explore the meaig of each oe with the studets. Talk through examples of each word, its use ad meaig. Studets use the job sectio i a local ewspaper to categorise differet types of job. Teacher may use a website such as loadzajobs.ie to show the differet job categories available. Studets complete Worksheet A; this ca be doe i paris. The teacher will read through the worksheet so that readig does t preset a difficulty to the studets ability to do the task. Activity 3 67 Studets use characters from popular soap operas of other TV programmes to idetify the types of icome that a teeager, a perso/family o social welfare, ad a perso/family i employmet might have. Studets work i groups to draw/make wall charts showig the possible sources of icome for each of the people idetified.

68 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Activity 4 Teacher reads the followig example with the studets. Studets work i pairs to aswer the questios ad complete the exercise. Worksheet B Extract from the Agoy Aut colum of a ewspaper. 1. Dear Miss Trust, Havig worked i a shop for 10 years I have just lost my job. I worked hard ad eared 250 every week. What will I do ow? I will have o moey at all, so how will I buy myself food or aythig else? Yours sadly, S Hopgirl. Dear Ms Hopgirl, Do t worry too much. You will get some moey from the Govermet eve though you are ot workig. They will give you moey every week, which is called Uemploymet Beefit util you start workig agai. Good luck with the job hutig! 68 Miss Trust. Ca you help Ms Hopgirl to get a job? Have a look at Worksheet A ad see if you ca suggest a job that she could apply for. Ca you take Miss Trust s place ad aswer a problem? Try to fill i the blaks usig the words at the bottom of the page. Dear Miss Trust, I am a old ma ad am about to retire from work. What will I do? If I am ot workig, I will ot ear ay moey. How will I pay my bills? Please help me. Yours, P. Esioer. Dear Mr. Esioer, Do ot worry. You will be able to your bills. The will give you moey every week. It is called the Old Age ad you will get 166 each. Miss Trust. Week Pay Pesio Govermet

69 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Activity 5 The teacher leads a discussio o the purpose of fiacial supports usig photocopies of a Social Welfare Book, o Old Age Pesio book, a Child Allowace book, etc. Welfare.ie is a useful site - if access is possuble. Studets the complete the followig excersie or similar matchig activity where examples are matched with appropriate services ad beefits. Worksheet C Who am I? Draw a lie from each descriptio i Colum 1 to a picture of a perso i Colum 2. Colum 1 Colum 2 Colum 3 I caot work every day because I am i a wheel chair ad I have to go to hospital very ofte. OAP book I used to be a maager i a office but I retired whe I tured 65 years old. Disability Allowace book 69 I have bee lookig for a job but have ot foud oe yet. Child Allowace book I have three childre that I love very much. Uemployet Beefit book Now, ca you match the perso with the right Social Welfare book? You ca draw aother lie from each picture i Colum 2 to the right picture i Colum 3.

70 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Activity 6 Teacher leads class discussio o part-time jobs studets may have. Discussio is led to explore why some people might choose to work part-time. They discuss The wages they ear How pay is orgaised Whether they get paid weekly Whether paymet is by time or by piece rate Activity 7 The teacher offers to pay studets a hourly rate for every hour i school today. Usig calculators, the studets, workig i pairs, calculate how much they are etitled to ear. Studets work i pairs to work out a weekly wage for 35 hours work. Activity 8 The teacher offers to pay studets a set rate for every page they have used i their copybooks (piece rate). Usig calculators, the studets calculate how much they are etitled to ear. 70 Studets work i pairs, usig calculators, to calculate a weekly wage beig paid to a perso for piece work. Activity 9 The teacher iitiates a geeral discussio about the cocept of workig more hours tha usual i a week. For example, i a school settig studets may be ivolved i sport or other extra-curricular activity. Itroduce the cocepts of overtime paymet ad double time. Studets may the work i pairs o completig Worksheets D,E, ad F. The teacher

71 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Worksheet D Ca you ad your parter work out how much these people will be paid for their week s work? Write the aswer i the boxes. 1. Paul has got a job i his local shop. He will work for thirty-five hours every week ad the ower will pay him 6 per hour. How much will he ear i a week? Aswer 2. Peter has bee employed by the local hospital as a urse. He will receive 15 for every hour that he works. How much will he be paid whe he works for a thirty-five hour week? Aswer 3. Elizabeth is goig to work i a office i tow. She must work for thirty-five hours ad will be paid 7.50 per hour. How much will her pay be? Aswer Kylie has got a job as a siger ad will ear 150 per hour. If she works for thirty-five hours per week what will she receive? Aswer 5. Robbie has joied a football club ad will ear 375 per hour. At the ed of a thirty-five hour week, how much will he be paid? Aswer Which job would you like to have? Ask your parter which job they would like best. Why do you thik some people are paid more tha others for a hour s work?

72 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Worksheet E Ca you ad your parter work out how much these people will be paid for their work? Write the aswer i the boxes. 1. Breda is a good cook ad he ca make lovely cakes. He is paid 7 for each cake he makes. If he makes four cakes o Moday how much will he ear? Aswer If he makes eleve cakes o Tuesday how much will he ear? Aswer Wedesday is his day off so he does ot make ay cakes at all. O Thursday he makes eightee cakes. What will he ear? Aswer 72 Friday is a busy day so he makes twety-five cakes. What will he be paid the? Aswer Saturday is busy too, so he makes thirty cakes. What will he be paid the? Aswer How much will Breda ear i the whole week? (Hit: Add together his pay for each day.) Aswer

73 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics 2. I Coroatio Street Mike Baldwi pays his staff for each item of clothes that they sew. Suppose he pays them 4 for each item. If a worker makes te items i a week how much will he/she be paid? Aswer If a worker makes sevety-five items i a week what will he/she ear? Aswer 3. If a worker works faster will he/she ear more moey or less moey tha before? Draw a circle aroud the right aswer below. More Less 73

74 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 5: Mathematics Worksheet F Ca you ad your parter work out how much these people will be paid for their work? Write your aswers i the boxes. 1. Sheila s boss has asked her to work i his shop o Sudays before Christmas. She usually gets paid 6 per hour, but the boss agrees to pay her double time for workig o Sudays. How much will she ear for every hour she works? Aswer If she works for seve hours o a Suday how much will she ear? Aswer 2. Steve is workig late this week. He is usually paid 15 per hour. 74 If he usually does thirty-five hours work durig the week how much will he ear? Aswer His boss has decided to ask Steve to do some extra work. He will pay him double time for workig i the eveigs. How much will his hourly rate be i the eveigs? Aswer He works for two hours overtime o Moday eveig. How much will he be paid for that? Aswer O Thursday eveig he does five hours overtime. What will he ear for that? Aswer How much will Steve ear for the whole week? (Hit: Add up his basic wage ad his overtime paymet for Moday ad Thursday.) Aswer

75 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Syllabus topic: The Busiess of Livig Aalysed Cash Books Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Measures Strad uit: Moey Strad: Data Strad uit: Represetig ad iterpretig data Juior Certificate (Ordiary level) Busiess Studies: The Busiess of Livig, Budgetig: Expediture. Juior Certificate School Programme Accoutig:Uderstad ad use basic budgetig ad accoutig methods ivolved i home, club ad compay accouts Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to seve class periods. The time scale ca be adjusted accordig to the teacher s assessmet of class/studet achievemet of targeted outcomes. Potetial areas of difficulty > Short-term memory (rememberig that debit side represets what goes i, etc.) > Poor vocabulary (difficulty with uderstadig termiology such as debit, credit, balace) > Spatial awareess (recogisig debit ad credit sides i Record Book, copig with the umber of aalysis colums, completig ad balacig the Cash Book i the required format) > Trasferrig learig to real life (recogisig the usefuless of recordig trasactios) > Performig calculatios 75 Strategies used i this exemplar Laguage developmet (developig a vocabulary of busiess terms, such as debit, credit, balace) Role-playig shoppig Pair/small group work Class discussio The use of Tossig the Coi game The use of cocrete materials The use of structured worksheets The use of visual material o spreadsheets or wallcharts The use of reiforcemet techiques The use of websites to reiforce the topic

76 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Resources Photocopies of the class roll book, a homework otebook, ad a diary Large cardboard or lamiated discs Moopoly/play moey Paper for wall charts Scissors A purse Calculators Iteret access to Computer spreadsheet package (optioal) 76

77 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of these activities studet should be eabled to 1. uderstad the cocept of keepig records 1. Iitiate a class discussio about the purpose of a class roll book, a homework otebook, ad a diary, usig photocopies of each as support. 1. Observe whether studets ca iterpret a sample roll book as show i Worksheet A. 2. explore differet reasos for keepig records 2. Followig o from Worksheet A, braistorm for ideas about who might keep records. Suggestios might iclude school records, doctors records, detists records, bak accouts, service providers (ESB), etc. 2. Observe studets participatig i a braistormig sessio ad explaiig the types of records that may be kept. 3. appreciate the beefits of keepig persoal fiacial records 3. Studets work i pairs to complete Worksheet B, sortig pictures of items ad moey ito those received ad those paid. 3. Observe whether studets ca describe why it is a good idea to keep fiacial records aalyse expediture uder appropriate headigs 4. Cocetratig o expediture, iitiate a class discussio to decide o aalysis headigs suitable for average family. 4. Observe studets usig Family Diary (Worksheet C) to group items of expediture uder give headigs. 5. uderstad how to keep persoal records of moey received ad moey spet 5. Studets work o worksheet D 5. Observe whether studets ca complete Worksheet D, dividig amouts of moey ito received ad paid. 6. uderstad the terms debit ad credit 6. Tossig the Coi game See Game 1, p Observe whether studets ca make five correct guesses as the coi is tossed. 7. trasfer that kowledge to bookkeepig 7. Use a chart or spreadsheet to demostrate the debit ad credit cash colums of a cashbook. 7. Observe whether studets ca complete Worksheet E, recordig moey received ad spet, usig small amouts. 8. calculate the remaiig balace 8. Role-play shoppig. (How much moey is left?) 8. Observe studets, usig play or Moopoly moey, role-playig the scearios o Worksheet E to calculate how much moey each perso would have remaiig.

