ERIC ED540544: The Power of Probability: Poster/Teaching Guide for Grades 6-8. Expect the Unexpected with Math[R]

2013·2.6 MB·English

by  ERIC

Lesson 1 Probability Basics continued Lesson 3 Compound Probability continued Lesson 1 Probability Basics
6. Atotwwahnsaoiokelnu.u swt lTg d (thhh hobae etertrhae e t1did hsa/sue r2w/ce ,pteo af.r uo5itololu,sbd roala oirpbnn wo5idiltes0i ittssa%yaitlb i li.tlyslsee /bor mohef ue flsdat,iec pdsoppsomi)i con.te uPgesord oa i fiannnnsetda 2 ohtl/ uwea4taon ,td s fhww aaaevent or wde r ovaoeubnnllede 8. D AoDcseofsee cukommo lusdoontt nnducbsos,de ttmae rruannaestdttesese dt w iihh,ffi oinittr.hhwedeoec. flt,eurh eisttpew sius asfos r uoa iypnnr .wo dg2saa asxym i tb2teaol xnbe d l t2oeae u l=to tec r8cor oam uo mtnirrn et2eeise3n .t fg dho ipera rtgnihnrueacm mifipbr.lse etr , 4. Athtpohhoneseekaien d ptihtfrsr eeot oiehanub ded taars ibte arhfli ogliaiiswrptt aya tiwm show ief.1ta htI/pyof2o rtns ouoosebti rcc na s5eagebsl0 tcist%tluhaiitnlrr yaoyeg t,roe e uf . 5p wtwewwawwch..aseccrAhstfu.odrsalohdartmsiimattil lfciT oo.achunnondema d Al/a utFcinorteneux.epaoe rrMgci/taaepldtr omhFgo arRatuhmen ssd/ofauotrr_ico ens ClaPIsonsssrtiodeoerm ® Grades 6–8 DWmCokeoeapnlrtpcoaehoow Srmrpltt erauTeodt negtgeiore taSa i Teotmchasf h neatthdo lePiae gpor rnmrdw:aesa ced, tt rwhiwc eoheimtif hct ahhP Nte rigCiocriTsvb sM eoaks fiab lspnlistlrdu ioa tdCbnyeoad,nmb atimsl ni toeynw. OS•tBu ucfpjdraeneaenrCdcnc Ttebteiisroenvs w ntteeaa,ixS lgnapl:—ed rd ;e te ashcsnaiemdtd pa alr,so obara ab ility
7. Nflecoxioppuwpllad eai dsbnk e th h huoroswewee da mt ttimorae neseyos d lo(vieuaeitg gtcrhhoaetmm ope,ur saot a cbtoraleemb mpleeo s,isn )os. raiAb nasln eko roisfgtr tuaghdnaeeni znciezotdesin d wt owlai syet.r e 9. Dcaonismstwrfioebrrutsat aebs lW ea oucrslakinsssgh. eaellt t 1h.r eEen spurroeb tahbailti tsyt umdeetnhtosd asr.e R eview a1.5 I5fn/0 t2dx%h ,.xe 5(f o1c. x5lr/a )2.ts 5hx sx r =5 ie1s 0e./ 1f% 2ah2 m e=5(a. i1o5ldi/r)as 8 rxi n wo5 rai0 t %hro e w(x.:5p)o n=e 1n2t.s5, %de omr o.1n2s5trate that ipnrNo tbheaiswb iolnitlyiSn setku ialdclste itvnoit th yOe, lnsptl uiRndiceekn Patsrno adbr Aeat cbhhiealniltlaey pn Clgahenda a lt lsoeu unmsgeme er PThewerofA PrPogram ofr The Actuarial Foubndation ability Dpsfertoouvregd rlreeoanapmlte sp’d stu hlbrerpysoo sTusohgenehss .A a aWccntteudi vha wirotioipaerelsk F sytohhoueaunet e dtunsas jtmeoi oymo nttaih,v ttihasht eenem e wat ics Ti•m uacceoans leuRdc n euttrtqhleiauneeti ge frdu eppindarrdgio:n ar3bcam0aimpb emlisneli,itn tttayuoal.t b else,s d, epending on how much review
the probability of any number of heads in a row equals concert tour. This activity allows students to use math for
Lesson 2 Simple Probability and Sampling real purposes, and is designed as an optional assignment program! the class needs, plus additional time for the worksheet
1/2 (number of flips). for in or out of the classroom. Poster/Teaching Guide for Grades 6–8 Materials:
OS•tBu ujSadeneniCdnmTetdirssv wpteSaiSlnlal:ed— mt hPaprt polriobnpaogrbtioinlsi ctayn 2. AS5t0suk%d w.e hTnhatste ytsh hmeoa upylr doc abinlacdbuiilclaiatttyee o tthfh irasot bl ltyihn weg rp airtnoin begav ebthnile int nyu umism b1be/er2 ri so.r 5. Oi=i.n nePd. (et,Ah pt)ehe. nePbd (opeBarno)r.tdb Ee,a xvwbepirnlliiatttesiyn: t o ththfhe tee wf pofoorr omrinmbudaulebalpai fl eioatnrny d cdoeo ftnm hAtap eotov cAuec nnuadtrnsr dpi:n rPBgo( baAdarBoebe) i sli ntyo,t E•x Cpoencvte trthieng U dneecximpaelcst, efrda cWtiiotnhs M, aantdh p®e Srceernietss:: Aligns with NCTM and Common Core State Standards STihnec eArcetluya,rial Foundation D••iR o WenoCerT kcisOohiNneSe (:tf o1r: d“Semmaorntspthraotnioe nT)est Prep”
be used to make predictions about of favorable outcomes (3) over the total number of Conversions Rock
affect the probability of B occurring, and vice versa. 1. Show the class a coin. Ask the class whether it will land
a population based on a sample; outcomes (6) to get 3/6, which should be reduced to • Graphing: Bars, Lines, & Pies Overview/Getting Started:
lowest terms (1/2). Show how they could also determine 6. Provide an example or two to show how the formula works. on heads or tails if flipped. Students should answer that
• identify the difference between • Perimeter, area, surface area, and volume: Setting the
outcomes and events; and this by adding the probability of each even outcome For example, if the probability of rain is 20% on Saturday Stage with Geometry This program is designed to supplement your existing it could land on either heads or tails. Ask if there is a
(1/6 + 1/6 + 1/6) to arrive at 3/6 or 1/2 or 50%. and 50% on Sunday, what is the probability of rain on instruction of these probability topics: way to quantify the chance that it will land on heads.
• add the probabilities of the both days? (20% times 50% = 10%). Demonstrate how • Pre-Algebra: Solving the Unknown with Algebra If the class doesn’t mention the word probability,
outcomes that are part of an 3. Explain that the even outcomes here are 2, 4, or 6. this could be done with fractions (2/10 times 1/2 = 2/20 • Probability: Shake, Rattle, & Roll • strategies to identify favorable and total outcomes; introduce it and note that it means “a fraction, decimal,
event to determine the probability of an event. Rolling an even number is called an event. The sum of which reduces to 1/10) or decimals (.2 times .5 = .10). • calculating simple probability; or percentage describing the likelihood of an event
Time Required: 30 minutes, depending on how much review the even outcomes equals the probability of an event. To reinforce the abstract concept of compound probability, Also Available: • sampling and proportions; occurring.” Explain how no event can have less than a
If necessary, repeat with other examples, such as the
the class needs, plus additional time for the worksheet use a tree diagram to demonstrate how rain on both days • The Math Academy Series: Using Math in the Real World • calculating compound probability; and 0% chance or more than a 100% chance of occurring.
probability of rolling a number other than a 3, the
Materials: represents one out of 10 possible outcomes. • Building Your Future: A Financial literacy Series • using probability concepts to solve real-world 2. Ask for examples of how probability is used in the real
probability of rolling a number less than 3, etc.
• one six-sided die (for demonstration) 7. D istribute Worksheet 3. Read the introduction and review the • Math Grant Opportunities problems. world. The topic of weather forecasts may be mentioned.
4. Distribute Worksheet 2 and calculators. Read the
• calculators introduction and review the facts with the class. facts with the class. Ask students to complete the worksheet. join Athena and Rick The materials are taught through this story line: Make sure the class understands that a 40% probability of
Review answers as a class. Athena and Rick are two middle-school students precipitation means that there is a 40% likelihood that
• Worksheet 2: “A Call for Assistants” 5. Ask students to complete the worksheet. Explain that precipitation will fall within a given area. Gaming/odds may
as they solve real-world admired for their powerful mathematical thinking and
DiReCTiONS: the bonus question requires them to apply what they also be mentioned. You can also introduce to students
real-world problem-solving skills. Asked by classmates
1. Show a single six-sided die to the class. Ask what the learned about probability in Lesson 1. Review answers as Worksheet Answer Key 3. 4 8 outfits (2 necklaces x 2 vests x 3 footwear Worksheet 3: “Math Masters” problems through that companies (insurance and financial companies in
for help preparing for a mathematics standardized
possible outcomes are. Record the outcomes on the a class. Make sure that the review includes a discussion Worksheet 1: “Smartphone Test Prep” x 4 headgear) 1. C ontestant A: 81.5% (.95 x .95 x .95 x .95) test, the duo develops a smartphone application with particular), statistical experts such as actuaries, and
board. Ask the class to calculate the probability of each of how proportions are used to make predictions about 1. 1 2 outfits: Now Try This: The probability of any one outfit Contestant B: 65.6% (.9 x .9 x .9 x .9) n. powerful mathematical practice math problems. The app, featuring a fictitious individuals in daily life use probability to make reasonable
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together, the sum is 1. 12/2,000 = x/50,000) and the validity of doing so. WTB WBCB WJHB WPHB W1.o rT khseh seaemt p2l:e “ iAs 2C%al lo ffo trh Ae spsoisptualnattiso”n .C9o5n)t estant B: 59.0% (.9 x .9 x .9 x .9 x .9) uarial F provides them with new opportunities and challenges. othna ht ethade sn (u1m/2er)a. tEonrs (u1r)e rtehparte tsheen tcsla tshse u nnudmerbsetra nodf s
PS PS PS PS (75/3,750). Contestant C: 32.8% (.8 x .8 x .8 x .8 x .8) e Act The program includes three lessons, each with a favorable outcomes (heads) while the denominator (2)
Lesson 3 Compound Probability T BC JH PH 2. 7 0% (the sum of the probabilities for 3. 21.9 % (.815 x .656 x .41) of Th corresponding worksheet. A bonus worksheet, which represents all possible outcomes (heads and tails). If
OBjeCTiveS: DiReCTiONS: Khaety):; HWTB ( (hwigohrk- tboopost)s;) B; CP H(b (ipkietrh c haepl)m; eTt ()t;i PaSra ()p;l JaHtf o(rjems tsehro’se s) 3. r2 e0v%en (uthese osuf m$2 o0f, 0th0e0 ,p $ro3b0a,0b0il0it,i easn dfo $r 50,000). NBoonwu Tsr yW Tohrikss: h5e4e.0t:% “ M(.i7n5d xY o.8u0r xO w.9n0 B)usiness!” demark aolpspoo prrtoumniotyte tso fianpapnlyc itahle l istkeirlalsc ya,n gdi vkenso swtlueddegnet st htehye' ve satlusod eanbtles htoa veexnp’rte msse tnhteio pnreodb aitb, ielintsyu arse . t5h oart 5th0e%y. are
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the probability of multiple independent events. three flips in a row could be depicted. at recorded all possible outcomes without double counting.
