SAMPLE YEAR 6 MASTERING THE MATHEMATICS CURRICULUM. Written by Laura Sumner. Including CD-ROM for whiteboard use or printing

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1 Including CD-ROM for whiteord use or printing MASTERING THE MATHEMATICS CURRICULUM YEAR 6 Written y Lur Sumner

2 MASTERING THE MATHEMATICS CURRICULUM YEAR 6 Written y Lur Sumner

3 Acknowledgements: Author: Lur Sumner Cover nd Pge Design: Jerry Fowler Illustrtion: Kthryn Wester The right of Lur Sumner to e identified s the uthor of this puliction hs een sserted y her in ccordnce with the Copyright, Designs nd Ptents Act 998. HedStrt Primry Ltd Elker Lne Clitheroe BB7 9HZ T E. info@hedstrtprimry.com All rights reserved. No prt of this puliction my e reproduced, stored in retrievl system, or trnsmitted in ny form or y ny mens, electronic, mechnicl, photocopying, recording or otherwise without the prior permission of the pulisher. Pulished y HedStrt Primry Ltd 08 HedStrt Primry Ltd 08 A record for this ook is ville from the British Lirry ISBN:

4 MASTERING THE MATHEMATICS CURRICULUM RATIONALE Bckground Techers Notes Yer 6 This ook hs een written tking into ccount the principles outlined in the current Mthemtics curriculum. It focuses on mstery pproch to teching mthemtics, s outlined y NCETM s director, Chrlie Stripp, in the short pper entitled Mstery pproches to mthemtics nd the new ntionl curriculum. In ddition, ccount is tken of the Oxford University Press series Teching for Mstery. Achieving mstery Emphsis is plced on the importnce of children fully mstering mthemticl concepts nd principles so tht, s well s eing le to complete mthemticl tsks, they re le to gin deep understnding out why mthemticl procedures work. Underlying this, is n expecttion tht ll children cn ccomplish high stndrds. Consequently, techers need to e le to focus their time on plnning highly effective strtegies to tech nd model mthemticl concepts for children. Chrlie Stripp highlights the vlue of well-plnned nd focused lessons, where techers explore nd enhnce children s understnding through highly effective nd precise questioning. Additionlly, he points to the importnce of effective prctice nd consolidtion of key concepts. Therefore, the over-riding im of this ook is to provide exmples for children to prctise the concepts they re eing tught, therey llowing techers more time to focus on chieving high qulity teching. Consequently, for ech ojective within the mthemtics curriculum, s outlined in the Sttutory requirements nd the Notes nd guidnce, there is t lest one pge of pertinent questions which children cn complete during lesson or for homework. For ojectives such s performing mentl clcultions, numer of pges re ville for children to prctise rnge of pproprite strtegies. Focused discussion, with techers nd other dults, out the concepts highlighted will enhnce children s depth of understnding nd mstery of the curriculum. Copyright HedStrt Primry Ltd YEAR 6