78 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Suggested outcomes Supportig activities Assessmet strategies 9. recogise ad become familiar with the relevat terms. 9. Usig play moey ad a purse the teacher demostrates that moey left to sped is available for spedig i the future. It may be appropriate to use basic terms such as balace. 9. Observe studets completig Worksheet F, usig a calculator to work out how much moey remais i the purse. 10. apply the terms to balacig a cashbook 10. Wall chart 1 A diagram of a old-fashioed weighig scale is used to reiforce the cocept of balace. 10. Observe studets completig Worksheet G to calculate the balacig amouts. 11. apply the techiques of balacig a cashbook 11. Use Worksheet H to reiforce the cocept of balacig. 11. Observe studets completig a wall chart/spreadsheet (Wall chart 2) idividually or i teams by affixig the correct amouts ad terms. 12. complete a Aalysed Cash Book 12. Usig a spreadsheet the teacher completes a Aalysed Cash Book. 12. Observe whether studets ca idicate the amout of moey remaiig i each cashbook revise what they have leared. 13. Usig studets ca revise the etire topic. 13. Observe whether studets ca allocate the expediture to the correct aalysis colum Ad if they are able to total ad balace the Cash Book. 14. Self-assessmet tests ad exercises are icorporated ito the lesso o

79 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet A A page from a school roll book Name Mo Tues Weds Thurs Fri Mo Tues Weds Thurs Fri 1. Joe Browe James Carroll m Sharo Darcy Kevi Fly 3 3 m Ciara Gly m Barry Hayes Deirdre Key Joae Kisella m m m m m Jim Marti Fioa O Brie m m 11. Breda Rya Paul Scully m m m Gemma Ward m Susa Ward m Note: The followig might be some questios that the class could discuss: How may people i the class? How may boys? How may girls? Who was abset o the first Moday? Fid someoe who was i school every day. Who had the most abseces? Why does a teacher keep a roll book? What other records does the school keep about studets? Why does the school keep these records?

80 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet B Ca you help Peter? He is i a awful muddle about his moey ad does t kow how much he spet or whether he should have ay moey left. Workig i pairs cut out the pictures at the top of the page ad stick them ito the correct colum. If Peter received moey put the pictures ito the Moey I colum. If he spet moey o them put the pictures ito the Moey Out colum. 80 Moey I Moey Out

81 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Maths Mathematics Worksheet C 81 Look at the thigs that the Mulle family bought last week. Workig i pairs cut them out ad stick them ito the correct colum. Groceries House Clothes Etertaimet Other

82 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet D Now you must put the figures i the correct colum. If Peter received moey write the amout ito the Moey I colum; if he spet moey write the amout ito the Moey Out colum. Peter got 30 for his birthday from his Gradmother. He bought a CD for 20 ad a book for 10 with this moey. Peter s Dad gave him 5 for washig the car ad he also eared 30 from his part-time job. He bought a ew t-shirt for 20, some sweets for 2, ad a ca of lemoade for 1. Moey I Moey Out 82

83 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet E Read the followig stories. You have to keep the records for each perso. If the perso gets moey i put the amout ito the Credit colum. If the perso speds moey put the amout ito the Debit colum. Sarah eared 25 for her Saturday job. She bought a magazie for 3 ad some make-up for 12. Debit Credit Magazie a Earigs a Make up a Michael received 50 as a birthday preset. He bought a DVD for 28, sweets for 3, ad a book for 8. Debit Credit DVD a Preset a Sweets a Book a 83 Mr. Johso received his wages of 350. He bought groceries i the supermarket for 70, spet 30 o petrol for his car, paid his mobile phoe bill for 60, ad bought a pair of shoes for 65. Debit Credit Groceries a Wages a Petrol a Mobile Phoe Bill a Shoes a This time you have to write the words as well as the amout of moey i the correct colum. Remember, if the perso gets moey i put the amout ito the Debit colum. If the perso speds moey put the amout ito the Credit colum. Broa wo 100 o the Lottery. She bought a pair of boots for 50 ad a top for 30. Debit Credit a a a

84 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Kevi eared 40 for babysittig ad 25 for deliverig leaflets. He bought a phoe card for 20, batteries for his Walkma for 6, ad a buch of flowers for his Mum for 9. Debit Credit a a a a a Mrs. Maguire received her wages of 500. She paid 40 to the detist, bought groceries i the supermarket for 80, ad paid 44 for the family to go to the ciema. She wo 10 o a Lotto card. Debit Credit a a a a a 84

85 a2 a5 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet F How much do I have left? Use your calculator to work out how much moey is left i each purse whe the thigs below it have bee bought. Write the aswer i the box give. Aswer: a1 a1 85 Aswer: a10 Aswer: a16 a15 Aswer:

86 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics a54 Aswer: 86

87 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet G Balacig How much would have to be added to the weighig scales each time so that it would be balaced? 55 = 53 5? 520 = ? = ? = ?

88 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Worksheet H Balacig a cashbook (i) Write the balacig figure i the box i each of these cashbooks. Debit Credit Earigs a25 Magazie a3 Make Up a12 Balace a Debit Credit Preset a50 DVD a28 Sweets a3 Book a8 Balace a 88 Debit Credit Wages a350 Groceries a70 Petrol a30 Mobile Phoe Bill a60 Shoes a65 Balace a Debit Credit Wages a350 Detist a40 Lotto a10 Groceries a80 Ciema a40 Balace a

89 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Balacig a cashbook (ii) Write the total figures i the boxes i each of these cashbooks. Debit Credit Earigs a25 Magazie a3 Make Up a12 Balace a12 a a Debit Credit Preset a50 DVD a28 Sweets a3 Book a8 Balace a11 a a 89 Debit Credit Wages a350 Groceries a70 Petrol a30 Mobile Phoe Bill a60 Shoes a65 Balace a125 a a Debit Credit Wages a500 Detist a40 Lotto a10 Groceries a80 Ciema a44 Balace a346 a a

90 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Balacig a cashbook (iii) Fill i the boxes to show the amout the perso has left i each of these cashbooks. Debit Credit Earigs a25 Magazie a3 Make Up a12 Balace a12 a25 a25 Balace a Debit Credit Preset a50 DVD a28 Sweets a3 Book a8 Balace a11 a50 a50 Balace a 90 Debit Credit Wages a350 Groceries a70 Petrol a30 Mobile Phoe Bill a60 Shoes a65 Balace a125 a350 a350 Balace a Debit Credit Wages a500 Detist a40 Lotto a10 Groceries a80 Ciema a44 Balace a346 a510 a510 Balace a

91 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 6: Mathematics Game 1 Tossig the Coi game Two large two-sided discs made from cardboard or lamiated paper are required by each pair or group of studets. Disc 1: I prited o oe side ad Debit prited o the other Disc 2: Out prited o oe side ad Credit o the other Oe perso tosses a coi (disc) ad whe the studet sees the side that is facig upwards he or she must guess the word o the other side. Note: A score may be kept i this game i order to ascertai a wier. Alteratively, each studet may be required to cotiue guessig o each toss util they have made five correct guesses. 91

92 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Maths Mathematics Syllabus topic: Statistics Collect, display ad iterpret Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Data Strad uit: represetig ad iterpretig data Juior Certificate (Ordiary level) Statistics 1. Collectig ad recordig data. Tabulatig data. Drawig ad iterpretig bar-charts, piecharts ad tred graphs. 2. Discrete array expressed as a frequecy table. Juior Certificate School Programme Sets, relatios ad charts: draw a bar chart/ tred graph, complete a frequecy table, work out the mode ad mea Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to twelve class periods. Potetial areas of difficulty > Uderstadig cocepts (such as mea, mode) > Trasferrig learig to real life (iterpretig graphs, uderstadig survey data) > Spatial awareess (difficulty with drawig graphs) > Laguage (uderstadig ad formulatig aswers to questios asked about graphs) 92 Strategies used i this exemplar Usig studets persoal experieces Usig appropriate ict resources Usig cross-curricular approaches Ecouragig studets to use relevat mathematical laguage situatig mathematics i real- life cotexts Adaptig the requiremets of the task Resources A selectio of ewspapers ad magazies, posters, coloured pes ad pecils, rulers, graph paper Appropriate ICT facilities (for example, a spreadsheet package) The classroom may eed to be rearraged to facilitate group work. Studets may eed some iput (o oral commuicatio skills) ad practice o presetig a project to the class if they have ot doe this before.