Time Required: 20–30 minutes, depending on how much 3. Ask what the probability of a coin landing on heads three BTC tphaasts tuhpe. p Aolttehnotuiaglh p trhoefirtes iasr neo t oriog ghot oadn stwo er, 23.. 11 5%% (3/20) With M What is an actuary? An actuary satnu odpetnitosn taol uassesi mgnamthe nfotr f orera iln p ourr opuots eosf, t ihse d celsaisgsnreodo mas. Suggest, for example, a tree diagram and model how it can
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Lesson 1 Probability Basics continued Lesson 3 Compound Probability continued Lesson 1 Probability Basics
6. Atotwwahnsaoiokelnu.u swt lTg d (thhh hobae etertrhae e t1did hsa/sue r2w/ce ,pteo af.r uo5itololu,sbd roala oirpbnn wo5idiltes0i ittssa%yaitlb i li.tlyslsee /bor mohef ue flsdat,iec pdsoppsomi)i con.te uPgesord oa i fiannnnsetda 2 ohtl/ uwea4taon ,td s fhww aaaevent or wde r ovaoeubnnllede 8. D AoDcseofsee cukommo lusdoontt nnducbsos,de ttmae rruannaestdttesese dt w iihh,ffi oinittr.hhwedeoec. flt,eurh eisttpew sius asfos r uoa iypnnr .wo dg2saa asxym i tb2teaol xnbe d l t2oeae u l=to tec r8cor oam uo mtnirrn et2eeise3n .t fg dho ipera rtgnihnrueacm mifipbr.lse etr , 4. Athtpohhoneseekaien d ptihtfrsr eeot oiehanub ded taars ibte arhfli ogliaiiswrptt aya tiwm show ief.1ta htI/pyof2o rtns ouoosebti rcc na s5eagebsl0 tcist%tluhaiitnlrr yaoyeg t,roe e uf . 5p wtwewwawwch..aseccrAhstfu.odrsalohdartmsiimattil lfciT oo.achunnondema d Al/a utFcinorteneux.epaoe rrMgci/taaepldtr omhFgo arRatuhmen ssd/ofauotrr_ico ens ClaPIsonsssrtiodeoerm ® Grades 6–8 DWmCokeoeapnlrtpcoaehoow Srmrpltt erauTeodt negtgeiore taSa i Teotmchasf h neatthdo lePiae gpor rnmrdw:aesa ced, tt rwhiwc eoheimtif hct ahhP Nte rigCiocriTsvb sM eoaks fiab lspnlistlrdu ioa tdCbnyeoad,nmb atimsl ni toeynw. OS•tBu ucfpjdraeneaenrCdcnc Ttebteiisroenvs w ntteeaa,ixS lgnapl:—ed rd ;e te ashcsnaiemdtd pa alr,so obara ab ility
7. Nflecoxioppuwpllad eai dsbnk e th h huoroswewee da mt ttimorae neseyos d lo(vieuaeitg gtcrhhoaetmm ope,ur saot a cbtoraleemb mpleeo s,isn )os. raiAb nasln eko roisfgtr tuaghdnaeeni znciezotdesin d wt owlai syet.r e 9. Dcaonismstwrfioebrrutsat aebs lW ea oucrslakinsssgh. eaellt t 1h.r eEen spurroeb tahbailti tsyt umdeetnhtosd asr.e R eview a1.5 I5fn/0 t2dx%h ,.xe 5(f o1c. x5lr/a )2.ts 5hx sx r =5 ie1s 0e./ 1f% 2ah2 m e=5(a. i1o5ldi/r)as 8 rxi n wo5 rai0 t %hro e w(x.:5p)o n=e 1n2t.s5, %de omr o.1n2s5trate that ipnrNo tbheaiswb iolnitlyiSn setku ialdclste itvnoit th yOe, lnsptl uiRndiceekn Patsrno adbr Aeat cbhhiealniltlaey pn Clgahenda a lt lsoeu unmsgeme er PThewerofA PrPogram ofr The Actuarial Foubndation ability Dpsfertoouvregd rlreeoanapmlte sp’d stu hlbrerpysoo sTusohgenehss .A a aWccntteudi vha wirotioipaerelsk F sytohhoueaunet e dtunsas jtmeoi oymo nttaih,v ttihasht eenem e wat ics Ti•m uacceoans leuRdc n euttrtqhleiauneeti ge frdu eppindarrdgio:n ar3bcam0aimpb emlisneli,itn tttayuoal.t b else,s d, epending on how much review
the probability of any number of heads in a row equals concert tour. This activity allows students to use math for
Lesson 2 Simple Probability and Sampling real purposes, and is designed as an optional assignment program! the class needs, plus additional time for the worksheet
1/2 (number of flips). for in or out of the classroom. Poster/Teaching Guide for Grades 6–8 Materials:
OS•tBu ujSadeneniCdnmTetdirssv wpteSaiSlnlal:ed— mt hPaprt polriobnpaogrbtioinlsi ctayn 2. AS5t0suk%d w.e hTnhatste ytsh hmeoa upylr doc abinlacdbuiilclaiatttyee o tthfh irasot bl ltyihn weg rp airtnoin begav ebthnile int nyu umism b1be/er2 ri so.r 5. Oi=i.n nePd. (et,Ah pt)ehe. nePbd (opeBarno)r.tdb Ee,a xvwbepirnlliiatttesiyn: t o ththfhe tee wf pofoorr omrinmbudaulebalpai fl eioatnrny d cdoeo ftnm hAtap eotov cAuec nnuadtrnsr dpi:n rPBgo( baAdarBoebe) i sli ntyo,t E•x Cpoencvte trthieng U dneecximpaelcst, efrda cWtiiotnhs M, aantdh p®e Srceernietss:: Aligns with NCTM and Common Core State Standards STihnec eArcetluya,rial Foundation D••iR o WenoCerT kcisOohiNneSe (:tf o1r: d“Semmaorntspthraotnioe nT)est Prep”
be used to make predictions about of favorable outcomes (3) over the total number of Conversions Rock
affect the probability of B occurring, and vice versa. 1. Show the class a coin. Ask the class whether it will land
a population based on a sample; outcomes (6) to get 3/6, which should be reduced to • Graphing: Bars, Lines, & Pies Overview/Getting Started:
lowest terms (1/2). Show how they could also determine 6. Provide an example or two to show how the formula works. on heads or tails if flipped. Students should answer that
• identify the difference between • Perimeter, area, surface area, and volume: Setting the
outcomes and events; and this by adding the probability of each even outcome For example, if the probability of rain is 20% on Saturday Stage with Geometry This program is designed to supplement your existing it could land on either heads or tails. Ask if there is a
(1/6 + 1/6 + 1/6) to arrive at 3/6 or 1/2 or 50%. and 50% on Sunday, what is the probability of rain on instruction of these probability topics: way to quantify the chance that it will land on heads.
• add the probabilities of the both days? (20% times 50% = 10%). Demonstrate how • Pre-Algebra: Solving the Unknown with Algebra If the class doesn’t mention the word probability,
outcomes that are part of an 3. Explain that the even outcomes here are 2, 4, or 6. this could be done with fractions (2/10 times 1/2 = 2/20 • Probability: Shake, Rattle, & Roll • strategies to identify favorable and total outcomes; introduce it and note that it means “a fraction, decimal,
event to determine the probability of an event. Rolling an even number is called an event. The sum of which reduces to 1/10) or decimals (.2 times .5 = .10). • calculating simple probability; or percentage describing the likelihood of an event
Time Required: 30 minutes, depending on how much review the even outcomes equals the probability of an event. To reinforce the abstract concept of compound probability, Also Available: • sampling and proportions; occurring.” Explain how no event can have less than a
If necessary, repeat with other examples, such as the
the class needs, plus additional time for the worksheet use a tree diagram to demonstrate how rain on both days • The Math Academy Series: Using Math in the Real World • calculating compound probability; and 0% chance or more than a 100% chance of occurring.
probability of rolling a number other than a 3, the
Materials: represents one out of 10 possible outcomes. • Building Your Future: A Financial literacy Series • using probability concepts to solve real-world 2. Ask for examples of how probability is used in the real
probability of rolling a number less than 3, etc.
• one six-sided die (for demonstration) 7. D istribute Worksheet 3. Read the introduction and review the • Math Grant Opportunities problems. world. The topic of weather forecasts may be mentioned.