5 MASTERING THE MATHEMATICS CURRICULUM Techers Notes Yer 6 Emedding mstery Opportunities for children to prctise nd demonstrte their mstery of mthemticl concepts run through ll the pges within the ook. So tht children cn gin n in-depth understnding of ech concept, the ook is designed to provide exmples precisely mtched to ech specific ojective. Hving this deep understnding will enle children to pply their knowledge nd skills to different contexts, sometimes requiring n understnding of rnge of ojectives nd concepts. Therefore, the ook lso includes further pges to provide n opportunity for children to prctise nd demonstrte this level of mstery. So, for ech domin within the curriculum, there re specific pges linked to ech ojective, s well s further mstery pges which drw together the concepts within the whole domin. DIFFERENTIATION The Teching for Mstery Oxford University Press series recommends tht the clss should work together on the sme topic, whilst t the sme time ddressing the need for ll pupils to mster the curriculum nd for some to gin greter depth of proficiency nd understnding. The NCETM pper Mstery pproches to teching mthemtics nd the new ntionl curriculum suggests tht differentition occurs in the support nd intervention provided to different pupils. The ook is designed to meet these recommendtions. Some groups of children my enefit from dditionl dult support nd intervention to complete the exmples, nd develop their proficiency nd understnding. In generl, the exmples re rrnged so tht they ecome progressively more difficult within ech question or on ech pge. The Teching for Mstery series suggests tht there should not e need for dditionl ctch-up progrmmes. However, some groups my require trgeted intervention to reinforce their understnding of their own yer group s concepts through crrying out work t level pproprite to their current ility. Therefore, some children could work on relevnt pges from the HedStrt ooks for other yer groups, whilst still working on the sme topic s the rest of the clss. ASSESSING CHILDREN S PROGRESS This ook is not designed to e used s summtive tool. Nevertheless, s the ook is sed on the Yer 6 expecttions within the mthemtics curriculum, it cn support techers in mking formtive ssessments out children s progress towrds those expecttions. Furthermore, the ook cn provide dignostic informtion out spects of the curriculum for which individul children, or groups of children, my need further support or enhncement. Copyright HedStrt Primry Ltd YEAR 6

6 MASTERING THE MATHEMATICS CURRICULUM Techers Notes Yer 6 USING THE BOOK The ook is designed so tht children re le to write nswers on the photocopied or printed sheets, which my e prticulrly useful if given s homework. However, for most pges, pupils cn esily trnscrie the work into their exercise ooks. If the children complete work on photocopied or printed sheets nd sustntil working out is to e completed, this my need to e crried out seprtely or in exercise ooks. In ddition to photocopying or printing the pges for the children s use, the enclosed CD cn e used to project pges onto n interctive whiteord, therey enling them to e used for modelling nd clrifiction purposes. Copyright HedStrt Primry Ltd YEAR 6

7 CONTENTS Numer numer nd plce vlue Pge Ojectives Pges Red nd write numers up to 0,000,000 Pge Compre nd order numers up to 0,000,000 Pge 4 Determine the vlue of ech digit in numers up to 0,000,000 Pge 5 Round whole numers to the nerest 000 Pge 6 Round whole numers to the nerest 0,000 Pge 7 Round whole numers to the nerest 00,000 Pge 8 Round whole numers to the nerest,000,000 Pge 9 Pge 0 Pge Pges 4 Round whole numers to required degree of ccurcy Clculte the difference etween numers cross zero Use negtive numers in context Solve prolems involving numer nd plce vlue Numer ddition, sutrction, multipliction nd division Pge Pges 5 6 Pges 7 8 Pges 9 0 Pge Pge Pges 4 Pges 5 6 Pge 7 Pge 8 Pges 9 7 Pge 8 Pge 9 Ojectives Multiply multi-digit numers up to 4 digits y two-digit whole numer using the forml written method of long multipliction Divide numers up to 4 digits y two-digit whole numer using the forml method of long division Divide numers up to 4 digits y two-digit whole numer, using long division, nd interpret reminders s whole numers, frctions or deciml frctions Divide numers up to 4 digits y two-digit whole numer, using long division, nd interpret reminders s whole numers, frctions or deciml frctions, s pproprite for the context Divide numers up to 4 digits y two-digit whole numer, using long division, nd round its reminder up or down, s pproprite for the context Divide numers up to 4 digits y two-digit whole numer using the forml written method of short division Divide numers up to 4 digits y two-digit whole numer, using short division, nd interpret reminders s whole numers, frctions or deciml frctions Divide numers up to 4 digits y two-digit whole numer, using short division, nd interpret reminders s whole numers, frctions or deciml frctions, s pproprite for the context Divide numers up to 4 digits y two-digit whole numer, using short division, nd round the reminder up or down, s pproprite for the context Perform mentl clcultions, including with mixed opertions nd lrge numers Identify common fctors Identify common multiples Copyright HedStrt Primry Ltd YEAR 6

