TJ Publishers Advantage Business Centre Great Ancoats Street Manchester M4 6DE

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2 TJ Pulishers Advntge Business Centre Gret Anots Street Mnhester M4 6DE Tel: Fx: e-mil: we pge: TeeJy Pulishers 2014 First Edition pulished y TeeJy Pulishers - August 2014 All rights in this ook re reserved. No prt of this ook my e opied or reprodued in ny formt, inluding eletroni, without the express permission of the uthors in ordne with the Copyright, Design nd Ptents At of Any person or orgnistion who mkes unuthorised opies of ny prt of this ook my e lile to proseution nd possile ivil lims for dmges. Printed y :- Elnders Ltd Merlin Wy New York Business Prk North Tyneside NE27 0QG Registered in Englnd numer pge (i)

3 Yer 6 Textook Book 6 Produed y memers of the TeeJy Writing Group. T Strng, J Geddes nd J Cirns. Front nd Bk Cover designed y Frser MKie. ( pge (ii) TEXTBOOK 6

4 Ntionl Curriulum Textook 6 This ook overs every outome of the Yer 6 ourse, s lid out in the Ntionl Curriulum Englnd Frmework Doument, (Septemer 2013). There re no A nd B exerises. The ook overs the entire Yer 6 ourse without the teher hving to pik nd hoose whih questions to leve out nd whih exerises re importnt. They ll re! The ook follows on diretly from TeeJy s Yer 5 Book nd inludes revision nd onsolidtion of the work overed in the Yer 5 ourse. The Yer 6 Book ontins n 8 pge Chpter Zero whih primrily revises every topi from the Yer 5 ourse nd n e used s dignosti tool. This ould e followed y TeeJy s dignosti ssessments * of the work overed in our Yer 5 ook. It lso ontins Chpter 21, whih revises every topi from the Yer 6 ourse, prior to n end of yer ssessment. Non-lultor skills re emphsised nd enourged throughout the ook. Eh hpter hs Revisit - Review - Revise exerise s summry. Homework*, mirroring exerise y exerise, the topis in this ook, is ville s photoopile pk. TeeJy s Assessment Pk* for Yer 6 work, is lso ville s photoopile pk, nd n e used topi y topi or omined to form series of Yer 6 Cumultive Tests. It lso ontins series of longer ssessments overing the Outomes s lid out in the Ntionl Curriulum Englnd Frmework Doument (Sept 2013). We mke no pologies for the multipliity of olours used throughout the ook, oth for text nd in digrms - we feel it helps righten up the pges!! T Strng, J Geddes, J Cirns (August 2014) * Aville for purhse seprtely. pge (iii)

5 Contents CH TOPIC EX CONTENT PAGES 0 Revision Revision of ll Yer 5 ook Whole No s 1 1 Ple vlue up to Rounding to ny degree of ury 11 3 Multiplition y single digit Multiplition y 2 digits Multiplition/Division y multiples of 10, 100, Revisit-Revise-Review 18 2 Negtive Numers 1 Negtive numers in ontext Adding integers (Extension) 23 Revisit-Revise-Review D Shpes 1 Drwing tringles (2 sides nd inluded ngle) Drwing tringles (2 ngles nd side) Drwing tringles (3 sides) Drwing qudrilterls nd regulr polygons The Cirle Revisit-Revise-Review 36 4 Whole No s 2 1 Division y single digit (Revision) 37 2 Division y 2 digits (no reminder) Division y 2 digits (with reminder) Addition, sutrtion, multiplition nd division Add, sutrt, multiply nd divide mentlly Rounding nd estimting 47 7 BOMDAS 48 Revisit-Revise-Review 49 5 Alger 1 1 Evluting expressions nd formule Construting nd evluting formule Sequenes Revisit-Revise-Review Multiples nd 1 Multiples nd lowest ommon multiple Ftors 2 Ftors nd highest ommon ftor Prime Numers 62 4 Prime Deomposition (Extension) 63 Revisit-Revise-Review 64 pge (iv)

6 CH TOPIC EX CONTENT PAGES 7 Frtions 1 1 Equivlent frtions (Revision) 65 2 Improper frtions nd mixed numers 66 3 Compring frtions (Revision) 67 4 Adding nd sutrting ny frtions Revisit-Revise-Review 71 8 Coordintes 1 Coordintes in ll 4 qudrnts Trnsltion nd refletion Revisit-Revise-Review 79 9 Rtio & Proportion 1 Understnding rtio Simplifying rtios Rtio lultions Proportion 87 5 Diret proportion Revisit-Revise-Review Perentges 1 Perentges without lultor Finding perentge using lultor (optionl) Revisit-Revise-Review Alger 2 1 Simple liner ptterns More diffiult liner ptterns Revisit-Revise-Review Are nd Perimeter 1 Are of right ngled tringle Are of ny tringle Perimeter/Are of squre, retngle nd tringle Are of prllelogrm Mixed exerise 115 Revisit-Revise-Review Deimls 1 Multiplying/dividing deimls y 10, 100, Multiplition y single digit Division y single digit Mixed prolems Chnging frtion to deiml 122 Revisit-Revise-Review 123 pge (v)

7 CH TOPIC EX CONTENT PAGES 14 Alger 3 1 Solving si equtions Hrder equtions Solving equtions with 2 vriles Revisit-Revise-Review Angles 1 Angles (Revision) Angles round point Vertilly opposite ngles Angles in tringles nd polygons Mixed exerise 138 Revisit-Revise-Review Frtions 2 1 Multiplying frtions Dividing frtion y whole numer Mixed Exerise 142 Revisit-Revise-Review Mesure 1 Converting units of metri mesure Metri nd Imperil units Approximte nd ext onversions Mixed prolems Revisit-Revise-Review Similr Shpes 1 Similr figures Revisit-Revise-Review Sttistis 1 Br grphs nd line grphs Interpreting nd drwing pie hrts Drwing pie hrts using protrtor The men nd the rnge Revisit-Revise-Review D nd Volume 1 3-D shpes (Revision) Volumes y ounting ues Volume of uoid - formul Volumes - the ui millimetre nd ui metre 174 Revisit-Revise-Review Revision Revision of ll Yer 6 work Answers Answers pge (vi)

8 Revision - Yer 5 1. Write the following numers out fully in words : A stellite flew totl of two hundred nd sixty thousnd, seven hundred nd five kilometres in one orit round the erth. Write this numer using digits. 3. Write down the numer tht is : less thn more thn Find the missing numers : , , , ,..., Round to the nerest 1000 :- (i) 8491 (ii) Round to the nerest :- (i) (ii) Round to the nerest :- (i) (ii) Round oth numers to the nerest 1000, then estimte : Wht Romn Numerls re used to write the numer : d 880? 8. Wht numers do these Romn symols represent :- CXLI CCCLXXXV CDLVII d CMXL? 9. Try these mentlly. Write down the nswers to : d e f Copy eh exmple nd work out the nswer : When Mr Brown retired, he hd in his svings ount. He used to uy unglow. How muh did Mr Brown then hve in his ount? Yer 6 Book - Chpter 0 pge 1 Revision Yer 5