93 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to recogise bar, tred, ad pie charts collect ad record simple data gathered from their classmates show simple data o a frequecy table represet simple data o bar/tred chart ad draw simple coclusios from the data idetify the mode (most frequet item) calculate the mea (average) from simple data commuicate their work to classmates use ICT to draw charts Studets gather ad discuss magazie ad ewspaper cuttigs of charts ad data. Refer to the bar-chart for ask the audiece results i Who Wats To Be a Millioaire. Uder the guidace of the teacher the studets each produce a tally chart for the class showig how studets travel to school, for example: Travel by Tally chart Number of studets Bus 7 Car 5 Walk 10 Bicycle 8 This leads to a frequecy table as follows: Trasport Bus Car Walk Bicycle No. of studets Studets the draw a bar chart ad a tred graph to represet the iformatio Questios will assist studets to draw coclusios (for example, Which method of travel is most/least popular? Why might this be? How may more studets walk tha come by car?). Note: Mea (average) does ot apply to this example. After workig through the above example studets ca udertake a statistics project as outlied i the Plaig for Statistics sheet o pages 94 to Studets complete a simple questioaire or worksheet after the iitial activities, but before startig the project. The teacher observes whether they recogise various kids of charts kow how to record data usig a tally chart kow how to use a frequecy table to record data ca costruct ad use various kids of charts kow how to calculate mea ad mode. The teacher ca use the feedback from these assessmets to assist i guidig studets towards suitable tasks durig the project (reiforcemet, gaiig of ew skills, etc.). As the project proceeds, the teacher ca assess further, by observatio, the studet s ability to collect, record, ad tabulate data, to choose ad draw charts, ad to commuicate the work. 93 These outcomes may be assessed by methods suggested followig the descriptio of the activities below. Cross-curricular liks: These skills ca be reiforced if similar cocepts i geography (data represetatio ad iterpretatio) ad CSPE (Actio project) are treated at the same time.

94 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Activity 6 Plaig for a Statistics Project The Project Plaig Sheet ad Six Steps i Project Work sheets outlied i the JCSP studet profile system hadbook offer a useful outlie for studets workig o projects, ad ca be adapted specifically for use with mathematics. A suggested adaptatio for both sheets is outlied below. Statistics Project Plaig Sheet Name of Studet Date Title ad Descriptio of Project 94 The title of my project is I will gather iformatio from my class about I will display the iformatio usig Other iformatio What I will lear from this project: Durig my work o this project I will lear how to

95 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Activities Decidig how to gather iformatio from the class Names of people resposible Whole group Desig a way to gather the survey iformatio Carryig out the survey Makig a table to show the iformatio gathered Draw a bar chart to show the iformatio Draw a tred graph to show the iformatio Fid the mea ad mode from the iformatio Write dow some coclusios that ca be made from the iformatio gathered Display the work o a poster Discuss what was leared from doig the project Whole group Preset the work to the class who explais what? Further Notes o a Statistics Project Whe studets are decidig o a topic o which to gather data from classmates the teacher could provide a list of possible topics to choose from, for example 95 favourite foods shoe sizes bed times heights of moutais favourite film stars favourite pop stars or groups pets birthdays area of hads temperatures traffic cout frequecy of occurrece of letters of the alphabet o a page of a book (why does e have the shortest symbol i Morse code?).

96 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Studets should decide o a suitable way to record the data (iformatio) ad test that it works by surveyig their ow group (for example, tally charts, frequecy table, pictorial represetatio). A simple spreadsheet package ca be used for drawig graphs o the computer. Studets eter the data i the form of a frequecy table. Studets the use various optios to choose which kid of chart they would like to use, for example: How we travel to school Bus Car Walk Bicycle No. of studets Studets may eed some assistace i drawig coclusios from their data. A list of questios could be provided to help them. 96 Note: The above series of activities is based o groups of studets workig o a statistics project. Activities ca be differetiated through extra guidace by the teacher ad with studets choosig to complete various tasks withi the group.

97 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Assessmet strategy 6 Sample assessmet istrumet for statistics project presetatios (peer, teacher, ad self-assessmet) Studets ad teacher each have a sheet like the oe below with headigs suggestig various criteria o which studets presetig projects ca be assessed. Each studet is also ivited to make a statemet of self-evaluatio uder these headigs. Marks (e.g. out of 20) could be assiged uder each headig, or studets could be asked to ote oe stregth of the presetatio ad oe area that could be improved. It is importat that feedback is of a positive ature. Group Number Explaatio of how the survey was completed (why a certai topic was chose, how data was gathered, etc.) Explaatio of charts (why a certai kid of chart was chose, how it was draw, use of ICT, etc.) Layout ad presetatio of project (colour, legibility, use of headigs, etc.) Ability to draw coclusios from the data ad express them What the group leared from doig the project (how to work as a group, how to do a survey, how to draw coclusios from the iformatio, etc.) Sample assessmet scheme for statistics project Studets are give a copy of the assessmet table before startig the project, ad the allocatio of marks is clearly outlied. This eables studets to esure that all of the headigs are covered i their fial presetatio. The table is the completed by the teacher who fills i a mark based o the assessmet criteria outlied o the followig pages ad, if appropriate, a commet. Alteratively, the teacher ca cosult with the group of studets ad agree a mark based o the assessmet criteria. 97 Writte Presetatio (10 marks) Format, layout, eatess, legibility Use ad quality of illustrative material (pictures) 0-5 marks 0-5 marks Cotet (30 marks) Itroductio (reaso for choice of topic) Collectig ad recordig data Orgaisatio of data usig a suitable table Use of charts (with ad without ICTs) Use of statistical calculatios (mea, mode) Statemet of coclusios based o data Oral Presetatio (10 marks) Oral skills (speaks clearly, expresses i ow words, addresses whole class) Uderstadig of material What was leared from doig the project 0-3 marks 0-4 marks 0-4 marks 0-10 marks 0-5 marks 0-4 marks 0-3 marks 0-4 marks 0-3 marks

98 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Criterio- refereced assessmet The followig criteria are suggestios to assist the teacher i the assigmet of marks uder the headigs give i the table o page 145. Writte Presetatio (10 marks) Format, layout, eatess, legibility Mark (5) Criteria 0-1 Little effort made to orgaise material, which is difficult to follow. 2-3 Some effort made to preset material i a suitable format. 4-5 A high stadard of writte presetatio with well orgaised material was evidet. Use ad quality of illustrative material (pictures) Mark (5) Criteria 0-1 Little or o use was made of appropriate illustrative material. 2-3 Basic use was made of illustrative material. 4-5 Illustrative material used is of high quality ad very relevat. 98 Cotet (30 marks) Itroductio Mark (3) Criteria 0-1 Little or o effort was made to itroduce the project. 2-3 The itroductio clearly outlies the cotet of the project. Collectig ad recordig data Mark (4) Criteria 0-1 Data are ot orgaised ito a table. 2-3 A table is used but could be more suitable. 4 Data are orgaised ito a suitable table. Orgaisatio of data usig a suitable table Mark (4) Criteria 0-1 There is little or o explaatio of methods of data collectio ad recordig. 2-3 Demostrates some kowledge of appropriate methods of data 4 Demostrates kowledge of appropriate methods of data collectio ad recordig ad gives reasos for selectio of particular methods.

99 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 7: Mathematics Use of charts (with ad without ICT) Mark (10) Criteria 0-2 Few or poorly produced/explaied charts are used. 3-5 Some charts are used, but more variety ad explaatio are eeded. 6-8 Good stadard of charts 9-10 Very high stadard of charts Use of statistical calculatios (Mea, Mode) Mark (5) Criteria 0-1 Little or o calculatios are show. 2-3 Some calculatios are show. 4-5 Shows a clear uderstadig of statistical calculatios. Statemet of coclusios based o data Mark (4) Criteria 0-1 Makes little or o attempt to state coclusio. 2-3 Some attempt is made to state coclusios. 4 Makes clear ad relevat coclusios. 99 Oral Presetatio (10 marks) Oral skills (speaks clearly, addresses whole class) Mark (3) Criteria 0-1 Needs to speak more clearly ad address the class. 2-3 Commuicates with the whole class about the project. Uderstadig of material Mark (4) Criteria 0-1 No real uderstadig of the material is show. 2-3 Ca explai his/her ow sectio of the project. 4 Talks cofidetly about the project material. What was leared from doig the project Mark (3) Criteria 0-1 No statemet is made o what was leared. 2-3 Commuicates what was leared from the project.

100 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Syllabus topic: Algebra Algebra Activity Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Algebra Strad uits: Variables, Equatios Juior Certificate (Ordiary level) Algebra: Meaig of variable, costat, term, expressio, coefficiet. Evaluatio of expressios. Juior Certificate School Programme Not applicable Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to fiftee class periods. Potetial areas of difficulty > Short term memory (rememberig algebraic procedures) > Uderstadig cocepts ad abstractios (What is a ukow? What is a variable?) > Trasferrig learig to real life (usig problem-solvig skills i everyday life) > Poor vocabulary/laguage (problems with uderstadig algebraic terms) 100 Strategies used i this exemplar Group discussio of ideas liked to studets experiece Usig cocrete materials Usig games to reiforce cocepts, operatios, ad problem-solvig skills Ecouragig studets to use relevat mathematical laguage Visual represetatio of algebra (usig couters, straws, etc.) Resources Sooker balls or differet coloured disks (Activity 2) Materials such as straws, Plasticie, ad couters used to make patters (Activity 3A) Studets should be ecouraged to record their observatios i some way. All activities ca be ru as a whole class activity or i small groups. This exemplar makes use of some of the lesso ideas outlied i the Juior Certificate Guidelies for Teachers: Mathematics. Asterisks are used to mark sectios of the extract that cotai material ot relevat to the Juior Certificate foudatio level course. Teachers may fid it useful to use ad adapt other lesso ideas from those guidelies. Algebra is a theoretical topic ad may prove particularly difficult for some studets with mild geeral learig difficulties. Teachers are ecouraged to choose the learig outcomes, learig activities, ad assessmet strategies that best suit the eeds of their studets.

