Introduction. Teacher s lesson notes The notes and examples are useful for new teachers and can form the basis of lesson plans.

Transcription

1 Introduction Introduction The Key Stge 3 Mthemtics series covers the new Ntionl Curriculum for Mthemtics (SCAA: The Ntionl Curriculum Orders, DFE, Jnury 1995, ). Detiled curriculum references re provided. Ech pck is designed to e flexile nd cn e used in vriety of wys: A complete course for Level 6 The worksheets cn e used to provide complete coverge of: Numer nd Alger; Shpe, Spce nd Mesures; nd Hndling Dt. The prolemsolving tsks provide experience for the pupils in Using nd Applying Mthemtics. Individul lessons The techer cn explin the tsks nd provide the worked exmples, either on the ord, s overhed trnsprencies or s photocopied sheets for the students. Students should then ttempt the exercises. Techer s lesson notes The notes nd exmples re useful for new techers nd cn form the sis of lesson plns. Asent students The notes, exmples nd exercises cn e used y students during longterm sence or to help students ctch up fter sence. Techer s sence If techer is sent, doule-sided worksheet (notes nd exmples on one side, exercises on the other) cn e provided for students. This will llow the students to continue with lerning the curriculum. Exmintion revision The notes nd exmples cn e issued to students shortly efore the exmintion for revision purposes. The pck includes: Notes nd worked exmples Exercises Coursework tsks for AT1 Using nd Applying Mthemtics Exmintion ppers contining Ntionl Curriculum-type questions Using nd Applying Mthemtics prolem-solving tsks Pupil s record form Answers. Using the notes nd exmples Pupils should fold the worksheet so tht the nswers cnnot e seen. They cn then red the notes, try the questions, nd then check their nswers. Exm ppers Ech pper is set on three or four sides of A4 pper. This will llow the exm pper to e plced on one sheet of A3, in order to remove the onerous tsk of writing nd stpling exm ppers. If oth ppers re set, the contents of Numer nd Alger, Shpe, Spce nd Mesures, nd Hndling Dt will hve een covered t Level 6. Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

2 Introduction Ech question is relted to specific prt of the Ntionl Curriculum s indicted on the chrt on pges 58 nd 59. It is lso possile to use ech exm pper s homework sheets in preprtion for the end of Key Stge 3 exmintions. Pupil s record form This form, provided on pge 60, llows the success of pupils to e recorded using the results on the exercises nd exm questions. Either tick/cross system or mrk system my e used. End of term ctivities The Qudrilterl Gme on pge 30 will help pupils to ecome fmilir with the nmes of qudrilterls. Experience will show them tht the proility of numers thrown with two dice re not equl. Using nd Applying Mthemtics Three prolem-solving ctivities re provided on pges 54 to 57. Dimonds is very interesting project for producing ptterns for wll displys. Stfford Burndred Octoer 1995 Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

3 Test 1 Test 1 1 Croline wnts to find the vlue of x in the eqution x 2 + x = First she tries = 30. The nswer is too high. Then she tries = 6. The nswer is too low. Continue using tril nd improvement methods to find the vlue of x correct to one deciml plce. 2 These four continers ech hold litre when full. Ornge sqush is poured in to the levels shown. 80% full 7/10 full 2/3 full Andre s continer Brend s continer Kren s continer Deorh s continer hs 0.65 litres c d Which continer hs the most ornge sqush? Explin how you worked this out. Which continer hs the lest ornge sqush? Explin how you worked this out. 3 Two shops re selling identicl television sets. In Blck s TV Store, ll items re for sle t 75% of their norml price. In White s Discount Wrehouse everything is for sle t 4/5 of its norml price. Television set normlly 400 Wht is the cost of the television in ech shop? Which shop should you uy from nd how much will you sve? Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