9 12. Nme eh of the ngles elow using 3 letters nd the! sign, nd stte wht type of ngle eh is :- F P A N Z X T d Y 13. Use protrtor to mesure eh of these ngles :- T F M G 14. Drw nd lel these two ngles :-!PQR = 47!FHG = How mny degrees will I turn through if I rotte lokwise from NW to SW? 16. Copy the following nd work out the nswers :- V D x 2054 d 3804 x 9. x 6 x 8 G I Q Z 17. Set down nd work out : x 2 4 x x ???? 18. Write down the nswer to eh of these :- 10 x x d Set down the following, show your working nd omplete eh lultion : d Yer 6 Book - Chpter 0 pge 2 Revision Yer 5

10 Ple Vlues Exmple :- In the numer , the 6 stnds for six million the 2 stnds for two hundred thousnd the 3 stnds for thirty thousnd the 4 stnds for four thousnd the 5 stnds for five hundred 500 the 9 stnds for nine tens 90 the 8 stnds for eight units (ones) Exerise 1 1. Wht do the following digits stnd for in the numer : d 5? 2. Wht does the 8 stnd for in eh of these numers : d ? 3. Write the following numers out fully in words : d e f g h Write the following numers using digits :- d e f five thousnd, six hundred nd twenty nine twenty thousnd nd twelve seven hundred nd eighty thousnd three hundred nd one six million, two hundred nd forty thousnd nd seven four million, four hundred nd seven thousnd nd three nine million, ninety thousnd nd nine Put the following sets of numers in order, lrgest first : , , , , , , , , , , Whole Numers 1 Understnd ple vlue for numers up to Six million, two hundred nd thirty four thousnd, five hundred nd ninety eight Yer 6 Book - Chpter 1 pge 9 Whole Numers 1????

11 6. Write down the numer tht is :- 500 more thn less thn more thn 7200 d 8000 less thn e more thn f less thn g more thn h less thn i more thn j less thn Look t these sles. Wht numers re represented y the letters A, B, C,...? H P D Q Wht numer lies hlfwy etween :- A B C R S L I M E T nd nd nd d nd e nd f nd ? 9. Write out in figures :- 7 million million million d million. J N F O U G K 10. Cornwll Rovers pid out 4 95 million for n interntionl golkeeper. Tht ws the lrgest trnsfer fee they hd ever pid. Write out this mount of money in full, in figures. Now write it out fully, using words. Yer 6 Book - Chpter 1 pge 10 Whole Numers 1

12 The 3 s R Revisit - Review - Revise 1. Wht does the 4 stnd for in eh of these numers : d ? 2. Write the following numers out fully in words : d Write the following numers using digits :- three hundred nd fourteen thousnd nd one six million, two hundred nd five thousnd nd seventy nine ten nd qurter million. 4. Write down the numer tht is : more thn less thn Round :- Smple Revision to the nerest to the nerest to the nerest 1000 d to the nerest e to the nerest f to the nerest Find :- All Chpters hve 145 x x x 500 d 123 x 8000 e f g h Mrtin n proess 4975 forms in dy. similr exerise How mny n he proess in five dy week? 8. A truk driver noted tht he trvels 1225 km eh week. How fr will he trvel over 8 weeks t this rte? 9. An eletril store hs 46 freezers for sle t 382 eh. How muh will the store tke in if ll re sold? 10. Use short or long multiplition to do these :- 237 x x x 26 d 4053 x 62. Yer 6 Book - Chpter 1 pge 18 Whole Numers 1

13 Negtive Numers in Context The set of Positive nd Negtive Whole numers, long with Zero re lled the set of Integers. Exmples of Integers :- 8, 25, 17, 76, 0, -14, 4003, Exerise 1 1. Wht tempertures re shown on these thermometers? Negtive Numers * Note 2 5, 1 3, 5 1, 3 25, et. re not integers Bnks del with positive nd negtive vlues of money. Working with positive & negtive numers nd zero in the rel world. Disuss :- (i) wht eing in the red or eing in the lk mens. (ii) Yer 6 Book - Chpter 2 pge 19 Negtive Numers d wht n overdrft is. 3. Gerry hs 100 in his nk ount. The nk omputer will show this s Mry hs overdrwn y 50. The omputer will show this s Smmi s ount shows Wht does this lne men? George s ount shows Wht does this lne men? Henry hd in his ount. He then withdrew Wht will his lne now show on the nk omputer? d Brend s lne lst week ws 20, ut she pid in 15. Wht s her new lne nd how muh more will she need to py in to ler her overdrft? e Len s nk lne showed 70. He ought lwnmower for 100 nd rke for 20, using his deit rd. How will his new lne show up on the nk omputer? C C C C

14 Negtive numers n e used in the ontext of time. The London Olympis were held in the yer 2012 A.D. (Anno Domini). This mens 2012 yers sine the irth of Christ. We n think of this s positive time, or Use + or signs to desrie the following dtes : (i) 1966 A.D. (ii) 312 A.D. (iii) 21 B.C. (iv) 729 B.C. The Romn Emperor Cludius ws orn in the yer 10 B.C. (efore Christ). This mens 10 yers efore the irth of Christ. We n think of this s negtive time, or -10. Bugtis Lvius ws orn in 100 B.C. nd died in 44 B.C. How old ws Bugtis when he died? Augustus Cesr ws orn in 63 B.C. nd died in 19 A.D. Wht ge ws Augustus when he died? d Minimus ws orn in 42 B.C. nd lived to the ge of 77. In whih yer did Minimus die? e Mximus died ged 63 in 54 A.D. In whih yer ws Mximus orn? f Annoyus Irritus died in 74 A.D. t the ge of 97. When ws he orn? 5. A fmous Greek Mthemtiin nmed Pythgors of Smos ws orn in 570 B.C. He died in 495 B.C. How old ws Pythgors when he died? 6. Write list of fmous people who were orn thousnds of yers go. d Find their dtes of irth nd dtes they died. Investigte wht mde them fmous. Crete poster of your findings. Yer 6 Book - Chpter 2 pge 20 Negtive Numers

15 The 3 s R Revisit - Review - Revise 1. Stte wht tempertures re represented on these thermometers : 2. On 29th Jnury, Alex s nk lne red Desrie lne of nother wy. His monthly slry of 1475 ws pid in the next dy. Alex then sent off heque for 175 for his seson tiket. Write down Alex s new lne. 3. In n experiment, sientist ooled flsk of liquid from 5 C down to -32 C. By how muh hd the liquid s temperture dropped? Sentor Rovius rrived in Britin in 23 BC. C C He siled k to Rome in the yer 19 AD. For how long hd Rovius een wy? A sumrine ws on the oen ed t depth of -155 metres. It rose to depth of -68 metres. It then dropped y further 52 metres. d Smple Revision. All Chpters hve similr exerise How fr ove the oen ed ws the sumrine t tht time? 4. Find the temperture tht is : 8 C up from 5 C 3 C down from 1 C 11 C up from 18 C d 9 C down from 12 C. 5. Find : 5 + (-7) 4 + (-3) 5!+ 5 d -6 + (-6) e 11 + ( 8) f 2 + ( 2) g h 20 + ( 20). C C Yer 6 Book - Chpter 2 pge 24 Negtive Numers

