Unit 3Collect, Organize, and Analyse Data

Grade?

Lesson Outline

BIG PICTURE

Students will:• organize and display data using different graphical representati(lll$;• ~. data to form hypotheses and ereate convincing llr~nts;• recognize that and graphs Cl'Ill he misinterpreted and Cl'Il'l be misleading;• understand meuures ofcentral tendency and the effect ofoutliers,

4 !Creating a I •

from at Database

7 IIntroduction to Circle I_Graphs •

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7m74, 7m7S, 7m79

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• Identify in data collection.• Coned primary data a• Orl!'anize primary data into a tallY chart.

• Interpret, display, graph. and draw conclusions

Make inferences and based on the ofdl'Itl'I.

• hetween primmy data.• Distinguish hetween a census and at sample.• ldentifv bias in data collection ~ltbO(ls.

•

•----

-•

••

or Data •

8 ICalculatingPercents!Angles forCircle Graphs

6 IThree

2 IDesigning andConducting a Valid

.5 I Who's the Author'!

:3

TIPS4RM: Grade 1: Unit :3 - Collect, Orgill'lize, and Analyse Data 1

• Identify trends fwDdin data and• Extend a papb to make predictions (extrapolate) bevond the

graphed area.• Determine if the extrapolated data sense.

• and mferenees.• to extract information from the data,

rel:aticrnskups within. the data, and use data wdraw conclU8ioos.• Interpolate to within the papbed region.

CaE

CaE 4b. 4f, So

1m1S,7m46,7m74.

1m71,7m?6

the ofoutliers on

U8ing a graph.Identify and biu in data.

IUmttate the same set ofdataU8~ a tally sheet. frequency table,bar graph, line graph,pi~h. and circle graph.Determine which graph bellt conveys the information (considerbias. audience).C~nJ)Itre features ofeach type ofpaph that would lend!!!!!!~ best to sumxm a statement.n:~_j~..

• ~. andmodethe meunres ofcentral tendency,

•

••

•

•

TIPS4RM: Grade 7: Unlt:.'l -CoUect. Organize, and ArnalySfl Data 2

~nit 3: Da¥ 1: What's the Sto~? Grade 7

•

.dJ lIImiog Gollf .. MlttDll!•... ...•. • M.,.. ake i·nfier·encc,·t; and arguments bued·. on.. the l.'IIlalysis ofda.ta. • SteM 3JJ

.. Distinguish between primary and $OOOOOary datL• Distinguish between a eenms and ft. sample,• IdentifY billl in data metbodll,

ASsessment

vs, women wbo lost

_ Minds On..,

_Action!

management" in the middle, and.~.. andaMWet'i that lead to some ~iOl1!l

tl1eise tlllrec~ 111l•• e.g" What data could we from the Internet aooutsurVe\I'inll ow: class? data)

Connecting/Oral Quatiorling/Ob&ervatiollMentai Note: Assellll stIl'ienltS'to connect the use ofdata to situations in their world.

i[ouu of 4 :t IllvestiSltionStudents examine and analyse the data and answer the questions (BLM 3.Ask (rom the chart to relate the data to the beadings.,

....--BLM3.U.

Who', Class:t Pilcy.ionDiseUllS the discfePlWCY between the numberlives,To demo1'l$trate a cenllUS '\1$. a by Ii sbowthe III the "women and first" rule Generalize fromobtainc~ that x % of tbe and tben survey theIntroduce tbe term in data coillection.

Think Utemcy:M$t~,

G~ 7-9, p. 2-4.

Pointout.lMIdIff~ in tn. iW()su~(onel$a

CtWIUliI oft~ de_,ather,s a

survey).

_ Consolidate Whole Class -+ DiscussionDebrief Revisit the terms introduced during Minds On... and Action! Students

evidence of when they were used duri.ng the lesson.

Home Activity or Further ClassfoomCon!ollgationFind current statistics in a newspaper, a magazine, 00 television, or on the Internetto answer the following Question aoout the data: What srory miRht the data teU?

T1PS4RM: Grade 1; Unit :3 - Collect Organize, aoo Analyse Data

Wall• ()tID$U$

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• prirl'Iarylsecondarydata

• bias

3

3..1 ..1: The Sinking of the Titanic

e E«ltucatioo Ol-lIwl, 1991)

Below is a summary of some data about the people saiting on the Titanic.Look at data on the chart and answer these questions:1. What was the total number of females aboard the Titanic? Males? <./ •

A

2. Were there more female or male deaths in the High Income category?

3. Which category (HlghiMiddlelLow Income) did most children belong to aboard the Titanic?

Low IncomeOtherTotal

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4, Compare the number of female deaths in the high and low income female category.Use ratios or percents to make your comparison. Explain why you think the results aredifferent

5, Is this data primary or (Circle one)

6. Is this data a census or a sample? Explain.

TIPS4RM: Grade 1: UI'lIt :3 - Collect, OrgM~, and ArmI)'H Dam <4

•

MJrtbJ,.ilamina Goals. . ~1.deD)titYbias.-. m'···•. ·· data··.· CCll..ecu·on...... . 'fJ:S.. 1,.,M 3,4.,1, j,:l.Z

.. primary data by conducting a l!l'UIVey, •(.W~

.. Orgmlize primary data into a tally chart, protractor

AsseumentOpportunities

• Minds 00,., Imlll GrRYQI 2 DilCUssl2JlStudents share stories from the Home Activity. l.

WIloll !<I.I :t SUMY:Survey the cmss by a show ofhands the number ofminutes that should be requiredfor homework time: Should homework in Grade 7 be limited to 15 minutes per

Record the responses on a yes~no tally chart.

Ask: Is this a ''fait'' or biased sample?

• Actiont )lYboll Ciasl :t DlsCussie.Lead a discussion ofthe criteria required to conduct a valid surveystudent volunteers to read the five scenarios on ml overhead ofBLMafter each scenario to of the questio:n,method ofdata collection.Student volunteers read aloud the deseripti011$ ofthe four on an. overhead of I Igl'(:MJf).