101 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to uderstad that algebra ivolves usig letters to represet thigs uderstad that a variable is somethig that ca take differet values recogise ad describe a patter usig a sequece of umbers use basic mathematical laguage to describe a patter or rule record umber pairs appropriately carry out simple calculatios i their heads orally solve simple verbal first degree equatios i oe variable demostrate some simple problem-solvig skills. 1. Use the Group discussio o algebra activity o page 102 to ecourage studets to thik of real-life situatios whe a letter or a symbol is used for short to represet somethig real-life situatios where a quatity varies. 2 Use Sookered! o pages & to itroduce the studets to the use of letters to represet umbers ad to the evaluatio of simple expressios. Note that a similar activity could be developed with scrabble letters Spot the patter (See page 112.) Guess my rule (see page 114.) This activity is based o the activity outlied i the Juior Certificate Guidelies for Teachers: Mathematics, Algebra lesso idea 3. Thik of a umber (see page 117.) 1. Observe whether studets ca give a simple verbal explaatio of what algebra is? give examples of a variable? 2. Have completed the worksheets i the Sookered! activity ad i pairs corrected the work. 3. Observe whether studets ca participate i the discussio outlied i this activity? describe what they are doig? state which quatities are variables? Observe how much directio studets eed. 4. Observe whether studets ca use appropriate laguage to describe the emergig patter or the rule. Oral calculatios quiz: The teacher goes aroud the class askig for aswers to simple calculatios (for example, 5 added to 2 gives? 10 mius 4 is? Double 3 to get?). The teacher should try to use a rage of differet terms for the same cocept ( subtract, mius, take away, less, etc.). 5. After activity 5 studets ca do the worksheet or role play (See page 117.). 101

102 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Activity 1 Group discussio o algebra A. For short Hold a group discussio o real-life situatios where a letter or a symbol is used to represet somethig. Some examples are icluded i the table below. Studets may eed hits from the teacher such as thik of clothes sizes. Letter or symbol Stads for z euro c cet p pece poud Letter or symbol s m l p Stads for small medium large page 102 Letter or symbol l m g Stads for litre metre gram Explai that algebra uses letters to represet thigs. Certai thigs ca be writte i a much shorter way i algebra tha i Eglish. Ecourage studets to thik of a shorter way to write each of the followig: Apple, Baaa, Coffee, Yoghurt, Pear. Ask studets to write a shorter versio of the followig shoppig list: 3 apples, 5 baaas, 1 jar of coffee, 4 yoghurts, 2 pears.

103 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics B.Thigs that vary Hold a group discussio o real-life situatios where thigs (umerical quatities) vary. Some examples are give i the table below. Studets may eed some examples to get them started. Ecourage discussio. For example, Why does it vary? What approximate values might it take, etc. Shoppig bill Cost of a pack of crisps Cost of a litre of petrol The amout of moey you have i your pocket Your shoe size Your age The mark you get i differet mathematics tests Time you sped asleep each ight The amout of rai that falls each day The temperature Explai that i algebra we are usually dealig with thigs that vary.these are called variables. For example, if we are measurig the temperature (T for short), it will probably be differet today tha it will be tomorrow. 103

104 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Activity 2 Sookered! The activity described here is reproduced from Algebra lesso idea 1 from the Juior Certificate Guidelies for Teachers: Mathematics. Title: Sooker balls ad variables! Topic: Algebra Aims: 1. To itroduce studets to the use of variables usig a sooker aalogy 2. To give the studets cofidece i usig variables algebra is ot just for the good classes Resources A set of sooker balls or differet coloured discs or coloured circles draw o the overhead or blackboard A large sheet showig the values of the differet coloured balls i sooker Pre-prepared worksheets 104 Method 1. Iitiate a opeig discussio about sooker. 2. Get the studets to give the value of differet sooker balls. Use a large sheet showig the values of differet coloured balls i sooker as a aid. 3. Write up a preted break o the board as follows: Red Blue Red Brow Ask studets to work out the value of the break score. More examples ca be doe ad the scores foud. 4. Studets ca be give a prepared worksheet (umber 1) to complete usig similar examples which ca be corrected immediately.

105 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics 5. The ext step is to ask studets to write out the preted break i words. The teacher should write clearly what each letter stads for: R = Red G = Gree U = Blue K = Black N = Brow Red Gree Red Gree Studets are asked: How may of each colour are there? Aswer: 2 red ad 2 gree (aswer to be give i this way). 6. Studets are the give aother worksheet (umber 2) with similar examples to complete. 7. Whe the secod worksheet is corrected a idetical worksheet (umber 3) is give out. O this occasio studets are asked to write the aswer as follows: Red Gree Red Gree 105 Aswer: 2R + 2G 8. The same worksheet (umber 4) is agai give to the studets. Now, studets are asked to substitute the value of each sooker ball ad arrive at the total break: Red Gree Red Gree Aswer: = 8 Example: 2R + 2G = 8

106 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics 9. A similar worksheet (umber 5) is give to studets to complete. O this occasio the variable expressio is give uder each example ad studets are asked to substitute the correct value ad arrive at the score break. The teacher shows a example first: Red Gree Red Gree Aswer: 2R + 2G = 2( 1) + 2( 3) = = 8 The studets are ow substitutig values for variables. The studets ca the progress to usig x ad y or other letters. It is possible for the teacher to combie the last two worksheets ito oe if so desired. Notes Classroom maagemet implicatios: Worksheets ca be doe idividually or i pairs. Strictly speakig, the letters i the above aalogy stad for objects ad ot variables per se. However, practisig teachers of mathematics have foud the lesso idea effective whe dealig with studets who fid algebra difficult. 106

107 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Worksheet 1 Sooker: work out that break! R = Red Y = Yellow G = Gree U = Blue K = Black N = Brow P = Pik Red 1 Yellow 2 Gree 3 Brow 4 Blue 5 Pik 6 Black 7 Work out the scores for each of the breaks below: 1. R U R G Break = R G R K R K Break = 3. R K R K R Pik R Break = 3. R U R N Break =

108 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Worksheet 2 Sooker: breaks ad words! R = Red Y = Yellow G = Gree U = Blue K = Black N = Brow P = Pik How may of each colour are i the followig breaks? 1. R G R G Total = 2. R Y R Y R 108 Total = 3. R P R P R P R Total = 4. R U R U Total =

109 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Worksheet 3 Sooker: breaks ad letters! R = Red Y = Yellow G = Gree U = Blue K = Black N = Brow P = Pik How may of each letter are i the followig breaks? 1. R G R G Total = 2. R Y R Y R 109 Total = 3. R P R P R P R Total = 4. R U R U Total =

110 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Worksheet 4 Sooker: letters ad additio! R = Red Y = Yellow G = Gree U = Blue K = Black N = Brow P = Pik Red 1 Yellow 2 Gree 3 Brow 4 Blue 5 Pik 6 Black 7 Work out the scores for each of the followig 1. R G R G Example 2R + 2G = R Y R Y R Total = 1. R P R P R P R Total = 1. R U R U Total =

111 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Worksheet 5 Sooker: letters ad substitutio! R = Red Y = Yellow G = Gree U = Blue K = Black N = Brow P = Pik Red 1 Yellow 2 Gree 3 Brow 4 Blue 5 Pik 6 Black 7 Work out the scores for each of the followig 1. R G R G Example 2R + 2G = 2( ) + 2( ) = R Y R Y R 3R + 2Y = 3( ) + 2( ) = 3. R P R P R P R 4R + 3P = 2( ) + 2( ) = 4. R U R U 2R + 2U = 2( ) + 2( ) =

112 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Activity 3 Spot the patter Studets take 4 straws ad arrage them i a square as show below. Studets cotiue to add straws i order to make more squares. Is there a patter to the umber of straws eeded to make a certai umber of squares? 2 squares are made from straws 3 squares are made from straws 112 Studets ca be ecouraged to fid a suitable way to record the iformatio. Oe possible example is the table show below: Number of straws Number of squares This activity could lead to a discussio istigated by questios such as: How may straws would you eed to make 5 squares? How may straws would you eed to make 8 square? How may straws would you eed to make 10 squares? Is there a way to fid out these aswers without havig to make all of the squares? Is there a patter to the list of umbers of straws eeded: 4,7,10,? (add 3) How could we describe this patter (startig at 4, go up i threes; treble the umber of squares ad add oe to get the umber of straws eeded.)? Ca we write this i mathematical terms? (for example, umber of squares = = 10 ). What chages or varies with each patter of squares? (The variables are umber of squares ad umber of straws.)

113 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Extesio activities The followig diagrams suggest other patters of shapes that could lead to similar discussio: Couters shaped as equilateral triagles: Number of rows of couters (x) Number of couters (y) Cubes made from plasticie: 113 Number of cubes across a row (x) Number of cubes i block (y)

114 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Activity 4 Guess my rule The activity described here is based o Algebra lesso idea 3 from the Juior Certificate Guidelies for Teachers: Mathematics. The lesso idea is also reproduced below i full for iformatio, although some of the cocepts icluded are ot appropriate for studets studyig the foudatio level course. Comparig this origial lesso idea with the modified exemplar shows how a idea ca be modified to suit studets with a mild geeral learig disability. Simplified example for Guess my rule The teacher thiks of the rule add 5. The studet says the umber 2. The teacher applies the rule ad says 7. The studet records 2 7 (or 2,7 or other suitable otatio). Aother studet says the umber 5. The teacher applies the rule ad says 10. The studet records The studet guesses rule correctly as add o 5. This studet ow makes up a ew rule ad the game cotiues. 114 The kid of rules used ca iclude add a umber, subtract a umber, multiply a umber, or a combiatio of these. It may be advisable to begi with a selectio of differet additio rules before progressig to the other operatios.