16 Drwing Tringles Given 3 relevnt piees of informtion out tringle, you should e le to drw it urtely. Two Sides nd the Inluded* Angle (* the ngle etween the 2 sides) Here is rough sketh of!abc. To drw it urtely :- Step 1 :- Step 2 :- Step 3 :- Drw line AB = 6 m. Ple your protrtor t A nd mrk n ngle of 50. Drw line AC, from A through the X, to point C. Mke sure it is 5 m long. A A 5 m 50 C 6 m 2-D Shpes Given 2 sides nd the inluded ngle, e le to drw tringle. 6 m A 6 m B 5 m C B B 50 Step 4 :- Join B to C to form the tringle ABC. A C 6 m B 5 m 50 A 6 m B Yer 6 Book - Chpter 3 pge 25 2-D Shpes

17 Exerise 1 You will require :- RULER, PROTRACTOR nd PAIR of COMPASSES. 1. Shown is rough sketh of!def. F Follow these instrutions to drw it urtely :- Step 1 :- Step 2 :- Drw line DE = 5 m. Put your protrtor t D nd mrk (with n X) n ngle of 30. Step 3 :- Drw line DF, from D through the X, to point F. (Mke sure it is 4 entimetres long). Step 4 :- Join E to F to mke the tringle. 2. Mke n urte drwing of this tringle :- 6 m 70 8 m 3. Mke urte drwings of these two tringles :- 9 m 30 7 m 9 m D 4 m 30 5 m E m 4. Mke urte drwings of the following tringles :- (Mke rough skethes of the tringles first efore drwing them urtely). Drw!KLM where KL = 10 m, KM = 8 m nd "MKL = 60. Drw!PUT where PU = 11 m, UT = 6 m nd "PUT = 120. Drw!XYZ where XY = 8 5 m, XZ = 8 5 m nd "YXZ = 60. Yer 6 Book - Chpter 3 pge 26 2-D Shpes

18 The 3 s R Revisit - Review - Revise 1. Mke n urte drwing of tringle PQR. Mesure nd write down the size of line RQ. 2. Drw urtely tringle DEF where :- DE = 8 5 m!def = 65!FDE = 25. Mesure nd write down the size of :- (i) line DF (ii) ngle EFD. W m Look t this sketh of tringle UVW. Mke n urte drwing of this tringle. Mesure nd mrk in the sizes of eh of its three ngles. 4. Drw kite with sides 5 m, 5 m, 8 m nd 8 m. 5. Mke net, urte drwing of this trpezium. 6 m Mesure the length of the 4th side. The ngle etween the 2 smller sides is to e The dimeter of irle is 16 entimetres. 6 m Smple Revision. U 5 m 8 m 5 m m V All Chpters hve 16 m 8 m Write down the length of its rdius. P R 68 8 m m Q 6 m 6 m similr exerise 7. Use pir of ompsses to drw irle with rdius of 3 5 m. 8. This shpe onsists of retngle mesuring 13 metres y 10 metres, with semi-irle on its end. Clulte the length of the shpe. (Do NOT mesure it with ruler). 10 m 13 m? m Yer 6 Book - Chpter 3 pge 36 2-D Shpes

19 Whole Numers 2 Division y Single Digit (Revision) Exmple :- Divide 5745 y r Be le to divide numer with up to 4 digits y single digit. Exerise 1 1. Set down the following in the sme wy s ove nd omplete eh lultion : d e f g 5033 h Find the reminder eh time : d Eggs re pked into oxes of 6. How mny oxes re needed to pk 4086 eggs? 4. Nine people won totl of If it is shred eqully mongst them, how muh will eh reeive? 5. Choolte isuits re pked into jrs of 8. If the ftory produes 7552 isuits eh dy how mny jrs re needed to pk them? 6. Blnk DVDs in their ses re pried t 9 for 10. How mny pks of 10 ould shopkeeper uy in with 3267? 7. A g ontins 135 sweets. They re shred eqully mongst 8 hildren. How mny will eh hild reeive? How mny sweets will e left over? 8. Tennis lls re pked into oxes of 6. How mny oxes re needed for 1000 lls? How mny tennis lls re left over? 9. Try this one : Yer 6 Book - Chpter 4 pge 37 Whole Numers 2

20 Division y Two Digit Numer (No Reminder) Exmple 1 :- Divide 3810 y 15. *Division y 2 digit numer is normlly done using long division. 15 x 2 15 x 5 15 x 4 Exerise Exmple 2 :- Divide 495 y 11. *Division y 11 or 12 my e done using short division. 1. Use short division to omplete eh lultion :- Be le to divide numer with up to 4 digits y 2 digit numer (no reminder) d e f g h Copy nd omplete : * Your teher will explin this tehnique of Long Division d Use long division to work out the nswer to eh of these divisions :- Divide - Multiply - Sutrt Cross down the next numer d e f g h i j k l m n o p Yer 6 Book - Chpter 4 pge 38 Whole Numers 2

21 Evluting Expressions nd Formule Exmples :- If p = 3, q = 4 nd r = -2, find the vlues of :- 1. 7p 2. 4p + r 3. q 2 p 2 = 7 x 3 = 4 x 3 + (-2) = (4 x 4) (3 x 3) = 21 = 10 = q p 2 + 6pq + r Exerise 1 = 7 = 2 x q x q x q = (5 x p x p) + (6 x p x q) + r = 2 x 4 x 4 x 4 = (5 x 3 x 3) + (6 x 3 x 4) + (-2) = 128 = = Find the vlue of eh of the following when = 3 :- Alger If C =, 4 find the vlue of C when when = 10 nd = 18. C = C = 4 28 C = 4 = d 5 14 e f 20 6 g 2 h 3 i 2 9 j 2 2 k 2 + l Find the vlue of eh of the following when x = 4 :- 5x 7x x 2 d 2x 2 e x 3 f 10x 2 g 20x 3 h 18 x Find the vlues of eh of the following :- *pq mens p x q g + 7 when g = 9 3h + 4 when h = 0 2p 9 when p = 25 d s + t when s = 9 nd t = 4 e 5ef when e = 4 nd f = 2 f 20 4 when = 1 nd = Given p = 1, q = 3 nd r = 7, lulte the vlue of :- Be le to sustitute numers for letters. p + q + r 2p + 5q + r q + p + 2r d pqr e 5p + 5q + 10r f pq + qr + pr g 3p + 2q r h 10pq 4r i 5pqr 100. Yer 6 Book - Chpter 5 pge 50 Alger 1