8 CONTENTS Pge 40 Pge 4 Pges 4 4 Pge 44 Identify prime numers Use knowledge of the correct order of opertions to crry out clcultions involving the four opertions Solve ddition nd sutrction multi-step prolems in context Solve multi-step prolems, using ll four opertions Frctions (including decimls nd percentges) Pge Pge 45 Pge 46 Pge 47 Pge 48 Pges Pge 5 Pge 5 Pge 5 Pge 54 Pges Pge 57 Pge 58 Pge 59 Pge 60 Pge 6 Pge 6 Ojectives Rtio nd proportion Pge Pges 6 65 Pge 66 Pge 67 Use common fctors to simplify frctions Use common multiples to crete equivlent frctions Use common multiple to express frctions in the sme denomintion Compre nd order frctions Add nd sutrct frctions with different denomintors nd mixed numers, using the concept of equivlent frctions Multiply simple pirs of proper frctions, writing the nswer in its simplest form Divide proper frctions y whole numers Associte frction with division nd clculte deciml frction equivlents Understnd the reltionship etween frctions nd division to find whole quntities Identify the vlue of ech digit to three deciml plces nd multiply nd divide numers y 0, 00 nd 000 giving nswers up to deciml plces Multiply one-digit numers with up to two deciml plces y whole numers Multiply one-digit numers with up to two deciml plces y whole numers in context Use written division methods in cses where the nswer hs up to two deciml plces, including rounding to specified degree of ccurcy Solve division prolems in context, rounding nswers s pproprite Recll nd use equivlence etween frctions, decimls nd percentges Recll nd use equivlence etween frctions, decimls nd percentges in different contexts Ojectives Solve prolems involving the reltive size of quntities using multipliction nd division Solve prolems involving the clcultion of percentges Solve prolems involving the use of percentges for comprison Copyright HedStrt Primry Ltd YEAR 6

9 CONTENTS Pges Pges 70 7 Alger Pge Pges 7 7 Pges Pge 76 Pges Pges Pge 8 Pge 8 Pges 8 84 Pges Pges Pges Pge 9 Pges 9 9 Mesurement Pge Pge 94 Pge 95 Pge 96 Pge 97 Pge 98 Pge 99 Solve prolems involving similr shpes where the scle fctor is known or cn e found Solve prolems involving unequl shring nd grouping using knowledge of frctions nd multiples Ojectives Use simple formule for re nd volume Use simple formul to find missing ngles Find missing co-ordintes Find one unknown numer where it is represented y symols or letters Generte nd descrie liner numer sequences Use formul to generte numer sequence Express missing numers lgericlly Use lgeric formul to solve missing numer prolems Solve equivlent equtions, where symol or letter represents one unknown numer Find pirs of numers tht stisfy nd eqution with two unknowns Enumerte the possiilities of two vriles Solve equtions using the correct order of opertions Solve equtions with n unknown numer on oth sides Ojectives Use, red, write nd convert etween stndrd units of mesure from smller to lrger unit nd vice vers, using deciml nottion of up to three deciml plces Solve prolems involving the clcultion nd conversion of units of length, using deciml nottion up to three deciml plces Solve prolems involving the clcultion nd conversion of units of mss, using deciml nottion up to three deciml plces Solve prolems involving the clcultion nd conversion of units of cpcity, using deciml nottion up to three deciml plces Solve prolems involving the clcultion nd conversion of units of volume, using deciml nottion up to three deciml plces Solve prolems involving the clcultion nd conversion etween nlogue nd digitl time Pges 00 0 Solve prolems involving the clcultion of time in timetles nd clendrs Pge 0 Solve prolems involving the clcultion nd conversion of units of time Copyright HedStrt Primry Ltd YEAR 6