BLM By a show ofhmlds, students select their favourite ride. Record resultson a taily chart.pltcus10n QutdmJI.. How reliable are these results for the decision being made?.. What are some other ways data could be collected?

SmJU.GroYRI.:t Inv,etlgltiRnStuden.ts investigate reasons why they e.g., music at admlce, fundrailling, school uniforms. withclass.

Small groups decide on a topic for which they would like to collect data anda survey.

Students consider:.. will the information collected be used?• How and why is important?.. What col1eetioo methods wilt be nsed?.. What is an appropriate sample• Are questions appropriately phrased?Smdents conduct their survey by the survey questions between groups.

fortMlr

• Consolidate Whole CIISS ~ DiicYI,IO!!Debrief Lead a discussion to identifY possible uses of the data collected in their surveys,

making the point that surveys should inform a decision of some type.

Reflecting!Application/Rating Scale: Individually student write II reflectionabout the kinds ofdecisions that could be made based on their survey data,

Home A.ctiv~ or Further Clanfoom Con$oUdatlonWrite a journal response:We live in. the Information Age. An informed citizen needs to be able toorgmlize, display, interpret information, and identifY bias. How can our study ofdata management help you become an informed decision maker'!

TIPS4RM: Grade 7: Unit 3 - Collect, and Analyse Data 5

3.2.1: Collecting Data

In each case, circie which type of sampling technique you would choose to collect data.

1. A donor gives the school $500 to spend on the students. The principal asks your class tocreate a survey to determine where to spend the money. Should your class:a) ask everyone who stayed after school for the basketball tryouts?b) ask people going In and out of the library at lunch?

randomly select 5 poopte from each class?

Justify your selection.A

2. To determine what students at your school think about sta.rting a lunch hour chess club,woLltdyou:a) ask everyone In Grade 4?b) ask. the teachers?

ask every tenth student as they enter the schoolln the morning?

Justify your selection.

3, To determine the most watched TV shows, would you:a) ask all the students In Grade 2?

(6)) call households between 4 and 6 p.m.?Cf send home a survey with each student?

Justify your selection.

~

Change the questions to match the purpose of the survey.

4, Anthea was carrying out a survey on favourite magazines. She asked "Do you like readingmagazines?"

5, Mike wants to find out what type of music people like to listen to. He asks "Do you like rap orpop music?"

TIF'S4RM: Graoo 7: Unit;) - Collect, Organize. and Analyse Data Ei

3..2 ..2: Paramount Canada's Wonderland

Scenario: Paramount Canada's Wonderland is considering opening an additional amusement:park. They need to know which ride they should promote as a key attraction for ages 11-13.

Cliffhanger: Cliffhanger is Paramount Canada's Wonderland's new super swing with attitudeand altitude. CUffhanger takes passengers through snap rollovers and unyIelding 360 degreetwists and turns as they are propelled through moments of zero gravity and finally quenched byan inescapable wall of water.

Meteor Attack: At Action FIX Theatre, there are non-stop thrills with Meteor Attack. Passeng.ersare taken on the flight of their lives, as they become the last line of defense against a full-scalealien invasion. Passengers are transformed into unsuspecting pilot trainees of the 23fd century,who are to save Rocketstation Outpost 769.

Dr012 Zon~ §tunt Tower: Drop Zone is Canada's tallest free~fall thrill ride: 23 stories high. Itfeatures a colourful, free-standing tower with open cockpit seats that drop at a speed of 100km/houf. Manufactured In Switzerland, five cars drop at a speed of 488 em/second and down a70 m drop. Drop Zone has an hourly capacity of 800 riders.

Water Park: Water Park is a million gallons of heated water funt Bring your bathing suit and ridethe waves at Canada's largest outdoor wave pool. Gently float 1.5 km on The Lazy River, orchoose from over 16 thrilling water slides.

Adapted from Clll1W'$ Woooerillfld webllite

TIPS4RM; Grade 7; Unit 3. - Collect, Organize, and Analyse Data 7

• BLM :3.3.1.. chart paper.. matkft'l>

OOl1clusionli from primary data.

.. x· ··s' and Preaentins Data ~~ ~

• Assessment

•all

mfill.'KIDsuabout

.ActJonl

CommunleatingfPresentatioa/Cheekbrk: AIlIlClls students' ability todatu to the purpose fClll.llts of their survey.

, l)ynamle stdsbl

• Consolidate Small (jrpuQI i ProtemalignDebrief Each small its results to the clallll. Students use the criteria on

3.3.1 as a for the ~J:'_..._

each peers conunent on criteria met and provide sUlitgesti<lnS

may have heen moreqmiSfit'll in tbe following way....

Word Wall.fmq~tabllil

Home t\etivtrl or Furth,.. Classroom ~onsolldltion

Complete worksheet 3.3.2 to reflect on your ptU'ticipation within your group.

Learning Skills (Teamwork)/ReflectionJAuK:dotaJ Notes: AssCIls students'self~ret1ection.

TIPS4RM: G~oo 7: Unit 3 - Cofllilct,Organlz:e, lilnd Anal~ Oata 8

3.3.1: Presentation of Primary Survey Data

Share the results of your survey with the class.Create a presentation on chart paper that Includes a relative frequency table, an appropriategraph, and a clear survey question.

Use the foUowing criteria as a checklist to ensure your presentation is complete:

• Our question/purpose of the survey is clearly stated.

• We can explain how we attempted to eliminate bias in our data collection method.

• Our frequency table is dearly displayed.

• All parts of our graph are labelled properly.

• Our graph summarizes our results.

• Our presentation takes between 2 and 3 minutes.

~----_.--~--------------------------~----------------- -----------------------_¥

Presentation of Primary Survey Data

Share the results of your survey with the class,Create a presentation on chart paper that indudes a relative frequency table. an appropriategraph. and a clear survey question.

Use the following criteria as a checklist to ensure your presentation is complete:

• Our question/purpose of the survey is clearly stated.

• We can explain how we attempted to eliminate bias in our data collection method.

• Our frequency table is clearly displayed.

• All parts of our graph are labelled properly.

• Our graph summarizes our results.

• Our presentation takes between 2 and 3 minutes.

TIPS4RM: Grade 7: Unit ::I - Collect, Organize, and Analyse Data 9

3.3.2: Reflecting on Your Work in the Group

Divide your circle into sections that reflect how much time you spent on each part of the groupactivity. Label each sacticn and justify the amount of the circle you have given to each section.

Discussing with groupmembers

Doing the work

Checking group workand revising

Off-task behaviour

ReflectionHow could you improve your project and presentation in the future?

~~------~---------------~---------------------------------------~-------------*

Divide your circle into sections that reflect how much time you spent on each part of the groupactivity. Label each section and justify the amount of the circle you have given to each section.

Discussing with groupmembers

Doing the work

Checking group workand revising

Off-task behaviour

ReflectionHow could you improve your project and presentation in the future?

TIPS4RM: Grade 7 Unit ::I - Collect, and AnaJysc& Pata 10

Unit 3: Dav 4: Creating a Spreadsheet from a Database

•

Math beaming Goal,. ... . .. c.• Ollec.t secondary.••. data from· a database (1m.nna..lly and/or electronically).

.. Organize secondary data ming a spreadsheet.

.. Identify correct data ll'Wlagemeut terminology.

Grade 1

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• Mll1ds On... Who. glall :i J;li,eusl120POle questions to students about wurees ofdata:.. How would you.make It doctor's appointment (phone caU and

It phonebook);.. How would you decide what to pack for a camping trip?

newspaper and electronic databases).

Ask:.. What is a database?.. What electronic and hard ropy have in cormnon?.. How are thev hl'llrrlid?

Enlpbasill:e that a database is an collection ofdata.Students ~ive other eXllltIl)les ofooth electronic hard copy databases.

Mae_mentOpportunities

Database Exampl$$• Statlsb Ca.Mda• ErIVlronment

CaMda

to make

• Actionl

• ConsoUdateDebrief

Practice

Plit! ~S"plomIQnDemoOltfate the features ofa database. introduce the termfield and how it relatesto the database. Select a for electronic data collection or provide data in hardcopy.Students explore the database,

Pllrs ~ RlSordim DmShow an example of It spreadsheet and model the transfer ofdata mto it. Introoucedataba:se vocabulary and bow it relates to spfiel:'ldsneets.Introduce features of an electronic spreadsheet, e,g., sort, sum, formulas, etc.Student'! transfer data into a or record the dataon a chart

Whole CI•• ~ DiscussionPose questions:.. Why are datablitSeS created?.. Why would someone transfer data from a database to a SprellldLSftClCt'?.. What can you do with data when it is in a format?

Conneettng:lOral Questioning/Mental Note: Note students'connections between spreadsheets. data, lm.u graphing,

Home Acth,ft\'. Qr Furth!r Cla,sroom ConsoUdationAnalyse the spreadsheet you created,.. What do you notice about the data you have collected?.. How c()uld you or someone else use this data?.. Why would somcone want to create a spreadlshc:et't

Word Wall• data.base• Iield• llpfudsheet• 0011$• rows• columns

T1PS4RM: Grade 7: UIlil3 Collee!, Organize, and Analyse Data 11

Grader

MI1tJ:iIII.. BLM 3.5.1,3.5.2

Assessment

_ Minds On." IhinlslfairISblre.~Reagins ~mRbIStudents examine the graphs on BLM 3.5, I 10 bypothes.ize whicb ofthe eban'tctcnlisted mtellina theStudents slwe their conjectures the reasons for their cnoroes,

$tud$Ou!fI'lllyiOOntify Iiooas the bellt waydlsptaytM~W(lfkdata.

Studet'lts can useTlflk~"llOftware for tl\l$liIdiV!ty

WotdWall0$Cla'-o Intervalo~o~in~

Whole Class -+•. Qi·uyssl2nDi~ how the same set ofdata em be used 10 luppM many different views.Students compare the graphs to determine which features (~. breabin were modifted for each to St:lppOrt I different view. W'hy wuthis done? Wbich ofthe graphs mmrepraent the data? Explain.

Group! qf -\ + InvestigationAssign each ifOUP a different role - Grade 7 teacher, Grade 7 student. parent ofaGrade 1 srudent. principal. They present a diffierent perspective on the data asdetermined by their assiped role (BLM 3.5.2)-Each that some or aU data from the point of

statement that tbe CMseo dam suppom>.The presents its graph smtement on a without revealing what itsoriigin;~l tller!lflective ormotivatiot:l was,For example, Parents choose Sept. May, and~ the horizontal axisshow during these months. The statement could be:Students in Grade 1 watch about I hour a day.

_ ConsolidatfJ Indiyjdu,l + JournalDebrief Smdents choose two or three of the displayed around the room and decide

what role the group wboproduce4 each of the graphs may have oel4, e.g., aparent. a principal. They justify their choices by different features

any misleading grapb.

Reasoning and ProvinglDemonstrationlRating Seale/Journal/Scoring Guide:Assess students' to based on the information In the

_Actionl

Home Activity gr Further Srtla$!room ConsoUd'tk!nPractice Set up It recording sheet for collecting dam on the amount of time you spend on

homework over the next week.

TIPS4RM: Gr<l<le 7: Unit 3 - Collect, and Data 12

3..5.1 : Whose Story Is It?

Examine the four' graphs below, Which of the Titanic charactersbelaw do you think could haveprepared ea.cngraph?