22 The Squre Root :- When you squre numer you multiply it y itself => 5 2 = 5 x 5 = 25. In reverse :- Ask yourself, Wht numer, times itself, gives 25? => The nswer of ourse is 5 (sine 5 x 5 = 25). We sy tht the squre root of 25 is 5 nd use the symol like this => 25 = 5. It reds s the squre root of 25 is 5. Here re some more exmples :- 16 = 4 (sine 4 x 4 = 16) 81 = 9 (sine 9 x 9 = 81) 1 44 = 1 2 (sine 1 2 x 1 2 = 1 44) = = 100 = If m = 3 nd n = 4, find the vlues of :- m 2 m 2 + n 2 (n m) 2 d n e (n + m) 2 f 2m 2 g 3mn h (m 2) 2 i 35 2n 2 j 40 4m 2 k m 2 + n 2 l (n 2 m 2 ) If x = 4, y = 2 nd z = 1, find :- 5x + y y + 5z x 2 d z 2 e x 2 + 3z 2 f z 2 + 2x 2 g 5x z + y h 6z 2 + y x i 3x 2 + y 30z. 7. Given = 2, = 8, = 10 nd d = 4, find :- d g ( + ) e 1 3 ( + d) f 1 ( ) ( 2) + h i Find the vlue of the letter sked :- P = q r find P, when q = 9 5 nd r = 2 5. D = S x T find D, when S = 60 nd T = 1 5. V = Ah find V, when A = 40 nd h = 2 5. d D = e x f x g find D, when e = 100, f = 5 nd g = 0 5. e N = z 100v find N, when z = 500 nd v = P = q r P = P =... Yer 6 Book - Chpter 5 pge 51 Alger 1

23 Multiples & nd Lowest Lowest Common Common Multiple Multiple In Yer 5, we found out the mening of the word multiple. Exerise 1 Multiples nd Ftors Exmples :- The 1st seven multiples of 9 :- (0), 9, 18, 27, 36, 45, 54. The 1st five multiples of 4 :- (0), 4, 8, 12, 16. * Sine 0 is lwys multiple, (the trivil multiple), in this hpter we will ignore it. Be le to find the lowest ommon multiple of numers (l..m.). In the following exerise you will not only e finding multiples of numers, ut lso the lowest ommon multiple (l..m.) of these numers. 1. List (not inluding 0) :- the first ten multiples of 4 the first eight multiples of 3 the first nine multiples of 5 d the first seven multiples of Write down ll the multiples of 3 etween 8 nd 25. Write down ll the multiples of 6 etween 29 nd 61. Write down ll the multiples of 8 etween 23 nd 73. d Write down ll the multiples of 9 etween 53 nd List the first ten multiples of 2. There is speil nme for the multiples of 2. Wht is it? Sutrt 1 from eh of the numers you hve in prt nd write them down. Is this set of multiples? d Wht is the speil nme for this group of numers? 4. {14, 21, 28, 35, 42} ould e desried s the multiples of 7 from 14 to 42. Desrie the following sets of numers in the sme wy : {44, 46, 48, 50, 52, 54, 56} {35, 40, 45, 50, 55, 60} {120, 130, 140, 150, 160} d {60, 66, 72, 78, 84, 90} e {81, 90, 99, 108, 117} f {60, 80, 100, 120, 140} g {15, 30, 45, 60, 75} h {600, 650, 700, 750, 800} i {39, 52, 65, 78, 91} j {500, 750, 1000, 1250, 1500}. Yer 6 Book - Chpter 6 pge 58 Multiples & Ftors

24 5. List the first twelve multiples of 3. List the first twelve multiples of 4. From nd, write down the multiples whih re ommon to oth lists. (The numers tht re multiples of oth 3 nd 4). d Wht is the lowest numer tht is multiple of oth 3 nd 4? This is lled the lowest ommon multiple of 3 nd 4 (the l..m.) 6. List the first ten multiples of 4. List the first ten multiples of 6. List the ommon multiples of 4 nd 6. d Wht is the l..m. of 4 nd 6? 7. Find the l..m. of eh of the following pirs of numers :- (Hint : go through the multiples of the lrger of the two numers until you reh numer into whih the smller numer divides extly). 2 nd 5 6 nd 3 4 nd 9 d 3 nd 4 e 9 nd 6 f 4 nd 10 g 5 nd 6 h 7 nd 8 i 10 nd 6 j 9 nd 8 k 9 nd 12 l 4 nd Find the l..m. of 2, 3 nd 5 3, 4 nd 8 2, 5 nd 8 d 2, 5 nd 10 e 2, 3 nd 7 f 3, 6 nd 9 g 6, 8 nd Howrd s timetle for his golf lessons is :- Driver lessons every 2 dys. Putter lessons every 4 dys. Snd Bunker lessons every 5 dys. He hd lesson on ll three on the sme dy. When will he next hve ll 3 lessons on the sme dy gin? 10. A Christms tree s lights re set so tht :- the lue lights flsh every 6 seonds. the green lights flsh every 8 seonds. the red lights flsh every 10 seonds. When they re swithed on, they ll flsh together. When will they ll next flsh together gin? Yer 6 Book - Chpter 6 pge 59 Multiples & Ftors

25 Frtions 1 Equivlent Frtions Rememer A frtion onsists of two prts :- Revision 3 5 numertor denomintor Be le to find n equivlent frtion. You n otin n equivlent frtion y multiplying the top nd ottom of frtion y the sme numer. Exmple :- Exmple :- 3 5 Exerise 1 n eome 3 x 2 = 6 12 simplified is 12 3 = 5 x Find two equivlent frtions for eh of the following : e i m f j n Simplify fully (where possile) : e f You n simplify frtion y dividing the top nd ottom of the frtion y suitle numer. g k o g d h l p d h i j k l m n o p Yer 6 Book - Chpter 7 pge 65 Frtions 1

26 Improper Frtions nd Mixed Numers Revision Rememer.. Exmple :- Chnging n improper frtion to mixed numer : Be le to onvert etween improper frtions nd mixed numers relly mens 23 4 => 4 23 (reminder 3) => note :- the 3 is divided y the 4 Exmple :- Chnging mixed numer to n improper frtion : Exerise = ((6 x 3) + 2) thirds = 20 thirds = Copy nd omplete the following :-... reminder relly mens 11 2 => 2 11 => reminder... relly mens => 3... => Chnge eh of the following to mixed numers nd simplify where possile :- e f 23 5 i Copy nd omplete : j = ((3 x 4) + 2) thirds = 14 thirds =... = ((... x...) +...) ninths =... ninths =... g k d h l Frtion s Yippee!!! 4. Chnge eh of the following mixed numers to improper frtions : d e f g h Yer 6 Book - Chpter 7 pge 66 Frtions 1