10 CONTENTS Pge 0 Pge 04 Pge 05 Pge 06 Pge 07 Pge 08 Pge 09 Pge 0 Convert etween miles nd kilometres Convert etween metric nd imperil units Recognise tht shpes with the sme re cn hve different perimeters nd vice vers Recognise when it is possile to use formule for re nd volume Clculte the re of prllelogrms Clculte the re of tringles Clculte nd compre the volume of cues nd cuoids using stndrd units Use compound units such s miles per hour Geometry properties of shpes Pge Pge Pge Pge Pge 4 Pge 5 Pge 6 Pge 7 Ojectives Drw -D shpes using given dimensions nd ngles Recognise nd descrie -D shpes Recognise nd descrie nets of -D shpes Compre nd clssify geometric shpes sed on their properties nd sizes Find unknown ngles in tringles, qudrilterls nd regulr polygons Illustrte, nme nd use fcts out prts of circle Recognise ngles where they meet t point, re on stright line or re verticlly opposite, nd find missing ngles Geometry position nd direction Pge Pge 8 Pge 9 Pge 0 Sttistics Pge Pge Pge Pge Pge 4 Pge 5 Ojectives Descrie positions on the full co-ordinte grid Drw nd trnslte shpes on the co-ordinte plne Drw nd reflect shpes in the xes of co-ordinte plne Ojectives Interpret nd construct pie chrts nd use them to solve prolems Interpret nd construct line grphs nd use them to solve prolems Connect mile/kilometre conversion to its grphicl representtion Know when it is pproprite to find the men of set of dt Clculte nd interpret the men s n verge Copyright HedStrt Primry Ltd YEAR 6

11 CONTENTS FURTHER MASTERY PAGES FOR EACH DOMAIN Pge Domin Pges 6 7 Further mstery numer nd plce vlue Pges 8 9 Further mstery ddition nd sutrction Pges 0 Further mstery multipliction nd division Pges Further mstery frctions nd decimls Pges 4 5 Further mstery rtio nd proportion Pges 6 7 Further mstery lger Pges 8 9 Further mstery mesurement Pges 40 4 Further mstery geometry Pges 4 4 Further mstery sttistics ANSWERS Pges Copyright HedStrt Primry Ltd YEAR 6

12 Numer Numer nd plce vlue Copyright HedStrt Primry Ltd YEAR 6

13 Nme Clss Dte Red nd write numers up to 0,000,000 c d e Write the following numers in digits. Eight thousnd, four hundred nd sixty-two Sixty two thousnd, eight hundred nd forty Seventy three thousnd, four hundred nd twenty-one Five hundred nd sixty-seven thousnd, nine hundred nd forty-two Two hundred nd eight thousnd, five hundred nd three A lottery gve out winnings. Complete the cheques elow y writing the mounts in digits. Py BIG BANK The Smith Fmily Nine million, seven hundred nd eighty seven thousnd, seven hundred nd ninety "456" pounds Dte 0//04 LUCKY LOTTERY Mr Silver BIG BANK Py The Friends Syndicte Two million, one hundred nd one thousnd nd ninety-nine "456" pounds Dte 0//04 LUCKY LOTTERY Mr Silver Copyright HedStrt Primry Ltd Numer numer nd plce vlue YEAR 6 Continued overlef

14 Nme Clss Dte 5 Julie hd trget time of 0 seconds to swim 5 m. She recorded ech of her ttempts ove nd elow her trget s follows. +4 seconds seconds 0 seconds + seconds seconds seconds c 6 7 IN OUT Wht ws the difference etween her fstest nd slowest time? How mny seconds ws her third fstest swim? In her next rce, her time ws 5 seconds. Wht would she hve recorded her time s? Aish ws writing horror story. The villin, Professor Freezem, tried to put victims in room which lowered the temperture t rte of 7 C per second. If the strting temperture of the room ws 8 C, wht would e the temperture fter 5 seconds. If the strting temperture ws 0 C, how long would it tke for the temperture to drop to 5 C? The numer function mchine tkes in numers nd then gives out numers which re 6000 less. Complete the functions elow , ,56 seconds seconds seconds o C seconds Copyright HedStrt Primry Ltd Numer numer nd plce vlue YEAR 6 4