4. Distribute Worksheet 2 and calculators. Read the
• calculators introduction and review the facts with the class. facts with the class. Ask students to complete the worksheet. join Athena and Rick The materials are taught through this story line: Make sure the class understands that a 40% probability of
Review answers as a class. Athena and Rick are two middle-school students precipitation means that there is a 40% likelihood that
• Worksheet 2: “A Call for Assistants” 5. Ask students to complete the worksheet. Explain that precipitation will fall within a given area. Gaming/odds may
as they solve real-world admired for their powerful mathematical thinking and
DiReCTiONS: the bonus question requires them to apply what they also be mentioned. You can also introduce to students
real-world problem-solving skills. Asked by classmates
1. Show a single six-sided die to the class. Ask what the learned about probability in Lesson 1. Review answers as Worksheet Answer Key 3. 4 8 outfits (2 necklaces x 2 vests x 3 footwear Worksheet 3: “Math Masters” problems through that companies (insurance and financial companies in
for help preparing for a mathematics standardized
possible outcomes are. Record the outcomes on the a class. Make sure that the review includes a discussion Worksheet 1: “Smartphone Test Prep” x 4 headgear) 1. C ontestant A: 81.5% (.95 x .95 x .95 x .95) test, the duo develops a smartphone application with particular), statistical experts such as actuaries, and
board. Ask the class to calculate the probability of each of how proportions are used to make predictions about 1. 1 2 outfits: Now Try This: The probability of any one outfit Contestant B: 65.6% (.9 x .9 x .9 x .9) n. powerful mathematical practice math problems. The app, featuring a fictitious individuals in daily life use probability to make reasonable
othuet cpormobea absi lait fireasc otifo anl l( i1n/d6iv fiodru eaal cohu)t.c Ionmdeicsa atere t hadadt ewdh en tphoell p oofp au slaamtiopnle a osf a t hweh tooleta bl yc uusstinomg tehr eb raesseu (lets.g o.f, a HTT HBCT JHHT PHHT bneeianrges ste tleencttehd o ifs a 1 p/e4r8c eonr t2)..1% (rounded to the 2. CC oonntteessttaanntt CA:: 4717..04%% ((..89 5x x.8 . 9x5 . 8x x.9 .58 )x .95 x oundatio thinking! cAethleebnrait ya ncdo uRpiclek adnedci tdhee tior pfoertm, i sa sbou ssuincecesss,s fwuhl itchha t 3. p Arsekd wichtaiotn tsh aeb poruotb tahbei lfiutyt uisre o af nad fl tiop paessde csos irnis lka.n ding
together, the sum is 1. 12/2,000 = x/50,000) and the validity of doing so. WTB WBCB WJHB WPHB W1.o rT khseh seaemt p2l:e “ iAs 2C%al lo ffo trh Ae spsoisptualnattiso”n .C9o5n)t estant B: 59.0% (.9 x .9 x .9 x .9 x .9) uarial F provides them with new opportunities and challenges. othna ht ethade sn (u1m/2er)a. tEonrs (u1r)e rtehparte tsheen tcsla tshse u nnudmerbsetra nodf s
PS PS PS PS (75/3,750). Contestant C: 32.8% (.8 x .8 x .8 x .8 x .8) e Act The program includes three lessons, each with a favorable outcomes (heads) while the denominator (2)
Lesson 3 Compound Probability T BC JH PH 2. 7 0% (the sum of the probabilities for 3. 21.9 % (.815 x .656 x .41) of Th corresponding worksheet. A bonus worksheet, which represents all possible outcomes (heads and tails). If
OBjeCTiveS: DiReCTiONS: Khaety):; HWTB ( (hwigohrk- tboopost)s;) B; CP H(b (ipkietrh c haepl)m; eTt ()t;i PaSra ()p;l JaHtf o(rjems tsehro’se s) 3. r2 e0v%en (uthese osuf m$2 o0f, 0th0e0 ,p $ro3b0a,0b0il0it,i easn dfo $r 50,000). NBoonwu Tsr yW Tohrikss: h5e4e.0t:% “ M(.i7n5d xY o.8u0r xO w.9n0 B)usiness!” demark aolpspoo prrtoumniotyte tso fianpapnlyc itahle l istkeirlalsc ya,n gdi vkenso swtlueddegnet st htehye' ve satlusod eanbtles htoa veexnp’rte msse tnhteio pnreodb aitb, ielintsyu arse . t5h oart 5th0e%y. are
S••tu up udsrseoeenb tatsah tbweri eilflieolt— rydm; i aaugnlarda fmor t coo dmepriovuen tdh ep rfoobrmabuillait fyo tro c coamlcpuoluatned 12.. Sp Rashreokco bafwoall rbt t hiahle ievt c yowo louoinfnr kttth eodee ot rchn oteeoi nc ienl alx aLspnsel dasasiinnnod gnh aoo1swn ko hnawel thla rtadehtes ei. sd o ituahtgecr oammess a fnodr 2. 2c h4a orutrtefiutsse, caonmd pornHiseTi nfogr t tweoa lt:r ees, onPJBeTHHC for 45.. rTsAa eehnnvreysver wrinecies ueirkse sw soa wi lfols lilf loob l$ srav1eia n1,ar0g0yk0 % mbe0uv o paetnr nnmoed.byi g$ aihs7b t,iul0 iinnt0ayc0 clt)uch.edapett ttahhbeal etn oerw 1. Iiwhw nnaoosvvurueetlrsh dettl omdeb sefaeas cn0.iclt% o faou.n rn Tatthlhsye est otUcs e.b gSrete. i rngfiieosckarva tefelrrlesny e mtc,oo es nbnose ttic dhwoeeomr ur eFilsDd k I C- h” is a registered tra www.actuaMrwioawlwrfoe.us cnFhdoraletaisoetni c.Mo.crogam/tp/hruon gPeraxrmpoescg/tferodarm_mtaetashc:hers.shtml lAuseus anemre pnmwreoe dbbr oiacnnbo uainl iscrt eeyora nstlk -ltiiwolnlouserr tl.cod hT hhacoileslnle potn enRgxlieitcn. ke e na agncadtg iAveitsth yse,t nuwdah epinclathsn at aoll ows 4. Apohoras kpsta shwiiablhszl/aeaht ri edof at uohdtrecsdo .ce mIorf,i es nast su i(skdi .flteehin.pe,t pmshe eb dhae odtgwwsin/o t t thatoieim loys e fccfsooe,urm e lo.dbgu im.nt,ca aohtkmeieoae ndsssus )i/rn eah areteh a edys
the probability of multiple independent events. three flips in a row could be depicted. at recorded all possible outcomes without double counting.
Time Required: 20–30 minutes, depending on how much 3. Ask what the probability of a coin landing on heads three BTC tphaasts tuhpe. p Aolttehnotuiaglh p trhoefirtes iasr neo t oriog ghot oadn stwo er, 23.. 11 5%% (3/20) With M What is an actuary? An actuary satnu odpetnitosn taol uassesi mgnamthe nfotr f orera iln p ourr opuots eosf, t ihse d celsaisgsnreodo mas. Suggest, for example, a tree diagram and model how it can
rMeavtieewri athlse: class needs, plus additional time for worksheets tdiimagersa imn ato r odwem woonusldtr batee. Wthaaltk tthheer est iusd oennet so tuhtcrooumgeh f ao rt ree [COLOR] WB PJHH tahded rsetussdeedn atss’ tthoeleyr daenfceen fdo rt hriesikr ashnoswuledr sb.e Ninodwic Tartye Tthhiast: tAhnes iwnevress wtmilel nvat riys, h biugth slyh roiuskldy with xpected iwsi athn beuxspienrets isne sst,a gtoisvteicrns mwhenot ws,o arknsd DevelOPeD WiTH IncBluodensu Onsl:in e A classroom poster displays strategies for identifying bthee u psreodb taob iidlietyn tisif fyo trh aen fyo ounr de ioffuetrceonmt oe u(t1c/o4m, .e2s5. ,A osrk 2w5h%at) .
•• c Wooinrk (sfhoere dte 3m: o“Mnsattrha tMioans)ters” tophurortecbeoa mbhieelaistd y(s Hi siHn o Tan, erHo oTwTu ,tw HohTfi Hleei, g tThhTetT r,oe Tr Ta1Hr/e,8 sT oeHvrT e1, nT2 H.u5Hn%f)a,. vsoor athbele PS PJBTHHC N12..o w34 03Tr0,y1 v 0Tih0e iwvsie:erws e (r5s0 (,5000,00/020,/020,00 0x0 1 x2 )1,724) a small probability of a significant profit. pect the Une otdhrisgec afinuptilziunaretei .to hAnacstt t uaoap rhpiealillep ss ct mhieeanmtche p ailsna ndth feo r StudeCnhta Pllreonbgaebility ouexunptdcreoersmssceeosdr e aasss t wah eeflr lac aocstni dcoeenpt,e ta rt mdheainct iipmnrgao lpb,r aoobrbi alai tbpyie lcirtacyne,n batnea dg e. 5. Mcoououtdcledol mb feoe rsu .ss tSeuedde te opn odtsset hteeorr wfmr oainn teta fbtohlere e onxrua ammnbp oelrerg oiaff nn piezocesedssi lbsiaslerty .
Ex statistical methods to assess risk.
