Series. Teacher. Fractions

Transcription

1 Series E Teher Frtions

2 Copyright 009 P Lerning. All rights reserved. First edition printed 009 in Austrli. A tlogue reord for this ook is ville from P Lerning Ltd. ISBN Ownership of ontent The mterils in this resoure, inluding without limittion ll informtion, text, grphis, dvertisements, nmes, logos nd trde mrks (Content) re proteted y opyright, trde mrk nd other intelletul property lws unless expressly indited otherwise. You must not modify, opy, reprodue, repulish or distriute this Content in ny wy exept s expressly provided for in these Generl Conditions or with our express prior written onsent. Copyright Copyright in this resoure is owned or liensed y us. Other thn for the purposes of, nd sujet to the onditions presried under, the Copyright At 9 (Cth) nd similr legisltion whih pplies in your lotion, nd exept s expressly uthorised y these Generl Conditions, you my not in ny form or y ny mens: dpt, reprodue, store, distriute, print, disply, perform, pulish or rete derivtive works from ny prt of this resoure; or ommerilise ny informtion, produts or servies otined from ny prt of this resoure. Where opyright legisltion in lotion inludes remunerted sheme to permit edutionl institutions to opy or print ny prt of the resoure, we will lim for remunertion under tht sheme where worksheets re printed or photoopied y tehers for use y students, nd where tehers diret students to print or photoopy worksheets for use y students t shool. A worksheet is pge of lerning, designed for student to write on using n ink pen or penil. This my led to n inrese in the fees for edutionl institutions to prtiipte in the relevnt sheme. Pulished P Lerning Ltd For more opies of this ook, ontt us t: Designed P Lerning Ltd Although every preution hs een tken in the preprtion of this ook, the pulisher nd uthors ssume no responsiility for errors or omissions. Neither is ny liility ssumed for dmges resulting from the use of this informtion ontined herein.

3 Series E Frtions Contents Topi Se on Working Answers with (pp. fr ons ) (pp. ) modelling working with fr ons ompring types of fr ons nd ordering fr ons fr ons, of deimls olle on nd perentges fr on word prolems fr on go fish pply Se on Assessment with nswers (pp. ) working with fr ons Topi Types of fr ons (pp. ) types of fr ons 9 fr ons, equivlent deimls fr ons nd perentges mixed numerls mixed numerls vity four in row fr ons pply Dte ompleted / / / / / / / / / / / / / / / / / / Topi Fr ons, deimls nd perentges (pp. ) wri ng tenths s deimls rel ng tenths, hundredths nd deimls introduing perentges 00 hundredths pply / / / / / / / / Series Author: Niol Herringer Copyright

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5 Working with frtions modelling frtions A fr on is prt of whole. This irle hd een divided into piees nd hs piees shded. shded prts prts ltogether The top numer is the numertor, the o om numer is the denomintor. Divide eh shpe into qurters. Shde one qurter: d Shde one third on eh shpe: d Wht fr on is shded? Fr on shded Fr on shded Fr on shded If this is of shpe, wht does the whole shpe look like? Frtions Copyright P Lerning E

6 Working with frtions modelling frtions Complete the tle for eh shpe. d e f Shpe d e f Fr on tht is shded Fr on tht is unshded This shpe hs piees. To show hlf, I hve shded piees. How mny different wys n you show hlf? Answers will vry. E Frtions Copyright P Lerning

7 E Frtions Copyright P Lerning Working with frtions ompring nd ordering frtions Connet the fr ons to their ples on the numer lines. d

8 Working with frtions ompring nd ordering frtions W Red Light green Purple Yellow Drk green Blk Brown Blue Ornge You will need opy of this pge. Colour eh strip in the digrm. If the ornge strip is whole, wht re the fr ons of the other strips? Lel the digrm. Cut out eh oloured fr on strip. opy Use the fr on strips tht you hve ut nd oloured to nswer these: If purple is, whih olour is whole? If red is, whih olour is whole? If lue is whole, whih olour is? Brown Brown Light green d If I onneted purple nd drk green together nd they equlled whole, wht is the vlue of eh? Purple 0 Drk green 0 e If I onneted red, light green nd purple nd they equlled whole, wht is the vlue of eh? Red 9 Light green 9 Purple 9 E Frtions Copyright P Lerning