27 Coordintes Coordintes in 4 Qudrnts Revision : You should know wht Coordinte digrm, (or Crtesin digrm), looks like. Be le to plot point with given oordinte in ny qudrnt. Rememer : x-xis (or horizontl xis). y-xis (or vertil xis). The origin (O). P is 3 (right) nd 4 (up) from the origin. => P(3, 4), hs x-oordinte 3 nd y-oordinte 4. Look t the numers on the x xes nd y xes. They now inlude NEGATIVE vlues. The point Q is 4 (to the right) nd 2 (down) from the origin > Q(4, 2). The point R is 2 (to the left) nd 3 (up) from the origin > R( 2, 3). y O P(3, 4) x If we now extend the set of x nd y xes kwrds nd downwrds, we rete four res where we n plot points. These re lled the 4 QUADRANTS. 2nd qudrnt R x y x x -1 S Q -2-3 x 1st qudrnt P(3, 4) x x The point S is 4 (to the left) nd 1 (down) from the origin > S( 4, 1). 3rd qudrnt -4 4th qudrnt Yer 6 Book - Chpter 8 pge 72 Coordintes

28 Exerise 1 1. Look t this oordinte digrm. The oordintes of A re A( 3, 4). Write down the oordintes of the other 8 points. 2. Write down the oordintes of ll the points : from J to T tht lie on the x-xis tht lie on the y-xis d tht hve n x-oordinte of :- (i) 4 (ii) 2 e tht hve y-oordinte of :- f g (i) 3 (ii) 1 tht hve the sme x-oordinte tht hve the sme x nd y-oordinte. 3. Copy the Crtesin oordinte grid from Question 2. Plot the following points on your digrm : A(4, 1), B( 2, 3), C( 1, 1), D(0, 3), E( 5, 0), F( 4, 3), G(0, 3), H(6, 3), I( 2, 3), J(5, 1), K( 3, 3), L( 3, 3). 4. Drw lrge set of xes ( 10 to 10 on oth sles). Plot eh set of points, join them up nd stte wht shpe is formed eh time : A(3, 3) B(5, 4) C(7, 3) D(5, 2) E( 7, 5) F( 5, 8) G(2, 8) H(0, 5) I( 10, 3) J( 8, 3) K( 9, 3) d L(1, 5) M( 4, 4) N( 5, 1) O(0, 0) e P(4, 5) Q(6, 7) R(5, 9) S(3, 9) T(2, 7) f U( 8, 3) V( 6, 3) W( 5, 5) X( 6, 7) Y( 8, 7) Z( 9, 5). Yer 6 Book - Chpter 8 pge 73 Coordintes A x K x y 4 y 4 E 3 x 2 3 R 2 x J x B x 1 G x x D -1 I C -2x x F H x -3 x 1-4 S x T N x -1 x L x M x -2-3x Q P x x x

29 Rtio & Proportion Understnding Rtio Rtios re used to ompre vrious numers of ojets. This piture shows 3 uses nd 4 rs. Be le to ompre different quntities using rtio. Exerise 1 1. Look t this piture. Write down the rtio of :- utterflies : irds irds : utterflies. 2. Write down the rtio of mie : ts. 3. In fe there re 9 tles nd 19 hirs. Write down the rtio of :- tles to hirs hirs to tles. Write down the rtio of ts : mie. 4. In n orhrd, there re 23 pple nd 29 per trees. 5. A mn owns seven pirs of shoes nd three pirs of triners. Write down the rtio of :- Wht is the rtio of :- shoes : triners triners : shoes. We sy tht :- the rtio of uses to rs is 3 to 4, or for short : uses : rs = 3 : 4. per trees to pple trees pple trees to per trees? Note : The rtio of rs to uses is 4 : 3. Yer 6 Book - Chpter 9 pge 80 Rtio nd Proportion

30 6. In her g, Grnny Smith hs 2 onions nd 15 pottoes. Wht is the rtio of :- onions to pottoes pottoes to onions onions to vegetles d vegetles to pottoes? 7. In shop window, there re pples, ornges, pers, nns nd pinepples. Wht is the rtio of :- pples : ornges nns : pers pers : pples d ornges : nns e pinepples : nns f pers : ornges g nns : other fruit? 8. Shown is frmed piture of Ben the Rottweiler. It is 43 m long nd 27 m rod. Write down the rtio, length : redth. Write down the rtio, redth : length. Write down the rtio, length : perimeter. 9. A mother sel is fed 20 fish for every 3 fish for its y. Write down the rtio of : 43 m 27 m fish for mother : fish for y. fish for y : numer of fish for oth. 10. During Septemer nd Otoer, there were 50 dys of reorded rinfll. Write down the rtio of : wet dys : totl dys. wet dys : dry dys. Yer 6 Book - Chpter 9 pge 81 Rtio nd Proportion

31 Clulting Perentge without Clultor Mny perentges n e redued into simple frtions for lultions without using lultor. Mny perentges n e lulted without lultor. Exmples : 1. Mke opy of the list shown elow nd LEARN it : Perentges 1. Find 3% of Find 70% of Find 11% of... Exerise 1 perentge 50% 25% 75% % 66 2 % 20% 40% 60% 80% 10% 30% 70% 90% 3 frtion Find 1% Find 10% Find 10%, find 1% then times y 3. then times y 7. then dd your two nswers note 2 3 note 2. Do the following, using their frtionl equivlents insted of the perentges :- 10% of % of % of 120 d 10% of 40 e 5% of 40 (hlf of 10%) f 75% of 240 g 33 1 % of 15 3 h 66 2 % of 15 3 i 25% of 140 j 30% of 140 k 20% of 760 l 60% of 350 m 33 1 % of 93 3 n 66 2 % of 93 3 o 50% of 3 p 75% of 36 q 10% of 180 r 5% of 180 s 1% of 700 t 2% of 700 u 3% of 700 v 75% of 480 w 33 1 % of 3900 x 5% of Hrder!! (no lultor). Disuss how, without lultor, you might find : 15% of something 2 1 % of something 7 1 % of something Be le to do some perentge lultions without lultor Find : 15% of 80 15% of 160 km 2 1 % of 1400 km 2 d 2 1 % of 4 2 e 7 1 % of 480 ml 2 f 12 1 % of 1600 mm 2 g 12 5% of 80 m h 7 5% of 1200 litres. Yer 6 Book - Chpter 10 pge 92 Perentges

32 5. A shool hs 420 pupils. 40% of the pupils re on trip. How mny pupils re there on the trip? 6. Five hundred trees re plnted in town. 15% of them re plnted in prk. How mny trees re plnted in the prk? 7. A reipe requires 680 g of flour. 30% of the flour is self-rising. How muh of the flour is self-rising? 8. A Ct nd Dog home hve 114 nimls % re ts. 3 How mny ts re there? 9. Aie hd 220. She spent 25% on weekend sp rek. How muh did Aie py for her rek? Ellie weighed 85 kilogrms. She went to helth resort for month nd lost 20% of her weight. (i) How mny kilogrms did she lose? (ii) How muh did she weigh fter her visit to the helth resort? Dr pid 75% deposit on 360 mountin ike. How muh ws his deposit? d Arnie does 150 sit-ups every dy. He does 60% in the morning nd the rest t night. (i) How mny sit-ups does he do in the morning? (ii) Wht perentge of the sit-ups does he do t night? e 75% of the nimls in frm yrd re hikens. If there re 96 nimls in the yrd, how mny re not hikens? 10. Very Diffiult. A ook prie hs een inresed y 20% nd now osts 24. How muh ws the ook efore the inrese? Yer 6 Book - Chpter 10 pge 93 Perentges