”
Lesson 1 Probability Basics continued Lesson 3 Compound Probability continued Lesson 1 Probability Basics
6. Atotwwahnsaoiokelnu.u swt lTg d (thhh hobae etertrhae e t1did hsa/sue r2w/ce ,pteo af.r uo5itololu,sbd roala oirpbnn wo5idiltes0i ittssa%yaitlb i li.tlyslsee /bor mohef ue flsdat,iec pdsoppsomi)i con.te uPgesord oa i fiannnnsetda 2 ohtl/ uwea4taon ,td s fhww aaaevent or wde r ovaoeubnnllede 8. D AoDcseofsee cukommo lusdoontt nnducbsos,de ttmae rruannaestdttesese dt w iihh,ffi oinittr.hhwedeoec. flt,eurh eisttpew sius asfos r uoa iypnnr .wo dg2saa asxym i tb2teaol xnbe d l t2oeae u l=to tec r8cor oam uo mtnirrn et2eeise3n .t fg dho ipera rtgnihnrueacm mifipbr.lse etr , 4. Athtpohhoneseekaien d ptihtfrsr eeot oiehanub ded taars ibte arhfli ogliaiiswrptt aya tiwm show ief.1ta htI/pyof2o rtns ouoosebti rcc na s5eagebsl0 tcist%tluhaiitnlrr yaoyeg t,roe e uf . 5p wtwewwawwch..aseccrAhstfu.odrsalohdartmsiimattil lfciT oo.achunnondema d Al/a utFcinorteneux.epaoe rrMgci/taaepldtr omhFgo arRatuhmen ssd/ofauotrr_ico ens ClaPIsonsssrtiodeoerm ® Grades 6–8 DWmCokeoeapnlrtpcoaehoow Srmrpltt erauTeodt negtgeiore taSa i Teotmchasf h neatthdo lePiae gpor rnmrdw:aesa ced, tt rwhiwc eoheimtif hct ahhP Nte rigCiocriTsvb sM eoaks fiab lspnlistlrdu ioa tdCbnyeoad,nmb atimsl ni toeynw. OS•tBu ucfpjdraeneaenrCdcnc Ttebteiisroenvs w ntteeaa,ixS lgnapl:—ed rd ;e te ashcsnaiemdtd pa alr,so obara ab ility
7. Nflecoxioppuwpllad eai dsbnk e th h huoroswewee da mt ttimorae neseyos d lo(vieuaeitg gtcrhhoaetmm ope,ur saot a cbtoraleemb mpleeo s,isn )os. raiAb nasln eko roisfgtr tuaghdnaeeni znciezotdesin d wt owlai syet.r e 9. Dcaonismstwrfioebrrutsat aebs lW ea oucrslakinsssgh. eaellt t 1h.r eEen spurroeb tahbailti tsyt umdeetnhtosd asr.e R eview a1.5 I5fn/0 t2dx%h ,.xe 5(f o1c. x5lr/a )2.ts 5hx sx r =5 ie1s 0e./ 1f% 2ah2 m e=5(a. i1o5ldi/r)as 8 rxi n wo5 rai0 t %hro e w(x.:5p)o n=e 1n2t.s5, %de omr o.1n2s5trate that ipnrNo tbheaiswb iolnitlyiSn setku ialdclste itvnoit th yOe, lnsptl uiRndiceekn Patsrno adbr Aeat cbhhiealniltlaey pn Clgahenda a lt lsoeu unmsgeme er PThewerofA PrPogram ofr The Actuarial Foubndation ability Dpsfertoouvregd rlreeoanapmlte sp’d stu hlbrerpysoo sTusohgenehss .A a aWccntteudi vha wirotioipaerelsk F sytohhoueaunet e dtunsas jtmeoi oymo nttaih,v ttihasht eenem e wat ics Ti•m uacceoans leuRdc n euttrtqhleiauneeti ge frdu eppindarrdgio:n ar3bcam0aimpb emlisneli,itn tttayuoal.t b else,s d, epending on how much review
the probability of any number of heads in a row equals concert tour. This activity allows students to use math for
Lesson 2 Simple Probability and Sampling real purposes, and is designed as an optional assignment program! the class needs, plus additional time for the worksheet
1/2 (number of flips). for in or out of the classroom. Poster/Teaching Guide for Grades 6–8 Materials:
OS•tBu ujSadeneniCdnmTetdirssv wpteSaiSlnlal:ed— mt hPaprt polriobnpaogrbtioinlsi ctayn 2. AS5t0suk%d w.e hTnhatste ytsh hmeoa upylr doc abinlacdbuiilclaiatttyee o tthfh irasot bl ltyihn weg rp airtnoin begav ebthnile int nyu umism b1be/er2 ri so.r 5. Oi=i.n nePd. (et,Ah pt)ehe. nePbd (opeBarno)r.tdb Ee,a xvwbepirnlliiatttesiyn: t o ththfhe tee wf pofoorr omrinmbudaulebalpai fl eioatnrny d cdoeo ftnm hAtap eotov cAuec nnuadtrnsr dpi:n rPBgo( baAdarBoebe) i sli ntyo,t E•x Cpoencvte trthieng U dneecximpaelcst, efrda cWtiiotnhs M, aantdh p®e Srceernietss:: Aligns with NCTM and Common Core State Standards STihnec eArcetluya,rial Foundation D••iR o WenoCerT kcisOohiNneSe (:tf o1r: d“Semmaorntspthraotnioe nT)est Prep”
be used to make predictions about of favorable outcomes (3) over the total number of Conversions Rock
affect the probability of B occurring, and vice versa. 1. Show the class a coin. Ask the class whether it will land
a population based on a sample; outcomes (6) to get 3/6, which should be reduced to • Graphing: Bars, Lines, & Pies Overview/Getting Started:
lowest terms (1/2). Show how they could also determine 6. Provide an example or two to show how the formula works. on heads or tails if flipped. Students should answer that
• identify the difference between • Perimeter, area, surface area, and volume: Setting the
outcomes and events; and this by adding the probability of each even outcome For example, if the probability of rain is 20% on Saturday Stage with Geometry This program is designed to supplement your existing it could land on either heads or tails. Ask if there is a
(1/6 + 1/6 + 1/6) to arrive at 3/6 or 1/2 or 50%. and 50% on Sunday, what is the probability of rain on instruction of these probability topics: way to quantify the chance that it will land on heads.
• add the probabilities of the both days? (20% times 50% = 10%). Demonstrate how • Pre-Algebra: Solving the Unknown with Algebra If the class doesn’t mention the word probability,
outcomes that are part of an 3. Explain that the even outcomes here are 2, 4, or 6. this could be done with fractions (2/10 times 1/2 = 2/20 • Probability: Shake, Rattle, & Roll • strategies to identify favorable and total outcomes; introduce it and note that it means “a fraction, decimal,
event to determine the probability of an event. Rolling an even number is called an event. The sum of which reduces to 1/10) or decimals (.2 times .5 = .10). • calculating simple probability; or percentage describing the likelihood of an event
Time Required: 30 minutes, depending on how much review the even outcomes equals the probability of an event. To reinforce the abstract concept of compound probability, Also Available: • sampling and proportions; occurring.” Explain how no event can have less than a
If necessary, repeat with other examples, such as the
the class needs, plus additional time for the worksheet use a tree diagram to demonstrate how rain on both days • The Math Academy Series: Using Math in the Real World • calculating compound probability; and 0% chance or more than a 100% chance of occurring.
probability of rolling a number other than a 3, the
Materials: represents one out of 10 possible outcomes. • Building Your Future: A Financial literacy Series • using probability concepts to solve real-world 2. Ask for examples of how probability is used in the real
probability of rolling a number less than 3, etc.
• one six-sided die (for demonstration) 7. D istribute Worksheet 3. Read the introduction and review the • Math Grant Opportunities problems. world. The topic of weather forecasts may be mentioned.
4. Distribute Worksheet 2 and calculators. Read the
• calculators introduction and review the facts with the class. facts with the class. Ask students to complete the worksheet. join Athena and Rick The materials are taught through this story line: Make sure the class understands that a 40% probability of
Review answers as a class. Athena and Rick are two middle-school students precipitation means that there is a 40% likelihood that
• Worksheet 2: “A Call for Assistants” 5. Ask students to complete the worksheet. Explain that precipitation will fall within a given area. Gaming/odds may
as they solve real-world admired for their powerful mathematical thinking and
DiReCTiONS: the bonus question requires them to apply what they also be mentioned. You can also introduce to students
real-world problem-solving skills. Asked by classmates
1. Show a single six-sided die to the class. Ask what the learned about probability in Lesson 1. Review answers as Worksheet Answer Key 3. 4 8 outfits (2 necklaces x 2 vests x 3 footwear Worksheet 3: “Math Masters” problems through that companies (insurance and financial companies in
for help preparing for a mathematics standardized
possible outcomes are. Record the outcomes on the a class. Make sure that the review includes a discussion Worksheet 1: “Smartphone Test Prep” x 4 headgear) 1. C ontestant A: 81.5% (.95 x .95 x .95 x .95) test, the duo develops a smartphone application with particular), statistical experts such as actuaries, and
board. Ask the class to calculate the probability of each of how proportions are used to make predictions about 1. 1 2 outfits: Now Try This: The probability of any one outfit Contestant B: 65.6% (.9 x .9 x .9 x .9) n. powerful mathematical practice math problems. The app, featuring a fictitious individuals in daily life use probability to make reasonable
othuet cpormobea absi lait fireasc otifo anl l( i1n/d6iv fiodru eaal cohu)t.c Ionmdeicsa atere t hadadt ewdh en tphoell p oofp au slaamtiopnle a osf a t hweh tooleta bl yc uusstinomg tehr eb raesseu (lets.g o.f, a HTT HBCT JHHT PHHT bneeianrges ste tleencttehd o ifs a 1 p/e4r8c eonr t2)..1% (rounded to the 2. CC oonntteessttaanntt CA:: 4717..04%% ((..89 5x x.8 . 9x5 . 8x x.9 .58 )x .95 x oundatio thinking! cAethleebnrait ya ncdo uRpiclek adnedci tdhee tior pfoertm, i sa sbou ssuincecesss,s fwuhl itchha t 3. p Arsekd wichtaiotn tsh aeb poruotb tahbei lfiutyt uisre o af nad fl tiop paessde csos irnis lka.n ding