4 Test 1 4 Kren hs ttempted the following five questions. Two of her nswers re wrong. Which nswers re wrong nd wht re the correct nswers? Cn you explin Kren s mistkes. Question 1 Write 5/8 s deciml Kren s nswer 5 8 = Question 2 Write 5/16 s percentge Kren s nswer 16 5 x100 = 320% Question 3 Write 20.8% s deciml Kren s nswer Question 4 Write 0.3 s percentge Kren s nswer 30% Question 5 Write 0.7% s deciml Kren s nswer 70% 5 These re the recipes for tod in the hole, one of the recipes is wrong. The other two re correct, identify the wrong recipe nd correct it. Recipe for 6 people Recipe for 8 people Recipe for 10 people Plin flour 300 g 420 g 500 g Slt 24 g 35 g 40 g Eggs Milk 420 ml 550 ml 700 ml Susge met 360 g 500 g 600 g 6 This is scle digrm of clssroom. The length of the clssroom is 6 m. 6 cm Express the scle s rtio in its simplest terms. Wht is the width of the clssroom? 2 cm 7 John s pttern 3, 7, 11, 15, 19, 23 Mndy s pttern 5, 8, 11, 15, 17, 20, 23 c Wht is the rule to produce John s pttern? Wht is the fifteenth term of John s pttern? Mndy hs mde n error in her pttern. Find the error nd correct it. How did you find the error? Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

5 Test 1 8 Jmes nd Zoe hve exctly the sme numer of sweets. Jmes hs two gs plus thirteen loose sweets Zoe hs five gs plus one loose sweet Ech g contins the sme numer of sweets. Form n eqution. Solve it to find the numer of sweets in ech g. 9 A mn uys B nns t Y pence. The totl cost is 48 pence. Form n eqution to show this. Use your eqution to find the vlue of B when Y = 6p. c Use your eqution to find the vlue of Y when B = Complete the tle nd then drw the grph of f(x) = x 2-6. x y 11 This is the net to mke die x Opposite fces of die dd up to 7, complete the numers on the net. Look t the edge mrked x indicte, using the letter Y, the other edge this will touch when the die is folded. Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

6 Test 2 Test 2 1 Nme this qudrilterl. Fill in the missing ngles. x y 2 This is regulr hexgon. Find the size of ech ngle shown. Explin how you found ech ngle. You must not use protrctor. c 3 Find the size of ngles, nd c. You must not use protrctor. c Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

7 Test 2 4 This is digrm of grden with n ornmentl pond. The reminder of the grden is lwn. 20 m 3 m Pond 6 m 10 m 3 m 6 m 2 m 6 m c d Wht is the perimeter of the pond? Wht is the re of the pond? Wht is the perimeter of the grden? Wht is the re of the lwn? T'' T Enlrge T y scle fctor of 4, centre of enlrgement is the point (16, 4) T is produced from T y n enlrgement. i ii Wht is the centre of enlrgement? Wht is the scle fctor of the enlrgement? Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

8 Test 2 6 These re the heights (in centimetres) of twenty people in room: Complete nd show this informtion in: A frequency tle A frequency digrm Height (cm) under under 150 Tlly Frequency Sixty people were sked to nme their fvourite television progrmme. Complete the tle nd pie chrt to show the informtion. Lel ech sector of the pie chrt. Progrmme Corontion Street Estenders Brookside Emmerdle Frequency Angle t the centre of the pie chrt Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

9 Test 2 8 Wht does this sctter grph tell you out the reltionship etween the numer of people on ech nd the temperture? Wht sort of correltion is shown? Temperture x x x x x x x x x xx x x Numer of people on ech 9 Pul decides to uy one ice-crem nd one sndwich. List ll of the possile comintions of ice-crem nd sndwich Pul cn uy. Ice-crem flvours Rsperry Vnill Sndwiches Hm Chicken Sld This g contins some red, yellow nd lue counters. The proility of picking red counter is 20%, the proility of picking yellow counter is 50%. i ii Wht is the proility of picking lue counter? Explin how you worked this out. Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

10 Ntionl Curriculum references Ntionl Curriculum references Numer nd Alger Level 6 Topic title Exm pper Question Pupils order nd pproximte decimls when solving numericl prolems nd equtions such s x 2 = 20, using tril-nd-improvement methods. Pupils re wre of which numer to consider s 100 per cent, or whole, in prolems involving comprisons, nd use this to evlute one numer s frction or percentge of nother. They understnd nd use the equivlences etween frctions, decimls nd percentges, nd clculte using rtios in pproprite situtions. When exploring numer ptterns, pupils find nd descrie in words the rule for the next term or nth term of sequence where the rule is liner. They formulte nd solve liner equtions with whole numer coefficients. They represent mppings expressed lgericlly, interpreting generl fetures nd using grphicl representtion in four qudrnts where pproprite. Tril nd improvement 1 1 Clculting frctions nd percentges Clculting frctions nd percentges Equivlences etween decimls nd percentges 1 4 Equivlences etween decimls, frctions nd percentges 1 4 Rtio Rtio Explore numer ptterns 1 7 Solving liner equtions 1 8 Formulting liner equtions 1 9 Grphicl representtion 1 10 Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