15 Numer Addition, sutrction, multipliction nd division Copyright HedStrt Primry Ltd YEAR 6

16 Nme Clss Dte Divide numers up to 4 digits y two-digit whole numer, using long division, nd round its reminder up or down, s pproprite for the context eggs were put into egg oxes holding eggs. How mny oxes were filled? A coch cn crry 4 pssengers. How mny coches will e needed to crry 798 pssengers? Rshid hd collected 64 footll stickers. He put them onto sheets with 4 stickers on ech sheet. How mny sheets hd stickers on? A group of rcheology students found 647 old coins. Forty six coins could e pcked in ox. How mny oxes were needed? 547 people go to the stdium. There re 5 sets in ech row. How mny rows were full of people? 6 The chocolte fctory mkes 846 chocoltes. Twenty-seven chocoltes fit in ech g. How mny full gs of chocoltes cn e mde? Numer ddition, sutrction, Copyright HedStrt Primry Ltd YEAR 6 multipliction nd division

17 Nme Clss Dte Identify common fctors 4 5 Write the common fctors for ech of the following sets of numers. (Don t include ) 8, 7, 6 Add the gretest common fctor to the smllest common fctor. ( Don t use ) 48, 64, 80 Write two numers in ech section of the sorting digrm. An exmple is shown. Complete the sentences elow. (Don t include ) Every numer with fctor of 6 must lso hve fctors of Every numer with fctor of 0 must lso hve fctors of Find the prime fctors of these numers. 0 = 0 = + =, 7 48, 44 Fctor of 4 Not fctor of 4 Fctor of 0 0 Not fctor of 0 c d c 5 = nd d 99 = Numer ddition, sutrction, Copyright HedStrt Primry Ltd YEAR 6 8 multipliction nd division

18 Nme Clss Dte Use knowledge of the correct order of opertions to crry out clcultions involving the four opertions B O D M A S rckets order division multipliction ddition sutrction ( + 4) (or other things mens the sme e.g. squres) s ( + 4) c d e Use BODMAS to complete the following. 76 _ 6 = (4 + 7) 9 = 8 = = = Give the correct nswer nd explin the error mde. EXAMPLE 48 + = 0 54 The ddition, rther thn division, ws clculted first = 60 ( + 6 7)6 + = 976 f g h i j (6 + 7 ) 0 = 4 6 = = 8 ( ) = (7 64 ) 8 + = Numer ddition, sutrction, Copyright HedStrt Primry Ltd YEAR 6 4 multipliction nd division

19 Numer Frctions (including decimls nd percentges) Copyright HedStrt Primry Ltd YEAR 6

20 49 Copyright HedStrt Primry Ltd YEAR 6 For ech of the following, dd the frctions y finding the lowest common denomintor. Now try sutrcting these frctions _ + _ + _ _ + = = = = = = + = = = = = = = = Nme Clss Add nd sutrct frctions with different denomintors nd mixed numers, using the concept of equivlent frctions Dte Continued overlef Numer frctions (including decimls nd percentges) c c d

21 Nme Clss Dte 4 5 Now use division to complete this tle. Numer in Divided y Numer out Complete the clcultions in the function mchine. Numer in Function Numer out Copyright HedStrt Primry Ltd YEAR 6 56 Numer frctions (including decimls nd percentges)

22 Nme Clss Dte Recll nd use equivlence etween frctions, decimls nd percentges Complete the tle elow to identify equivlent frctions, decimls nd percentges. Frction 0.75 Drw lines etween ny vlues which re equivlent. 60% 5% % 70% Put the vlues in the correct position on the numer line. For some, you will need to estimte the position. For ech vlue, write the equivlent frction, deciml nd percentge. An exmple is shown. 0 5 Deciml Percentges % % Copyright HedStrt Primry Ltd YEAR 6 6 Numer frctions (including decimls nd percentges)