33 Alger 2 Simple Liner Ptterns It is esy to spot numer pttern from digrm or tle. Exmple :- Eh hoolte sponge hs 4 ndles. Be le to identify pttern from tle nd mke up rule for extending it. Drwing up tle helps you see the pttern :- No. of Sponges (S) No. of Cndles (C) ??? Cn you see tht for every new sponge => the numer of ndles rises y 4? => We n write, in words :- Numer of Cndles = 4 x no. of Sponges => or in symol form :- C = 4 x S * For 12 sponges, you would need C = 4 x 12 = 48 ndles. Exerise 1 1. In shool lirry, the tles re set out so tht 3 hildren sit round eh tle. 1 tle 2 tles 3 tles 3 hildren 6 hildren 9 hildren Drw the next pttern of hildren sitting round 4 tles. Copy the following tle nd omplete it :- No. of Tles (T) No. of Children (C) 3 6 9?????? For every extr tle, how mny extr hildren re seted? Yer 6 Book - Chpter 11 pge 98 Alger 2

34 1. d Copy nd omplete the formul :- Numer of hildren =... x Numer of tles. e Now write down the formul using symols :- C =... x T. f Use your formul to deide how mny hildren the lirry n tke if there re 20 tles in it. 2. Look t the str shpes with irles t eh end point. 1 str 2 strs 3 strs 5 irles 10 irles 15 irles Drw the next pttern of strs nd irles. Copy the following tle nd omplete it :- For every extr str, how mny extr irles re needed? d Copy/omplete the formul :- numer of irles =... x numer of strs. e Write down the formul using symols C =... x S. f No. of Strs (S) No. of Cirles (C) 5 10??????? Use your formul to deide how mny irles re needed for 40 strs. 3. Here is glss of strwerry juie whih needs 6 strwerries per glss to mke it. Copy nd omplete the tle listing the numer of strwerries per 1 glss :- No. of Glsses (G) No. of Strwerries (S) 6????? How mny strwerries re needed for 7 glsses? Copy/omplete :- numer of strwerries =... x numer of glsses. d Write the formul using symols onneting S nd G. e??? Use your formul to sy how mny strwerries would e needed to mke 10 glsses of the juie. Yer 6 Book - Chpter 11 pge 99 Alger 2

35 Are & Perimeter Are of Right Angled Tringle To lulte the re of Right Angled Tringle, use two steps s follows :- Be le to work out the re of right ngled tringle. Step 1 Clulte the re of the surrounding retngle Exerise 1 => Are = 6 x 3 = 18 m 2. Step 2 Now simply hlve the nswer you otined => Are = 1 of 18 = 9 m2 2 Eh ox in this exerise represents 1 m Mke n urte drwing of this right ngled tringle. d Complete the figure y drwing the surrounding retngle. Clulte the re of the retngle. Now write down the re of the tringle m Mke n urte drwing of this right ngled tringle. 3 m d 3 m 4 m 6 m Complete the figure y drwing the surrounding retngle. 5 m Clulte the re of the retngle. Now write down the re of the tringle. 3. Mke n urte drwing of this right ngled tringle. d Complete the figure y drwing the surrounding squre. Clulte the re of the squre. Now write down the re of the tringle. 5 m Yer 6 Book - Chpter 12 pge 107 Are & Perimeter 5 m

36 4. Use 1 m squred pper to drw these right ngled tringles : (i) Mke n urte drwing (ii) Drw the surrounding retngle (iii) Find the re of the retngle (iv) Clulte the re of the tringle. d f Are (retngle) = L x B = 8 x 5 5 m = 40 m 2 10 m 8 m 12 m 5 m e g Are (tringle) = 1 2 of 40 =... m2 4 m 11 m 11 m 9 m 8 m 10 m 6 m 2 m 14 m 5. This is not right ngled tringle. Clulte the re of the dotted retngle. Wht do you think the re of the shded tringle will e? 3 m Wht does this tell you out finding the re of ANY tringle? (Investigte). 6 m Yer 6 Book - Chpter 12 pge 108 Are & Perimeter

37 Deimls Multiplying/Dividing Deimls y 10, 100, 1000 To multiply y 10, 100 or 1000, you move the figures one, two or three ples to the left. Be le to multiply/ divide numer with up to 3 deiml ples y 10, 100, To divide y 10, 100 or 1000 you move the figures one, two or three ples to the right. We will now look t exmples involving 3 deiml ples. The multiplition or division is done using the ext sme method s efore. Exmples : x 10 = x 100 = x 1000 = = = = Exerise 1 1. Write down the nswers to the following multiplitions : 2 5 x x x 10 d x 10 e 6 2 x 100 f 5 76 x 100 g x 100 h x 100 i 1 8 x 1000 j 0 77 x 1000 k x 1000 l x 1000 m x 10 n x 100 o x 1000 p x Write down the nswers to the following divisions : d e f g h i j k l m n o p A piee of rd is entimetres thik. How thik is pk of 1000? Joe trvels to his offie nd home gin 5 times per week. He overs totl of km eh week. How fr does Joe live from his offie? If lok of plsti weighs kg wht will 100 loks weigh? Yer 6 Book - Chpter 13 pge 117 Deimls

38 Multiplition y Single Digit Those multiplition tles AGAIN!!! Exmple : x 4. Exerise 2 note tht the deiml points should line up x Copy the following nd omplete the lultions : d e f g h 2. Rewrite eh of these in the ove form nd omplete the lultions :- Be le to multiply deiml y single digit. 8 7 x x x 5 d x 9 e 8 x f 3 x 8 38 g x 7 h 6 x Show your working in nswering the following questions :- x 4 x 8 x 2 x 9 A pket of gums weighs 32 7 grms. Wht is the weight of 8 pkets? Henry the heting engineer erns per hour x 7 How muh does he ern for working one dy from 8.30 m till 2.30 pm? x x 6 x 3 By Joe gined 28 9 grms per week over the pst 7 weeks. How muh is this weight inrese in totl? d By how muh is 7 x 0 82 less thn 6 x 0 97? e f The weight of r of hoolte is grms. How muh will 9 rs weigh? A fully lden rgo ship overed km in 1 hour. At this speed, how fr will it trvel in 6 hours? Yer 6 Book - Chpter 13 pge 118 Deimls