11 Ntionl Curriculum references Shpe Spce nd Mesures Level 6 Topic title Exm pper Question Pupils recognise nd use common 2-D representtions of 3-D ojects. They know nd use the properties of qudrilterls in clssifying different types of qudrilterl. They solve prolems using ngle nd symmetry properties of polygons nd properties of intersecting nd prllel lines, nd explin these properties. They devise instructions for computer to generte nd trnsform shpes nd pths. They understnd nd use pproprite formule for finding circumferences nd res of circles, res of plne rectiliner figures nd volumes of cuoids when solving prolems. They enlrge shpes y positive whole-numer scle fctor. 2-D representtion of 3-D shpes 1 11 Properties of qudrilterls 2 1 Regulr polygons 2 2 Intersecting nd prllel lines 2 3 Not included. Suggestion: Use computer pckge eg DART Circumferences nd re of circle, res nd volumes 2 4 Enlrgement 2 5 Hndling Dt Level 6 Pupils collect nd record continuous dt, choosing pproprite equl clss intervls over sensile rnge to crete frequency tles. They construct nd interpret frequency digrms. They construct pie chrts. Pupils drw conclusions from sctter digrms, nd hve sic understnding of correltion. When deling with comintion of two experiments, pupils identify ll the outcomes, using digrmmtic, tulr or other forms of communiction. In solving prolems, they use their knowledge tht the totl proility of ll the mutully exclusive outcomes of n experiment is 1. Collect nd record continuous dt in frequency tles nd frequency digrms 2 6 Constructing pie chrts 2 7 Sctter digrms 2 8 Proility 2 9 Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

12 KS3 Mthemtics B: Level 6 Pupil s record form Pupil s record form Nme: Techer: Form: Test mrks: Exercises Exm Exm questions completed pper nswered Numer nd Alger Tril nd improvement 1 1 Clculting frctions nd percentges Clculting frctions nd percentges Equivlences etween decimls nd percentges 1 4 Equivlences etween decimls, frctions nd percentges 1 4 Rtio Rtio Explore numer ptterns 1 7 Solving liner equtions 1 8 Formulting liner equtions 1 9 Grphicl representtion 1 10 Shpe, Spce nd Mesures 2-D representtion of 3-D shpes 1 11 Properties of qudrilterls 2 1 Regulr polygons 2 2 Intersecting nd prllel lines 2 3 Circumference nd re of circle, res nd volumes 2 4 Enlrgement 2 5 Hndling Dt Collect nd record continuous dt in frequent tles nd frequency digrms 2 6 Constructing pie chrts 2 7 Sctter digrms 2 8 Proility 2 9 Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

13 Answers Tril nd improvement (pge 4) c 2 d 7 e 10 f 15 g 18 h 7 i 20 j 10 Clculting frctions nd percentges (pge 6) 1 15% % 3 40% 4 56% /4 11 1/ 4 c 4 1/ 2 d 10 1/ 8 e 6 f 135 g h 180 i c 3 d 5 e 4.20 f 5.20 g 8.40 h i % 25% c 45% 8 7% d 60% e 90% f 85% g 34% h 36% i 41% j 65% Clculting frctions nd percentges (pge 8) c 304 d 4 e 2.40 f g 3.60 h 2.88 i 5.76 j 4.28 k 6.12 l i 840 ii 1595 iii 1110 iv i ii iii iv v vi c AA Electrics, 23 less Equivlences etween decimls nd percentges (pge 10) c 0.06 d 0.26 e 0.8 f 0.05 g 0.45 h 0.03 i 0.6 j 0.07 k l 0.25 m n 0.4 o Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