23 Rtio nd proportion Copyright HedStrt Primry Ltd YEAR 6

24 Nme Clss Dte Solve prolems involving the clcultion of percentges Numer of pges 4 In Mr Seedt s clss, 40% of the 0 children were girls. How mny girls were there? The clss mde dges for usiness enterprise. The tkings were 0 nd 60% ws profit. How much profit ws there? Nick is writing n essy. He writes 0 pges. He drws r chrt to show the numer of words on ech pge he writes. c < >4 Numer of words on pge Wht percentge of the pges hve 40 words? Wht percentge hve 0 words or fewer? Which of the rnges shown ove represents 5% of the pges? There were 60 pupils in Yer 6. 0% liked swimming est. 5 liked footll. 5% liked thletics nd the rest did not know. How mny children liked thletics est? Wht percentge liked footll est? c How mny children knew which sport they liked est? % % % Copyright HedStrt Primry Ltd Rtio nd proportion 66 YEAR 6

25 Alger Copyright HedStrt Primry Ltd YEAR 6

26 Nme Clss Dte Use simple formule for re nd volume Are = 6 cm 6 cm = Volume = 4 cm 4 m = or The formul to find the re of rectngle is A (Are) = l (length) w (width). Use this to find the missing vlues in the tle elow. cm Rectngle A Rectngle B Rectngle C Rectngle D Rectngle E 5 cm 4 cm = cm cm cm or 6 cm = cm cm cm l 4 cm 8 cm m 5 m mm w 5 cm 9 cm 9 mm m m A 6 m 7 mm 45 m Use the formul V (Volume) = l w h (height) to find the volume of the cuoids. cm cm V = 5 m V = cm cm Not to scle cm cm cm 5 m m Use the formule ove to identify two possile sets of missing vlues (ech side is whole numer). cm m Continued overlef Copyright HedStrt Primry Ltd Alger 7 YEAR 6

27 Nme Clss Dte Use simple formul to find missing ngles The sum of the interior ngles in tringle = 80 The sum of the ngles on stright line = 80 The sum of the ngles t point = 60 The sum of the interior ngles in qudrilterl = 60 The sum of the interior ngles in pentgon = 540 Use the formule ove to find the missing ngles. c Angle = c Angle c = 9 98 e Angle = Angle e = Angle c = d e 4 70 c 8 Continued overlef Copyright HedStrt Primry Ltd Alger 74 YEAR 6

28 Nme Clss Dte Solve equtions using the correct order of opertions To mke sure we crry out clcultions in the correct order, we use BODMAS. B O D M A S rckets order division multipliction ddition sutrction ( + 4) (or other things mens the sme e.g. squres) s ( + 4) Use BODMAS to find the missing vlues. c d = ( 0 + ) 7 e = ( 8 4 ) + 5 = = = 6 ( ) = x = x = y = ( 4 4 ) y = f g 6y = 55 9 y = = ( 6 4 ) 5 = h 9x = 6 + ( 68 7 ) x = Copyright HedStrt Primry Ltd Alger YEAR 6 9

29 Mesurement Copyright HedStrt Primry Ltd YEAR 6

30 Nme Clss Dte Solve prolems involving the clcultion nd conversion etween nlogue nd digitl time 4 5 Drw lines to mtch up to the times shown. One is done for you. 8:00 5:40 04:0 8:0 07:5 Sophie s wtch showed time of qurter pst 7. Her lrm went off 5 minutes lter. Wht time did her lrm go off? Give your nswer s digitl time. The wtch shows the time in the morning when Nfis set off to her cousin s house. The digitl 4-hour clock shows the time she rrived. How long did it tke her? 4:08 hours Jessic, Jmes nd Amy set off on school trip t 8:0. They rrived t their destintion t qurter pst eight the next morning. For how mny hours nd minutes were they trvelling? hours minutes One of the clocks is 5 minutes fst. One is minutes slow. Wht is the correct time? : : : minutes Copyright HedStrt Primry Ltd 99 Mesurement YEAR 6