Director of White Star Lines: Conclusion: "Lots of people were saved,"

Suzie Moneypenny: Conclusion: "Most of the people who died were poor:

Lord I. M, Gallant: Conclusion: "The males were brave,"

Jay Crew (a cook on board): Conclusion: "Working on ships is safe,"

600

400

200

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I·TC~1 I• Dead

550

500

450

400

350

300

250

200

150

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ToUlI Oelitths

.Passengers I

(A~ from hltp:!!r.;lllXri,cuhlm,l~ed.qld.g(lv.llUi·klai'edai

Education~llIDd, 1997)

TIPS4RM: Grade 7: Unit:; - Collect, Organize, <lnd Arlalyl'll'il Oa~ 13

3.5..2: Homework Data

3

73%73%75%70%68%66%69%700/072%71%

641161832122052151981688345

2820

TIPS4RM: Gra~ 1: Unll 3 - Collect, Organize, and AMlylile Data 14

Unit 3: DaX 6:.Three T~pel of Data Orade 1

•

MdJ bUtI'd"" Gotl! . .. .. NM'dtll. .. .. ]Jist'.j.np..••.•••..•..•t...•Ih•.•....~..•.•••••.•• 11... typeg.• ofgraphs that eOOlP.are q.wmtities:·.fbat~h. double bar • BLM 3.6.1

~)md.··~dhtt show change over time (brokenmulti,l, lme~hi),

.. Diswpilh bltwllm discrete. categorical, md continuous data.As~ent

Fimttwoda~

are categoriclill.Third dataset isoontmuous. Lastdataset is dIS(ll1')te.

pasisible to

(Answer: Only

grouping or a

I"sltxldlgl 2 ADlIYH ¥arioHI ReQresematic;m, of DamG"ut BLM 3.6,1 into 16 pieces and uk each student to choose one piece. Students

ifoupl offour by matching their representation of a set ofdata with otherrepresentations ofthe same data,To h,lp stndents decide whether have dis(;rete. cClUtir:lI10!J1S,data,_:.. Which

.. 'Ifmen group Bas oata

..

..

_ Minds On,,,

_Action!

h~dinll:s:cl>nti,nU(>UI, discrete, and

Some OO!>sible answers:

EMUre that at! threetypeslill'8~.

continuous, and

"'''''VIA", data that was conti:nunus,

of data and decides how to collectexperiment. They collect and represent

.. Who. """'"

.. Continuous:

shoe?_ ......, _,..I...., are in each ofyour shoes?

.. are your shoes?

.. Discrete:

..

Curdeulum ElpeetatMmllDemoDstnttion/Ch~kbric:Assess students'their tor it their choice

collected and the ways in which they orgmizedStudents explain why their graphical representation is consistent

the mte o:r data collected.

Home Activity or Furth,r Classroom ConsotidationIdentify some data. Choose a topic such as growth ofplants,Provide examnles ofall three ofdata, and explain how you would collect

data.Practu:t

II•ConsolidateD,bdef

TlPS4RM; Grade"; Unit :3 - Collect, and Analyse Data 15

3 ..6 ..1: Discrete, Categorical, and Continuous Data

JanuaryJanuaryDecemberMarchAprilJuneJuneJuneAugustDecemberMard"lJune

Mard"IFebruaryDecemberAugustAugustJuneJuneJulySeptemberJanuaryMard"lJuneOCtot;)er

i

1

! :i:

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.J.FaM.A.M.J.J.A.5.0aN.0

Therefore,mostpeopfawere bornlnttlemonth ofJune.

Therefore,moreboys thengirls wereborn inthe firsthalf of theyear,

So A

s.aon.MaIe .Fema&e

Winter(M)(M)

lAutUmn (F)SUrnmer(M)Summer (F)Spring (M)Spring (M)summer(M)SUmmer(M)Winter (F)Winter (M)Spring (M)Autumn (F)

Winter(M)Winter (F)Autumn (M)Wl1'Iter (F)Spring(M)Spring (M)Spring (M)Spring (F)Summer(M)Autumn (F)Winter(M)Spring (F)

First week 12Second week 10Third week 8

70lao~50

.540:!300)20! 10

o

Therefore,the planthas beangrowingsteadiiyover threeweeks.

First week 78Second week 126Third week 117

1 40.:. 30

J 20

10

oOct Oct Oct Oet Oct

7 11 15 21 26

Therefore,Allysonread moretowardsthe end ofthe threeweeksthan atthebeginning,except forthe lastday.

TIPS4RM: Grade 7: Unit :3 - C~, and ArnilyD Data 16

Unit 3: Day 7: Introduction to Circle Grafh8 Graft 7

Ft1fdh Lllrnlng 92,11 M*11I11.. Create circle graphs using different methods, • string.. Estimate the percents, hetionJi, and degrees found in circle graphs, • muking~.. Undmctand that a circle graph represents part!l ofa whole, • coloured Sticky

notes• BLM3:U

Assessment

Whgle CUI'S ~ .. COM!!Pose the question: Do you think school uniforms should be mandatory? Students:proceed to acomer ofthe room bued 00 their opinion (agree, agree but. disagree,disagree but). Provide a different colour sticky note at each comer, To identifytheir opinion,. they wem a sticky note, e,g., agreeing students wear a greenstickynote.

Whgle.!t1ils ~ KlntUll~h!tic GraphingStudents liue up to make a human bar graph based Oil their opinion. Point out thisis one way to their (categorical) data. Students think ofanother method.The whole class fOfl:M a circle, keeping opinion groups (same colour sticky notes)togethier 00 the circumferen~ ofthe circle. Place tape on the floor to show central

Place the ends of four long to the floor at the centre of the circle,extend them to the at each where the opinions change.

Ask: How is this new iimilar to the bar graph? different? What does itshow?Discuss characteristics of the circle graph with a focus on the relationship of theparts: to a. whole. Record data for future use.

Wh21' CIII! :t DllcuUI2UStudents record characteristies ofa circle graph. Ask:.. Ifthe whole that school uniforms should be mandatory, how many

deglrees would that degrees).. whole class was in disagreement with school uniforms being mandatory,

percent of the class would that be? (lOO%) How many degrees is that on lit

circle What ifhalf the students agreed? (percent, degrees, fraction,Students selectedpms ofthe circle t, t, t, t, )as a fraction,decumu, and percent on BLM 3.7,1.Use the school opinion data to create Ii. sample circle graph as a model forstu<lenlts, on an overhead of BLM 3.7.1.

Individual :t GrlPhlcl1 Reprlunlat!2UStudents use spreadsheet data colleeted in Day 4 or use other data provided, tocreate a circle graph (BLM 3.7.1). They include a title, label percents, etc.Stu;dents: provide a written description ofthe storY the data tells and explain and

how tbev divided their circle.

• Minds On...

• Actionl

RepreseJ'ltinglDemonstrationfCbed<bric: Assess students'data and explain their rea,sollil'lig.

to represent

Lead lIitlJd~ tosay a~ graph, If~.

WordWaI• circle graph• OOI1trm Mgle

Reinforce the ideathat circle grapMare used torlllpresent andcompare parts of awl'lol$.

).

• Consolidate Whgl' Cl,ss ~.QilCUl!k>nDebrief Discuss strategies for comparing and connecting, fractious, percentages, and

central Ask: What is a circle graph used for?Students: with examples of when a circl.e graph is used to display data.

Home Aetivlty; or Furtf1,r Classroom ConsolidationRepresent the data with a circl.e graph and write an explanation of the story thedata teUs. Be prepared to share your ideas with the class.

TIP$4RM: Grade 7: Unit :3 - Collect. OrganIZe, and Analyse Data

SEllect textbookqUft$tioos that lilre00 a total of 100OOIleS. and lll$utt insimple fraetkll'ls

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Unit 3: Da

•8: Calculatina PercentsfAngles for Circle Graphs

MaSh bIImlng GQlII• Create a circle graph by calculating peroontages to determine th.e central q!e8.• Ule a measure the central angle8.

GtH&7

Mltm:iIJJ• BLM 3.8.1.. f'rlwtion circle'S.. protl'aCWfS

A&se$sment

• Mindr> On", Sm," irgup. :t 12I,c:us,kmStudents share their circle graphs and eltpLanations from previOUll day's HomeActivity. Cironlate to identify students who may have selected a strategy that canbe used when uncommon fractions are involved, (to calculate central

WbOI! !tIft" -tl2tmgD!lratlgnUsing an overhead, demonstrate the steps and strategies to create a graph.Ule fra<:tion circle pieces to reinfcree the ecnneetioo between fractions, pel100u1ts,and they have calculated the they use a Pfctractor toaccumtely measure and coost:l'Uet cmtral ofthe circle

Differentiated Instruction.. Provide circle showing 1()Oil! increment!> around the diameter... Provide circle showin~ in of I ()o!i>•

This Iead$ to~for_e

~:

1:1 of the whole) x 300or centnd angles In~ .. (pereentof whole) x 300.

tothe

ell" i: C9o.!tYBID9.!ilrc:', GrIPb!Students display data represented in a relative frequency tsfile (Bl.M 3.lS.l) as a

CBLM 3.7.1). relate frequencies to fractions. to and

Curriculum ExpeetationslApplicatjou!Cbeekbrie: A!:l~~ students'understanding of the betwem percent!>

in adrcle

.Actionl

• Consolidate Whol, !i'll' -t 0lley"ionDebrief Reinforce the strategies and steps used to create a circle include probing

qWl:Stj4~ such as:.. If the calculated pel1oou:mgcl:S add up to 110, what does this indicate?.. If the total have a !111m of 340 what should you do?Reinforce the coneeptl> that the sum for the percents must be 100 and the sumthe angles must be 360 degrees.

r".."",,,, Practtee

l:jome Ac:t!vlty or Fut'therCII"room ConsoltgatlOflChoose some data and create a circle graph. List the you took to nmke thecircle graph and prove with more than one strategy that your circle ~raDh isaccurate,

Suggest~s.

l'IlIilgm:!l'le$.~,etc.,as

$OUroliIIil of data,Or. provide vmiool!lMt$ of data from

$tl.ldMltsmakel!l~.

TIPS4RM: Graoo 7: Urdl3 - Collect, Organize. and Data 19

3..8..1 :. Creating a Circle· Graph

Surveyresulm of favourite sports in Grade 7.

Survey results for the favourite types of music of students in Grade 7.

Survey results of number of slbflngs.

T1PS4RM; Grade 7; Unit 3 - Coflect, OrgMiD, and Analyse Oata 20

Unit 3: Dav 9: Which Graph Is Best?

•"alb L.arnlng Qall• Illustrate the same set ofdata using a taUy sheet, frequency table, bar graph, line

mle Jl1.lPh.• ~em)l;ne wrllen If'IPh best conveys the informatiQQ (COO$ider oi8$, audience).• Compare~ ofeach type ofJl1.lPh that would lend th~lves best to support

a statement.

Grade 1

_tm,ls• BLM3.9.1.~with

~t

paper

Asu$sment

• Minds On...

• Action!

• ConsolidateDebrief

Thlnk/Pair/Sha,e :t 6nticipatiin GuidI (1 oral question only)POle the I can 'use any type of grapeh Iwish to repruent data. Agree ordisagree? Students indieate or di.llapement Quickly record the datafrom this survey.

Whole Class -+ Orientation to the ProbltmUsing an overhead of the data (on BLM 3.9.n,bave the nrohlem. read aloud.POie the quel~tim:l$:

• What point do you want to~?• What type ofJl1.lPh would you use?

Plitt :t AnIIDID" QflpblStudents examine several ofgraphs 00 the same data. BLM In

they the pros and COM ofeadl.

Re.allOning and Proving!ApplicatioB/Ratmg Scale: Assess students' abHitv tochoose a graph to display data. nodng the reasooinl.! rel.a:ted tochoice.

Whot, CIa,s :t DiscussionDevelop a Venn diagram on the differences and similarities between two types of

or data representation e.g., It line graph and a tally sheet. Studentsthe Anticipation Guide. Ask the oral question from Minds On... again.

Indlvigual:t ReprlHntingStudents complete an individual Verm diagram on two different Of grapns ordata representation tools of their choice. Collect theie and provide individualfeedback, as required,

Home Activity or Further Ch~s$room Con@olld@tion.Find examples Qfgraphic representation ofdata (in textbooks. newspapers,Internet. magazines, etc.) Reflect on whether that is the best representation for the

considering the audience and the title (statement),

POlI$lble thelml$ 'forthe letter to theedltorll'l~:

.ge~are

rhIlng• geprldng

favooflll l..oeatloo Bresk.'kmts

TIPS4RM: Graoo 1: Unit :) - Collect, Organize, and AfIl!.llyH Data 21

3..9..1: Average Gas Prices

Analyse the data and decide what statement you want to make about gas prices. Choose thegraph that best supports your statement and justify your choice. Write a letter to the news.papereditor to support your statement. Indude the graph.

Data

TIPS4R:M:Grade 1: UnIt:3 - Colilwt, Organize, and Data 22

"

f I i IS ! -.. !iII

I•• '. lll

!i ! ! -I

II.. I $

8' a I

Unit 3: Day 10: GOins Around in Circles Of... ?

•

Math L,eacnins Goa" ...,.. .... Display data usmg a cirele graph. .. BLM :U&.l

. .. Identify irw::euraci~ and bias in data. .. l'lprogram

AueumentOppoftumtlu

_ Minds On,..

_ACtionl

iroURS of'" :t AqiXltins erlor Know".Cut out and place the 10 bottom cells 00 BLM 3.HU in envelopes. Distribute oneenvelope to .eh aroop. the descriptions under the proper categorythe chart.

Whole Clm :t DiscuI,logUBe Day 5's collection ofdata 00 the amQoot oftime spent 00 h<:tmeWm'k todifiCUfis where there oould have been sourccs or bias in tbe datacollection, e,g., Does ·'b<:tmeWo!'k time" include time spent off task, asa taking lit phone can?Lead a ~ 00 the data you have I that the$tuJbtfi in oor school, 00 the averaae, minute!> 00 1lorlle\l'ori,"!"OifiCUfis how this: may be biased since ooly Grade 7 was !lUnfeveid.DiSl:iU$S that the data that is. a census for the class data {ifaU students provided

now~nts lit for the rcst of the rather than a census.

Individual :t erld!i!Students use a sp~bect program or create a circle by band based 00 thedata collected about homework, Pft)i)Ortion ofthehomework time actually on.

write "the that the that can be drawnfrom the grapb. graph with it.

CommunleatinglDemnnstration/Checkbric:A~s students' to int(~rpret

lit and to describe words.

~

~:Studenls~homework data fromTuesday tllroughFrtday.

CODed and provide~tol.ndMdual$t~as required

• Consolidate Whole Cia" .. $ummarl%lnsDebrief Prepare a sharedwrlting note to summarize bias in data ooltleetiOltl,

graphs, and data that either a sample or it

population. under ootlsidlm.ttiion.Revisit the di~lon about accnraey ofthe data cmlc:elmilllamount oftime !!pent on homework to set fmtbe nextround ofdata collectioo.

$$& Thinktopic SI1amdWritlng,

Hpme As;ttvttx or FYah!r<;lassroom ConlofidationSet up a recording sheet based on the criteria tor time spent on homeworkidentified in class, and collect detailed data on exactly bow the time is used.the data to with the class.Prepare a circle

TIPS4RM: Gr~ 7: Urllt 3 - COllEict, Orgart~e. arid AnalyM Oatil 24

3.10.1: What Doesn't Fit?

_~~ __ •• _~ ~ .. _~ __ ~~~._~~$~.~WM_~~_.~ __ ~ •• __ .~ _

~. Has a scale

: Represents data with pictures~~.~._._._._._.~.~._._._.~.~.-.-._.~._._._._.-._.-.~.~.~:~.~._.~._._.~._._.~.~._._._._._._.-.~._.~._._._.~.~'-'-'-

: Displays categorical data

: Has a title : A graph that shows data points

: Has a vertical axis

: Displays continuous data ' Uses fractions or percents

: Com.pares the parts to the whole : Divides a circle into categories

TIPS4RM: Gmoe 7: Unit;; - Coillilet, and Data 25

Unit 3: DaX.11: Investigating Mean•.Median, Mod.e, and. Outliers Grade 1

•.·i ~~-'::_ofQ1lti~ODd>e_Ofr()ll~tkI.~uh'll·(lltlll~

.. II_1m!: CU.,."lli

SeeUAS~

"MyProf~Praotk:e~ for a videoc:flp lWlmple.

Word Wall.. 0tl1ller

AssosmentOpportunities

Who'l C'MI :! BlvlU!Revi~ mean, median, and mode and informally usess prior knowledie ofthe

using an dataooBLM3.11.1.DiscWlS how meuUl'eS ofcentral tendency belp us to interpret data. Use coloured

cubes in columns 00, 4, 5,6, 7 tu represent these quantities and tudetllOfllltrate mean, median, and mode. R~ge oobm:lns ofcubes to clearlyUlumate the ofmean, and mode.Add asixth column cubes. mean, median, and mode. Rearratllecubeti; to reinforce increase in :mean and minimal increase inmedian. Note mean is altered by extreme values (outliers),the median is not lIigttific;antly a:l:'fec:ted

CumculumExpe.::tatwDll/Oral QnestiQuil:l.glMeutal Note: Assess students'

• MindsOn'H

• Actionl Whml Cia•• :! Data S!ltherlnsStudents illther dllta 00 the Might ofadults ~musicians, hockey players, relatives,teache:N.I in etc. and record it in centimetres.

InglXldual 7 C;onstructlng SIem-rang-Leaf PI.Students use collected dllta to construct a stem..and..le:afplot. calculating .mean,m~UaJl, and mode for the dllta set. Add ofbasketball players to the stem..an<lf·l~lf nl:ot Recalculate mean, mode.

Muresilltl, 231 em; Bogues, 160 em; Yao Ming,em: leBron em.

ComltruooooofllI.em-and4Mf ptQt!MY need to bemlewed,

StuderWl rmry Wl.mtto update ttI4s datawith the I't'lO$t~tNBAdatlii forpr~S$iooal

basketball playetli.

• Consolidate Who'l ClaM 7 01$%""_Debrief Discuss the effect ofadding beights ofbasketball n1avers (outliers) on each

measureAsk:... Was each measure affected Mllllathl?

.. Which mea~'tn'e would be most accurate of the expanded data

Thedl$~and

1.m$W$tli ... vary~il'l9 00 thesla of each dataset,

Stll,dettts :ll.:lSltify their answers.

Practice

l12me A;tivttx or Further Clas$room ConsolidationThe following test marks were collected: 75, 68.,47,55,88,16, 79,80,70,64, 73,Create a and calculate the mean, median, and. mode. Threestudents wrote the test late. Their marks were 98, 92,94.Did the new outlim affect the median more than the mean'! What is the bestmeuure for this data? your tbittkin:g.

TIPS4RM: Grade 7: Unlt:3 - CoUlllCI. and Data 26

3.11.1: Mean, Median, Mode

Measures of Central Tendency

Definitions and exampfel

M.e.AN' tA. ..)= sum of alt data"""'" •v·~v~ ,. pieces of data

, 4+7+13+11+19 6l>e,g" the mean of4,7, 13, 17, 191$ • ."" - '" 12

I) 5MODE: the number that oecul'S most often In the data set

e,g., for 3, 4, 6, 6, 6. 1, 7, 9 the~ Is £)

MEDIAN: obtained by arranging the numbel'lllin order and chooliling the middle number; where there is a evennumber of numbers, take the mean of the two middle numbel'Se,g" for 1 3 1 9 13. the median is 1

The measure of central tendency you use depends on the situation and what you are trying to discoverfrom the data,

Sam's record for the last 11 games:o 10 9 10 0 0 1 4 5 9 8

Coach has two strong basketball players. She needs to review both of their free-throw recordsas part of their MVP evaluation,

Robin's record for the last 11 games:2 6 6 8 0 2 6 10 6 6 4

Calculate the mean, median, and mode for both basketball records.What is the best record?

How do you know?

TIPS4RM: GI'~ 1: Unit 3 - COiled, Organlztft, and Data 21

Unit 3: Dar 12: And the Data SalSm Grade"

•

. Milt! wmina isll Mmldlll• Distinguish between facti and inferences. • BLM 3.12.1,• Analyse g1"l1phs to extrl'1ct informatioo from the data, rel~,tior,t$hilps within the

data, and use data to dnlw conclusions.• lnterpolate to make predictions within the StiPbed ~on.

AsllleumfitntOpportunities

• NtlnasOn... .. Corntfl :t BfllMIgtllPlace one ofthe following statementl in each. ofthe four oom.et$ ofthe room: DatIis Uke alipt...camem•.•library.• ,music Studentlgo to one ofthefour 00m.et$, based on their choice. In their comers, groupsdi~ the an~llOlY,

md then s.hare r~ and ideas with the larlergroup.

Alta~..~-foeu$QI1

the m.aSOl'ling.

ExU,fj GrgYH .. JlguwIn the same groups. oHom, each student selects ooe

etc., form and interpret the mean.ing ofthe "stI'aigibtgraph. The groups and make coovinl~ing argt1tmmtsgraph. Studentl return to their origmal groups and report on the WscU!l,sion.

groygs of .. :t lov,stisallODStudents discus and complete the on BLM 3.12.2 to coosolidate thecoocept of fact versus inference, mteroolate to malre medictious within the

ues. in each e.g., The .._"..... '" Sample at'IlIWem:F&W!aftw~_: torok 2 mintb$to get to tbe store.~twefor2

mlrn.lte$, took 5mlrn.lte$ to~ baek,~:~to the $lOre andI:laekata~rate, After 1 minuteJIiWd Is I'taffway tothe storllI•

H·tl1O'mllbie. Groups.

and what inferences.

00 each axis..

vv nat- mcu. CfID we be surecan be made?

•

Group! 2f .... R,adIDS gfleblForm offour with one student from etlCbdiscuss. complete the BLM :l.12.1 ,jm:tif}Jing

Whole Qlus .. Olscu!!loDGuide eft di~ioo 00 the 1imellingdjstalll::te from John'sStudents place appropriateAsk:• Arethe

• ActiOnl

Curriculum Expmations/Observatlon/Cherkbric: Observe students.' ability toand extract information from the data,

• Consolidate Whot, Cfa" -+ Di.saYSfi9"Debrief Discuss answers from 3.12.2,. paying particular attention to Part qu¢stions :;

and 4, and Part B, questions 4 and ,.

Home ActMtv or Further Clalsroom ConsolidationC~te a graph to teU the story ofyour trip to and from schoul. Write thewords.

in

TIPS4RM: Graoo 1: Unit 3 - Coliect. Organize, and AoolyseOata 28

3.12.1: Where Are They Going?

Match each graph to a story below. Write each letter beside Its story.

o "''''-----------108642

OK ~

500

11000

108642

500

11000

500

11000

Ok': 02 4 6 8 10 2 4 6 8 10

500

11000

Jared hurries to the store before It closes, buys then drives home more slowly.

Mona bikes to her work, but then remembers that she has forgotten her purse. She bikes- back home, picks up the purse, and bikes back to work.

