MEP Scheme of Work: YEAR 8A

Transcription

1 MATHEMATICAL DIAGRAMS. Milege Chrts Extrcting distnces from milege chrt The distnces etween sttions on the GNER rilwy re 4 York shown opposite Doncster () Complete the top row Peterorough () Wht is the distnce etween London nd York?. Stevenge London. Using Flow Chrts to Pln With/without decisions Give instructions for shutting down computer. Prcticl Tsks With/without loops Pln wllppering room. Pln clss trip to theme prk. Emphsise cross curricul links Pln school disco..3 Using Flow Chrt for Clssifiction Cross curricul links, e.g. insect identifiction, Design flowchrt to clssify qudrilterls. plnt identifiction Design flowchrt to clssify numers..4 Networks Constructing nd interpreting network digrms Find shortest nd longest routes from S to T through this network: Shortest nd quickest routes through network 4 3 S Criticl Pth Anlysis Simple exmples; time for criticl pth, flot times Orgnising school ply. Plnning trip to London. Activity networks will normlly e given. T

2 FACTORS. Fctors nd Prime Numers Multipliction nd division fcts up to 00 () 4 8 =? () 4 6 =? (c) 6 7 =? Recp on fctors nd multiples Write down ll the fctors of: () 0 () 64 Simple tests for divisiility, i.e. y, 3,, 0 Definition of prime numers Write down ll the prime fctors of. Sieve of Ertosthenes Write down the first prime numers. Find the numer of prime numers in the intervls 0-9, 0-9, 0-9,..., Prime Fctors Fctor trees Wht re the prime fctors of? Express ny numer s product of its prime fctors Write 00 s the product of prime fctors..3 Index Nottion Lws of indices not included Write using index nottion. Using the x y 4 3 key on clcultor Wht is the vlue of 3?.4 Highest Common Fctor (HCF) nd Finding HCF nd LCM y oservtion nd y Find the HCF nd LCM of 30 nd 36. Lowest Common Multiple (LCM) listing ll prime fctors Express 60 nd 0 s the product of prime fctors. Common multiples of numers Hence deduce the HCF nd LCM of 60 nd 0.. Squres nd Squre Roots Squres of integers from - 0 nd corresponding Using = 44, wht is the vlue of 44? squre roots Squre root function on clcultor Relting squres nd squre roots to res of squres nd lengths of sides of squres Use prime fctors to find. Estimting squre roots of ny positive integer Show tht 7 < 3 < 8. Wht is the smllest numer y which 4 must e multiplied to mke it perfect squre? The re of squre is 3 cm. Wht is the length of side?

3 3 3 PYTHAGORAS' THEOREM 3. Pythgors' Theorem Hypotenuse nd right-ngled tringles For right-ngled tringles, + = c Developing Pythgors' Theorem y investigting squres on sides of right-ngled tringles Proof of Theorem (Bronowski) Verify Pythgors' Theorem for this tringle: 3 3. Clculting the Length of the Approprite degree of ccurcy Find the length of hypotenuse for these tringles: () 3 () (c) 4 4 Hypotenuse ( d.p. or nerest whole numer) Clculting the Lengths of Other Sides Find the unknown side in ech of these tringles: () () (c) 6 0 z Isosceles nd equilterl tringles Find the perpendiculr height 7 cm 7 cm x y of this isosceles tringle: 6 cm 6 cm 3.4 Prolems in Context Perimeters of trpezium nd prllelogrm Wht is the re of this prllelogrm: Use of N, S, E, W in prolems 3. Constructions nd Angles + = c right - ngled c + > c cute - ngled + < c otuse - ngled Constructing tringles cm cm A ldder of length 8 m is plced ginst wll, m from its se. Wht is the height of the ldder? Which of these tringles re right-ngled, cute or otuse? () 7 6 () 0 (c) 8 cm 6 7 Using ruler nd pir of compsses, construct tringle with sides of lengths 9 cm, cm nd cm. Is it right-ngled? 8 m 8 m