31 Nme Clss Dte Clculte the re of prllelogrms Look t the prllelogrms on the centimetre grid. Clculte their res. A A prllelogrm hd n re of 0 cm. Its se mesured 4 cm. Wht ws the perpendiculr height? Complete the tle elow. Prllelogrm A Prllelogrm B Prllelogrm C C B A = B = C = D = length (cm) D cm cm cm cm Perpendiculr Height (cm) 4 6 Are (cm) cm Copyright HedStrt Primry Ltd Mesurement YEAR 6 07

32 Geometry Properties of shpes Copyright HedStrt Primry Ltd YEAR 6

33 Nme Use pper or your exercise ook to nswer the following questions. Drw the following rectngles s ccurtely s you cn. Drw the following tringles. Clss Drw D shpes using given dimensions nd ngles c Length 5 cm, width cm Length 6 cm, width 6 cm An equilterl tringle with sides mesuring 4 cm. 5 5 cm 4 cm Not ctul size Not ctul size Juli mde screcrow using D shpes. Use the informtion elow to drw Juli s screcrow s ccurtely s you cn. You will need to use your knowledge of the properties of shpe. Not ctul size Prt of screcrow top of ht rim of ht hed ody rms fingers legs feet uttons knee ptches eyes nose mouth c d Length 4 4 cm, width cm An isosceles tringle with se of 4 5 cm nd n interior ngle of 50º t either side of its se. d Length cm, width 6 cm 4 5 cm 6 cm Shpe 8 cm rectngle rectngle circle rectngle rectngles right ngle tringles prllelogrms rectngles equilterl tringles squres circles tringle rc of circle Dte Dimensions 0 5 cm cm 0 4 cm cm dimeter cm 4 cm 6 cm 5 cm cm se 0 4 cm height cm cm 4c m 60 0 cm cm sides cm cm dimeter 0 cm (pprox) sides pprox 0 cm to fit Copyright HedStrt Primry Ltd Geometry properties of shpes YEAR 6

34 Nme Clss Dte Find unknown ngles in tringles, qudrilterls nd regulr polygons A Without using protrctor, work out the size of Angle A in ech of the shpes elow. c 60 5 cm 5 cm A A 6 cm 6 cm cm 90 not ctul sizes Clculte the vlue of the missing ngles. A 40 cm 70 A A 75 4 cm 4 cm 4 cm 40 4 cm cm 4 cm 4 cm A 4 cm 4 cm 50 = c = c = The shded shpe shows n isosceles tringle drwn inside regulr pentgon. Wht is the size of Angle A? Explin how you worked out your nswer. d e f Copyright HedStrt Primry Ltd 5 Geometry properties of shpes YEAR 6

35 Geometry Position nd direction Copyright HedStrt Primry Ltd YEAR 6

36 Nme Clss Dte Drw nd trnslte shpes on the co-ordinte plne Sketch the new position of the shpe fter it hs een trnslted units up nd units to the left. Sketch the position of the shpe fter rottion of A 0 B C Aove is sequence of rectngles. Write the co-ordintes for ech vertex of the next rectngle (, ) (, ) (, ) (, ) 0 0 Copyright HedStrt Primry Ltd Geometry position nd direction YEAR 6 9