115 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Algebra lesso idea 3 Title: Guess my rule Topic: Elemetary algebra Aim: To develop the cocept of a variable Method 1. The teacher thiks of a simple (verbal) rule such as double ad add 1, ad challeges the studets to guess what this rule is. The teacher asks the studets to put forward umbers betwee, say, 0 ad 20. A studet the provides a umber. The teacher gives the result of applyig the rule ad this cycle is repeated several times. At ay stage a studet may offer a guess as to what the rule is. If the guess is wrog the studet may ot guess agai (or put forward aother umber) durig this game. Evetually (hopefully) the studets guess the rule. The teacher speds some time checkig to see that all studets uderstad ad ca apply the rule. Note At this stage symbols should be avoided ad the rule formulated i words (uless the studets themselves suggest some symbolic represetatio) The game is played agai, usig a differet rule (perhaps formulated by, or with iput from, the studet who idetified the rule correctly i the first game). If the studets have ot already see the eed to record umber pairs systematically the teacher suggests the strategy ad a appropriate format is agreed. 3. The studets form small groups ad play the game. The oe who guesses the rule formulates the ext rule. The teacher arbitrates where ecessary ad checks that the rules are beig applied correctly. The studets have to write the rules i their ow words ad explai them to the teacher whe she/he visits the group. 4. For homework, studets are asked to try out the game at home, ad to report ay iterestig icidets the ext day. O this day the teacher asks for feedback, askig, for istace, if ayoe suggested a short cut, but ot yet itroducig symbolic otatio uless the studets suggest it.

116 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Classroom maagemet implicatios Ideally, it is helpful if the studets are used to workig i groups, ad to egotiatig ad sortig out problems themselves before appealig to the teacher as referee. Note 1. The game ca be played with various types of rule for some time. Evetually, whe the studets are tired of writig the rules i Eglish, symbolic otatio ca be itroduced i stages, for example 2 umber + 1 ad after a while 2 N + 1 (or usig some symbol of the studets choice i place of N, but evetually itroducig a letter to stad for ay umber ). The multiplicatio sig should be retaied for some time (as i the Primary School Curriculum). 2. This itroduces the idea of a variable (which ca take may values) rather tha a ukow (which has a specific value, for example as i x + 7 = 10 ). Startig with a variable may help to avoid problems, which ca arise, for example, with the similar game my umber plus 7 is 10, what is my umber? This ca lead evetually to protests of the form but yesterday we decided x was 6 3. The game ca be used also to itroduce the idea of a fuctio. 116

117 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Activity 5 Thik of a umber This activity is a itroductio to solvig simple equatios. Studets must uderstad that each basic operatio has a iverse or a opposite. For example: Addig ad subtractig are opposites. Multiplyig ad dividig are opposites. The teacher ad studet activities are outlied i the examples below: Example 1 Teacher: I am thikig of a umber. Whe I add 4 to it I get 9. What was my umber? Studet: Your umber was 5. Teacher: Why? Studet: 9 take away 4 gives 5. Example 2 Teacher: Thik of a umber ad write it dow secretly. 117 Studet: (Thiks of 4 ad writes it dow.) Teacher: I your head, add the umber you wrote dow to itself (or double the umber). Studet: (Thiks of 8.) Teacher: Add 5 to this umber. Studet: (Thiks of 13.) Teacher: Tell me your aswer. Studet: The aswer is 13. Teacher: By my powers of deductio I ca tell you that the origial umber you thought of was (Thiks: 13-5 = 8; 8 2 = 4.) four. The steps from start to fiish ca be as simple or as complicated as is appropriate for the studets. The example above could be represeted by the equatio: 2x + 5 =13 Studets ca the take it i turs to act as the leader. Assessmet Note: Studets ca use the followig worksheet i twos, with oe role-playig the cartoo character i the worksheet ad the other tryig to guess the rule. Studets the switch roles. I this way studets are assessig each other s ability to make ad guess a rule. I such a activity studets should be ecouraged to describe how they worked out the iitial umber.

118 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 8: Mathematics Assessmet strategy 7 Thik of a umber worksheet Studets are ecouraged to describe how they worked out the missig umber. I m thikig of a umber If I take 6 from it, the aswer is 3 What umber was I thikig of? Aswer: 118 I m thikig of a umber If I add 7 to it, I get 13 What umber was I thikig of? Aswer: I m thikig of a umber If I multiply it by 3, I get 12. What umber was I thikig of? Aswer:

119 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Syllabus topic: Fuctios ad Graphs Plottig Poits Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Data Strad uit: Represetig ad iterpretig data Juior Certificate (Ordiary level) Fuctios ad graphs: Cocept of a fuctio Juior Certificate School Programme Graphs, Costructios ad trasformatios Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to six class periods. Potetial areas of difficulty > Studets may experiece: difficulty i perceptual skills, visual, tactile, ad auditory perceptio > Short term memory (rememberig to plot the horizotal co-ordiate before the vertical co-ordiate) > Uderstadig cocepts ad abstractios (What is a poit?) > Vocabulary/laguage (uderstadig mathematical istructios to plot poits) 119 Strategies used i this exemplar Usig cocrete materials Usig games to reiforce cocepts ad operatios Usig cross-curricular approaches Plottig poits that form ames ad shapes that are familiar to studets Resources A rage of draughts or chess boards or equivalet 8 8 grids, draughts pieces or other couters A scrabble board with raised edges (may also be useful ad may suit studets with a visual impairmet) OHP A spreadsheet program ca also be used for this activity Some aspects of the topic Relatios, fuctios ad graphs are theoretical ad may prove particularly difficult for some studets with mild geeral learig disabilities. Teachers are ecouraged to choose the learig outcomes, learig activities, ad assessmet strategies that best suit the eeds of their studets.

120 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. state some situatios whe you eed to give your positio to someoe 2. uderstad that graphig ivolves horizotal ad vertical positioig 3. read co-ordiates of poits from a basic square grid 4. place a couter o the correct square of a basic square grid give its coordiates 5. place several couters o a grid give a list of coordiates ad recogise ad ame the shape produced 6. place a shape of couters o a grid ad make a list of the co-ordiates. 1. Studets egage i a structured discussio ad other activities o the purposes of usig graphs ad co-ordiates to give your positio, ad o the merits of graphs over tables. 2. Studets complete the Graphig the classroom activity. 3. Usig a draughts or chess board tape letters alog the horizotal ad umbers alog the vertical of a grid. The teacher has a overhead projector grid prepared with a umber of couters placed. The teacher leads the studets i amig the positios of various couters (for example, A2, F5). 4. Studets work i pairs. Oe studet places a couter o the grid ad the other ames its positio. 5. Studets work i pairs. Oe studet gives the co-ordiates for a couter ad the other places the couter i the correct positio. 6. The teacher puts a list of coordiates o the board or overhead projector. Studets are challeged to make the shape/letter/umber usig couters o their grid. 7. Studets work i pairs. Oe studet makes a shape with the couters o the grid ad records the co-ordiates i secret. The other studet is the give the list of co-ordiates ad the empty grid ad tries to replicate the shape. 1. Observe whether studets ca state two situatios whe it is importat to kow your positio. 2. Observe whether studets, startig from a agreed iitial positio, ca pace out a give umber of horizotal ad vertical steps to get to a particular place i the classroom (for example take 4 horizotal steps ad 3 vertical steps. Where are you?). 3. Studets work i pairs as i activities 4 ad 5. Observe whether studets keep a record of how may correct aswers their parter gives. 4. After the activity each studet otes ay difficulties they had with certai co-ordiates (for example switchig letters ad umbers, misreadig the grid). 5. Studets complete the worksheet o page 125 ad compare their results i pairs to fid their errors. The teacher observes studets as they work to see if they have progressed beyod the difficulties expressed i assessmet strategy Cross-curricular liks: These skills ca be reiforced if grid refereces i geography are treated at the same time. Possible extesio activities are suggested.

121 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Activity 1 Let s talk about graphs ad co-ordiates Structured Discussio The teacher iitiates a structured discussio about the purposes of usig co-ordiates ad graphs. Some possible questios to iitiate the discussio might iclude the followig. How are ciema ad theatre seats laid out? Why is a letter ad a umber (for example, D7) commoly used? Why ot just a umber? Have you ever heard ayoe i a film say, What are your co-ordiates? What does this mea? (Where are you? What is your positio? Where are you o the map?, etc.) I Star Trek before they get beamed up they sometimes say, Lock oto my co-ordiates. What does this mea? A boat at sea is i trouble because of a storm. They radio for help. A search-ad-rescue helicopter is set out to fid the boat. What iformatio must the boat ower give o the radio to help the helicopter crew to fid the boat? (Latitude ad logitude, distace from lad, compass directio travelled from lad, etc.) Has ayoe played the game Battleships? How do you tell your oppoet where you are bombig? (Give a letter for horizotal positio ad a umber for vertical positio, for example D3). Liks to geography, for example map refereces, ca be oted. Whe might we use graphs? (to show uemploymet figures over time, to show attedace at school, how the weight ad height of a child o a graph ca show if the child is gettig eough ourishmet). Graphs from magazies ad ewspapers may be a useful resource. 121 Why two co-ordiates? Studets are show the diagram below o the board or o the OHP ad asked to describe the positio of the perso queuig at the bus stop who is wearig the hat. Most will aswer 4. Other similar examples of whe a sigle umber ca give someoe s positio ca be examied such as a perso i a lift, a ame o a roll book, a house o a street. Referrig back to the discussio o fidig your seat i a ciema, remid the studets that two pieces of iformatio are eeded to fid a positio. Now set up the classroom seats i a grid. Give each row a letter (say A to D) ad umber the seats i each row (say 1 to 5). The teacher calls out a studet s ame ad a seat positio (say B3). The studet must fid the correct seat ad sit dow. Differet studets ow select a studet ad a seat positio ad the activity cotiues util everyoe is seated. Other examples of situatios like this ca be discussed. Studets should uderstad that whe somethig is o a grid (i two dimesios) we eed two pieces of iformatio to fix its positio. Usually (although this is ot the case i the ciema) the first umber (or letter) tells you the positio across (horizotally) ad the secod umber tells you the positio up (vertically).