together, the sum is 1. 12/2,000 = x/50,000) and the validity of doing so. WTB WBCB WJHB WPHB W1.o rT khseh seaemt p2l:e “ iAs 2C%al lo ffo trh Ae spsoisptualnattiso”n .C9o5n)t estant B: 59.0% (.9 x .9 x .9 x .9 x .9) uarial F provides them with new opportunities and challenges. othna ht ethade sn (u1m/2er)a. tEonrs (u1r)e rtehparte tsheen tcsla tshse u nnudmerbsetra nodf s
PS PS PS PS (75/3,750). Contestant C: 32.8% (.8 x .8 x .8 x .8 x .8) e Act The program includes three lessons, each with a favorable outcomes (heads) while the denominator (2)
Lesson 3 Compound Probability T BC JH PH 2. 7 0% (the sum of the probabilities for 3. 21.9 % (.815 x .656 x .41) of Th corresponding worksheet. A bonus worksheet, which represents all possible outcomes (heads and tails). If
OBjeCTiveS: DiReCTiONS: Khaety):; HWTB ( (hwigohrk- tboopost)s;) B; CP H(b (ipkietrh c haepl)m; eTt ()t;i PaSra ()p;l JaHtf o(rjems tsehro’se s) 3. r2 e0v%en (uthese osuf m$2 o0f, 0th0e0 ,p $ro3b0a,0b0il0it,i easn dfo $r 50,000). NBoonwu Tsr yW Tohrikss: h5e4e.0t:% “ M(.i7n5d xY o.8u0r xO w.9n0 B)usiness!” demark aolpspoo prrtoumniotyte tso fianpapnlyc itahle l istkeirlalsc ya,n gdi vkenso swtlueddegnet st htehye' ve satlusod eanbtles htoa veexnp’rte msse tnhteio pnreodb aitb, ielintsyu arse . t5h oart 5th0e%y. are
S••tu up udsrseoeenb tatsah tbweri eilflieolt— rydm; i aaugnlarda fmor t coo dmepriovuen tdh ep rfoobrmabuillait fyo tro c coamlcpuoluatned 12.. Sp Rashreokco bafwoall rbt t hiahle ievt c yowo louoinfnr kttth eodee ot rchn oteeoi nc ienl alx aLspnsel dasasiinnnod gnh aoo1swn ko hnawel thla rtadehtes ei. sd o ituahtgecr oammess a fnodr 2. 2c h4a orutrtefiutsse, caonmd pornHiseTi nfogr t tweoa lt:r ees, onPJBeTHHC for 45.. rTsAa eehnnvreysver wrinecies ueirkse sw soa wi lfols lilf loob l$ srav1eia n1,ar0g0yk0 % mbe0uv o paetnr nnmoed.byi g$ aihs7b t,iul0 iinnt0ayc0 clt)uch.edapett ttahhbeal etn oerw 1. Iiwhw nnaoosvvurueetlrsh dettl omdeb sefaeas cn0.iclt% o faou.n rn Tatthlhsye est otUcs e.b gSrete. i rngfiieosckarva tefelrrlesny e mtc,oo es nbnose ttic dhwoeeomr ur eFilsDd k I C- h” is a registered tra www.actuaMrwioawlwrfoe.us cnFhdoraletaisoetni c.Mo.crogam/tp/hruon gPeraxrmpoescg/tferodarm_mtaetashc:hers.shtml lAuseus anemre pnmwreoe dbbr oiacnnbo uainl iscrt eeyora nstlk -ltiiwolnlouserr tl.cod hT hhacoileslnle potn enRgxlieitcn. ke e na agncadtg iAveitsth yse,t nuwdah epinclathsn at aoll ows 4. Apohoras kpsta shwiiablhszl/aeaht ri edof at uohdtrecsdo .ce mIorf,i es nast su i(skdi .flteehin.pe,t pmshe eb dhae odtgwwsin/o t t thatoieim loys e fccfsooe,urm e lo.dbgu im.nt,ca aohtkmeieoae ndsssus )i/rn eah areteh a edys
the probability of multiple independent events. three flips in a row could be depicted. at recorded all possible outcomes without double counting.
Time Required: 20–30 minutes, depending on how much 3. Ask what the probability of a coin landing on heads three BTC tphaasts tuhpe. p Aolttehnotuiaglh p trhoefirtes iasr neo t oriog ghot oadn stwo er, 23.. 11 5%% (3/20) With M What is an actuary? An actuary satnu odpetnitosn taol uassesi mgnamthe nfotr f orera iln p ourr opuots eosf, t ihse d celsaisgsnreodo mas. Suggest, for example, a tree diagram and model how it can
rMeavtieewri athlse: class needs, plus additional time for worksheets tdiimagersa imn ato r odwem woonusldtr batee. Wthaaltk tthheer est iusd oennet so tuhtcrooumgeh f ao rt ree [COLOR] WB PJHH tahded rsetussdeedn atss’ tthoeleyr daenfceen fdo rt hriesikr ashnoswuledr sb.e Ninodwic Tartye Tthhiast: tAhnes iwnevress wtmilel nvat riys, h biugth slyh roiuskldy with xpected iwsi athn beuxspienrets isne sst,a gtoisvteicrns mwhenot ws,o arknsd DevelOPeD WiTH IncBluodensu Onsl:in e A classroom poster displays strategies for identifying bthee u psreodb taob iidlietyn tisif fyo trh aen fyo ounr de ioffuetrceonmt oe u(t1c/o4m, .e2s5. ,A osrk 2w5h%at) .
•• c Wooinrk (sfhoere dte 3m: o“Mnsattrha tMioans)ters” tophurortecbeoa mbhieelaistd y(s Hi siHn o Tan, erHo oTwTu ,tw HohTfi Hleei, g tThhTetT r,oe Tr Ta1Hr/e,8 sT oeHvrT e1, nT2 H.u5Hn%f)a,. vsoor athbele PS PJBTHHC N12..o w34 03Tr0,y1 v 0Tih0e iwvsie:erws e (r5s0 (,5000,00/020,/020,00 0x0 1 x2 )1,724) a small probability of a significant profit. pect the Une otdhrisgec afinuptilziunaretei .to hAnacstt t uaoap rhpiealillep ss ct mhieeanmtche p ailsna ndth feo r StudeCnhta Pllreonbgaebility ouexunptdcreoersmssceeosdr e aasss t wah eeflr lac aocstni dcoeenpt,e ta rt mdheainct iipmnrgao lpb,r aoobrbi alai tbpyie lcirtacyne,n batnea dg e. 5. Mcoououtdcledol mb feoe rsu .ss tSeuedde te opn odtsset hteeorr wfmr oainn teta fbtohlere e onxrua ammnbp oelrerg oiaff nn piezocesedssi lbsiaslerty .
Ex statistical methods to assess risk.
”
Worksheet #1 Worksheet #2 Worksheet #3 Bonus Worksheet
Smartphone Test Prep A Call for Assistants Math Masters Mind Your Own Business!
Athena and Rick, two middle-school How can we help everyone Athena and Rick’s app is a huge hit, so they If no one buys the After only six months, R App is making a R App has been in business for a while and I think it would be
students frequently called upon for their with their math questions? form a company: R App Inc. Some customers tutoring service, On the other hand, Let's conduct a sizable profit. “We should donate some of Maybe we should donate Athena and Rick have turned a profit. The two smart to invest our money
powerful math skills, have been flooded ask for a new service: math tutoring. it cobuulsdi nheusrst. our mwoen ecyo utlod h mealpk eu s market survey and our profits to a worthy cause,” Athena thinks somae woofr otuhry pcraoufsiet.s to have always saved some of the money they to make more money.
How about a then decide!
expand. made for extra things they wanted. “It would
with numerous student requests for help smartphone app After estimating that it will cost $14,000 a aloud. Rick replies, “How about a donation But how can we predict
with the dreaded upcoming mathematics withp rfoubnl epmrasc?tice year to hire tutors, the duo wonders what to to our school because they made us the compHeotwit iaobno tuot aaw ard be nice to spend this money, but it’s also if an investment is risky?
smart to invest it to make even more money,”
standardized test. “Wow, how are we do. “If no one buys the service, the additional mathematicians we are today?” “Our gift a math scholarship!
Athena mentions. “But how can we predict if
going to get to everyone in time?” cost might sink us,” fretted Rick. Athena might inspire others to excel in math, too,”
an investment is risky? I certainly don’t want
wondered Athena. responded, “But if we do nothing, we could chimes in Athena.
to lose any money!” replied Rick.
lose income that could help R App grow.”
Rick had a flash: How about a After considering gifts like a random lunch That’s a
smartphone app that provides our To make an informed decision, Athena menu generator for the cafeteria and a statue great idea! The pair decides to email their questions to
classmates with fun practice problems? suggests doing a market survey. The pair of Isaac Newton, the grateful duo donates a Joe, an actuary, whose daily work involves
The pair got to work on their first set of decides to survey 75 randomly selected users scholarship to the first contestant to correctly using statistics to help predict risk. Joe
math problems. (out of 3,750 users) to find out how much answer four challenging problems in a row in suggests that Rick and Athena apply their
additional revenue they can expect. knowledge of mathematical probability to
a math competition.
help them make smart investment choices.

WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.)
1. Lee and Lily Limelight, the famous celebrity couple Amount of Revenue Probability For the first scholarship competition, there are three contestants: Rick and Athena discover thousands of investment choices, but they limit
(famous for what, we don’t know!), love to dress Iggy, their research to the following:
$1,000 10% or 1/10 Contestant Average Math Test Score
their pet iguana, for photographers. Iggy’s hats include NOW TRY THIS $7,000 10% or 1/10 NOW TRY THIS Contestant A 95% NOW TRY THIS • A one-year bank certificate of deposit paying 1% simple interest NOW TRY THIS
a diamond tiara, a leather biker cap, a silk jester’s hat, Contestant B 90% annually. (The U.S. government protects the value of these accounts,
$14,000 10% or 1/10
and a bejeweled pith helmet. Iggy’s footwear consists of Contestant C 80% and historically, no one has ever lost their money, even if the bank
$20,000 20% or 1/5
hot pink high-top sneakers, rhinestone work boots, and If the Limelights reach into Iggy’s Sampling their customer base gives Rick and Working with compound probability for goes out of business.) Making reasonable predictions about
$30,000 25% or 1/4 1. What is the probability that each of the contestants will answer
three-inch platform shoes. Using a table, determine how closet and pick one complete Athena an idea for new problems for the app: the contest gave Athena and Rick ideas • Shares in a mutual fund, representing an investment in the stocks of the future gives Athena and Rick
many outfits the Limelights can make for Iggy, assuming $50,000 25% or 1/4 four questions in a row correctly?
