Including CD-ROM for whiteboard use or printing. Primary THE ALGEBRA BOOK. Written by Laura Sumner

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1 Inluing CD-ROM for whiteor use or printing Primr THE ALGEBRA BOOK Written Lur Sumner

2 Primr THE ALGEBRA BOOK Written Lur Sumner Primr

3 Aknowlegements: Author: Lur Sumner Cover n Pge Design: Kthrn Wester The right of Lur Sumner to e ientifie s the uthor of this pulition hs een sserte her in orne with the Copright, Designs n Ptents At HeStrt Primr Lt Elker Lne Clitheroe BB7 9HZ Primr T E. info@hestrtprimr.om All rights reserve. No prt of this pulition m e reproue, store in retrievl sstem, or trnsmitte in n form or n mens, eletroni, mehnil, photooping, reoring or otherwise without the prior permission of the pulisher. Pulishe HeStrt Primr Lt 2018 HeStrt Primr Lt 2018 A reor for this ook is ville from the British Lirr - ISBN:

4 HeStrt Primr: THE ALGEBRA BOOK Rtionle n ook orgnistion Approhes to tehing lger Introution Primr These questions hve een written in line with the ojetives from the Mthemtis Curriulum. Alger is not inlue s seprte ontent omin until the Yer 6 Progrmme of Stu, when hilren re epete to use letters to represent unknown numers. However, the onepts whih hilren nee to grsp in orer to gin full unerstning of lgeri priniples re evelope within the mthemtis urriulum from Yer 1. Prt 1 (pge 1-36) of this ook is se on pre-yer 6 epettions n provies tehers with the opportunit to revise those onepts t n pproprite level for Yer 6 pupils. Therefore, it is epete tht tehers will use the first prt of the ook, s neessr, for the whole lss or groups of hilren. It m e tht tehers eie to give the erlier pges s homework, prior to eginning the Alger topi. Alterntivel, Prt 1 n e use in erlier er groups in preprtion for Yer 6, s pproprite. Prt 2 is se on the Yer 6 epettions n inlues questions to reflet ll the Yer 6 ojetives from the Mthemtis Curriulum Alger ontent omin. In ition, using the orret orer of opertions (tken from the Yer 6 Numer ition, sutrtion, multiplition n ivision omin) n solving equtions with n unknown numer on oth sies (hllenge eon tht epete within the Yer 6 urriulum) is pplie to lger. In orer to support the tehing of lgeri onepts, reminers of pproprite strtegies, whih moel importnt priniples in lger, re ientifie on some pges. It is unerstoo tht shools m vr their tehing pproh from the moel shown. In suh ses, tehers shoul sustitute the pproprite shool moel. Copright HeStrt Primr Lt

5 When multipling in lger, ommon prtie is to omit the multiplition smol. However, so tht hilren n fous on the onept of letters representing missing numers, the erl pges within the Yer 6 Epettions o inlue the smol. Lter pges introue the prtie of omitting the multiplition smol. Differentition In generl, the questions re rrnge so tht the eome progressivel more iffiult on eh pge. Aitionll, for eh ojetive, there is pge or pges whih give the opportunit to prtise the ojetive t stnr level (reltivel simple lultions e.g. smller numers, limite rossing of the tens ounr et.), s well s prllel pge or pges t more hllenging level (more omple lultions, lrger numers et.). This is inite h t the ottom right hn orner of the pge. Consequentl, to i ifferentition, those hilren who nee to fous purel on the lgeri onepts re le to work on reltivel simple lultion spets, whilst those hilren who re ple of unerstning lger with more hllenging lultions re lso provie for. It m e pproprite for some hilren to ttempt the simpler pges efore moving on to the hllenging pges. The lst ojetive Solve equtions with n unknown numer on oth sies, onl ontins hllenging pges s the onept overs hllenge eon tht epete within the Yer 6 urriulum. Using the worksheets The ook is esigne so tht hilren re le to write nswers on the photoopie sheets, whih m e prtiulrl useful if given s homework. However, shoul it e more pproprite, pupils n esil trnsrie the work into eerise ooks. Where sustntil working out nees to e omplete, this m hve to e rrie out in eerise ooks or on seprte pper. Copright HeStrt Primr Lt

