SAMPLE A) B) C) D) Tip. Rate = 1L/ hr. Rate = 10L/ hr. Time = 3 hours. Time =? hours. Volume = 5.5 L. Volume =?L. Rate =?L/ hr.

Size: px

Start display at page:

Download "SAMPLE A) B) C) D) Tip. Rate = 1L/ hr. Rate = 10L/ hr. Time = 3 hours. Time =? hours. Volume = 5.5 L. Volume =?L. Rate =?L/ hr."

Delilah Richardson
5 years ago
Views:

Many ancint civilisations had mthods of kping tim. Th ancint Egyptians usd what was calld a watr clock. This involvd watr dripping into a jug from anothr containr.

2 Many ancint civilisations had mthods of kping tim. Th ancint Egyptians usd what was calld a watr clock. This involvd watr dripping into a jug from anothr containr. Q1 Jordan has constructd his own watr clocks; som work wll but most of thm ar faulty. Th faulty clocks ithr hav no markings on th sid or hav an unknown rat. Hlp Jordan work out th unknown (tim, volum, or rat) for ach of his watr clocks blow. A) B) Rat = 10L/ hr Tim = 3 hours Volum =?L C) D) Rat = 2L/ hr Tim = 8.5 hours Volum =?L Rat = 1L/ hr Tim =? hours Volum = 5.5 L Rat =?L/ hr Tim = 3 hours Volum = 75 L Tip R : V : T Covr th quantity you want to find, and follow th stps. R = rat, V = volum and T = tim For xampl, rat = v/t

Ancint Egyptians mad us of boats to transfr matrials. Nubi nds your hlp to calculat th amount of ston that h rcivd on various days during th wk, so that h is not punishd by th Pharaoh.

On th Wdnsday thr was a grat storm up th rivr which limitd th numbr of boats arriving to 3 pr day. How many blocks arrivd on Wdnsday?

3 Ancint Egyptians mad us of boats to transfr matrials. Nubi nds your hlp to calculat th amount of ston that h rcivd on various days during th wk, so that h is not punishd by th Pharaoh. Q1 Q2 Q3 Q4 On Monday th rat at which boats arriv is 10 pr day and ach boat can hold 7 blocks of ston. Th rat of blocks arriving is 7 blocks pr boat. How many blocks arrivd on Monday? On th Wdnsday thr was a grat storm up th rivr which limitd th numbr of boats arriving to 3 pr day. How many blocks arrivd on Wdnsday? If 35 blocks arrivd at th sit on Thursday, how many ships arrivd on that day? On both Friday and Saturday th sailors wr slow to arriv, dlivring only 56 sandston blocks ovr both days. How many ships arrivd pr day, if an qual numbr of boats arrivd ach day?

4 In ancint civilisations it was important to mak sur that thr was nough frsh food for vryon to surviv. Awan is an Egyptian councilman, and th Pharaoh has snt him a dcr asking him to find which livstock is most common.! c f Solv th quations on th following pag to uncovr which livstock was th most common on th Pharaoh s land. Matching th answrs and qustion lttr to th colour in th puzzl blow. For xampl th answr to qustion a) is 3 so you would colour in th a squars grn. d i a g d j h b c g j d b c b g j f i f h b d a b b c Answ r Colour Gr n Blu Brown Gr n Whit Brow n Black Whit

5 Q1 Solv th following quations and us th tabl to colour in th corrct squars. a) If 21 dr wr caught by th Egyptian huntsmn in on wk, how many dr did thy catch pr day? b) In Dcmbr, thr wr 31 calvs born on on farm. What was th rat at which th calvs wr born pr day? c) If Amir workd svn days a wk and arnd gold coins at a rat of 2 pr day, how many gold coins did h arn in a wk? d) How many gold coins would Maht arn if h workd 2 days at a rat of 5 gold coins pr day? ) How many ships would arriv at th Tarmu port in 3 days, if thy arrivd at a rat of 3 pr day? f) If Bahim s farm producs what at a rat of 1 tonn pr month during summr and spring, how many tonns dos h produc? g) How many days would it tak Bari to craft 16 bows if h can crat thm at a rat of 2 pr day? h) If Kbi, th halr, tratd 20 patints in 10 hours, what was th rat that sh tratd patints pr hour? i) If a cart travls 7 kilomtrs an hour, how many hours would an 84km journy tak? j) Th ancint Egyptian Pharaoh, Khufu ruld for 33 yars and a pyramid was finishd vry 3 yars. How many pyramids wr built during his rign?