4 4 4 ROUNDING nd ESTIMATING 4. Revision of the Four Rules: Simple ddition, sutrction, multipliction nd 3 + 6, , 8 7, 4, 4 7, 33, 3 3, 900 Whole Numers division in liner form nd in verticl form Revision of the Four Rules: Decimls Addition, sutrction, multipliction nd Work out (without using clcultor): division () () (c) 8. 7 (d) (with / without clcultors) (e) 8. (f). 4 (g) Order of Opertions BODMAS Clculte: () () 8 3 (c) 8 7 (d) (e) Prolems in Context Relevnt contexts How mny miniuses, ech seting 7 pupils, re needed to trnsport 0 pupils? How much is the cost of 7 clcultors t.99 ech? 4. Rounding Rounding to nerest whole numer, 0, 00 nd 000 Wht is: () 4.3 ().07 (c) 9.8 (d) 7. to the nerest whole numer? Deciml plces nd significnt figures Round 64. to nerest: () whole numer () 0 (c) 00 (d) 000. Give: () 4.34 () 4.07 (c).9 (d) 0.03 to one deciml plce. Give: () 4837 () (c) 7.36 to two significnt figures. 4.6 Estimting Emphsise the importnce of ESTIMATE, CALCULATE nd CHECK Estimte the cost of oxes of Christms crds t 3.99 per ox. Common sense rounding of numers when estimting Is Knowing when clculted nswer is incorrect pproximtely () 3 () 30 (c) 300? ( ) Clcultor Logic - Brcket nd Note different logic used y different clcultors Clculte () (). 07. ( ) 3. Memory Keys giving nswers to (i) significnt figures, (ii) deciml plces.

5 DATA ANALYSIS. Frequency Tles: Discrete Ungrouped Tllying rw dt to produce frequency tle () The results of mths test, out of 0, for clss re: Dt Illustrting dt from frequency tle with line Construct frequency tle nd illustrte the dt in line grph. grph or pie chrt Interprettion of the illustrtions () The NC levels chieved t Key Stge 3 for clss (in mths) were: Construct frequency tle nd illustrte the dt with pie chrt.. Men, Medin, Mode nd Rnge Note tht men, medin, mode re ll types of 'verge', i.e. mesures of centrl tendency Finding mode nd rnge from frequency tle Finding medin from frequency tle when totl frequency is: () odd, () even Finding men vlue from frequency tle Find the mode nd rnge for exmples () nd () ove. Find the medin for exmples () nd () ove. Find the medin of the vlues Find the medin of the dt in exmples () nd (). Copy nd complete the tle elow, nd find the men score mde y the golfer: Golf Score Frequency Score Frequency fi x Use of nottion; men vlue, x = fi nd n = f i Deciding which verge is most pproprite i =

6 6 6 NETS nd SURFACE AREA 6. Common -D nd 3-D Shpes Revision of nmes, with definitions Wht could e the nme of the -D shpe with 4 sides, which hs ll ngles of equl size? 6. -D Representtion of 3-D Shpes Nmes of -D nd 3-D shpes. Wht re the nmes of these shpes: Accurte drwing of rectngles using ruler nd () () protrctor Accurte drwing of tringles using ruler nd compsses Use of squre dotted pper for cues nd cuoids Use of isometric pper On isometric pper, drw cuoid of dimensions cm 3 cm 4 cm. 6.3 Plns nd Elevtions Strightforwrd exmples Sketch the pln nd elevtion for this uilding: m m m 3 m m 6.4 Nets nd Surfce Are of Cues nd Also include other simple shpes Drw n ccurte net for: () cm cue, Cuoids () cm 3 cm 4 cm cuoid. Algeric formule for surfce re of cue nd cuoid Wht re the totl surfce res for () nd () ove? 6. Nets of Prisms nd Pyrmids Design suitle continer for gift Drw n ccurte net for ech of the following shpes: () () cm cm 3 cm 0 cm All lengths re 4 cm

7 7 7 RATIO nd PROPORTION 7. Equivlent Rtios Revise fctors nd highest common fctors Wht re the fctors of: () 6 ()? Wht is the HCF of 6 nd? Simplify to n : m, where n nd m re coprime Simplify the rtios: () 4 : 0 () 4 : 7 Write the rtio : in the form : n. Use of : n nd n : Note tht A : B B : A (A B) On mp, scle : 0 000, wht is the ctul length represented y cm length? 7. Direct Proportion Numericl exmples 6 copies of ook cost. How much do 7 copies cost? Unitry method 7.3 Proportionl Division By unit shre Divide 0 in the rtion : 3 :. 7.4 Liner Conversion Recp concepts If is worth $.63, how much is Currency conversion investigte chnging s to () 7.0 in dollrs, Euros directly compred with to $ nd then $ to () $. in s? Euros 7. Inverse Proportion Numericl exmples How much time is sved on 00 mile journey y driving t 80 mph rther thn t 60 mph?

8 8 8 ALGEBRA: BRACKETS 8. Expnsion of Single Brckets Revise directed numers nd BODMAS Expnd: () x + Tulr method, e.g. x + ( ) () 7( x 3) ( ) represented y: (c) x ( 3 + x) (d) x ( x y) x x x 0 (e) x x 4 ( ) (f) 3x ( x ) 8. Liner Equtions Solving equtions y expnsion Solve for x: () ( x + ) = () ( x ) = Common Fctors Simple exmples Fctorise: () x + 4 () 4x + 3x (c) x + 0x (d) xy+ xz (e) 3xy+ xyz ( )( + ) 8.4 Expnsion of Two Brckets Strightforwrd exmples Expnd: () x + 3 x 4 ( ) ( ) ( )( ) Tulr method, e.g. x x represented () x + x ( )( ) y: (c) x + x x x x x x x + (Extension Pscl's tringle) (d) ( x ) ( )( + ) (e) x + x

9 9 9 ARITHMETIC: FRACTIONS nd PERCENTAGES 9. Revision of Opertions with Frctions Use of simple frctions Wht is 4 of 0? Addition, sutrction, multipliction nd division Clculte: () (d) 8 (g) 4 + () 3 4 (e) 4 (h) 9. Frctions in Context Including use of frctions utton on clcultor Clculte the re of rectngle which mesures 4 3 (c) (f) (i) 4 4 m y m Conversion of Frctions nd Also decimls, where helpful Write: () 0% () % (c) 66 3 % s frctions. Percentges Write: () 3 () (c) s percentges Finding Percentges Chnging rtios to percentges Clculte: () 0% () 40% of. Finding 0%, %, 0%, 7% of quntity Wht is 36 out of 80 s percentge? VAT t 7 % using % Wht is VAT on ill of 0? 9. Incresing nd Decresing Quntities Applictions including: simple interest, popultion Increse 0 y: () 0% () %. y Percentge growth, infltion The popultion of town is Wht is the totl popultion fter % increse? (Extension: compound interest) Equivlent multipliction, e.g. 0% increse multiply y. Wht is the multiplier for 0% reduction? 9.6 Finding the Percentge Increse nd Including percentge profit/loss The numer of lions in Indi hs reduced in the lst 0 yers from 600 to Decrese Wht is the % reduction? A television priced t 00 is reduced in the sle to 400. Wht is the % reduction? 9.7 Reverse Percentge Clcultions Simple exmples A video recorder is sold for 30 fter reduction of 0%. How much ws the originl price? A ill which includes VAT is 9.. Wht is the ill without VAT?

10 0 0 PROBABILITY - TWO EVENTS 0. Recp: Bsic Proility for One Event Applictions with coins, dice, crds Wht is proility of throwing fir dice nd otining: () () numer greter thn 4, (c) n even numer? 0. Outcomes with Two Events Systemtic listing List ll the outcomes when throwing two fir dice. Two wy tles Tree digrms Use tree digrm to find ll the outcomes when two lls re drwn from g contining red, white nd lue lls. 0.3 Proility Using Listings Simple exmples with dice nd coins When you toss n unised coin nd throw fir dice, wht is the proility of otining 'Hed' nd '6'? 0.4 Multipliction Lw for Independent Independent events Events Smpling with replcement Wht is the proility of otining two '6s' when throwing fir dice twice? Use of tree digrms or wy tles A g contins red, 3 white nd lue lls. Two lls re chosen, one t time, with replcement. Wht is the proility of otining: () two red lls, () two lls of the sme colour? 0. Conditionl Proility Smpling without replcement A g contins red, 3 white nd lue lls. Two lls re chosen, one t time, without Use of tree digrms replcement. Wht is the proility of otining: () two red lls, () two lls of the sme colour?

11 ANGLES, BEARINGS nd MAPS. Angle Mesures Types of ngles Mesure the ngles mrked: () () (c). Prllel nd Intersecting Lines Corresponding, lternte, supplementry ngles Determine the sizes of the ngles mrked: () () Verticl opposite ngles c 6 c.3 Berings Eight points of the compss Wht ngle hve you turned through from N to SW? Three figure erings Find the ering of: () B from A, () A from B. N A 0 B.4 Scle Drwings Journeys including erings The journey from A to B to C is shown elow: Two stge journeys Mesure the ering of C from A. N N 0 60 B A km 0 km C N