~ Tanlka engages in her choice of daily physical education by jogging to school at aconstant rate of speed.

-L.....1-- John gets a ride to a friend's house. waits while his friend gets ready, then walks toschool with his friend.

TIPS4RM: Gfl\lde 7: Unlt 3 Colled. and AnalyM Data 29

3.12.2:. Mona's Bicycl.e Ride from Home to Work

1000

900

- llOl)e

I:J500J400!300

200

100

0

Mona's Bicycle

D

? 3 .. $ e 1 a i 10

rllTle(~)

Part A: InterPolating to Determine FactiUse information from the graph to help you determine the answers to the following questions.1, How far did Mona ride in the first 2 minutes (point A)?

How do you know?

2. How long, after retuming home, did it take Mona to travel 300 m (point D)?How do you know?

iY\i

Make up your own questions about points Band C:3,

4.

TIPS4RM: Grade 7: Unit;; - Collect, Organize, and Arl'\IJye Data 30

3..12..2: Mona'5 Bicycle Ride from Home to Work (continued)

Part B: Inferences1, Are there any stop signs between Mona's house and her work?

How do you knoW?

2, Was the purse close to the door?How do you know?

3, Could Mona come home for lunch?How do you know?

4, Work with your group to make up your own inference about Mona's bike ride,

5, Based on these questions and on your answers, what do you think is the difference betweena fact and an inference?

part c: Ton~ Has aGI,ss of Milk

~400~

¥ 300 , \:e I..15 2001::~100<:

o1 2 '3 4

Time (Seconds)

Are the following statements facts or inferences?

1. Tony drank the entire glass of milk. , ~> '1

2, Tony likes milk, _,,-<::>,,~'If::'

3. The glass was refilled only halfway, ,_-,

4, Tony asked for more milk after drinking the first glass, '" '-' __, .'-"'-

5, State a fact about Tony's drink of milk.

6. State an inference about Tony's drink of milk.

TIPS4RM: Grade 1: Unit ::I - Collect, aod Analy$li! Data 31

Unit 3: Da'

•13: Trends of Generosi

Malt belmlng GQlII,. Identify trends found in. data and graphs,• Bxtend a graph to make predictions (extrapolate) beyond the graphed a:rea.• Determine ifthe extrapolated data makes sense,

Grader

Mattd,ts• BLM3.13J.pl~

.ov~of

:u:u

Maeel.mentOpportunitieel

_ Minds On".

_Actionl

• Con$olidateDebrief

groups of .4 :t PIUImiSPresent the following data about test seores: ''Test I 89%. Test 2 93%.Test 3~ 97%. Bued on these rest scores. what mark: can. I expect to get onTest 81" JU$tify your answer.

student responds to the question individually. then they eonsotidateresponses in the centre space.Each group shares their group's response. Compare respoU$es.Lead students to understand that extendinll data to make prediction bas limitations,

Iml" GrOuQI :t f;;am'gfllRnStudents preview and orally identify featu.res of the text on BLM :3.13.1.Ask leading to help students lOOl1te the information.Students individually fiU in all ofthe missing information as indieated by shadedareas. They read the information that is given to complete the graphs or charts andwrite the textual information that is missing. based on data in charts or graphs,Students who finish earty can make an overhead of their graph for question 2.

Curriculum Exptletadons/AppUcadon/Rubric/Marking Scheme: Assessstudents' tointerotet and represent data.

Wnglt Cllss :t OiUYIsionDiscuss the answers from BLM 3.13.1 a vmety ofstudent "'. "4V"''''

Lead students to realize that 2,3,5, and 6 will have a variew ofoorrectanswers.

Home Activity or Further Chlls:room S:;;ons:olldltionWrite a note that summarizes and iIlU$trates the use ofdata to ideatify trends,Create a concept map all ofthe words on oW' Word Wall.

see Think' "",n,,,,,v'Math&mettiC6,~s 7-Q, pp, 2., S

CoflCept map(seelThlflkl.~Methelml!JtJC6.Grades 7-9, p.

TIPS4RM:Graoo 7: !Jolt 3 - Collect, and Oata 32

3.13.1: Generosity in Canada

Generosity in Canada: Trends in Personal Gifts and Charitable Donations overThree Decades, 1969 to 1991

for All Canadian Homesyears, the total average gifts or oontributioosper Canadian home rosein 1969 to $2018 In 1997 (includes money and gifts).

How generous are Canadians? How much of our lnoomas do we give to others? Are theredifferences in the generosity of people in different regions? Has our generosity changed overthe past 30 years?These are some of the questions addressed in a research report prepared by Senior SocialScientist Paul B. Reed as part of Statistics Ca.nada's Nonprofit Sector Knowledge Base Project.

Findings1. Average GM

Over the past.steadily from

$1293 1$1003 1$1151 I $1427 I $1751 I $2292 I$2018 I

1969 I 1978 1982 1992 11996 11997 I

2. The graph below shows the information above in graph form. and extends the data to showthe trend aU the way to the present (Make a graph by hand or electronically.)

'1 o;:::l~

3. Having data given in this way allows us to make inferences about charitable donations inCanada.It would be unreasonable to make the inference that in 10 years donations will double;however, here are some inferences that we made, based on the data given:

TIPS4RM: Gra<:Ie 1: Unit:.'} .. CoIl«:t, and Analyse Data 33

3.13.1 : Generosity In Canada (continued)

Data by.'.gion4, The chart below shows average donations for some of the regions of Canada,

This is a graphical representation of the same data,

;;;.-

1969 1918 1982 1986 1991 1_Yean;

5. Here are some other interesting facts about the data above:

6. Are there any aspects of the presentation Of this data that may be misleading?

A~mnn Statistk;$C~: Sector, Clll:af",gue

iIPS4RM: Gra<:I& 7: Unit 3 - Collect, and AMly" Dam

7SFOO33MIE, Issue 00, 4

M