37 Sttistics Copyright HedStrt Primry Ltd YEAR 6

38 Nme Clss Dte Interpret nd construct pie chrts nd use them to solve prolems c There re children in the clss. Mths English 45 P.E Art 45 Science 7 people were sked out their fvourite sport. Their nswers re shown in the tle. Use this informtion to complete the pie chrt. netll Griel nd Isc collected utumn leves. They ech mde pie chrt of their collection. Griel 7 leves How mny children liked Science est. How mny children liked Art est? Wht percentge of the clss did not choose Mths or English? Wht frction of the clss chose P.E? rugy 9 Isc 60 leves sh ok ok sh elm eech elm eech c d swimming Griel sid, Our pie chrts show tht we hve collected the sme numer of ok leves. Explin why he is wrong. 9 netll 8 footll 7 Who collected the most sh leves? tennis How mny eech leves were collected ltogether? 9 % Copyright HedStrt Primry Ltd Sttistics YEAR 6

39 Nme Clss Dte Clculte nd interpret the men s n verge 4 Tom drew the grph elow to show the distnce he jumped over 5 stnding jumps. distnce (metres) jumps Tom only jumped 0 6 m for his 6th jump. To the nerest centimetre, wht ws his new verge? Any is sving for some triners which cost On verge, how much would she need to sve ech week for 5 weeks? Linzi collects 8.6 for chrity. Roert collects 7.54 nd Joseph collects 9.0. Wht is the verge mount collected? Wht ws the verge distnce Tom jumped? Dle ws investigting how long he could stnd on one foot. His results re shown in the tle elow. ttempt time in seconds 8 Wht ws his verge time? seconds m cm Dle wnted to increse his verge to 8 seconds. For how mny seconds would he hve to stnd on one foot in his sixth ttempt to chieve this? seconds Copyright HedStrt Primry Ltd Sttistics YEAR 6 5

40 Further mstery Copyright HedStrt Primry Ltd YEAR 6

41 Nme Clss Dte Further mstery frctions nd decimls c c For ech of the following, write >, < or = to mke the numer sentence correct c d 8 5 Put whole numer less thn 0, in ech ox, to mke the numer sentence correct. There my e more thn one possile nswer. 6 = = 5 This time, put whole numer less thn 0 in ech ox. < 4 8 = _ = 6 = 6 d d = 4 = Copyright HedStrt Primry Ltd YEAR 6 Further mstery frctions nd decimls Continued overlef

42 Nme Clss Dte 4 5 Use your knowledge out re of rectngles to explin how you cn find the re of this tringle. Then explin your working. cm 0 cm 5 cm Not ctul size cm cm Are = The dimeter of sphere is cm. Which of the following oxes could hold 0 spheres? (ech with dimeter of cm). 0 cm Box Box How mny spheres would fit in the other ox? Explin your nswer. cm cm 4 cm A cue weighs 0 4 kg. A cuoid weighs times s much s cue kg How much does cylinder weigh? Give your nswer in kilogrms nd grms. kg g Copyright HedStrt Primry Ltd Further mstery mesurement YEAR 6 9

43 Nme Clss Dte Further mstery sttistics c d cr cycle wlk 5% trin 5% us Wht percentge of the 500 people trvel to work y cr? How mny people cycle to work? The pie chrt shows the results of survey of 500 people s mode of trvel to work. Some percentges re shown. Four times s mny people trvel to work y us thn wlk nd twice s mny people cycle to work thn wlk to work. How mny more people trvelled to work y cr thn wlked? If the survey hd included nother 00 people nd the proportions of mode of trvel to work remined the sme, how mny people would hve used ech mode of pulic trnsport? cycle wlk us trin cr A shoe compny wnted to know which shoe size they should mke the most of. The mnger thought tht finding the men verge shoe size for 5000 people would generte the dt needed. Do you think tht ws sensile ide? Explin your nswer. % Copyright HedStrt Primry Ltd Further mstery sttistics YEAR 6 4 Continued overlef

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45 MASTERING THE MATHEMATICS CURRICULUM YEAR 6 covers ll Ntionl Curriculum ojectives focuses on the mstery pproch supports lesson plnning nd sves techer time provides evidence for formtive progress judgements ISBN T E. info@hedstrtprimry.com