122 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Graphs or tables? The teacher distributes a hadout with a table of figures o it to oe half of the class, ad a hadout with a graph o it to the other half. (See sample table ad graph below.) I pairs, studets try to iterpret the table or graph. Studets are ot told iitially that the table ad graph represet the same iformatio. The teacher ecourages the studets to commet o how easy the graph ad table are to iterpret. Simple questios ca be put to the studets to see whether those with the table or graph ca fid the aswers more quickly. Sample questios Describe the growth of the plat? (goig up gradually) How high did the plat grow? (2cm) What was the biggest icrease i the growth of the plat? (0.5cm betwee days 4 ad 6) Were there ay days that the plat had ot grow at all? How do you kow? Durig the discussio the followig poits may be raised. Graphs are easier tha tables to take i at a glace. O a graph you ca look for peaks ad slopes ad beds more easily tha o a table. Keywords Keywords ad phrases relevat to this topic should be itroduced to the discussio or the follow-up activities as appropriate. Suitable words ad phrases iclude graph, graph paper, horizotal, vertical, axis, grid, couples, positio, co-ordiates, poit, ame a poit, plot, tred, icrease, decrease, graph raifall agaist time. 122 Growth of Plat What ca you tell from the followig graph? 2.5 Growth of plat height of plat i cm umber of days What ca you tell from the followig table? Number of days after platig Height of plat i cm

123 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Activity 2 Graphig the classroom All studets are give a copy of a grid map of the classroom ad several pictures represetig items or people i the classroom. The class first discusses where to place the door so that they all have the same orietatio. The the studets cut out each of the pictures below ad stick them oto the correct positio o the grid map of the classroom. Follow-up discussio ca brig out ideas such as horizotal positio ad vertical positio. Classroom map Classroom map 123 The Door My desk My fried s desk The board The cupboard The bookshelves

124 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Activities 3, 4, 5, 6, ad 7 Placig couters o a grid Resources A selectio of draughts or chess boards, ideally oe for every two studets, with letters taped alog the horizotal ad umbers alog the vertical of the grid as show i figure 1 below. The co-ordiates of the poits o the grid i figure 1 are: A2, B7, C4, D6, F5, G A B C D E F G H

125 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Assessmet strategy 5 Plot the co-ordiates worksheet Put couters o the followig co-ordiates. What letter is produced? B2, B3, B4, B5, B6, B7, C6, D5, E4, F3, G2, G3, G4, G5, G6, G7. My ame is Joseph. I have put my age ito co-ordiates for you to plot. What age am I? A6, B1, B2, B3, B4, B5, B6, B7, D1, E1, F1, F2, F3, F4, E4, F5, F6, F7, E7, D7. My ame is Marie. My favourite shape is the shape of my favourite toy o widy days. The coordiates for this shape are: B5, C6, C4, D3, D7, E2, E8, F3, F7, G4, G6, H5. What is my favourite shape? What is my favourite toy? My ame is Jo. List the co-ordiates eeded to spell out my ame as show i the grid below: A B C D E F G H

126 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Solutios The letter N A B C D E F G H I am 13 years old 126 A B C D E F G H My favourite shape is a diamod (or a rhombus) ad my favourite toy is a kite A B C D E F G H The co-ordiates eeded to spell out JO are: A7, B7, C7, D7, C6, C5, C4, C3, B2, A3, F6, F5, F4, F3, G2, H3, H4, H5, H6, G7.

127 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 9: Mathematics Possible extesio activities (a) Replace the letters o the horizotal lie with the umbers as show i figure 2 below ad repeat a selectio of the above activities. The co-ordiates of the poits o the grid i figure 2 are: 1,2; 2,7; 3,4; 4,6; 6,5; 7, (b) Replace the umberig of the grid spaces with umberig of the grid lies as show i figure 3 below. The co-ordiates of the poits o the grid i figure 3 are: (1,2); (2,7); (3,4); (4,6); (6,5); (7,4) (c) The hit ad miss activity i geometry lesso idea 13 o page 71 of the Juior Certificate Guidelies for Teachers: Mathematics, ca be used. (d) Studets ca lear to draw their ow co-ordiate grid ad ca practise similar activities to those outlied above.

128 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Syllabus topic: Geometry What kid of triagle is it? Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Shape ad Space Strad uits: 2-D shapes, Lies ad agles Juior Certificate (Ordiary level) Geometry: Sythetic geometry: Triagle (scalee, isosceles, equilateral), rectagle, square, circle Juior Certificate School Programme Maths: Perimeter, Area ad Volume. Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to four class periods. Potetial areas of difficulty > Uderstadig cocepts (isosceles triagle) > Trasferrig learig to real-life (seeig commo geometrical shapes i the eviromet, comparig ad cotrastig shapes) > Spatial awareess (drawig triagles) > Laguage (uderstadig keywords such as scalee, equilateral) > Cofusio with sigs ad symbols (markig agles ad sides i a triagle as equal) 128 Strategies used i this exemplar Usig cocrete materials Adaptig the materials give to a group Adaptig the resposes required Idetificatio ad specific targetig of mathematical laguage Usig cross-curricular approaches Resources Worksheet, cut-out versio of worksheet, rulers, protractors, set squares, strig, paper, trasparet paper This exemplar makes use of some of the lesso ideas outlied i the Juior Certificate Guidelies for Teachers: Mathematics. Teachers may fid it useful to use ad adapt other lesso ideas from these guidelies. Some aspects of geometry are theoretical ad may prove particularly difficult for some studets with mild geeral learig disabilities. Teachers are ecouraged to choose the learig outcomes, learig activities, ad assessmet strategies that best suit the eeds of their studets. The activities preseted i this exemplar illustrate how a activity ca be modified to suit studets with special eeds.

129 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. idetify simple geometrical shapes i their eviromet 2. use ad uderstad some geometrical words ad symbols 3. compare the legths of sides i a triagle 4. compare the measures of agles i a triagle 5. recogise a right agle 6. use mathematical equipmet (ruler, protractor, set square) more accurately) 7. describe a triagle i terms of the umber of equal sides ad equal agles (for example, this triagle has 2 equal sides ad 2 equal agles) 8. state whether a triagle is scalee, isosceles, equilateral, or right-agled, ad give reasos. 1. Spot the shape This activity ivolves studets fidig items i the classroom or the school that match give shapes. 2. Let s talk about shapes This activity ecourages the studets to use ad uderstad some geometrical terms by makig a pictorial ad symbolic dictioary. 3. What kid of triagle is it? This activity is based o Geometry lesso idea 1 o page 58 of the Juior Certificate Guidelies for Teachers: Mathematics. Differetiatio: Suggestios for differetiatig activity 3 are give. 1. Observe whether studets ca give two examples of thigs shaped like give shapes (for example triagle, square, rectagle, parallelogram, quadrilateral). 2. Observe as, i pairs, oe studet says a word from the geometrical dictioary ad challeges the other studet to draw the relevat diagram. If the studet draws the icorrect diagram the first studet explais the word to him/her. This cotiues. 3. Assess studets progress by observig their record of work o the triagles worksheet. Ca the studet recogise whe sides of a triagle are the same legth? Ca the studet recogise whe agles of a triagle are the same measure? Ca the studet recogise a right agle? How accurate is the studets i usig mathematics equipmet? 129 Ca the studet state correctly which triagles have equal sides ad agles? Does the studet uderstad the meaig of the terms scalee, isosceles, equilateral, right agle Cross-curricular liks: These skills ca be reiforced if similar cocepts i Techical Graphics ad Materials Techology (Wood) are treated at the same time.

130 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Activity 1 Spot the shape Studets work i small groups. Each group is give a card to complete as show i the examples below. The objective is to record as may differet items they ca see i the classroom (or aroud the school) that are the same shape as the oe o their sheet. Group 1: Your shape is a CIRCLE. List all of the thigs you ca see that are shaped like a circle. 130 Group 2: Your shape is a RECTANGLE. List all of the thigs you ca see that are shaped like a rectagle. Group 3: Your shape is a SQUARE. List all of the thigs you ca see that are shaped like a square.