outfit at random, what is the The Limelights are negotiating with Lowest for new problems for the app. the largest U.S. companies. Over the past 20 years, this has increased another app idea:
they pick one hat and one set of footwear. Contestant A Contestant B Contestant C
probability that the outfit will 1. Common Denominator Cable to produce a reality Iggy the iguana has become a an average of 7%. In the past 20 years, the increase has been over 10% Because Iggy is so popular, the
What percentage of the population is the sample?
include a tiara, high-tops, teal show starring (you guessed it!) the Limelights. Hint: You can assume the probability of a contestant answering a single breakout reality star! Iggy’s agent has eleven times and the decrease has been over 10% three times. Limelights come up with a money-
2. Lee decides to purchase two vests for Iggy, one
vest, and silver necklace? The cable company has 50,000 customers. To make question correctly equals his or her average test score. successfully negotiated an appearance • A share of a new company developing an app to chart the quickest path making idea to build upon his star
chartreuse and the other teal. Using a tree diagram,
2. What is the probability that the new service will sure there are enough viewers, the cable company on the hit show “You Want Me to Do through school hallways. Rick estimates that there is a 99% chance status. They collect a few of his scales
determine how many outfits he could make with one hat, Hint: Think about probability make money? surveyed 2,000 customers. Twelve customers said 2. If Athena and Rick decided to make the competition more What?!” To win the grand prize for the that the company will not make money. and plan to clone Iggy replicas to
one vest, and one set of footwear. (You can use the tree as the number of outcomes
they would watch “Life With the Limelights.” When difficult by adding a fifth question, what would the probability Love a Lizard Foundation, Iggy must sell to the public for outrageous
diagram on the classroom poster as an example.) meeting the requirements out of 3. What is the probability that the new service will Suppose Athena has $1,000 to invest:
asked if they would watch a show featuring Iggy of winning be for each contestant? complete three wacky but dangerous prices. The Limelights' investment
the total number of equally likely lose money? 1.
the iguana, the number spiked to 1,724 customers. Contestant A Contestant B Contestant C challenges: Dodge the Doberman (75% What is the probability that the certificate could become worthless? advisor estimates that a $100,000
3. Lily then purchases a little bling for Iggy: one silver outcomes.
necklace and one gold necklace. Using the fundamental 4. Why don’t your answers to the first two questions 1. How many customers do you predict would probability of winning), Root Canal 2. What is the probability that the mutual fund will lose more than investment will be necessary, and
counting principle, determine the number of outfits add up to 100%? watch “Life With the Limelights”? 3. What is the probability of all three contestants answering four (80% probability of winning), and Is It 10% of its value in the next year? that the business has a 10% chance
questions in a row correctly? Spoiled? (90% probability of winning). of making $1,000,000 but a 90%
she could make with one of each category of clothing,
5. What do you think Athena and Rick should do? 2. How many customers do you predict would
What is the probability of Iggy winning 3. What is the probability that the start-up company will become chance of going bankrupt. What
including footwear, one hat, one vest, and one necklace.
Explain your thinking. watch a show starring Iggy?
the grand prize? successful? should the Limelights do?
Worksheet #1 Worksheet #2 Worksheet #3 Bonus Worksheet
Smartphone Test Prep A Call for Assistants Math Masters Mind Your Own Business!
Athena and Rick, two middle-school How can we help everyone Athena and Rick’s app is a huge hit, so they If no one buys the After only six months, R App is making a R App has been in business for a while and I think it would be
students frequently called upon for their with their math questions? form a company: R App Inc. Some customers tutoring service, On the other hand, Let's conduct a sizable profit. “We should donate some of Maybe we should donate Athena and Rick have turned a profit. The two smart to invest our money
powerful math skills, have been flooded ask for a new service: math tutoring. it cobuulsdi nheusrst. our mwoen ecyo utlod h mealpk eu s market survey and our profits to a worthy cause,” Athena thinks somae woofr otuhry pcraoufsiet.s to have always saved some of the money they to make more money.
How about a then decide!
expand. made for extra things they wanted. “It would
with numerous student requests for help smartphone app After estimating that it will cost $14,000 a aloud. Rick replies, “How about a donation But how can we predict
with the dreaded upcoming mathematics withp rfoubnl epmrasc?tice year to hire tutors, the duo wonders what to to our school because they made us the compHeotwit iaobno tuot aaw ard be nice to spend this money, but it’s also if an investment is risky?
smart to invest it to make even more money,”
standardized test. “Wow, how are we do. “If no one buys the service, the additional mathematicians we are today?” “Our gift a math scholarship!
Athena mentions. “But how can we predict if
going to get to everyone in time?” cost might sink us,” fretted Rick. Athena might inspire others to excel in math, too,”
an investment is risky? I certainly don’t want
wondered Athena. responded, “But if we do nothing, we could chimes in Athena.
to lose any money!” replied Rick.
lose income that could help R App grow.”
Rick had a flash: How about a After considering gifts like a random lunch That’s a
smartphone app that provides our To make an informed decision, Athena menu generator for the cafeteria and a statue great idea! The pair decides to email their questions to
classmates with fun practice problems? suggests doing a market survey. The pair of Isaac Newton, the grateful duo donates a Joe, an actuary, whose daily work involves
The pair got to work on their first set of decides to survey 75 randomly selected users scholarship to the first contestant to correctly using statistics to help predict risk. Joe
math problems. (out of 3,750 users) to find out how much answer four challenging problems in a row in suggests that Rick and Athena apply their
additional revenue they can expect. knowledge of mathematical probability to
a math competition.
help them make smart investment choices.

WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.)
1. Lee and Lily Limelight, the famous celebrity couple Amount of Revenue Probability For the first scholarship competition, there are three contestants: Rick and Athena discover thousands of investment choices, but they limit
(famous for what, we don’t know!), love to dress Iggy, their research to the following:
$1,000 10% or 1/10 Contestant Average Math Test Score
their pet iguana, for photographers. Iggy’s hats include NOW TRY THIS $7,000 10% or 1/10 NOW TRY THIS Contestant A 95% NOW TRY THIS • A one-year bank certificate of deposit paying 1% simple interest NOW TRY THIS
a diamond tiara, a leather biker cap, a silk jester’s hat, Contestant B 90% annually. (The U.S. government protects the value of these accounts,
$14,000 10% or 1/10
and a bejeweled pith helmet. Iggy’s footwear consists of Contestant C 80% and historically, no one has ever lost their money, even if the bank
$20,000 20% or 1/5
hot pink high-top sneakers, rhinestone work boots, and If the Limelights reach into Iggy’s Sampling their customer base gives Rick and Working with compound probability for goes out of business.) Making reasonable predictions about
$30,000 25% or 1/4 1. What is the probability that each of the contestants will answer
three-inch platform shoes. Using a table, determine how closet and pick one complete Athena an idea for new problems for the app: the contest gave Athena and Rick ideas • Shares in a mutual fund, representing an investment in the stocks of the future gives Athena and Rick
many outfits the Limelights can make for Iggy, assuming $50,000 25% or 1/4 four questions in a row correctly?
outfit at random, what is the The Limelights are negotiating with Lowest for new problems for the app. the largest U.S. companies. Over the past 20 years, this has increased another app idea:
they pick one hat and one set of footwear. Contestant A Contestant B Contestant C
probability that the outfit will 1. Common Denominator Cable to produce a reality Iggy the iguana has become a an average of 7%. In the past 20 years, the increase has been over 10% Because Iggy is so popular, the
What percentage of the population is the sample?
include a tiara, high-tops, teal show starring (you guessed it!) the Limelights. Hint: You can assume the probability of a contestant answering a single breakout reality star! Iggy’s agent has eleven times and the decrease has been over 10% three times. Limelights come up with a money-
2. Lee decides to purchase two vests for Iggy, one
vest, and silver necklace? The cable company has 50,000 customers. To make question correctly equals his or her average test score. successfully negotiated an appearance • A share of a new company developing an app to chart the quickest path making idea to build upon his star
chartreuse and the other teal. Using a tree diagram,
2. What is the probability that the new service will sure there are enough viewers, the cable company on the hit show “You Want Me to Do through school hallways. Rick estimates that there is a 99% chance status. They collect a few of his scales
determine how many outfits he could make with one hat, Hint: Think about probability make money? surveyed 2,000 customers. Twelve customers said 2. If Athena and Rick decided to make the competition more What?!” To win the grand prize for the that the company will not make money. and plan to clone Iggy replicas to
one vest, and one set of footwear. (You can use the tree as the number of outcomes
they would watch “Life With the Limelights.” When difficult by adding a fifth question, what would the probability Love a Lizard Foundation, Iggy must sell to the public for outrageous
diagram on the classroom poster as an example.) meeting the requirements out of 3. What is the probability that the new service will Suppose Athena has $1,000 to invest:
asked if they would watch a show featuring Iggy of winning be for each contestant? complete three wacky but dangerous prices. The Limelights' investment
the total number of equally likely lose money? 1.
the iguana, the number spiked to 1,724 customers. Contestant A Contestant B Contestant C challenges: Dodge the Doberman (75% What is the probability that the certificate could become worthless? advisor estimates that a $100,000
3. Lily then purchases a little bling for Iggy: one silver outcomes.
necklace and one gold necklace. Using the fundamental 4. Why don’t your answers to the first two questions 1. How many customers do you predict would probability of winning), Root Canal 2. What is the probability that the mutual fund will lose more than investment will be necessary, and
counting principle, determine the number of outfits add up to 100%? watch “Life With the Limelights”? 3. What is the probability of all three contestants answering four (80% probability of winning), and Is It 10% of its value in the next year? that the business has a 10% chance
questions in a row correctly? Spoiled? (90% probability of winning). of making $1,000,000 but a 90%
she could make with one of each category of clothing,
5. What do you think Athena and Rick should do? 2. How many customers do you predict would
What is the probability of Iggy winning 3. What is the probability that the start-up company will become chance of going bankrupt. What
including footwear, one hat, one vest, and one necklace.
Explain your thinking. watch a show starring Iggy?
the grand prize? successful? should the Limelights do?