14 Answers p 0.5 q r 0.75 s t % 72% c 47% d 54% e 63% f 60% g 3% h 90% i 27.2% j 45.3% k 10% l 1% m 2% n 24% o 40% p 372% q 201% r 410% s 0.72% t 10.4% 3 50% 25% c 75% d 33.3% e f g 0.1 h 0.01 Equivlences etween decimls, frctions nd percentges (pge 12) 1 39 /50 93 /100 c 47 /100 d 3 /5 e 4 /5 f 1 /20 g 7 /100 h 49 /50 i 63 / c d e 0.3 f 0.7 g 0.58 h 0.87 i , 56.25% 17 /50, 34% c 51 /200, d 28 /125, 22.4% e 0.875, 87.5% f 1 /25, 4% 4 75% 50% c 37.5% d 80% e 10% f 20% g 93.75% h 62.5% i 85% 5 1 /4 47 /100 c 7 /25 d 37 /100 e 39 /100 f 427 /1000 g 3 /5 h 3 /10 i 2 /25 Rtio 1 (pge 14) 1 60 g, 240 ml, 1 egg 180 g, 720 ml, 3 eggs c 300 g, 1200 ml, 5 eggs g, 25 g, 1 onion, 300 g, 175 g 660 g, 75 g, 3 onions, 900 g, 525 g c 1100 g, 125 g, 5 onions, 1500 g, 875 g 3 1:4 1:2 c 5:3 d 5:2 e 6:4:3 f 3:5: c 3 d 4.5 e cm 8.2 cm c 13.5 cm Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

15 Answers Rtio 2 (pge 16) 1 2:3 5:6 c 3:2 d 5:1 2 1:50 1:1000 c 1:2000 d 1:200 e 1:1600 f 1: , 1500, , , 160, cm 30 m c 2.5 cm d 0.5 cm e 12 m Explore numer ptterns (pge 18) 1 2N 30 c N 90 c N 45 c N-2 58 c N-2 73 c N+3 33 c N+1 46 c N-7 53 c N-8 37 c N c N+1 76 c N c , 8, 11, 14, , 15, 19, 23, , 5, 7, 9, , 11, 17, 23, , 2, 5, 8, , -6, -4, -2, 0 Solving liner equtions (pge 20) Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

16 Answers Formulting liner equtions (pge 22) Grphicl representtion (pge 24) 2 5, 0, -3, -4, -3, 0, 5-7, -2, 1, 2, 1, -2, -7 c -1.5, -4, -5.5, -6, -5.5, -4, , 7, 5, 3, 1, -1, -3 22, 7, -2, -5, -2, 7, 22 c 7.5, 5, 3.5, 3, 3.5, 5, 7.5 d 6, 3, 2, 3, 6, 11, 18 2-D representtion of 3-D shpes (pge 26) 1 cylinder 2 c nd d Properties of qudrilterls (pge 29) 1 rectngle rhomus c trpezium d prllelogrm e squre 2 rhomus prllelogrm c kite d rectngle e trpezium f squre = 50, = 130, c = 130 c d = e = 140 Regulr polygons, intersecting nd prllel lines (pge 33) 1 72, , 120 c 40, 140 d 36, 144 e 30, c c 18 4 x = 60, y = 120 = e = g = 50, = c = d = f = 130 c x = z = 45, y = 135 d = 110 e = 80, = 40, c = 60 f x = 50 Circumference nd re of circle, res nd volumes (pge 35) cm, 78.5 cm m, 452 m 2 c 44.0 m, 154 m 2 d 20.1 cm, 32.2 cm 2 e 37.7.cm, 113 cm 2 f 62.8 m, 314 m 2 g 28.3 cm, 63.6 cm 2 h 15.1 m, 18.1 m m m 2372 m m 138 m m 2 Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

17 Answers Enlrgement (pge 38) 1 top left hnd coordinte is (13, 12) 2 top left hnd coordinte is (5, 13) 3 top left hnd coordinte is (8, 30) 4 (5, 10) SF2 5 (6, 17) SF3 Collect nd record continuous dt (pge 40) under under under under Constructing pie chrts (pge 42) 1 112, 32, 100, , 72, 96, 84, , 90, 40, , 80, 60, 70 Sctter digrms (pge 44) 1 positive correltion 2 no correltion 3 negtive correltion 4 positive correltion Proility (pge 46) 3 UU, UD, DU, DD 4 CB, CP, LB, LP, OB, OP 5 36 c i 5 /36 ii 6 /36 = 1 /6 6 3 /11 8 / Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