131 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Activity 2 Let s talk about shapes Further discussio ca take place after the hut for shapes as to reasos why certai thigs are certai shapes, for example: Mahole covers ad bath-plugs are usually circular, so that the lid caot fall ito the hole. Wheels are roud, so that they make a ride smooth. Drai-pipes are rouded, or cylidrical, so that thigs caot get stuck i corers. Books are usually rectagular. Packets of food are usually rectagular, for ease of storage. Bricks are usually rectagular, so that they ca be easily built o top of each other. Keywords Studets eed to be familiar with appropriate geometrical key words ad symbols. Geometrical words iclude lie, agle, shape, triagle, scalee, isosceles, equilateral, quadrilateral, parallelogram, rectagle, square, legth, measure, equal, same, differet. Studets also eed to be able to ame ad use geometrical istrumets, icludig ruler, compass, set squares, protractor. 131 Makig a dictioary Studets are guided i the makig of a dictioary as they come across geometrical words. Some sample etries are show i the table below. Studets are ecouraged to suggest etries for the dictioary. Word Diagram Symbol Explaatio Triagle A shape with 3 sides Isosceles triagle A triagle with two equal sides ad two equal agles Agle a abc The space or corer b formed whe two lies c meet Legth of a lie ab = 3cm How log a lie is 3cm a b

132 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Activity 3 What kid of triagle is it? This is based o Geometry lesso idea 1 o page 58 of the Juior Certificate Guidelies for Teachers: Mathematics. The lesso idea is reproduced below i full for iformatio. Comparig this origial lesso idea with the modified exemplar shows how a idea ca be modified to suit studets with a mild geeral learig disabilities. Geometry lesso idea 1 Title: Differet types of triagle Topic: Triagles Aim: 1. That studets will be able to recogise various types of triagles. 2. That studets will be provided with cocrete experieces dealig with triagles. Resources The worksheet with various types of triagles is o the ext page. Method The studets are itroduced to a series of triagles o a worksheet, a example of which is preseted o page 133. The triagles comprise a mixture of isosceles, right-agled, scalee, ad equilateral triagles. The studets task is to determie the legths of the sides, the magitudes of the agles ad cosequetly the type of each triagle preseted. The results ca be preseted i tabular form, as show. 132 Classroom Maagemet Implicatios Studets ca work idividually o the above exercise but should the be ecouraged to share ad discuss their results with their peers as the exercise goes o. Note The worksheet below was costructed usig a stadard word processig package that icorporated a basic set of drawig tools. Teachers familiar with dyamic geometry software will kow that such packages ca be used to prepare these worksheets also. A additioal advatage is that they ca also provide a teacher s master copy with a pritout of the legths of sides ad agles i the give triagles. Familiarity with isosceles (from isos, equal ad skelos, a leg) ad equilateral triagles ca be further ehaced if studets use cut-out triagles from the same sheet. The sides of each triagle ca be compared by foldig alog a suitable axis. The Irish phrases used to describe these differet types of triagles ca give a isight ito their properties. Thus, for example, triatá comhchosach (equal legs) describes the isosceles triagle, while triatá comhshleasach (equal sides) describes the equilateral triagle.

133 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Studet Worksheet Triagles A B C D 133 E F Triagle A Agle 1 Agle 2 Agle 3 Side 1 Side 2 Side 3 Equilateral Isosceles Right- Agled Scalee B C D E F

134 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 10: Mathematics Differetiatig geometry activities Some of the skills required by the above activity iclude the ability to measure the legth of a lie with a ruler measure a agle with a protractor compare measuremets use kowledge of geometrical terms to ame triagles correctly. However, some studets may have difficulties with some of these skills. For example, a studet who has difficulty usig a ruler accurately ca still compare the legths of the sides of a triagle with the aid of a piece of strig or a strip of paper. The measure of agles i a triagle ca be measured ad compared with the aid of a protractor a set square (for right agles) a piece of trasparet paper (tracig a agle to see if it fits ito ay of the other two agles) cut-out versios of the triagles o the worksheet (rotatig the triagle aroud to see which agles fit ito each other, or tearig off oe corer ad compare it to others). 134 I this way studets may lear to recogise the various kids of triagles without gettig a exact measuremet for legths of sides or measure of agles. Some studets may also be able to apply certai terms to the triagles. For studets that have difficulties with laguage, the table of triagles could be adapted to have headigs: o sides the same istead of scalee, 2 sides the same istead of isosceles, ad all sides the same istead of equilateral. I this way studets ca experiece a activity without ecessarily beig able to achieve all of the learig outcomes.

135 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 11: Mathematics Syllabus topic: The busiess of livig Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Measures Strad uits: Moey Juior Certificate (Ordiary level) The Busiess of Livig: Persoal icome ad expediture Juior Certificate School Programme Persoal Fiace: Maage persoal fiaces i the areas of icome, expediture ad budgetig Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to four class periods. Potetial areas of difficulty > Laguage: uderstadig terms > Uderstadig cocepts icome ad expediture > Trasfer to real life > Usig charts appropriately > Takig roles 135 Strategies used i this exemplar Laguage developmet (busiess terms, such as household, icome, expediture, budget, cosumer, cash flow) Matchig sources of icome ad expediture Settig up a system of barter (exchage) usig school ad persoal objects Role-playig cosumers ad retailers usig play moey ad household objects Measurig ad recordig icome ad expediture i charts (i tabular form) Measurig ad recordig usig a spreadsheet Discussig choice, opportuity, cost, impulse buyig, ad plaig Ivestigatig applicatios of plaed spedig ad plaed savigs Settig priorities i expediture Resources Magazies, toys, games, cards Moopoly/play moey Items of household cosumer goods Computer with spreadsheet

136 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 11: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of these activities studets should be eabled to 1. idetify sources of icome 2. idetify expediture o household goods 3. classify household expediture ad calculate lists. 1. Teacher-led class discussio 2. Playig differet roles i a retail outlet 3A. Studets costruct a chart of importat items for a household 3B.Studets calculate cost of eeds/bills i a household for a week 3C.Studets prepare a chart to illustrate a budget Teacher observatio of studets 1. discussig ad describig where people source icome ad sped cash 2. settig up a retail outlet to sell goods carryig out the trasactio of exchagig cash for household goods icludig recordig the cash received by the retail outlet explaiig to classmates why cash was spet o the items chose, ad each retailer explaiig his/her pay slip completig a record of moey spet 3. costructig a chart of the expediture of a household 136 preparig a pla (budget) matchig icome ad expediture (o paper or o a spreadsheet)

137 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 11: Mathematics Activity 1 Studets, usig magazie ad ewspaper advertisemets, discuss icome from differet sources, such as pocket moey, employmet, social welfare. Activity 2 Divide the studets ito two groups: retailers ad cosumers. Distribute moopoly/play moey to the groups. Costruct a retail outlet (a table filled with cosumer goods ad stadard household goods) with prices attached to the items. Studets barter for goods or exchage play moey for goods ad keep records of the trasactios. Itroduce the cocept of icome for work by providig pay slips for retailers. Exchage/barter role playig Two studets begi the process of egotiatig a fair exchage. Two more studets take up positios betwee these ad egotiate a differet exchage. Through this exercise the studet comes to uderstad that exchage may differ depedig o how a perso values a item. 137 Retailer/cosumer role playig The terms employer/retailer/employee ad cosumer are itroduced. A retail outlet is set up displayig household goods with prices attached. Studets could set their ow prices for products displayed. Whe play moey has bee distributed two studets are allocated more tha the others. Whe trasactios take place each studet is asked to record what they bought ad the price of same. Choices made are compared. Through this exercise the studets come to uderstad that items for a household may be see as more or less importat depedig o how a perso values them. The studets with more play moey allocated to them display their purchases ad costs. The remaiig moey is couted ad compared with what they received. This demostrates the cocept of choice.

138 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 11: Mathematics Activity 3A Studets costruct a chart of importat items for a household, classifyig them uder very importat ad less importat. Prepare a wall chart classifyig household expediture, use calculators/computer spreadsheet for calculatios. The terms savigs/spedig/plaig/budget are itroduced. A class chart is prepared outliig ad classifyig various items purchased. The cocept of fixed/regular bills (ESB, ret, heatig, ruig a car) are itroduced to illustrate other expediture. Studets are the helped to desig the costs of ruig a household. These costs are listed very importat/ importat. Calculators are used to add up the cost of these items. A computer spreadsheet is set up to record the trasactios of the household. Through this exercise the studets come to uderstad that households differ but that each eeds to pla spedig. A quiz ca be prepared settig priorites for differet households (ordiary households/footballers/ movie stars). The studets should discuss why plaig a budget is useful for ay household. This demostrates the cocept of plaig expediture to cover priority items. 138 Activity 3B Studets discuss the eeds/bills of a household ad calculate the cost of these eeds for a week. Activity 3C A pie chart of household expediture The classified household expediture is graphed i a pie chart. This looks at the costs i terms of ecessity ad discretioary icome, ad illustrates priorities i a household.