Worksheet #1 Worksheet #2 Worksheet #3 Bonus Worksheet
Smartphone Test Prep A Call for Assistants Math Masters Mind Your Own Business!
Athena and Rick, two middle-school How can we help everyone Athena and Rick’s app is a huge hit, so they If no one buys the After only six months, R App is making a R App has been in business for a while and I think it would be
students frequently called upon for their with their math questions? form a company: R App Inc. Some customers tutoring service, On the other hand, Let's conduct a sizable profit. “We should donate some of Maybe we should donate Athena and Rick have turned a profit. The two smart to invest our money
powerful math skills, have been flooded ask for a new service: math tutoring. it cobuulsdi nheusrst. our mwoen ecyo utlod h mealpk eu s market survey and our profits to a worthy cause,” Athena thinks somae woofr otuhry pcraoufsiet.s to have always saved some of the money they to make more money.
How about a then decide!
expand. made for extra things they wanted. “It would
with numerous student requests for help smartphone app After estimating that it will cost $14,000 a aloud. Rick replies, “How about a donation But how can we predict
with the dreaded upcoming mathematics withp rfoubnl epmrasc?tice year to hire tutors, the duo wonders what to to our school because they made us the compHeotwit iaobno tuot aaw ard be nice to spend this money, but it’s also if an investment is risky?
smart to invest it to make even more money,”
standardized test. “Wow, how are we do. “If no one buys the service, the additional mathematicians we are today?” “Our gift a math scholarship!
Athena mentions. “But how can we predict if
going to get to everyone in time?” cost might sink us,” fretted Rick. Athena might inspire others to excel in math, too,”
an investment is risky? I certainly don’t want
wondered Athena. responded, “But if we do nothing, we could chimes in Athena.
to lose any money!” replied Rick.
lose income that could help R App grow.”
Rick had a flash: How about a After considering gifts like a random lunch That’s a
smartphone app that provides our To make an informed decision, Athena menu generator for the cafeteria and a statue great idea! The pair decides to email their questions to
classmates with fun practice problems? suggests doing a market survey. The pair of Isaac Newton, the grateful duo donates a Joe, an actuary, whose daily work involves
The pair got to work on their first set of decides to survey 75 randomly selected users scholarship to the first contestant to correctly using statistics to help predict risk. Joe
math problems. (out of 3,750 users) to find out how much answer four challenging problems in a row in suggests that Rick and Athena apply their
additional revenue they can expect. knowledge of mathematical probability to
a math competition.
help them make smart investment choices.

WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.)
1. Lee and Lily Limelight, the famous celebrity couple Amount of Revenue Probability For the first scholarship competition, there are three contestants: Rick and Athena discover thousands of investment choices, but they limit
(famous for what, we don’t know!), love to dress Iggy, their research to the following:
$1,000 10% or 1/10 Contestant Average Math Test Score
their pet iguana, for photographers. Iggy’s hats include NOW TRY THIS $7,000 10% or 1/10 NOW TRY THIS Contestant A 95% NOW TRY THIS • A one-year bank certificate of deposit paying 1% simple interest NOW TRY THIS
a diamond tiara, a leather biker cap, a silk jester’s hat, Contestant B 90% annually. (The U.S. government protects the value of these accounts,
$14,000 10% or 1/10
and a bejeweled pith helmet. Iggy’s footwear consists of Contestant C 80% and historically, no one has ever lost their money, even if the bank
$20,000 20% or 1/5
hot pink high-top sneakers, rhinestone work boots, and If the Limelights reach into Iggy’s Sampling their customer base gives Rick and Working with compound probability for goes out of business.) Making reasonable predictions about
$30,000 25% or 1/4 1. What is the probability that each of the contestants will answer
three-inch platform shoes. Using a table, determine how closet and pick one complete Athena an idea for new problems for the app: the contest gave Athena and Rick ideas • Shares in a mutual fund, representing an investment in the stocks of the future gives Athena and Rick
many outfits the Limelights can make for Iggy, assuming $50,000 25% or 1/4 four questions in a row correctly?
outfit at random, what is the The Limelights are negotiating with Lowest for new problems for the app. the largest U.S. companies. Over the past 20 years, this has increased another app idea:
they pick one hat and one set of footwear. Contestant A Contestant B Contestant C
probability that the outfit will 1. Common Denominator Cable to produce a reality Iggy the iguana has become a an average of 7%. In the past 20 years, the increase has been over 10% Because Iggy is so popular, the
What percentage of the population is the sample?
include a tiara, high-tops, teal show starring (you guessed it!) the Limelights. Hint: You can assume the probability of a contestant answering a single breakout reality star! Iggy’s agent has eleven times and the decrease has been over 10% three times. Limelights come up with a money-
2. Lee decides to purchase two vests for Iggy, one
vest, and silver necklace? The cable company has 50,000 customers. To make question correctly equals his or her average test score. successfully negotiated an appearance • A share of a new company developing an app to chart the quickest path making idea to build upon his star
chartreuse and the other teal. Using a tree diagram,
2. What is the probability that the new service will sure there are enough viewers, the cable company on the hit show “You Want Me to Do through school hallways. Rick estimates that there is a 99% chance status. They collect a few of his scales
determine how many outfits he could make with one hat, Hint: Think about probability make money? surveyed 2,000 customers. Twelve customers said 2. If Athena and Rick decided to make the competition more What?!” To win the grand prize for the that the company will not make money. and plan to clone Iggy replicas to
one vest, and one set of footwear. (You can use the tree as the number of outcomes
they would watch “Life With the Limelights.” When difficult by adding a fifth question, what would the probability Love a Lizard Foundation, Iggy must sell to the public for outrageous
diagram on the classroom poster as an example.) meeting the requirements out of 3. What is the probability that the new service will Suppose Athena has $1,000 to invest:
asked if they would watch a show featuring Iggy of winning be for each contestant? complete three wacky but dangerous prices. The Limelights' investment
the total number of equally likely lose money? 1.
the iguana, the number spiked to 1,724 customers. Contestant A Contestant B Contestant C challenges: Dodge the Doberman (75% What is the probability that the certificate could become worthless? advisor estimates that a $100,000
3. Lily then purchases a little bling for Iggy: one silver outcomes.
necklace and one gold necklace. Using the fundamental 4. Why don’t your answers to the first two questions 1. How many customers do you predict would probability of winning), Root Canal 2. What is the probability that the mutual fund will lose more than investment will be necessary, and
counting principle, determine the number of outfits add up to 100%? watch “Life With the Limelights”? 3. What is the probability of all three contestants answering four (80% probability of winning), and Is It 10% of its value in the next year? that the business has a 10% chance
questions in a row correctly? Spoiled? (90% probability of winning). of making $1,000,000 but a 90%
she could make with one of each category of clothing,
5. What do you think Athena and Rick should do? 2. How many customers do you predict would
What is the probability of Iggy winning 3. What is the probability that the start-up company will become chance of going bankrupt. What
including footwear, one hat, one vest, and one necklace.
Explain your thinking. watch a show starring Iggy?
the grand prize? successful? should the Limelights do?
Worksheet #1 Worksheet #2 Worksheet #3 Bonus Worksheet
Smartphone Test Prep A Call for Assistants Math Masters Mind Your Own Business!
Athena and Rick, two middle-school How can we help everyone Athena and Rick’s app is a huge hit, so they If no one buys the After only six months, R App is making a R App has been in business for a while and I think it would be
students frequently called upon for their with their math questions? form a company: R App Inc. Some customers tutoring service, On the other hand, Let's conduct a sizable profit. “We should donate some of Maybe we should donate Athena and Rick have turned a profit. The two smart to invest our money
powerful math skills, have been flooded ask for a new service: math tutoring. it cobuulsdi nheusrst. our mwoen ecyo utlod h mealpk eu s market survey and our profits to a worthy cause,” Athena thinks somae woofr otuhry pcraoufsiet.s to have always saved some of the money they to make more money.
How about a then decide!
expand. made for extra things they wanted. “It would
with numerous student requests for help smartphone app After estimating that it will cost $14,000 a aloud. Rick replies, “How about a donation But how can we predict
with the dreaded upcoming mathematics withp rfoubnl epmrasc?tice year to hire tutors, the duo wonders what to to our school because they made us the compHeotwit iaobno tuot aaw ard be nice to spend this money, but it’s also if an investment is risky?
smart to invest it to make even more money,”
standardized test. “Wow, how are we do. “If no one buys the service, the additional mathematicians we are today?” “Our gift a math scholarship!
Athena mentions. “But how can we predict if
going to get to everyone in time?” cost might sink us,” fretted Rick. Athena might inspire others to excel in math, too,”
an investment is risky? I certainly don’t want
wondered Athena. responded, “But if we do nothing, we could chimes in Athena.
to lose any money!” replied Rick.
lose income that could help R App grow.”
Rick had a flash: How about a After considering gifts like a random lunch That’s a
smartphone app that provides our To make an informed decision, Athena menu generator for the cafeteria and a statue great idea! The pair decides to email their questions to
classmates with fun practice problems? suggests doing a market survey. The pair of Isaac Newton, the grateful duo donates a Joe, an actuary, whose daily work involves
The pair got to work on their first set of decides to survey 75 randomly selected users scholarship to the first contestant to correctly using statistics to help predict risk. Joe
math problems. (out of 3,750 users) to find out how much answer four challenging problems in a row in suggests that Rick and Athena apply their
additional revenue they can expect. knowledge of mathematical probability to
a math competition.
help them make smart investment choices.

WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.) WORK THE MATH (Show your work on separate paper.)