7 Firstly, thank you for your support of Mighty Minds and our rsourcs. W ndavour to crat highquality rsourcs that ar both ducational and ngaging, and rsults hav shown that this approach works. To assist you in using this rsourc, w hav compild som brif tips and rmindrs blow. About this rsourc This Mighty Minds Fundamntals Lsson focusss on on subtopic from th NAPLAN Tsts and prsnts this skill through a thm from th Australian Curriculum (History, Scinc or Gography). This lsson is also targtd at a crtain skill lvl, to nsur that your studnts ar complting work that is suitd to thm. How to us this rsourc Our Fundamntals Lssons ar split into two main sctions, ach of which contain diffrnt typs of rsourcs. Th studnt workbook contains Th main titl pag; and Th blank studnt workshts for studnts to complt. Th tachr rsourcs sction contains This st of instructions; Th Tachr s Guid, which offrs information that may b ndd to tach th lsson; Th Itm Dscription, which givs a brif ovrviw of th lsson and its aims, as wll as xtnsion idas; Th studnt answr shts, which show modl rsponss on th studnt workshts to nsur that answrs to th qustions ar clar; Th tachr s answr shts, which provid a mor dtaild xplanation of th modl rsponss or answrs; and Finally, th nd of lsson markr. W suggst that you print th studnt workbook (th first st of pags) for th studnts. If studnts ar complting this lsson for homwork, you may also lik to provid thm with th studnt answr pags. Fdback and contacting us W lov fdback. Our policy is that if you mail us with suggstd changs to any lsson, w will complt thos changs and snd you th rvisd lsson fr of charg. Just snd your fdback to rsourcs@mightyminds.com.au and w ll gt back to you as soon as w can.

8 A rat is a typ of ratio that rlats two diffrnt masurmnts to ach othr by using th word pr or th forward slash symbol (/). Rats ar frquntly usd in vryday lif, for instanc whn purchasing ptrol, convrting currncy, working out a wkly wag or purchasing a phon plan. Th units of both forms of masurmnt ar includd in th rat, for xampl, th cost of ptrol is xprssd in cnts pr litr, or /L. Th first quantity is usually masurd rlativ to on unit of th scond quantity for as of undrstanding paying 146 /L for ptrol is much asir to comprhnd than paying 1022 /7L, vn though thy man th sam thing. For this rason, whn working with rats, studnts nd to b abl to simplify ratios. This involvs convrting btwn various units of masurmnt by using multiplication and division. Convrsions Ensur your studnts ar familiar with th following units of masurmnt and convrsion rats. Mass: Volum: Distanc: Tim: 1000 milligrams (mg) = 1 gram (g) 1000 grams (g) = 1 kilogram (kg) 1000 kilograms (kg) = 1 tonn (t) 1000 millilitrs (ml) = 1 litr (L) 1000 litrs = 1 kilolitr (kl) 10 millimtrs (mm) = 1 cntimtr (cm) 100 cntimtrs (cm) = 1 mtr (m) 1000 mtrs (m) = 1 kilomtr (km) 60 sconds (s) = 1 minut (min) 60 minuts (min) = 1 hour (h) 24 hours (h) = 1 day 365 days = 1 yar Currncy: 100 cnts ( ) = 1 dollar ($) Exampls of Common Rats Dollars pr hour, which would b a rat usd to masur incom arnd at a job. E.g. If I arnd $100 for 10 hours work at McDonalds, my hourly rat would b $100/10hrs = $10/hr Spd, which is masurd in distanc/tim (i.. mtrs pr scond or kilomtrs pr hour). E.g. If I was travlling at a spd of 1m/s, that would b qual to 3600m/hour. This is 3.6km/h This taching guid is continud on th nxt pag...

9 ...This taching guid is continud from th prvious pag. Ptrol, which is masurd in cnts pr litr. E.g. If ptrol was 145c/L today and my car s ptrol tank taks 40L, I would spnd 145 x 40 = 5800 = $58 Grocris, many of which ar masurd in dollars pr kilogram E.g. If bananas ar $3/kg and my bunch wighd 2kg, thy would cost m $6. Phon cards, which offr chap long-distanc calls for a crtain pric pr minut. E.g. If calls from Australia to Pakistan wr 2 /minut and I spok to my aunty for 1 hour and 23 minuts, I will hav usd 166 or $1.66. Forign currncy xchang, which swaps on country s mony for anothr according to a crtain rat. E.g. If th Australian dollar was worth 52 Indian rups, it could b xprssd as 52INR/AUD. Howvr, currncy rats tnd not to b xprssd in this mannr, and instad look lik this: 1AUD = 52INR. If I xchangd $1000AUD, I would nd up with 52000INR.