39 Alger 3 Solving (Bsi) Equtions Rememer - we n solve equtions y over up (using finger). Be le to solve si equtions. x + 5 = 9 x = 4 We n lso use our over up method for these type of equtions : 3x mens 3 times x. There re vrious other wys of solving equtions :- Exerise 1 p 3 = 12 p = 15 3x = 12 x = 4 the over up method the method of equl ddition the hnge side < > hnge sign rule. You my ome ross these lterntive methods lter. y 7 = 1 y = 8 2k = 10 k = 5 3 x = Copy nd solve eh eqution y finding the vlue of the letter :- 7y = 56 y = 8 x + 3 = 7 x + 9 = 12 x + 1 = 17 d y + 11 = 21 e y 3 = 6 f y 1 = 21 g p 10 = 0 h p 50 = 10 i p + 6 = 6 j k 18 = 0 k h + 15 = 30 l g 40 = 40 m 5 q = 1 n 8 + w = 11 o 9 z = 0 p 71 + f = 111 q 145 x = 77 r y = Copy eh eqution nd find the vlue of the letter : 3 times wht equls 12? 3x = 6 4m = 20 5p = 30 d 7q = 28 e 6t = 36 f 6 = 60 g 3 = 36 h 8d = 48 i 2x = 24 j 2p = 22 k 4p = 56 l 6m = 54 m 10x = 110 n 8t = 64 o 14p = 42 p 2 = 5 q 2 = 9 r 2n = 19 s 4x = 21 t 10x = 34 u 5x = 24. Yer 6 Book - Chpter 14 pge 124 Alger 3

40 Hrder Equtions Look t these equtions whih involve oth ddition/sutrtion nd multiplition. Be le to solve n eqution. Exmple 1 :- Exmples :- 3x 2 = 25 3x = 27 x = 9 Exerise 2 2x + 1 = 7 2x = 6 x = 3 4x 6 = 6 4x = 12 x = 3 2x + 1 = 7 Ask yourself - wht, dd 1, gives 7? The nswer is 6 - this mens 2x = 6 2 x = 6 Now sk yourself - 2 times wht, gives 6? The nswer is 3 - this mens x = 3 Cn you see we n still use the over up method? Disuss eh of these exmples with your teher. 1. Find the vlue of x y solving eh eqution elow. Copy nd omplete : 2x + 5 = 11 3x + 1 = 13 2x = 6 3x =... x =... x = Find the vlue of x :- (Set down your 3 lines of working refully). 4x 5 = 15 4x =... x =... 2x + 3 = 5 3x + 6 = 21 4x + 7 = 23 d 5x + 2 = 42 e 2x 4 = 6 f 3x 3 = 24 g 4x 1 = 35 h 3x 6 = 0 i 6x 1 = 53 j 7x 2 = 68 k 8x + 4 = 28 l 9x 2 = 61 m 2x 12 = 2 n 4x + 10 = 22 o 5x + 20 = 20 p 5x 1 = 24 q 5 + 2x = 12 r 6x 3 = Look t the piture showing 2 rods end to end. x m 8 m Write down n expression, in terms of x, for the totl length of the 2 rods. Given tht the totl length of the rods is tully 21 entimetres : (i) mke up n eqution involving x. (ii) solve it to find the vlue of x. Yer 6 Book - Chpter 14 pge 125 Alger 3

41 Angles Angles Revision Exerise 1 1. Use right, stright, ute, otuse or reflex to desrie eh of these ngles : d 303 e Use protrtor to drw eh of the ngles in Question Wht is the :- omplement of 70 omplement of 4 supplement of 110 d supplement of 5? 4. Copy nd omplete eh digrm elow, filling in ll missing ngles : 28 d e f * * 5. Shown is retngle ABCD. 12 * * * 133 * * * * * 156 A B D C Mke lrge sketh of ABCD (You do NOT need to e urte). Show ll prllel lines nd equl sides. Fill in the sizes of ll the missing ngles. Yer 6 Book - Chpter 15 pge 130 Angles

42 Angles Round Point The ngles round point must totl 360. (2 stright ngles). In the digrm shown Exmples : Exerise d = = 360 => = 360 => = 110. d 1. Clulte the vlue of the ngles mrked : = 360 => = 360 => = 70. d e f g h * Be le to lulte missing ngle round point. * * * i j k l Sketh some digrms similr to Question 1. Get your prtner to find the missing ngles. Yer 6 Book - Chpter 15 pge 131 Angles

43 Frtions 2 Multiplying Frtions The rule for multiplying two proper frtions is very simple. Be le to multiply one frtion y nother. = 3 4 x 3 5 3!!!3 4!!!5 = 9 20 Exerise 1 To multiply 3 5 x x 5 6 = 20 4!!!5 ( 30 5!!!6 ) = 2 3 (simplified) > 3 5 x 4 7 = 3!!!4 Exmple 1 :- Exmple 2 :- Exmple 3 :- 8 9 x 3 4 = = Copy eh of the following nd omplete :- = = 3 4 x 4 5 3!!!4 4!!!5? 20 =?? = 5 6 x 1 3 5!!!7 = !!!1 6!!!3 Bsi Rule :- 2. Multiply the following frtions nd simplify (where possile) :- =?? Multiply the 2 numertors. Multiply the 2 denomintors. Simplify where possile. 4 5 x x x 5 6 = 3!!!5 4!!!6 =? 24 =? x 4 9 d 4 7 x 5 6 e 5 8 x 4 5 f 7 12 x 6 7 g x 2 3 h 2 9 x 9 10 i 2 3 x 4 5 x 3 4 j 4 5 x 1 2 x 5 6 k 1 2 x 3 5 x 2 3 l 2 3 x 3 4 x Clulte the re of retngulr sheet of metl mesuring 5 6 metre y 3 8 metre. Yer 6 Book - Chpter 16 pge 140 Frtions 2

44 Dividing Frtions y Whole Numer Imgine you hve qurter of pizz nd you wnt to shre it with one other person. Be le to divide frtion y whole numer. This mens you wnt to divide your qurter pizz y 2, (or find hlf of the qurter). Cn you see from the piture tht this mens you end up with n eighth of pizz? To divide y 2, is the sme s finding 1 2 :- => = 1 2 x 1 4 = 1 8 Exmple 1 :- Exerise 2 1. I hve I hve Copy nd omplete :- 4. Find : = 1 2 x 1 2 = 1 4 To divide y 3, is the sme s multiplying y 1 3. To divide y 4, is the sme s multiplying y 1 4. To divide y 5, is the sme s multiplying y 1, nd so on... 5 Exmple 2 :- Exmple 3 : = 1 3 x 1 5 = 1 15 pizz. It is ut into 4 equl its. Wht frtion of pizz is eh it? of pizz ut into 4 its. Wht frtion of pizz is eh it? = = = d = = x = 1 6 e f g h Billy nd his three friends won n equl shre in the lottery. Billy deided to give his portion of the winnings eqully to his 3 dughters. Wht frtion of the lottery win will eh dughter reeive? Yer 6 Book - Chpter 16 pge 141 Frtions 2