1. Lee and Lily Limelight, the famous celebrity couple Amount of Revenue Probability For the first scholarship competition, there are three contestants: Rick and Athena discover thousands of investment choices, but they limit
(famous for what, we don’t know!), love to dress Iggy, their research to the following:
$1,000 10% or 1/10 Contestant Average Math Test Score
their pet iguana, for photographers. Iggy’s hats include NOW TRY THIS $7,000 10% or 1/10 NOW TRY THIS Contestant A 95% NOW TRY THIS • A one-year bank certificate of deposit paying 1% simple interest NOW TRY THIS
a diamond tiara, a leather biker cap, a silk jester’s hat, Contestant B 90% annually. (The U.S. government protects the value of these accounts,
$14,000 10% or 1/10
and a bejeweled pith helmet. Iggy’s footwear consists of Contestant C 80% and historically, no one has ever lost their money, even if the bank
$20,000 20% or 1/5
hot pink high-top sneakers, rhinestone work boots, and If the Limelights reach into Iggy’s Sampling their customer base gives Rick and Working with compound probability for goes out of business.) Making reasonable predictions about
$30,000 25% or 1/4 1. What is the probability that each of the contestants will answer
three-inch platform shoes. Using a table, determine how closet and pick one complete Athena an idea for new problems for the app: the contest gave Athena and Rick ideas • Shares in a mutual fund, representing an investment in the stocks of the future gives Athena and Rick
many outfits the Limelights can make for Iggy, assuming $50,000 25% or 1/4 four questions in a row correctly?
outfit at random, what is the The Limelights are negotiating with Lowest for new problems for the app. the largest U.S. companies. Over the past 20 years, this has increased another app idea:
they pick one hat and one set of footwear. Contestant A Contestant B Contestant C
probability that the outfit will 1. Common Denominator Cable to produce a reality Iggy the iguana has become a an average of 7%. In the past 20 years, the increase has been over 10% Because Iggy is so popular, the
What percentage of the population is the sample?
include a tiara, high-tops, teal show starring (you guessed it!) the Limelights. Hint: You can assume the probability of a contestant answering a single breakout reality star! Iggy’s agent has eleven times and the decrease has been over 10% three times. Limelights come up with a money-
2. Lee decides to purchase two vests for Iggy, one
vest, and silver necklace? The cable company has 50,000 customers. To make question correctly equals his or her average test score. successfully negotiated an appearance • A share of a new company developing an app to chart the quickest path making idea to build upon his star
chartreuse and the other teal. Using a tree diagram,
2. What is the probability that the new service will sure there are enough viewers, the cable company on the hit show “You Want Me to Do through school hallways. Rick estimates that there is a 99% chance status. They collect a few of his scales
determine how many outfits he could make with one hat, Hint: Think about probability make money? surveyed 2,000 customers. Twelve customers said 2. If Athena and Rick decided to make the competition more What?!” To win the grand prize for the that the company will not make money. and plan to clone Iggy replicas to
one vest, and one set of footwear. (You can use the tree as the number of outcomes
they would watch “Life With the Limelights.” When difficult by adding a fifth question, what would the probability Love a Lizard Foundation, Iggy must sell to the public for outrageous
diagram on the classroom poster as an example.) meeting the requirements out of 3. What is the probability that the new service will Suppose Athena has $1,000 to invest:
asked if they would watch a show featuring Iggy of winning be for each contestant? complete three wacky but dangerous prices. The Limelights' investment
the total number of equally likely lose money? 1.
the iguana, the number spiked to 1,724 customers. Contestant A Contestant B Contestant C challenges: Dodge the Doberman (75% What is the probability that the certificate could become worthless? advisor estimates that a $100,000
3. Lily then purchases a little bling for Iggy: one silver outcomes.
necklace and one gold necklace. Using the fundamental 4. Why don’t your answers to the first two questions 1. How many customers do you predict would probability of winning), Root Canal 2. What is the probability that the mutual fund will lose more than investment will be necessary, and
counting principle, determine the number of outfits add up to 100%? watch “Life With the Limelights”? 3. What is the probability of all three contestants answering four (80% probability of winning), and Is It 10% of its value in the next year? that the business has a 10% chance
questions in a row correctly? Spoiled? (90% probability of winning). of making $1,000,000 but a 90%
she could make with one of each category of clothing,
5. What do you think Athena and Rick should do? 2. How many customers do you predict would
What is the probability of Iggy winning 3. What is the probability that the start-up company will become chance of going bankrupt. What
including footwear, one hat, one vest, and one necklace.
Explain your thinking. watch a show starring Iggy?
the grand prize? successful? should the Limelights do?
Lesson 1 Probability Basics continued Lesson 3 Compound Probability continued Lesson 1 Probability Basics
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the probability of any number of heads in a row equals concert tour. This activity allows students to use math for
Lesson 2 Simple Probability and Sampling real purposes, and is designed as an optional assignment program! the class needs, plus additional time for the worksheet
1/2 (number of flips). for in or out of the classroom. Poster/Teaching Guide for Grades 6–8 Materials:
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be used to make predictions about of favorable outcomes (3) over the total number of Conversions Rock
affect the probability of B occurring, and vice versa. 1. Show the class a coin. Ask the class whether it will land
a population based on a sample; outcomes (6) to get 3/6, which should be reduced to • Graphing: Bars, Lines, & Pies Overview/Getting Started:
lowest terms (1/2). Show how they could also determine 6. Provide an example or two to show how the formula works. on heads or tails if flipped. Students should answer that
• identify the difference between • Perimeter, area, surface area, and volume: Setting the
outcomes and events; and this by adding the probability of each even outcome For example, if the probability of rain is 20% on Saturday Stage with Geometry This program is designed to supplement your existing it could land on either heads or tails. Ask if there is a
(1/6 + 1/6 + 1/6) to arrive at 3/6 or 1/2 or 50%. and 50% on Sunday, what is the probability of rain on instruction of these probability topics: way to quantify the chance that it will land on heads.
• add the probabilities of the both days? (20% times 50% = 10%). Demonstrate how • Pre-Algebra: Solving the Unknown with Algebra If the class doesn’t mention the word probability,
outcomes that are part of an 3. Explain that the even outcomes here are 2, 4, or 6. this could be done with fractions (2/10 times 1/2 = 2/20 • Probability: Shake, Rattle, & Roll • strategies to identify favorable and total outcomes; introduce it and note that it means “a fraction, decimal,
event to determine the probability of an event. Rolling an even number is called an event. The sum of which reduces to 1/10) or decimals (.2 times .5 = .10). • calculating simple probability; or percentage describing the likelihood of an event
Time Required: 30 minutes, depending on how much review the even outcomes equals the probability of an event. To reinforce the abstract concept of compound probability, Also Available: • sampling and proportions; occurring.” Explain how no event can have less than a
If necessary, repeat with other examples, such as the
the class needs, plus additional time for the worksheet use a tree diagram to demonstrate how rain on both days • The Math Academy Series: Using Math in the Real World • calculating compound probability; and 0% chance or more than a 100% chance of occurring.
probability of rolling a number other than a 3, the
Materials: represents one out of 10 possible outcomes. • Building Your Future: A Financial literacy Series • using probability concepts to solve real-world 2. Ask for examples of how probability is used in the real
probability of rolling a number less than 3, etc.
• one six-sided die (for demonstration) 7. D istribute Worksheet 3. Read the introduction and review the • Math Grant Opportunities problems. world. The topic of weather forecasts may be mentioned.
4. Distribute Worksheet 2 and calculators. Read the
• calculators introduction and review the facts with the class. facts with the class. Ask students to complete the worksheet. join Athena and Rick The materials are taught through this story line: Make sure the class understands that a 40% probability of
Review answers as a class. Athena and Rick are two middle-school students precipitation means that there is a 40% likelihood that
• Worksheet 2: “A Call for Assistants” 5. Ask students to complete the worksheet. Explain that precipitation will fall within a given area. Gaming/odds may
as they solve real-world admired for their powerful mathematical thinking and
DiReCTiONS: the bonus question requires them to apply what they also be mentioned. You can also introduce to students
real-world problem-solving skills. Asked by classmates
1. Show a single six-sided die to the class. Ask what the learned about probability in Lesson 1. Review answers as Worksheet Answer Key 3. 4 8 outfits (2 necklaces x 2 vests x 3 footwear Worksheet 3: “Math Masters” problems through that companies (insurance and financial companies in
for help preparing for a mathematics standardized
possible outcomes are. Record the outcomes on the a class. Make sure that the review includes a discussion Worksheet 1: “Smartphone Test Prep” x 4 headgear) 1. C ontestant A: 81.5% (.95 x .95 x .95 x .95) test, the duo develops a smartphone application with particular), statistical experts such as actuaries, and
board. Ask the class to calculate the probability of each of how proportions are used to make predictions about 1. 1 2 outfits: Now Try This: The probability of any one outfit Contestant B: 65.6% (.9 x .9 x .9 x .9) n. powerful mathematical practice math problems. The app, featuring a fictitious individuals in daily life use probability to make reasonable
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together, the sum is 1. 12/2,000 = x/50,000) and the validity of doing so. WTB WBCB WJHB WPHB W1.o rT khseh seaemt p2l:e “ iAs 2C%al lo ffo trh Ae spsoisptualnattiso”n .C9o5n)t estant B: 59.0% (.9 x .9 x .9 x .9 x .9) uarial F provides them with new opportunities and challenges. othna ht ethade sn (u1m/2er)a. tEonrs (u1r)e rtehparte tsheen tcsla tshse u nnudmerbsetra nodf s
PS PS PS PS (75/3,750). Contestant C: 32.8% (.8 x .8 x .8 x .8 x .8) e Act The program includes three lessons, each with a favorable outcomes (heads) while the denominator (2)
Lesson 3 Compound Probability T BC JH PH 2. 7 0% (the sum of the probabilities for 3. 21.9 % (.815 x .656 x .41) of Th corresponding worksheet. A bonus worksheet, which represents all possible outcomes (heads and tails). If
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the probability of multiple independent events. three flips in a row could be depicted. at recorded all possible outcomes without double counting.
Time Required: 20–30 minutes, depending on how much 3. Ask what the probability of a coin landing on heads three BTC tphaasts tuhpe. p Aolttehnotuiaglh p trhoefirtes iasr neo t oriog ghot oadn stwo er, 23.. 11 5%% (3/20) With M What is an actuary? An actuary satnu odpetnitosn taol uassesi mgnamthe nfotr f orera iln p ourr opuots eosf, t ihse d celsaisgsnreodo mas. Suggest, for example, a tree diagram and model how it can
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