139 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Syllabus topic: Number Systems, Applied arithmetic ad measure Home Ecoomics: Food Studies/Culiary Skills Desig ad make a pizza Primary School Curriculum (5th ad 6th classes) Mathematics Strad: Number Strad uits: Fractios Strad: Measures Strad uits: Weight, Time, Moey Juior Certificate (Ordiary level) Mathematics: Number systems Applied arithmetic ad measure Home ecoomics: Food Studies / Culiary skills: Juior Certificate School Programme Food Studies ad Culiary Skills SPHE Strad: Myself Strad uit: Takig care of my body Health ad well beig Food ad utritio Time scale: The full rage of learig ad assessmet activities preseted i this exemplar may take up to eight class periods. 139 Potetial areas of difficulty > Short term memory (rememberig recipe amouts ad stages) > Short attetio spa ad lack of cocetratio (difficulty stickig to the task ad followig the recipe through the differet stages) > Uderstadig cocepts (difficulty with weighig ad measurig, costig ad comparig costs) > Spatial awareess (difficulty with orgaisig workspace ad fidig thigs as they are eeded) > Trasferrig learig to real-life (difficulty trasferrig kowledge gaied i mathematics about how to measure ad calculate) > Relatig skills ad cocepts to those already leared > Poor vocabulary/laguage (difficulty i followig recipes as they are traditioally writte, difficulty with the laguage used to evaluate products) > Visual sequecig (difficulty with copyig from the board)

140 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Strategies used i this exemplar Usig a flow chart istead of traditioal style recipes Usig a map for settig up the uit-part of the preparatio class Usig visual clues where appropriate Breakig the task ito stages Ecouragig studets to reward themselves with a visual tickig system as they complete each stage Referrig back to skills ad kowledge previously leared, for example scoe makig Ecouragig studets to use the relevat termiology Usig a simple worksheet with a strog visual compoet for evaluatio Usig cross-curricular liks to mathematics Resources Igrediets ad equipmet for makig pizzas A selectio of differet coveiece pizzas, for example Frech bread pizzas, idividual pizzas, froze pizzas, ad deli pizzas Stickers, for example happy faces, to mark off stages as completed Activity sheets Outcomes, activities ad assessmet strategies which have a direct mathematical applicatio are marked with a asterisk. 140

141 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Suggested outcomes Supportig activities Assessmet strategies As a result of egagig i these activities studets should be eabled to 1. record the prices of a variety of pizzas ad igrediets for makig the pizza 2. calculate the cost of the fresh pizza ad compare it to the cost of a coveiece pizza 3. uderstad what a pizza is ad how it is made 4. recall the healthy eatig guidelies ad foods from the four food groups ad relate these to the chose pizza 5. weigh ad measure the igrediets required 6. set up equipmet o the allocated workspace 7. draw up a time pla ad follow this durig the cookery class 8. set the ove to the required temperature 9. divide the pizza ito eight equal parts 10. evaluate the pizza i relatio to the others i the class ad i relatio to a coveiece pizza. 1. Let s go Shoppig: Studets visit the supermarket to research the differet pizzas o the market ad to research the costs of pizzas ad igrediets. (Activity Sheet 1) What is a pizza? Studets idetify the differet parts of the pizza, base, sauce ad toppigs. Desig ad make a pizza: Recap o healthy eatig guidelies ad the four food groups. Studets are guided through the desig process to desig their ow pizza. 2. Flowchart : The teacher ad studets complete a flow chart for the cookery class, icludig times. (Activity Sheet 2) 3. Equipmet list ad uit map: Recap o weighig ad measurig. (Activity Sheet 3) 4. Cookery class: Studets follow time plas to make the pizza. The teacher demostrates each stage to reiforce skills. Studets tick the smiley face o their flow charts to idicate the completio of each stage. 1&2. The teacher observes studets recordig the prices of two differet brads of each product, selectig the best value i each case. 3&4. The teacher observes studets writig four poits to show they kow what a pizza is ad to illustrate how the four food groups ca be icluded. 5. The teacher observes studets completig the process of desigig their ow pizzas (workig i pairs). 6. Teacher observes the studet performig the followig: weighig ad measurig igrediets settig up equipmet o the allocated workspace followig flowchart ad time-pla food preparatio skills settig ove to correct temperature dividig the pizza ito eight equal parts. 141

142 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Suggested outcomes Supportig activities Assessmet strategies 5. Studets divide the pizza ito eight equal portios ad discuss how may portios would make ½, ¼, ¾, etc. 6. At the ed of the cookery class studets carry out a brief evaluatio of the fiished pizzas. Durig the ext class a more detailed evaluatio ca be carried out. The teacher could cook a coveiece pizza to allow studets to compare these with their fresh pizza. (Activity Sheet 4). 7. Evaluatio Sheet: Studets calculate the cost of the pizza ad compare it to the cost of a coveiece pizza. The studet is asked to give his or her ow pizza marks out of te ad give reasos why marks are beig deducted. 142

143 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Activity 1 Let s go shoppig Some preparatio work will have to be doe before the supermarket visit. Studets might draw a pla of the supermarket ad mark o it where to look for the differet items. Data ca be gathered o the visit to the supermarket. Studets ca work i pairs. The task ca be divided up amog studets. For example, each pair of studet could be assiged two or three igrediets to research ad oe coveiece pizza. Results ca the be compiled back i the classroom. Havig the calculatios doe i a mathematics class ca ecourage cross-curricular liks with mathematics. Let s go shoppig Pricig igrediets for my pizza PRODUCT BRAND NAME PRICE WEIGHT PRICE PER 25g (Or each) Self-raisig flour 143 Milk Olive oil Oio Ca of tomatoes Tomato puree Mozzarella cheese Pepperoi Ca of pieapple Gree pepper

144 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Let s go shoppig Coveiece pizzas 1. Make a list of all the differet types of coveiece pizzas you ca thik of i colum 1 of the table below. PIZZA TYPE BRAND NAME PRICE WEIGHT PRICE PER 100g For example, Frech bread pizza 144 Best value pizza Which pizza is the best value for moey? Give two reasos why 1. 2.

145 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Activity 2 Makig my pizza (flowchart) The flow chart ca be worked o durig a preparatio class ad further iformatio ca be filled i as required. The differet stages of the flow chart should have eough space to add further otes. The callouts o the left side of the sheet are for the time pla. The teacher ad studets ca sped time workig out the time pla durig the preparatio class. The smiley faces o the right side of the page are for studets to to tick as they complete each stage. 145

146 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Makig my pizza Startig time: SET UP UNIT USE UNIT MAP SET OVEN C GAS PREPARE INGREDIENTS FOR SAUCE PREPARE TOPPINGS MAKE SAUCE

147 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics MAKE DOUGH ASSEMBLE PIZZA BAKE TIDY UNIT WASH UP 147 REMOVE PIZZA FROM OVEN SERVE PIZZA AND DIVIDE INTO EIGHT EQUAL PORTIONS EVALUATION Fiish time:

148 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Activity 3 Equipmet list ad uit map The uit map will help the studet to set up the uit correctly before they start the class. It will beefit studets who have spatial awareess difficulties if it is used costatly. The map give icludes oly the basics. It ca be completed durig the preparatio class. Studets would beefit from some revisio of weighig ad measurig durig the preparatio class. Equipmet list ad uit map Class: Make a list of all the equipmet you will eed for your cookery class i Colum 1 ad the tick it off i Colum 2 as you collect it. Equipmet Tick 148

149 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Uit map Food Food Used Cutery Food Sieve Bowl Activity Evaluatio - Pizzas The Pizza I made Cost Coveiece Pizza Cost Igrediets Weight Cost Brad ame of Pizza Weight Cost Total cost: Cost per portio: Marks out of 10: Total cost: Cost per portio: Marks out of 10:

150 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Exemplar 12: Mathematics Give reasos why you deducted marks i each case. 150 Best Pizza

151 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Appedix 1 Real-world mathematics The tables preseted below offer suggestios for likig some aspects of mathematics to the world of the studet. Table 1 gives a real-world situatio ad suggests a variety of mathematical etry poits that relate to it. Table 2 takes a mathematical cocept ad suggests where it ca be foud i real-world situatios. The tables are icluded here to suggest possible startig poits i the mathematics classroom. They are by o meas all-iclusive. Table 1 Situatio Railway, bus statio, or airport Road trasport Post office Garde Pets Weather Car park Cookig DIY Mobile phoes Shoppig Mathematical etry poits Timetables Ticket fares Shapes (i the statio, o the trai/bus) Geometry (parallel lies, right agles) Plaig a jourey (time, distace, speed) Maps (distace, scale) Price of stamps Weight of parcel/evelope Area of evelope required to hold a card Iterest o savigs Plaig ad pricig the desig of a garde (legth, area, moey) Buyig garde equipmet (use of brochures to compare prices) Buyig food Vet charges Distace walked with dog Legth ad width of keel/hutch Volume of water i bowl How ofte to chage the water How ofte to feed the pet Chartig raifall, hours of sushie, wid speed Graphig the umber of cars agaist time Cost Area of ordiary car-park space, of ivalid space, of paret-ad-child space, of car park Recipes Plaig a dier Weighig Costig Temperature Cookig time Measurig (legth, perimeter, area) Costig the decoratio of a room Pricig tools Which compay offers the best value? How much call credit left, how may calls/texts ca be made for this amout? At what time is it cheaper to make calls or sed texts? Moey Special offers Price per weight/volume VAT 151

152 Guidelies Mild Geeral Learig Disabilities / Mathematics / POST-PRIMARY Table 2 Cocept Number Shape Time Measure Liks to the world aroud us Patters o floor or ceilig tiles The caledar Bookig/fidig seats i a ciema/theatre Wall ad floor patters Straight lies, right agles i the classroom Symmetry i a butterfly, i our bodies (sort of) Various boxes, cas, bottles from the supermarket Why is a mahole cover or bath-plug roud? Timetables Joureys by walkig, cyclig, car, bus, trai, aeroplae Times we do thigs i school or at home Graphs of time spet watchig TV, sleepig Old uits of measure based o the body (for example, the use of hads to measure the height of a horse) Estimatig ad measurig legth for DIY tasks Distace o maps, heights of moutais Capacity of various tis, cas, cartos Weight of items, of persos 152