18 Answers Test 1 (pge 47) 1 tle (2 mrks) 3.7 (2 mrks) 2 Andre (2 mrks) explntion (1 mrk) c Deorh (2 mrks) d explntion (1 mrk) 3 Blck s 300 (2 mrks) White s 320 (2 mrks) Blck s 20 (2 mrks) 4 Question x 100 = 31.25% (2 mrks) correct explntion (1 mrk) Question 5 0.7% = (2 mrks) deciml point moved the wrong wy (1 mrk) 5 8 people wrong. Should e 400 g, 32 g, 4, 560 ml, 480 g (3 mrks) 6 1:100 (1 mrk) 2 m (1 mrk) 7 4N-1 (2 mrks) 59 (2 mrks) c 5, 8, 11, 14, 17, 20, 23 (2 mrks) dd 3 ech time (1 mrk) 8 2B+13 = 5B+1 (2 mrks) 4 (2 mrks) 9 BY = 48 (2 mrks) B = 8 (1 mrk) c Y = 4 (1 mrk) 10 3, -2, -5, -6, -5, -2, 3 (2 mrks) 11 correct grph y 5 4 (2 mrks) 6 (2 mrks) (2 mrks) Totl 50 mrks Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

19 Answers Test 2 (pge 50) 1 trpezium (1 mrk) x = y = 130 (2 mrks) explntion (2 mrks) 30 + explntion (2 mrks) c 90 + explntion (2 mrks) 3 50 (1 mrk) 40 (1 mrk) c 90 (1 mrk) m (2 mrks) 64.3 m 2 (3 mrks) c 60 m (2 mrks) d 98.7 m 2 (3 mrks) 5 top left corner (4, 24) (3 mrks) i (10, 4) (2 mrks) ii SF3 (2 mrks) 6 frequency 3, 4, 5, 5, 3 (3 mrks) correct digrm (3 mrks) 7 114, 102, 60, 84 (4 mrks) pie chrt (3 mrks) 8 higher the temperture, the more people on the ech (2 mrks) positive (1 mrk) 9 RH, RC, RS, VH, VC, VS (2 mrks) i 30% (2 mrks) ii must dd up to 100% (1 mrk) Totl 50 mrks Blocks (pge 54) A Tringle numers, Formul H(H+1) 2 Height of 10 = 55 Height of 20 = 210 Height of 100 = 5050 B Formul H(H+1) Height of 16 = 272 Height of 30 = 930 Height of 200 = C Squre numers Formul H 2 Height of 10 = 100 Height of 15 = 225 Height of 100 = Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

20 Answers Dimonds (pge 55) Stge Squre Stge Squre Stge Squres Stge Squres Dimond squres t stges: 2, 4, 8, 16 32, etc. Note: Stge 5 = Stge 9 Stge 6 = Stge 10 Stge 7 = Stge 11 Stge 8 = Stge 12 Stge 5 x 3 = Stge 13 Stge 6 x 3 = Stge 14 Stge 7 x 3 = Stge 15 Stge 8 x 3 = Stge 16 The Symmetry Puzzle (pge 57) Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx

21 Contents Introduction... 1 Numer nd Alger Tril nd improvement... 3 Clculting frctions nd percentges... 5 Equivlences etween decimls nd percentges... 9 Equivlences etween decimls, frctions nd percentges Rtio Rtio Explore numer ptterns Solving liner equtions Formulting liner equtions Grphicl representtion Shpe, Spce nd Mesures 2-D representtions of 3-D shpes Properties of qudrilterls Regulr polygons Intersecting nd prllel lines Circumference nd re of circle, re nd volumes Enlrgement Hndling Dt Collect nd record continuous dt in frequency tles nd frequency digrms Constructing pie chrts Sctter digrms Proility Tests Activity nd investigtion Blocks Dimonds The Symmetry Puzzle Ntionl Curriculum references Pupil s record form Answers Person Pulishing, Chesterton Mill, French s Rod, Cmridge CB4 3NP Tel Fx