10 Itm Dscription Plas not: any activity that is not compltd during class tim may b st for homwork or undrtakn at a latr dat. Watr Clocks, Egyptian Shipping and Th Animal Encryption Activity Dscription: In this activity, studnts will b rquird to complt a varity of qustions rlating to rats and Ancint Egypt. Th first activity, Watr Clocks,, introducs studnts to th concpts of rat, tim and volum. It asks thm to find unknown variabls with th hlp of a simpl diagram. In th scond activity, Egyptian Shipping, studnts ar rquird to solv wordd problms involving unknown variabls. In th third activity, Th Animal Encryption, studnts ar rquird to solv wordd rat problms in ordr to uncovr a hiddn pictur. Purpos of Activity: Th purpos of this activity is to nhanc studnts abilitis to solv rat problms in a rang of situations. KLAs: Mathmatics, History CCEs: Visualising (β50) Analysing (θ43) Stting out/ prsnting/ arranging/ displaying (π20) Calculating with or without calculators (Ф16) Suggstd Tim Allocation: This lsson is dsignd to tak approximatly on hour to complt 20 minuts pr worksht. This Itm Dscription is continud on th nxt pag...

11 Itm Dscription continud This Itm Dscription is continud from th prvious pag. Watr Clocks, Egyptian Shipping and Th Animal Encryption Taching Nots: Studnts should complt all activitis individually bfor discussing solutions as a class. Studnts will rquir colouring pncils to complt this activity. If studnts ar struggling show thm how to complt part of th activity. This should assist thm in answring th rmaining qustions To challng th studnts ask thm to complt th activitis without a calculator. Studnts should hav a basic concpt of rat bfor bginning this activity. Follow-up Qustions: Whn do you think th watr clock was abolishd? Is th cow still th biggst livstock producr? If not, what is? What othr ways othr than boats do w transfr matrials? What is Egypt famous for? What landmarks?

12 Many ancint civilisations had mthods of kping tim. Th ancint Egyptians usd what was calld a watr clock. This involvd watr dripping into a jug from anothr containr. Q1 Jordan has constructd his own watr clocks; som work wll but most of thm ar faulty. Th faulty clocks ithr hav no markings on th sid or hav an unknown rat. Hlp Jordan work out th unknown (tim, volum, or rat) for ach of his watr clocks blow. A) B) Rat = 10L/ hr Tim = 3 hours Volum =?L C) D) Rat = 2L/ hr Tim = 8.5 hours Volum =?L A) Rat = 10L/hr Tim = 3 hrs Volum = 10 x 3 = 30L C) Rat = 2L/hr Tim = 8.5 Volum = 8.5 x 2 = 17L Rat = 1L/ hr Tim =? hours Volum = 5.5 L Rat =?L/ hr Tim = 3 hours Volum = 75 L Tip R : V : T Covr th quantity you want to find, and follow th stps. R = rat, V = volum and T = tim For xampl, rat = v/t B) Rat = 1L/hr Volum = 5.5 Tim = 5.5 / 1 = 5.5 hrs D) Volum = 75L Tim = 3 hrs Rat = 75 / 3 = 25L/hr

13 Watr Clocks Qustion On: Studnts wr rquird to calculat a sris of unknown valus whn givn spcific information about a watr clock. Th studnts wr givn ithr th tim and rat, th tim and volum, or th volum and rat and askd to find th unknown. a) For this qustion studnts wr rquird to calculat volum whn givn rat and tim. Rat = 10L/hr Tim = 3 hrs Volum = rat x tim = 10 x 3 Thrfor volum = 30 L b) For this qustion studnts wr rquird to calculat tim whn givn rat and volum. Rat = 1L/hr Volum = 5.5 Tim = volum / rat = 5.5 / 1 Thrfor tim = 5.5 hours c) For this qustion studnts wr rquird to calculat volum whn givn rat and tim. Rat = 2L/hr Tim = 8.5 Volum = tim x rat 8.5 x 2 Thrfor volum = 17 L d) For this qustion studnts wr rquird to calculat rat whn givn tim and volum. Volum = 75L Tim = 3hrs Rat = volum / tim = 75 / 3 Thrfor rat = 25L/hr