6 CONTENTS Prt 1: Pre-Yer 6 Epettions Yer 6 Pre-Yer 6 Epettions Pge Ojetives Pge 1 Use the reltionship etween ition n sutrtion to solve missing numer prolems Pge 2 Use the reltionship etween ition n sutrtion to solve missing numer prolems h Pge 3, 4 Use the reltionship etween ition n sutrtion to solve missing numer prolems Pge 5, 6 Use the reltionship etween ition n sutrtion to solve missing numer prolems h Pge 7, 8, 9 Pge 10, 11, 12 Pge 13 Use the reltionship etween ition n sutrtion to solve missing numer wor prolems Use the reltionship etween ition n sutrtion to solve missing numer wor prolems h Use the reltionship etween multiplition n ivision to solve missing numer prolems Pge 14 Use the reltionship etween multiplition n ivision to solve missing numer prolems h Pge 15, 16 Pge 17, 18 Pge 19, 20, 21 Pge 22, 23, 24 Use the reltionship etween multiplition n ivision to solve missing numer prolems Use the reltionship etween multiplition n ivision to solve missing numer prolems h Use multiplition or ivision to solve missing numer wor prolems Use multiplition or ivision to solve missing numer wor prolems h Pge 25 Unerstn tht n smol n e use to represent numers Pge 26 Pge 27 Unerstn tht n smol n e use to represent numers h Unerstn tht n smol n e use to represent numers. Use the reltionship etween opertions Pge 28 Unerstn tht n smol n e use to represent numers. Use the reltionship etween opertions h Pge 29, 30, 31, 32 Pge 33, 34, 35, 36 h h Mke oth sies of n eqution equl, where one sie ontins missing numer Mke oth sies of n eqution equl, where one sie ontins missing numer h h h Copright HeStrt Primr Lt

7 CONTENTS Prt 2: Yer 6 (n eon) Epettions Pge Ojetives Pge 37, 38 Pge 39, 40 Pge 41, 42, 43 Pge 44, 45, 46 Begin to use letters to represent vriles Begin to use letters to represent vriles h Yer 6 (Strteg moelle) Solve equtions where letters represent missing numers (Strteg moelle) Solve equtions where letters represent missing numers h Pge 47 Solve equtions where letters represent missing lengths Pge 48 Pge 49 Pge 50 Pge 51, 52 Pge 53, 54 Solve equtions where letters represent missing lengths h Solve equtions where letters represent missing lengths in shpes Solve equtions where letters represent missing lengths in shpes h Solve equtions where letters represent missing o-orintes Solve equtions where letters represent missing o-orintes h Pge 55 Solve equtions where letters represent missing ngles Pge 56 Pge 57, 58, 59 Pge 60, 61, 62, 63 Pge 64, 65, 66, 67 Pge 68, 69, 70, 71 Solve equtions where letters represent missing ngles h Use simple formule Use simple formule h Generte n esrie liner numer sequenes Generte n esrie liner numer sequenes h Pge 72 Use formul to generte numer in numer sequene Pge 73 Pge 74, 75 Pge 76, 77 Pge 78, 79 Pge 80, 81 Pge 82, 83, 84 Pge 85, 86, 87 Use formul to generte numer in numer sequene h Epress missing numer prolems lgerill Epress missing numer prolems lgerill h Yer 6 Epettions Solve equivlent epressions, where letter represents one unknown numer Solve equivlent epressions, where letter represents one unknown numer h Fin pirs of numers tht stisf n eqution with two unknowns Fin pirs of numers tht stisf n eqution with two unknowns h Copright HeStrt Primr Lt

8 CONTENTS Prt 2: Yer 6 (n eon) Epettions (ontinue) Pge 88, 89, 90 Pge 91, 92, 93 Pge 94, 95 Pge 96, 97, Pge 98, 99, 100 Enumerte the possiilities of two vriles Enumerte the possiilities of two vriles h (Strteg moelle) Solve equtions using the orret orer of opertions Yer 6 Yer 6 Epettions (Strteg moelle) Solve equtions using the orret orer of opertions h (Strteg moelle) Solve equtions with n unknown numer on oth sies h Copright HeStrt Primr Lt

9 Prt 1 Pre-Yer 6 Epettions This setion will help ou prepre to stu lger! Copright HeStrt Primr Lt

10 Nme Use the reltionship etween ition n sutrtion to solve missing numer prolems Complete the following e Now tr these. Hve go t these f Clss e f e Dte f Copright HeStrt Primr Lt 1 ALGEBRA

11 Nme Clss Dte Use the reltionship etween ition n sutrtion to solve missing numer wor prolems. 1 Re eh prolem elow. Put irle roun the eqution ou woul use to solve the prolem. There re 56 lue n re rs in the grge. 23 re lue. How mn re rs re there? 23 Mrs Shh ke 86 kes for her ughter s irth prt. After the prt, 25 were left. How mn kes were eten t the prt? From Mon to Thurs, Esme ollete 43 house points. On Fri she gine nother 14. How mn house points i Esme ollet ltogether? Copright HeStrt Primr Lt Continue overlef ALGEBRA 7

12 Nme Clss Dte 2 3 Now tr this Jne s fmil h to rive 1652 kilometres to their holi estintion. On the first, the rove 967 kilometres. How muh further i the hve to rive? Use the eqution ou hve hosen to fin the nswer to the prolem. Hve go t this one pupils tten Sunnsie High Shool re os. How mn re girls? Use the eqution ou hve hosen to fin the nswer to the prolem Copright HeStrt Primr Lt Continue overlef h ALGEBRA 11

13 Prt 2 Yer 6 (n eon) Epettions You re now re to stu lger n prtise our skills! Copright HeStrt Primr Lt

14 Nme Clss Dte Begin to use letters to represent vriles. 1 2 Put the missing numers in the oes e f g h In lger, inste of smols to represent numers, we n use letters Copright HeStrt Primr Lt Continue overlef ALGEBRA 37

15 Nme Clss Dte Begin to use letters to represent vriles. 1 2 Put the missing numers in the oes e f g h In lger, inste of smols to represent numers, we n use letters Copright HeStrt Primr Lt Continue overlef h ALGEBRA 39

16 Nme Clss Dte Now tr to fin or in these equtions Wht is the vlue of or? 7 5 Fin the vlue of the letters in these mie multiplition n ivision equtions Clue: Whtever ou o to one sie ou must o to the other. (8 mens the sme s 8 ) e Emple: To fin the vlue of, ivie oth sies 4. So Copright HeStrt Primr Lt Continue overlef ALGEBRA 42

17 Nme Clss Dte The formul for the re of prllelogrm is A (se) h. Use this to omplete the tle elow. Prllelogrm A Prllelogrm B Prllelogrm C Tringle A Tringle B Tringle C 300m 2 496m 2 In the formul D 2r, D represents the imeter of irle n r represents the rius. Use the formul to fin the missing vlues. 156m 2 374mm 2 m 2 A m 2 8m 5m 12m 15m 22mm m 29m 16m 1240m 265m m 16m Use the formul elow to fin the missing vlues in the tle elow. A Cirle A Cirle B Cirle C Cirle D A h or 1/2 h 2 h D m m h m mm r 57m 7.25m m m Copright HeStrt Primr Lt Continue overlef h ALGEBRA 61

18 Nme Clss Dte Epress missing numer prolems lgerill. 1 Complete the following. Jz h 16 preious oins. He gve oins to Afzl. He h 7 left. Cirle the eqution whih woul show how mn preious oins Jz gve to Afzl. 16 Dvi ought 8 pkets of isuits. Eh pket h the sme numer of isuits. There were 208 isuits ltogether. Cirle the eqution whih oul e use to work out how mn isuits were in eh pket (). 8 There re 18 tennis lls in the g. 7 re green n re ornge. Cirle the eqution whih oul e use to fin. Moll hs 4. She spens t the shop. She hs 1.50 left. Cirle the eqution whih oul e use to fin Copright HeStrt Primr Lt Continue overlef ALGEBRA 74

19 Nme Clss Dte 2 Write own suitle eqution ou oul use to solve the prolems. Then solve them people tten the Li Bk Leisure Centre over one weeken. 652 re femle. How mn re mle ()? There were three times s mn tiles in the lrge pool s in the smll pool. The smll pool h 876 tiles. How mn tiles were in the lrge pool ()? Mrs Shh shre evenl etween her three hilren. How muh i the eh get ()? Megn spent 2.64 on nekle, 1.25 on some sweets n on present for her mum. How muh i she spen ltogether ()? Write the full eqution on the line. Copright HeStrt Primr Lt h ALGEBRA 77

20 Nme Clss Dte Solve equtions using the orret orer of opertions. To mke sure we rr out lultions in the orret orer we use BODMAS. B O D M A S rkets orer ivision multiplition ition sutrtion 2 (3 4) (or other things mens the sme e.g. - squres) s 2 (3 4) 1 Use BODMAS to fin the missing numers in these equtions. ( 8 2 ) 3 e 14 ( 8 3 ) 15 ( 1 2 ) f g h 27 ( ) You re oing gret! Copright HeStrt Primr Lt Continue overlef ALGEBRA 94

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22 Primr THE ALGEBRA BOOK inlues Pre-Yer 6 preprtion n prtie for Alger overs ll Y6 Ntionl Curriulum Alger ojetives inorportes high level of hllenge n mster for Y6 n eon fetures uilt-in ifferentition n progression Primr T E. info@hestrtprimr.om