9 Working with frtions ompring nd ordering frtions If the purple strip is equl to whole, wht fr ons would these strips now e: Light green Red White If the rown strip is equl to whole, wht fr ons would these strips now e: Purple White Red If the drk green strip is equl to whole, wht fr ons would these strips now e: Yellow Light green or White 7 This piture shows hlves. The red strip is nd eh white strip is. Red White Use your strips to rete piture tht shows whole, hlves nd qurters. First hoose strip tht is equl to whole, then hoose different olours for the hlves nd the qurters. Pste your strips in the spe elow: Purple Red White Frtions Copyright P Lerning E

10 Working with frtions frtions of olletion Finding fr on of different mounts is like division. Look t this rry of dots. Finding one qurter is the sme s dividing y. of Cirle the fr on given for eh group nd omplete the sttements: of pentgons of of strs of of tringles of Shde for you. of these grids nd omplete the sttements. The first one hs een done 9 of of of 9 E Frtions Copyright P Lerning

11 Working with frtions frtions of olletion Shde on these grids nd omplete the sttements: of of of Shde on these grids nd omplete the sttements: 0 0 of 0 of of 0 Find the fr ons of these numers: of of of 9 d of e of f of 0 Complete this piture to show tht of these oys re wering hts: First work out wht of is then mes y. Frtions Copyright P Lerning E 7

12 Working with frtions frtions of olletion Josie onneted ues. were red, were yellow nd the rest were lue. Wht fr on of the whole were lue? or Red: of Yellow: of Blue R R R Y Y Y B B B B B B 7 Answer these ue prolems: Amy onneted ues. were green, nd the rest were lue. were red How mny were lue? Green: of Red: of Joel onneted ues. were lue, were ornge nd the rest were purple. How mny were purple? Blue: of Ornge: of Ntlie onneted 0 ues. were yellow, were green nd the rest were ornge. How mny were ornge? Yellow: of 0 Green: of 0 Amer s ered pket of Smr es on her desk to see how mny lue ones there were. Below is list of wht ws in the pket. Shde them s shown: were red were pink were yellow d were green e The rest were lue. How mny were lue? R R Y R R Y Y R R P G G G G Y Y Y Y P P Y B B B E Frtions Copyright P Lerning

13 Working with frtions frtion word prolems Jess spent hlf of her poket money on mgzine. If she gets $0 poket money, how muh ws the mgzine? of $0 $ or $0 $ $ If one qurter of pket of sweets is sweets, how mny sweets re there in the whole pket? sweets Mrley nd M shred pizz tht hd een ut into piees. Mrley te of the pizz nd M te. How mny piees were le? Mrley te of piees Mtt te of piees piees left Amy mde upkes. She ied of them pink, of them lue nd le the rest plin. How mny plin upkes were there? of pink upkes of lue upkes 9 plin upkes Josie ordered two pizzs ut into eighths. If he te of pizz, how muh ws le? So is left. pizzs Frtions Copyright P Lerning E 9

14 Frtion go fish pply Ge ng redy This is gme for either or plyers. Eh plyer will need to ut out opy of the rds on pge. Wht to do Choose one person to e the deler. Eh plyer uts out the rds nd gives them to the deler. The ojet of this gme is to ollet s mny pirs of rds showing the sme fr on s possile. The deler shuffles the rds well nd dels rds to eh plyer. The remining rds re pled fe down in the pond in the middle with plyers si ng round the pond in irle. The plyer on the deler s right egins y sking ny plyer for speifi rd. For exmple: Amity do you hve rd tht shows? If Amity hs rd she must hnd over tht rd nd the sme plyer sks nyone in the group for nother rd. If plyer does not hve the rd tht ws sked for they must sy, Go fish. Then the person sking must tke rd from the pond nd it is the next person s turn. Ply on nues un l there re no more rds le in the pond. The plyer with the most sets is the winner. 0 E Frtions Copyright P Lerning

15 Frtion go fish pply opy Frtions Copyright P Lerning E

16 Types of frtions equivlent frtions Different fr ons n hve the sme mount. They re equivlent. This pizz hs een ut into prts. hs een eten. This pizz hs een ut into prts. hs een eten. Here we re going to explore equivleny. You will need opy of these fr on strips. whole opy First olour in eh strip different olour, then follow these steps: Strip : Cut out the first strip nd write whole. Strip : Cut out the seond strip, fold it in hlf nd ut the equl size piees. Lel eh piee. Strip : Cut it out, fold it in hlf nd hlf gin. Cut the piees nd lel eh piee. Strip : Cut out the next strip nd fold into eighths. How will you do this? Cut the piees nd lel eh piee. Strips nd : The lst strips hve een mrked for you. Count the mrkings. Wht fr ons re they? 0 Ple ll of these strips into pls sleeve to keep them ll in one ple. This is your fr on kit. E Frtions Copyright P Lerning

17 Types of frtions equivlent frtions Use the equivlent fr on strips to nswer these: How mny qurters in one hlf? How mny eighths in one hlf? How mny fi hs in one whole? d How mny tenths in one hlf? 0 Use the equivlent fr on strips to ply these gmes. Both gmes re for plyers only. You will need: your fr on kit die Numer on die Fr on piee from kit or red or yellow or ornge Gme The im of this gme is to e the first to revel the whole piee of pper from your fr on kit. Strt the gme with the whole overed with hlves. Plyer rolls the die nd tkes off tht fr on. Plyers my need to swp piees from their own kit first. For exmple, if you roll first, you need to swp for, then you n tke off. Plyer rolls the die nd tkes off tht fr on, swpping piees if needed. The winner is the plyer who is the first to revel the whole piee of pper first. opy Gme The im of this gme is e the first plyer to omplete wholes. plyers use oth sets of fr on strips. Line up the wholes together. Plyer rolls the die nd ples the fr on piee on top of one of the wholes. Plyer rolls the die nd ples tht fr on piee on top of one of the wholes. Plyers tke turns. The winner is first plyer who is the first to ple the lst piee tht overs wholes. You nnot go over wholes. Your lst piee must fit extly. Frtions Copyright P Lerning E

18 Types of frtions equivlent frtions Shde nd lel these models to show equivlent fr ons: Answers will vry. d 0 Write either T for true or F for flse under eh sttement: > 0 0 < < 0 T F F d > 7 0 e < f 0 < T T F E Frtions Copyright P Lerning

19 Types of frtions mixed numerls A mixed numerl is whole numer nd fr on. For exmple, sy we onneted 0 mul link ues nd nmed this s whole. If we then piked up more mul link ues we hve nother tenths. 0 0 In eh of these prolems, 0 mul link ues represent whole. Write the mixed numerl for eh set of mul link ues Write the mixed numerls tht these fr on models re showing: d Frtions Copyright P Lerning E

20 Types of frtions mixed numerls Shde these fr on models to show the mixed numerls: Answers will vry. d 0 e f Complete these numer lines: E Frtions Copyright P Lerning

21 Types of frtions mixed numerls tivity A group of friends hs formed Cookie Clu. They ke ookies t home nd shre them in shool every Fridy. Help the group shre the ookies firly. You will need opy of pge 0. Cut out the shpes for the following prolems nd figure out the nswers. One you re hppy with your solu ons, pste the piees next to eh person nd write your nswer s mixed numerl t the o om of eh pge. Prolem : Sqi rought in doule ho hip ookies. Show him how he ould shre these mong Cookie Clu memers. Hint: Cut eh ookie into qurters. This mens there re now totl of 0 piees to shre mong memers. Shre these piees evenly mong memers: How mny ookies does eh memer get? Frtions Copyright P Lerning E 7

22 Types of frtions mixed numerls tivity Prolem : Vni rought in 7 doule ho hip ookies. Show him how he ould shre these mong Cookie Clu memers. Hint: Cut eh ookie into piees. This mens there re now totl of piees to shre mong memers. Shre these piees evenly mong memers: How mny ookies does eh memer get? E Frtions Copyright P Lerning

23 Types of frtions mixed numerls tivity Prolem : Rex rought in doule ho hip ookies. Show him how he ould shre these mong Cookie Clu memers. Hint: Cut eh ookie into piees. This mens there re now totl of 0 piees to shre mong memers. Shre these piees evenly mong memers: How mny ookies does eh memer get? Frtions Copyright P Lerning E 9

24 Types of frtions mixed numerls tivity Copy nd ut out the following shpes: Prolem opy Prolem Prolem 0 E Frtions Copyright P Lerning

25 Four in row frtions pply Ge ng redy This is gme for to plyers. You will need the plying ord elow, die nd eh plyer will need different set of oloured ounters. Wht to do The im of this gme is to lim squres in row y overing the mixed numers with your ounters. You n go horizontlly, ver lly or digonlly. Plyer rolls die nd retes mixed numer with the numers. For exmple, if plyer rolled, nd, they ould put their ounter on or or. If plyer nnot mke fr on to lim or it is lredy limed, they miss turn. Note: Mke sure the numertor is smller thn the denomintor. Frtions Copyright P Lerning E

26 Frtion frenzy pply Ge ng redy This is gme for plyers. You will need opy of the plying rds on this pge nd pge. Cut them out nd shuffle them well. Plyers tke turns eing the deler. opy Wht to do The im of this gme is to get rid of ll the rds. The deler dels out ll the rds evenly so eh plyer hs the sme mount of rds. Eh plyer keeps their rds in pile fe down. On the ount of, plyers turn over the top rd nd ple them on the tle. The plyer who hs the greter fr on wins the round nd the other plyer dds oth rds to their pile. If the fr ons re equivlent, ply on nues un l plyer wins the round. The winner is the first plyer to get rid of ll their rds E Frtions Copyright P Lerning

27 E Copyright P Lerning Frtions Frtion frenzy pply opy

28 Frtions, deimls nd perentges writing tenths s deimls Tenths re wri en s deimls like this: Shde the fr on strips so eh one mthes the fr on or the deiml: Order eh set of fr ons nd deimls from smllest to lrgest: 0., 0., 0, , 0.,.0, 0 0., 0, 0., 9 0., 0 0, 9 0,.0 Show the ple vlue of these deimls y wri ng them in the tle: Ones Tenths 7 Ones Tenths The deiml point signls the ple vlue of numers smller thn. This numer is nd 0 or nd 0.. Connet the mthing fr ons nd deimls: E Frtions Copyright P Lerning

29 Frtions, deimls nd perentges writing tenths s deimls Lel this se on of ruler s en metres in deimls. The first ox hs een done for you. (Note this digrm hs een enlrged so you n see the lines lerly.) 0. m. m. m.7 m These ts were the finlists in the F est Ct Compe on. Fill in the lnks elow: Felix. kg Leroy.9 kg Mosley. kg Felix is hevier thn Leroy y 0 Leroy is hevier thn Mosley y 0 of kilogrm. of kilogrm. Mosley is lighter thn Felix y 7 0 of kilogrm. 7 Write the mss of eh t nd < or > to mke the sentene true. Felix Leroy Mosley Felix >. kg.9 kg. kg. kg < The omined weight of whih two ts is.7 kg? Felix nd Mosley Frtions Copyright P Lerning E

30 Frtions, deimls nd perentges writing tenths s deimls whole 00 hundredths 0 tenths 0 00 is the sme mount s 0. We n divide whole into one hundred prts. These re lled hundredths. Hundredths re mde up of 0 lots of tenths. Show how these mounts re the sme: 0 00 is the sme mount s is the sme mount s is the sme mount s 0. d is the sme mount s 7 0. Shde these mounts on the hundred grids: d 0 E Frtions Copyright P Lerning

31 Frtions, deimls nd perentges relting tenths, hundredths nd deimls This digrm shows hundredths shded or 00. Fr ons n e wri en s deimls. As deiml, this mount is wri en s: Ones Tenths Hundredths 0 Complete this tle to show the mounts s tenths, hundredths nd deimls: Tenths Tenths Hundredths 0 Hundredths 0 Deimls 0. Deimls 0. Hundredths Deimls is sme s.0. d Hundredths Deimls Show the ple vlue of these deimls y wri ng them in the tle: Hundreds Tens Ones Tenths Hundredths..7. d Frtions Copyright P Lerning E 7

32 Frtions, deimls nd perentges relting tenths, hundredths nd deimls Shde the fr ons on the grid nd show them s hundredths nd deimls: d Express these ommon fr ons s hundredths nd s deimls: d e f Show where the deimls fit on the numer lines: E Frtions Copyright P Lerning

33 Frtions, deimls nd perentges introduing perentges A perentge is n mount out of % Colour this hundred squre ording to the dire ons: G P B B O O Y Y R R G P B B O O Y Y R R G P B B O O Y R R G P B B O O Y R R G P B B O O Y R R G P B O O Y R R G P B O O Y R R G P B O O Y R R P B O O Y R R P B O O Y R R % green 0% pink % rown d 0% ornge e % yellow f 0% red g Leve the rest lnk. Wht perentge is this? % The most ommonly used perentge mounts re in the tle elow. Complete the tle nd shde hundredth grid for eh mount. The first one hs een done for you. d e Perentge 0% % 0% 7% 0% Hundredths Deiml Fr on 0 0 or Hundredth grid Frtions Copyright P Lerning E 9

34 Frtions, deimls nd perentges introduing perentges O en you n see perentges in shops when it is sle me. Work out the sle prie of these items: End of yer sle, ll items 0% off! Sle prie: $0 $ Sle prie: $ $ $0 d e $0 $00 Sle prie: $0 Sle prie: $ Sle prie: $00 Pie hrts re used to show inform on lerly nd re o en olour oded. Complete the pie hrts ording to the inform on. Eh whole pie hrt is 00% nd eh segment is 0%. Choose olour for eh it of inform on. 00 people were surveyed out their fvourite weekend vi es. R G Go to resturnt... 0% Go to the eh... 0% R R R P O B P See movie... 0% Go shopping... 0% Ply sport... 0% G O O B B P A perentge is n mount out of 00, so 00 0 would e the sme s people were surveyed out their fvourite food. P R G B Pizz... 0 Hmurgers... 0 Pst... 0 Curry... 0 R P R P G P G P G B 0 E Frtions Copyright P Lerning

35 00 hundredths pply Ge ng redy This is gme for plyers. Eh plyer will need opy of this pge nd opy of the plying rds on pge. opy Wht to do The ojet of this gme is to e the first plyer to olour whole grid. Eh plyer uts out the plying rds. The plyers join the rds nd shuffle them. There will e rds. Ly rds out in row, ensuring oth plyers n see them. The rest of the rds go fe down in pile. Plyer tkes rd from the row of nd olours in tht mount on one of their hundred grids. Then they put tht rd t the o om of the pile nd reple it with one from the top of the pile. Plyer repets this proess. Plyers tke turns un l plyer hs filled in 00 hundredths or whole. (If you go over 00 hundredths or whole, it does not ount s win. You must reh extly whole.) There re grids so ply the est out of. Frtions Copyright P Lerning E

36 00 hundredths pply % opy % % 00 % % E Frtions Copyright P Lerning

37 Working with frtions Nme Write the fr on shown on eh shpe: d Show in different wy on eh shpe: Show on eh shpe: Skills Not yet Kind of Got it Interprets the numertor nd denomintor of fr on Represents hlves nd qurters of n ojet in different wys Interprets the numertor nd denomintor of fr on Copyright P Lerning Series E Topi Assessment

38 Working with frtions Nme Write the fr on shown on eh shpe: 7 0 d Show in different wy on eh shpe: Answers will vry. Show on eh shpe: Answers will vry. Skills Not yet Kind of Got it Interprets the numertor nd denomintor of fr on Represents hlves nd qurters of n ojet in different wys Interprets the numertor nd denomintor of fr on Series E Topi Assessment Copyright P Lerning

39 Working with frtions Nme Connet the fr ons to their ples on the numer line: Cirle the igger fr on in eh pir: nd nd nd d nd e nd f nd 0 Write T for true or F for flse next to eh pir of fr ons: > < d Skills Not yet Kind of Got it Orders ommon fr ons with different denomintors Finds equivlene etween hlves, qurters nd eighths Copyright P Lerning Series E Topi Assessment

40 Working with frtions Nme Connet the fr ons to their ples on the numer line: Cirle the igger fr on in eh pir: nd nd nd d nd e nd f nd 0 Write T for true or F for flse next to eh pir of fr ons: > < d T T F T Skills Not yet Kind of Got it Orders ommon fr ons with different denomintors Finds equivlene etween hlves, qurters nd eighths Series E Topi Assessment Copyright P Lerning

41 Working with frtions Nme 7 Cirle the fr on given for eh group nd omplete the sttements: of tringles of strs Find the fr on of these numers: of of 9 of d of e of 0 f of Solve these fr on word prolems. Josh s ered pket of jelly ens onto his desk. of the jelly ens were lk. How mny jelly ens were NOT lk? Nin nd Drew mde pizz nd ut it into piees. Nin te nd Drew te. How mny piees were le? Skills Not yet Kind of Got it Finds fr on of olle on of ojets Finds fr on of whole numer Copyright P Lerning Series E Topi Assessment 7

42 Working with frtions Nme 7 Cirle the fr on given for eh group nd omplete the sttements: of tringles of strs Find the fr on of these numers: of of 9 of d of e of 0 f of Solve these fr on word prolems. Josh s ered pket of jelly ens onto his desk. of the jelly ens were lk. How mny jelly ens were NOT lk? 0 0 Nin nd Drew mde pizz nd ut it into piees. Nin te nd Drew te. How mny piees were le? + 7 Skills Not yet Kind of Got it Finds fr on of olle on of ojets Finds fr on of whole numer Series E Topi Assessment Copyright P Lerning

43 Types of frtions Nme Shde nd lel these models to show equivlent fr ons: d Mke the fr ons equivlent: 0 d Complete this numer line: 0 Skills Not yet Kind of Got it Finds equivlene etween fr ons Shows mixed numerls on numer line Copyright P Lerning Series E Topi Assessment 9

44 Types of frtions Nme Shde nd lel these models to show equivlent fr ons: Answers will vry. d 0 Mke the fr ons equivlent: d 0 Complete this numer line: 0 Skills Not yet Kind of Got it Finds equivlene etween fr ons Shows mixed numerls on numer line 0 Series E Topi Assessment Copyright P Lerning

45 Frtions, deimls nd perentges Nme Shde the numer of hundredths on eh grid: Show eh grid s hundredths nd deimls: Hundredths Deimls Hundredths Deimls Complete eh olumn in this tle. The first one hs een done for you. Perentge 0% % 0% Hundredths 0 00 Deiml 0. Fr on Skills Not yet Kind of Got it Uses deiml not on for tenths nd hundredths Finds equivlene etween tenths, hundredths nd deimls Reltes ommon perentges suh s 0%, % nd 0% to fr on or deiml Copyright P Lerning Series E Topi Assessment

46 Frtions, deimls nd perentges Nme Shde the numer of hundredths on eh grid: Show eh grid s hundredths nd deimls: Hundredths Deimls Hundredths 7 0. Deimls 0.7 Complete eh olumn in this tle. The first one hs een done for you. Perentge 0% % 0% Hundredths 0 00 Deiml Fr on 0 Skills Not yet Kind of Got it Uses deiml not on for tenths nd hundredths Finds equivlene etween tenths, hundredths nd deimls Reltes ommon perentges suh s 0%, % nd 0% to fr on or deiml Series E Topi Assessment Copyright P Lerning