14 Ancint Egyptians mad us of boats to transfr matrials. Nubi nds your hlp to calculat th amount of ston that h rcivd on various days during th wk, so that h is not punishd by th Pharaoh. Q1 Q2 Q3 Q4 On Monday th rat at which boats arriv is 10 pr day and ach boat can hold 7 blocks of ston. Th rat of blocks arriving is 7 blocks pr boat. How many blocks arrivd on Monday? Numbr of boats = 10 Rat = 7 blocks/boat Numbr of Blocks = Numbr of boats x Rat = 10 x 7 = 70 blocks On th Wdnsday thr was a grat storm up th rivr which limitd th numbr of boats arriving to 3 pr day. How many blocks arrivd on Wdnsday? Numbr of Blocks = 35 Rat = 7 Blocks/Ship Numbr of boats = 3 Rat = 7 blocks/boat Numbr of Blocks = Numbr of boats x Rat = 3 x 7 = 21 blocks If 35 blocks arrivd at th sit on Thursday, how many ships arrivd on that day? Numbr of ships arrivd = Numbr of blocks / Rat = 35/7 = 5 ships On both Friday and Saturday th sailors wr slow to arriv, dlivring only 56 sandston blocks ovr both days. How many ships arrivd pr day, if an qual numbr of boats arrivd ach day? Numbr of Blocks = 56 Rat = 7 Blocks/Ship Numbr of ships arrivd = Numbr of blocks / Rat = 56/7 = 8 ships Boats / Day = Total numbr of boats / numbr of days = 8/2 = 4 boats pr day

15 Egyptian Shipping Qustion On: Studnts wr rquird to calculat a sris of unknown valus whn givn spcific information about a shipping manuscript. Th studnts wr givn a combination of information rlating to th numbr of ships that arrivd and th amount of tim it took to dlivr th blocks or th numbr of blocks that wr dlivrd. Thy wr givn a constant rat of 7 blocks pr ship to calculat th unknown valus. 1. For this qustion studnts wr rquird to calculat th amount of blocks that arrivd on a spcific day. Th numbr of boats that arrivd on Monday was 10 and as ach boat can carry 7 sandston blocks th numbr of blocks that wr dlivrd was 70. Rat= 7 blocks/boat Numbr of boats = 10 Numbr of blocks = numbr of boats x rat = 10 x 7 Thrfor th numbr of blocks = For this qustion studnts wr again rquird to calculat th amount of blocks that arrivd on a spcific day. Th numbr of boats that arrivd on Wdnsday was 3, as ach boat can carry 7 sandston blocks th numbr of blocks that wr dlivrd was 21. Rat= 7 blocks/boat Numbr of boats = 3 Numbr of blocks = numbr of boats x rat = 3 x 7 Thrfor th numbr of blocks = For this qustion studnts wr rquird to calculat th numbr of boats that arrivd, givn th numbr of blocks dlivrd. Numbr of blocks dlivrd = 35 Rat = 7 blocks/boat Numbr of boats = numbr of blocks/ rat = 35/7 Thrfor th numbr of boats = 5 4. For this qustion studnts wr rquird to calculat th numbr of boats that arrivd, givn th numbr of blocks dlivrd ovr a priod of two days Numbr of blocks dlivrd = 56 Rat = 7 blocks/boat Numbr of boats = numbr of blocks/ rat = 56/7 Thrfor th numbr of boats = 8 Numbr of boats pr day = Total numbr of boats / numbr of days Thrfor numbr of boats pr day = 4

16 In ancint civilisations it was important to mak sur that thr was nough frsh food for vryon to surviv. Awan is an Egyptian councilman, and th Pharaoh has snt him a dcr asking him to find which livstock is most common.! c f Solv th quations on th following pag to uncovr which livstock was th most common on th Pharaoh s land. Matching th answrs and qustion lttr to th colour in th puzzl blow. For xampl th answr to qustion a) is 3 so you would colour in th a squars grn. d i1 a g d j h b c g j d b c b g j f i f h b d a b b c Answ r Colour Gr n Blu Brown Gr n Whit Brow n Black Whit

17 Q1 Solv th following quations and us th tabl to colour in th corrct squars. a) If 21 dr wr caught by th Egyptian huntsmn in on wk, how many dr did thy catch pr day? 3 dr/day b) In Dcmbr, thr wr 31 calvs born on on farm. What was th rat at which th calvs wr born pr day? 1 calf born/day c) If Amir workd svn days a wk and arnd gold coins at a rat of 2 pr day, how many gold coins did h arn in a wk? 14 gold coins d) How many gold coins would Maht arn if h workd 2 days at a rat of 5 gold coins pr day? 10 gold coins ) How many ships would arriv at th Tarmu port in 3 days, if thy arrivd at a rat of 3 pr day? 9 ships f) If Bahim s farm producs what at a rat of 1 tonn pr month during summr and spring, how many tonns dos h produc? 6 tonns g) How many days would it tak Bari to craft 16 bows if h can crat thm at a rat of 2 pr day? 8 days h) If Kbi, th halr, tratd 20 patints in 10 hours, what was th rat that sh tratd patints pr hour? 2 patints/hour i) If a cart travls 7 kilomtrs an hour, how many hours would an 84km journy tak? 12 hours j) Th ancint Egyptian Pharaoh, Khufu ruld for 33 yars and a pyramid was finishd vry 3 yars. How many pyramids wr built during his rign? 11 pyramids