45 Converting Units of Metri Mesurement Exerise 1 Chnge : entimetres to millimetres millimetres to entimetres Revision In Yers 4 nd 5, you lerned to hnge from one unit to nother. Exmples : L = 0 85 x 1000 = 850 ml 3820 m = = 3 82 km 20 g = = 0 02 kg 0 4 m = 0 4 x 10 = 4 mm 1 m = 10 mm 1 km = 1000 m 1 litre = 1000 ml Mesure entimetres to millimetres millimetres to entimetres metres to entimetres entimetres to metres metres to entimetres entimetres to metres kilometres to metres metres to kilometres kilometres to metres metres to kilometres metres to millimetres millimetres to metres millimetres to metres kilometres to entimetres kilometre to millimetres entimetres to kilometres millimetres to kilometres kilometres to entimetres litres to millilitres litres to millilitres millilitres to litres millilitres to litres millilitres to litres litres to millilitres kilogrms to grms grms to kilogrms grms to kilogrms grms to kilogrms kilogrms to grms grms to kilogrms. Be le to onvert etween different units of metri mesurement. 1 m = 100 m 1 kg = 1000 g Yer 6 Book - Chpter 17 pge 144 Mesure

46 Metri & Imperil Mesurement (Conversion) Exerise 2 For lss disussion 1. How muh do you lredy know out Imperil Mesurement? Choose one nswer eh time :- 5 m is round out (i) 2 feet or (ii) 2 inhes? 8 km is round out (i) 5 miles or (ii) 5 feet? 1 oune is round out (i) 28 grms or (ii) 28 kilogrms? d 30 m is round out (i) 12 feet or (ii) 1 foot? e 1 pints is round out (i) 1 litre or (ii) hlf litre? f 1 gllon is round out (i) 4 5 litres or (ii) 4 5 millilitres? g 2 5 m is round out (i) 5 inhes or (ii) 1 inh? h 1 kilogrm is round out (i) 2 2 ounes or (ii) 2 2 pounds? i 1 litre is round out (i) 1 75 gllons or (ii) 1 75 pints? Ext nd Approximte Conversions For disussion. Use the tle shown opposite to disuss the est wy of onverting from metri to old imperil units nd kwrds. The tle gives quik onversions nd more urte onversions. You my wnt to use omputer to find n even more urte wy of onverting. Be le to onvert from metri to imperil mesurement nd vie vers. unit pproximte more urte 1 entimetre = little less thn 1 2 n inh 0 39 inh 1 inh = out entimetres 2 54 m 1 metre = little more thn 3 feet 3 28 ft 1 foot = out 1 3 or 3 10 of metre 0 30 metre 1 kilometre = out 5 8 or 0 6 of mile 0 62 mile 1 mile = out 8 5 or just over km 1 61 km 1 kilogrm = just over 2 pounds (ls) 2 2 pounds (ls) 1 pound (l) = out 1 2 kilogrm 0 45 kg 1 oune (oz) = out grms 28 3 grms 1 grm = out 1 25 of n oune (oz) 0 04 oune (oz) 1 litre = out 1 5 gllon or pints 0 22 gl or 1 76 pt 1 gllon = out litres 4 55 litres 1 pint = just over 1 2 of litre 0 57 litre Yer 6 Book - Chpter 17 pge 145 Mesure

47 Similr Figures Two figures re sid to e CONGRUENT in Mths if they re extly the sme. (One figure should e le to e lifted nd pled on top of the other extly). These 2 retngles re ongruent. Two figures re sid to e SIMILAR if : they re silly the sme shpe ut Exerise 1 4 m one is n enlrgement (or redution) of the other. 2 m 8 m Sine the ove 2 squres re the sme si shpe, ut the 2nd shpe is 2 times s ig s the first, they re sid to e SIMILAR. 1. Look t the following 10 shpes. Mth up CONGRUENT pirs : Similr Shpes A retngle, mesuring 8 m y 2 m is not similr to either of these shpes. Cn you explin why? 2 m 4 m 4 m 8 m Be le to lulte the missing side in similr shpe. 4 m A B C D E F G H I J Yer 6 Book - Chpter 18 pge 150 Similr Shpes

48 2. Look t this retngle. Whih two of the 4 shpes elow is mthemtilly SIMILAR to this shpe - P, Q, R or S? 3. You need ruler here!! P Q R S Mesure the length of oth the smll nd lrge retngle elow. l =? w =? L =? Now divide the ig length (L) y the smll length (l) nd write down the vlue of L l. Mesure the width of the smll nd lrge retngles. d Write down the vlue of W w =? e The nswers to nd d should e the sme. Are they? This numer is lled the SCALE FACTOR (or the mgnifition ftor). W =? 4. These re skethes of figures. S 12 m R D 4 m C 9 m 9 m 3 m 3 m A 6 m B P 18 m Compre the 2 sides AB nd PQ nd divide to find the sle ftor. Q => PQ AB = 18 6 =... Yer 6 Book - Chpter 18 pge 151 Similr Shpes

49 Br Grphs nd Line Grphs Exerise 1 1. The r grph shows the numer of people who donted lood in the trnsfusion vn one week lst winter. How mny people gve lood on : (i) Mondy (ii) Tuesdy (iii) Fridy (iv) Thursdy? How mny people gve lood in totl? The trnsfusion vn s heting system roke down one dy nd the stff were sent home. Whih dy ws tht? Give reson for your nswer. 2. This r grph shows the numer of footll tops sold in shop in Oldhm, during the World Cup. How mny Spnish tops were sold? Wht ws the lest populr strip sold? d Whih two strips sold the sme numer nd how mny of eh ws tht? Stte n ovious reson for the high sles of English tops in this sports shop? e How mny more Englnd thn Germn tops were sold? 3. Yer 6 were sked wht they preferred to et with rie, from menu. How mny of Yer 6 preferred :- (i) Chilli Beef (ii) Prwns (iii) Pork (iv) Chiken? Wht ws the most liked food with rie? How mny more hose prwns thn pork? d How mny less hose stir fry thn hiken? e How mny were sked ltogether? 3G p.133 Q4 30 up in 2 s Sttistis Be le to interpret nd drw r grph nd line grph. Mon Tues Wed Thu Fri Dy Yer 6 Book - Chpter 19 pge 155 Sttistis No. People Blood Dontions Numer of Tops Menu Spin Chilli Beef Prwns Pork Stir Fry Chiken Portugl Englnd Tems Oldhm Sports Itly Germny This is lled Horizontl Br Grph Like With Rie

50 4. The owner of smll shop sked 30 ustomers wht kind of tinned soup they liked. The results re shown in the tle :- pe/hm tomto hiken lentil oxtil minestrone Drw nd lel net r grph to show this informtion. 5. Kerry's Eletril Store rried out survey into whih TV hnnel their ustomers preferred to view. Here re the results of tht survey :- Deide on suitle sle nd drw/lel net r grph to show these findings. 6. A ptient s temperture ws tken every hour from 6 m until 1 pm. The results re shown in this line grph. Temperture ( F) pe/hm ITV 1 BBC 1 Ch 4 Ch 5 Sky 1 Sky Sports Sky Movies Ptient s Temperture 6 m 7 m 8 m 9 m 10 m 11 m noon 1 pm Time When ws the ptient s temperture t its lowest? When ws it t its highest? By how mny degrees did it rise etween 6 m nd 8 m? d At whih two times did the temperture egin to rise? e At 9 m, his temperture egn to fll. For how long did this lst nd y how mny degrees did it fll? f Wht ws his estimted temperture t m? Yer 6 Book - Chpter 19 pge 156 Sttistis