18 Th Animal Encryption Qustion On: Studnts wr rquird to calculat a sris of unknown valus whn givn information about diffrnt situations in Egypt. Th studnts wr givn a combination of qustions whr thy wr rquird to calculat ithr a rat, tim or volum, whn two othr valus wr givn. Thy wr thn rquird to us th answrs to ths qustions to solv a pictur puzzl by colouring th corrct boxs and larning a fun fact about Egypt. a) In this qustion studnts wr rquird to calculat th rat at which dr wr caught in th last wk, givn that 21 dr wr caught in 7 days. Rat at which th dr wr caught = numbr of dr /days takn to catch thm Rat at which th dr wr caught = 21 dr / 7 days Rat at which th dr wr caught = 3 dr/day b) In this qustion th studnts wr rquird to calculat th rat at which calvs wr born in Dcmbr, givn that 31 calvs wr born. Rat at which calvs wr born= numbr of calvs / days in Dcmbr Rat at which calvs wr born= 31 calvs / 31 days Rat at which calvs wr born= 1 calf /day c) In this qustion studnts wr rquird to calculat th amount of gold coins that Amir arnd considring h arns 2 gold/day and workd 7 days. Gold arnd = days workd x rat of gold arnd Gold arnd = 7 days x 2 gold/day Gold arnd = 14 gold coins d) In this qustion studnts wr rquird to calculat th amount of gold coins that Maht arnd considring h arns 5 gold/day and workd 2 days. Gold arnd = days workd x rat of gold arnd Gold arnd = 2 days x 5 gold/day Gold arnd = 10 gold coins ) In this qustion studnts wr rquird to calculat th numbr of ships that would arriv at Tarmu port in 3 days if ships arrivd at a rat of 3 ships/day. Ships arrivd = numbr of days x th rat of ships arriving Ships arrivd = 3 days x 3 ships/day Ships arrivd = 9 ships f) In this qustion studnts wr rquird to calculat how much what was producd by Bahim s farm if it producd 1 tonn/month in summr and spring. What producd = numbr of months x rat of production What producd = 6 months x 1 tonn/month What producd = 6 tonns This answr guid is continud on th nxt pag...

...This answr guid is continud from th prvious pag. g) In this qustion studnts wr rquird to calculat th numbr of days it would tak for Bari to craft 16 bows, at a rat of 2 bows pr day.

19 ...This answr guid is continud from th prvious pag. g) In this qustion studnts wr rquird to calculat th numbr of days it would tak for Bari to craft 16 bows, at a rat of 2 bows pr day. Numbr of days = numbr of bows / rat of production Numbr of days = 16 bows / 2 bows pr day Numbr of days = 8 days h) In this qustion studnts wr rquird to calculat th rat at which Kbi tratd patints pr hour, if sh tratd 20 patints in 10 hours. Rat of tratmnt = numbr patints / tim Rat of tratmnt = 20 patints / 10 hours Rat of tratmnt = 2 patints/ hour i) In this qustion studnts wr rquird to calculat how many hours it would tak a cart to complt a journy, if it was travlling at 7 kilomtrs/ hour and had to travl 84 kilomtrs. Tim takn = distanc/rat Tim takn = 84 kilomtrs/ 7 kilomtrs pr hour Tim takn = 12 hours j) In this qustion studnts wr rquird to calculat how many pyramids wr built during th 33 yar rign of Pharaoh Khufu, whn a pyramid was built vry 3 yars. Numbr of pyramids built = tim takn /rat Numbr of pyramids built = 33 yars / 3 yars pr pyramid Numbr of pyramids built = 11 pyramids Aftr complting ths problms th studnts thn had to dcod th colour puzzl, by comparing th qustion lttr, and th tabl showing th answrs and colours. For xampl, th answr to qustion a is 3, thrfor th studnts must look on th tabl for th numbr thr, which corrsponds with th colour grn. Thy can thn colour in all th boxs lablld with an a with a grn pncil. Thy should do this for all answrs and colours until th pictur of th animal is rvald, which is a cow. Th compltd puzzl should look as follows:

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation