Contents of Grade Level Planning Supports

Page'Circles

Talking about Clrel.Mysterious Circles• Investigating C and d using GSPCirCUlating Problems• Can You Hear the Radio?• Who Gets Wet?• Estimating the Area of a CircleParts and WholesGetting Your Piece of the PizzaComposition with CirclesRound Up - Performance Task

7275

78

86879094

Lesson Outline: Days Circles

BIGPlmYBI

Grade 8

••

•••

constant

18

19 Parts

•

•

•

1:1

cir'cuml:emeni~e and area of

Section Queen's Printer for Qntario 2004 (modified by n"Vi;;'t:\!

rulersa•

Da116: Talklna About Clrcl.. Grade 8I)tIcriptIon Mattrt••• Use circle vocabulary .. ~JlilldriCld objects

M i I:; • 'I .. chart peper• ' easure parts am Icatures em:: e, ..cir.cun1felreOice and the of

.. BLM 16,1. 16,2

.. hillJI!i~l:llers

~$flt

OpportunHiee

container !ids,cans. CDs, coins,circles on gymfloor, paper cups,clock faces, etc,

When returning

'I/Va'{8 to measurecircumference;Flexible tapemeasure,

me:aswred, e.g.,string/ruler combination.

Carrk1tJum E~peetatioIWQatlJMarJd.1 Key:

Whole CI_ ~ DIIcuntgnInform students that they will be

Discuss different thata ruler. Tlte G't;Y)Hltfter :f SA<,!/(~ftptf(i .("Discuss how to accurately measure a diameter.

ImJII Gf9UPI ~ PlaHmtdStudents fbm> small groups around a placemat with the question, Whatare some different and features ofa circle? After some individualresponse time, students a response in the centreplacernaL Facilitate a whole class that thedis:culsskm there will a assessment.Students C(}mplete a (BLM 16.1). Write a on the board for

the assessment ll{)w if a cifcle tltt:' s'(:tHle as or

Stress carefulmea$urementStudents shouldrecord theirobservalions to thenearesllenth of aem Student valuesfor C ... d may vsryfrom 2,810

used todemonstrateof a circlecoli$truction andmeasurement offeatures of a circle

to use calipers

Pan? Inv!fV.gationNumber a collection of objects with circular faces and in onelocation in the classroom, selects one item,1,"'1"""'" the instructions on BLM J6.2. Students the item after!1U';£ll:llrlrW it Students take measurements fur at least 6 itemsthe This and 'no' eXlJlmJ;llesconstant measurernent between circumference

division: 'no'

•

• COrl$olidamcDebrief

WboltCIIH_~Jivmmll'lzlna\'AI"'.)'''' '' the data collected, Be to discuss out! iers (data that doesn'tfit due to incorrect measurements or Discuss responses t()qwestl1cms 6 and 7, Guide to the that there is a relationshipbetween the circumference and diameter,

Home Activity or Further Cla••room Con.olloatiorl('JIU'l'lH Find other circular o!:liects at home in something that has a very

e.g" vehicle culvert, tree stumn. etc, Confirm that the rule works f{)f these

TiPS Section :3 Grade 8 Queen's Prinler for Qnlano, 2004 (modified bv 72

16.1: Looking at Circles

Highlight the indicated feature on each diagram.

centre-

arc

radius-

TIPS Section 3 Grade 8 Queen's Printer for Ontario, 2004 i.mm,,,,y~ by

16.2: Exploring Relationships Within the Circle

1 Select an object with a circular face,

2, Measure the circumference (C) to the nearest 0,1 cm. Record the measurement

3, Measure the diameter (d) to the nearest 0,1 cm, Record the measurement

4, Repeat the first three steps with different objects,

5, Do the calculations indicated in the chart Use a calculator and round answers to the nearest0,1 cm,

Object C d Calculations

C-d C+d C+d Cxd

6, Examine the "calculations" columns. What patlem(s), if any, do you see?

7, If possible, state a mathematical rule for any pattern you observed,

TIPS SectIon 3 Grade Queen's Prthter for Ontario. 2004 (modified by HeeS8) 74

Circles (GS~4 file)Circles,gso

Circles

---Radius:::: 2,0 emDiameter:::: 4.0 cm

Circumference :::: 12,6 em

Area:::: 12.7 cm2

Chord:::: 3.2 emF

G Drag to change size

Questions:1) Is there a numerical relationship between the lengths of the diameter and radius?2) Is a diameter also a chord?

TIPS4RM Grade B oow GSP lesoon -Insert after page 74 in Notable Stmlel'l~$

Day 17: Mysterious Cire_

PtHriltkm• fhrmulas for clr'curnte~rellce of a circle,

GradeS....- computer- ClllcullltofS

-BLMlfl,112-os!' !7.1

AuM......m

The TfPS Grade 7#Glilzcbo"

value ofrr

3.14 is an

De$crloo the home

liPIl,roxlima'tkm fOrrr. should

how

when therr button is uSfldon the calculator.Be cOl'lsi&tent anduse the rr buttonfOr aU calculatorcalculations

811:57 pm.

March 14 is calledrr and why

occur

InCludes dynamicsketches that canbe used to showanother method fordiscovering the

accuracy canchangillg the

Fa(oHiltate a about how to apply this about the lr ratio.Ask how the can be used to the circumference iHhediameter or radius is known and vice verS!l, Do the on BLM 172

Ensure that students know how to use the n: on a calculfatllfStudents work in to BLM 17:2

ClIrrieuJa.. ExpeaatioulObservatioDIMeatal NoW: Cin::ulalc to forUlH:It"f:;tarldillg how to use the circumference tormtlla,

'al" '7ED'orationStudents use the instrtlctions on BLM 17,1 to constrtlct a modelall<::rmltively use OSP 17.1 to exnlorethe ratio. data that confirms or

WJJ9It CIM '7 DilMJl<mDiscuss the dynamic exploration and wnetnierthe ratio to the dialme1:erName the constant as lr

two different exr1Iorati()l1

maCIm =t pilHlltQnfacilitate a discussion about the nh.,t>ftrldi,rtn<: from the preliiOlls

stui:lents to the that the of theCirl:unlfel'enl:e to the in any is a constant Describe the next

computer that will simulate what student'> did in the

• ConsollftteDe:brief

• Actionl

Home Activity or Futtbm: ClIUroom CoD!!2liddonStart your IT project"A Taste of PI." Your pr~lect can take the form

letter to the editor, or letter, some intlere:stirtgand List the first oftt Include an c>Q,tallation

11: is called an number. YOil canTwo websites }OU can are:

Yom ass.es:,ed fl)( accuracy lind eflective communication,

TIPS Sect,on 3 Grade 8 Queen's Printer lor Cotano. 2004 {modified by HCDS8\ Page 75

17.1: Investigating the Relationship between C and dUsing Thtl Geomettlr's Sktltchpad~

1, Construct a circle.Draw a line segment from the centre of the circle to the outside edge and label it torepresent the radius,Construct a line perpendicular to through the centre of the circle,Construct points where the perpendicular line and circumference meetHide the perpendicular line,Draw a line segment between the two points,label the new line segment"d' for diameter,label the circumference "" »

2, Measure the length of the radius (I) and diameter (0;,Measure the circumference (C).Calculate: C + d, C ~ d, C )( d, and C -+ dHighlight the four calculated values and create a table..Change the size of the circle by dragging the size control point.Double click on the table to enter another value.Repeat this step 5 times then look for a pattern in one of the columns.

17.1: Investigating the Relationship between C and dUsing The Geometer's Sktltchpad~

1. Construct a circle.Draw a line segment from the centre of the to the outside edge and label it torepresent the radius.Construct a line perpendicular to through the centre of the circle.Construct points where the perpendicular line and circumference meet.Hide the perpendicular line.Draw a line segment between the two points.label the new line segment"d' for diameter.label the circumference "C.

2. Measure the length of the radius (I') and diameter (0;,Measure the circumference (C).Calculate: C + d, C ~ d, C )( d, and C -+ dHighlight the four calculated values and create a table.Change the size of the circle by dragging the size control point.Double click on the table to enter another value.Repeat this step 5 times then look for a pattem in one of the columns.

TIPS Section:3 Grade 8 Queens Printer for Ontario. 2004 (modified 16

Investigating Regular Polygons (GSPI,l4 flle)Investigating Regylar Polygons,gsp

Investigating Regular Hexagons

A and notice whichmeewrementi change,

Colleet Evidence:To ida a new entry to the table, dragpoint A then double click in the table,Add severalltlWS to the fable,

Measurements

length of one side "" 1,98 emPerimeter = 11,88 emlength of Diagonal =3,96 em

Perimeter------ :; 3.00(Length of DIagonal)

PerimeterI length of Diagonal Perimeter (Length of DIagonal)

3.96 em 11.88 cm3,OO

-

TIPS4RM - Gmde 8 new GSP les$OO - insert alter page 77 in Notable Strategies

Investigating Regular Octagons Mea.u........ng

A and notice whichmeasurements change,

Collect EvIdence:To aaa a new entry to the table, dragpoint A then double click in the table.Add leveral rows to the table.

/~A

III.I1JIIlli_

5.09 em

Length of one $ide '" 1,95 emPerimeter:;: 15.57 emLength of Diagonal FG '" 5.09 em

Perimeter--------:;: 3.00(Length of Diagonal FG)

TIPS4RM ~ Grade e new GSP lesson - insert after page 77 in Notable Strategies

Investigating Regular Polygons (GSP~4 file continued)

Investigating Regular Decagons Measurement&

t A and notice whichmeasurements change.

Collect Evidence:To add a new entry to the tabfe, dragpoint A then double click in the table.Add NveraJ rowa to the tabfe.

Length of one aide:: 1.16 emPerimeter=: 11.51 emLength of Diagonal =3.7'" em

Perimeter-------:: 3.09(Length of Diagonal)

TIPS4RM - Grade 8 new GSP lesllOfl lnSl'.ut after page n in Notable Strategies

length of OM Side::: 0.44 emPerimeter::: 13.21 emlength of Diagonal =4.21 em

Perir'ltetEIr---..............--=314(length of Diagonal) .

4.21

,t A and notice whichmeasurements change.

CoIled. Evidence:To add a I'IGW entry to the table, dragpoint A then double ckk in the table.Add several rows to the table.

Investigating Regular Polygons with 30 SidesMeasurements

__iIII..: _: .. , :' ""."'.' ._,..",,,,,,,.,,.,,_, "'C'-"',··,.,·"'> _,,_', __ ' .. ", ,', _' "; ,8:1.., _,"", .,,_.'.'._ .._','' """,','"-. :_' ._.""" .' ..'.,'."',..,,_•.,.,:_., ;., 0,.5 _.• ".',,-.,,"'_ , __ .•., .., .•.,..•0; ..

TIPS4RM Grode e new GSP 16ssoo - insert after page 77 in Notable Strategies

Investigating Regular Polygons (GS~4 file continued)

Investigating Regular PentagonsB!!?re:•rag point A and notice which

measurements change.

Collect Evidence:To ida a new entry to the table, dragpoint Itt. then double click in the table.Add several rows to the table.

Aof Symmetry

4.09 em

Mea.u.......n.length of one side;:: 2.66 emPerimeter lit 13.30 emUne of Symmetry '" 4.09 em

Perime1er------ '" 3.25(line of Symmetry)

Perimeter

(line of Symmetry)3.25

TIPS4RM - Grade 8 new GSP lesson - insert after page 7710 Notable Stratliilgies

Investigating Regular Polygons with 15 Sides

:3.15

---=:3,15(Une of SymmelI')')

Measurements

Length of One Side :::: 1.11 emPerImeter::::: 16.69 emUne of Symmetry:::: 5.29 em

Perimeter

5.29 em

Collect Evidence:To .aa • new entry to the table, dragpoll'll A then double click in the table.Add severa! rows to the mble.

A and OOQ whiChmeasurements change.

A./--'"/"

( )\~

--

TIPS4RM - Grade 8 new GSP lesson - Insert after page 17 in Notable Strategies

17..2: Circus of Circles

Calcula. the miaaing meaaur•. Use a ca.lculator. Show your work.

a) hoop

d:::.:r=C:::.:

d) base of tent

r:::.:

b} surface of drum

d:::.: 40cmr=C=I

e) hoop waist

C:::.: 210 cmd:::.:r =;:) ...,.2.:;) (no,

c) surface of circular barrel

C=2.5mr:::.: ~ ""'"'d:::.: 1II ~

f) unicycle wheel

r:::.: 30 cmd:::.: It''1f)(

C:::.:

The unicycle wheel in part (f) made 1000 complete revolutions as it traveled down a road. Whatdistance did the rider travel?

''8

Queen'$ Printer lor Ontario. 2004 (modified by HCDSB) 77

a.pply the t<mnula the area circle, - llCissofs, lap<:/IlJue• paper (If

various-Ht,M lSI, 18J"

lS3

~nt

SOW' GroYI! -7 Brainatorm :t Inv!dIationPose the following problem:A is O!! fl chal!! that ,;, attache" to a staKe ill 17t<, an~a IIlat the,11'1'7 t''/m (J(.'Ct0I;f ir needy mbe ret;,itl{¥'d 1+/,~t.It,><"".

How can,lYJIf {~5'1illlat{' the (lI!lOtI!l/

Guide to corlcllrdeModelarea.

BLM IS.! and the rest BLM 182.their problem. The purpose ofthese two activities is

a forumla for the area ofa circle.

half of the smallthe instructions

to establish a need

• Action! ..,I GroUI!-7 §gIgmtionThe fi.rst three activities on BLM 18J involve the exploration of the area of a

l11e activities vary in Each group works on one of theactivities. group their actlvlllvClU'l'ieulum ExpeetatioulObservatioDIMeBta.1 N.te: tocommtmicatirm and

The radius of theis the

maximum dil'Jtancethe signal willreach Acircle withthis radius w!l!show themaximum area the

will cover

• ConsolidateDebrief

Whole CIm :t DllcupionDiscuss the mathematical students used in each activity Discuss thepros and cons method the area of a circle.Guide students to conclusion that the fbmmla f'()r the area ofa circle is A

the fi:lnnula to the word walLModel how to use the formula by the area of the circle f1.mnd onBLM 18.1 andior HLM 18.2.

Home Activit! or Further Ci_mom Con$OlidationComplete Activity 4 on the worksheet

Explain theinstructions for

4

TiPS Seclion 3 Grade 8 Queen's Printer for Ontario, 2004 (mc)dlfileld by HCDSB) 78

18.1: Can You Hearths Radio?

The radio station located at the satellite icon on the map broadcasts to most of Centraland Southem Ontario. Construct a circle surrounding the station to represent itsbroadcast area. Assume the signal comes from the tip of the antenna.

Determine where you would place a radio station in Northern Ontario so it covers thelargest possible area in Northern Ontario. The broadcast signal of this new station willhave the same strength the sOlllbern station.

(

TIPS Section *' Grade 8 Queen's Printer lor Ontario, 2004 (modified by HCDSB) 79

18..2: Who Gets Wet?

It is a hot day in June and to cool off, the class decides to use its outside activity break to play asponge toss, The students line up in rows as shown with 'fair ground' anywhere within therectangular outline shown, Students stretch on the spot The person near the middle of the fieldgets to throw out the first toss, He can throw it far enough to reach the person standing one rowahead of him, one place to the right Construct a circle to show all possible 'fair' landinglocations for the sponge,

~

~

~

t

t

t

~

t

~

~

~~/ ~

~

~

t

t

t~

~

t

~

~

t~

t

t

The person standing in the upper right corner of the diagram can throw the sponge the samedistance. Construct a model of the possible 'fair' landing area for this student's sponge.

is the total possible 'fair' landing area for the sponge from tosses of the two sponges?~(!f\IO:t~many students might get wet from these two sponges? q _\

TIPS Section :3 ~ Grade 8 Queens Printer for Qntario. 2004 (modified by HCDSB) 80

18..3: Estimating the Area of a Circle

Activity 1: Circles Inscribed in Squares

Materials:Circle inscribed in a square, scissors, tape or glue, highlighter

Instructions:

Shade the square as illustrated in the diagram,What is the length of one side of 'IWhat is the area of the square? 'X. 0Use words to compare the area of the square to the area of one-quarter of

circle, greater than, than, equ

Shade a congruent square adjacent to the first square as illustrated in thediagram, Use words to compare the area of the two squares to the area ofone-half of the circle.

Shade a congruent square adjacent to the second square as illustrated.Use words to compare the area of the three squares to the area of three­quarters of the circle.

Cut away the three shaded areas covered by the squares which are not part of the inside of thecircle. Fit the cut out shaded area pieces onto remaining quarter of the circle. The piecesmay need to be cut into smaller pieces to fit inside the circle,

Compare the area of 3 squares to the area of the circle.Do the shaded pieces completely cover the remaining part of the circle?

Jason said: The area of a circle is just a little more than three times its radius squared,(Area of a circle) > 3r

Confirm or deny his statement based on your exploration.

TIPS Sechon:3 Grade 8 Queeo's Printer for Ootano. 2004 (modified by

18.3: Estimating the Area of a Circle (continued)

Queen's Printer for Ontario, 2004 (modified by HenSB) 82

3.9.2: Unusual Dart Board

This dart board Is designed with a squareInside a circle and a square outside thesame circle,

Assign numerical values of 2, 5, and 6 tothe three coloured regions on the dart boardsuch that regions with smaller areas areassigned higher scores.

Justify your solution.

r..-···~li•.'lr.../.. /1l"'\ . . ... I

L::~,,~~_J

TIPS4RM - Grade 8 -ln~ after page ae in Notable Strategies

paper

• scisSOl'll

AssessmentOpportunities

Wholl CIUI ~ Small GrgupStudents discuss their Home Activity explaining their reasoning, andwrite up a solution to share. The class goes on a gallery walk to view thevarious solutions.

Curriculum Expectatiolls/QuizlMarking Key: Students cOlnpllete:t9J).

•Unit 3: Day 9: Unusual Dart Board Grade 8

Mlth bgm'ag iill, MI{.datl• Apply formula for area ofcircles in problem-solving situations. • BLM 3.9.1,

3.9.2

• Minds On

• Action! Small Group! 'iASlxIYDiscuss th.e pme ofdarts and how scoring works to set the context for theproblem. Use dart board problem from Continuum. and Connections ~

and Volume, Pl'. 25~31. Select groups to record then solve onchart paper (BLM

• ConsolidateDebrief

Whole GrQup 'i Ol,eu!sGroups their solutions. Share as ll'lI.'tfiy solutions a,'l possiblle.

In!flvid"al -+ Bispon,e JoumllStudents reflect on aU the different ways that the dart board prOblem wassolved writinst up at least two different solutions.

Home Activity or Further Classroom Consolldgtlon

6cm

----:rocm--+

I. The clock in Ii ha,,, the dimensions shown. Explain how youwould determine the surface area ofthe fuune ofthe

2. Describe how you would determine what of the surface area. isface ofthe clock.

\

18.3: Estimating the Area of a Circle (continued)

Activity 4: Triangles from S·quar. on Circles

Diagram 1:The length of the side of the square is the same as the length of the radiusof the circle,

Diagram 2:Kim cut the square into 4 congruent triangles and placed the squares ontothe circle as shown in the second diagram.

Questions:How many squares will Kim need to completely cover the circle? !(Notice that part of each triangle extends outside the circle),If the side of the square is 5.0 cm long, thena) what is the area of one square?b) what is the area of one circle?Give reasons for your answer.

Diagram 1 Diagram 2

TIPS Section - Grade 8 Queen's Printer for Ontario (modified HCDSB) 85

formulas f'hr and area i.n SOlVing

GradelMItmjJII• tmelion circles• chart pilper,

marker• index cards

An~

Cooslderconlpll!l~ing III fewindElx illadval"lt:e. Thesecan be usedstudents whonot thellSl'lignmel'lt butwho can stltl~nefit from this

new

in the call;;ulation

the assij~nments (sroden!ts

WbRIt ClaM ~ ilvlOot=GttOoeStudents share one interesting point from their

shares one fromnartner<; andDraw the on a Cluun n problem oncomer of It rectangular doghouse, Illustrate a ofchain that is

the lenlrth Students describe how toaccess· to, Facilitate a that results

Students identify a that the

,.191.'7 BtfIectkmDistribute one index card to

it that

an answer,

Calculatorkeystrokes mayneed to bereviewed,

Stress goodcommunication,

quarter {nr <:nrt>l{'''''''

a marker and one fraction......rim..t"'r and area of their fraction

callculat!ing the .....1';"''''1<.,.

Palra ~ PmSleeStudents determine the surface area ofa penny,~. ,_.. ".""'"'~ in the cfnl)sn:,omi),

Curriculum E~.~"atioul5lMe.taJ Note: ,"",,,.,,,,,,,,,,ufthe fbrmul~ and use Qrder of"pe"1'ltl,)llS,

lmall GmJmJ 7 DIHuM'ou<Jive t¥dch group one piece ofcharta set of fracltlon

• Action!

• COMoSI..l)ebrtef

small imp! ~ PlJItntationaEach gmup its solutions on chart paper,

students

ExtendingQues.Uon ,can beoffered as achallenge to some

Hom! Aclbfty PI' Fw:tbl! C""room CPDIOlidaUqnResearch: Call two pizza restaurants or use thelntemet to find and record thesize the numher and the fhrpejpptlrOl11 and cheese Make sure you ask whether the measurements are

in centimeters or inches,the problem the dUlln the side

do~~house is 2m x 3m and the chain iscan walk ifthe chain is

can walk on?

TiPS Section:3 Grade 8 Queen's Printer for Ontario, 2004 HCDSBl 86

18..3: Estimating the Are. of a Circle (continued)

Activity 2: Clrcl•• and Parallelograms

Materials:Fraction circles

Instructions:

Arrange the eight, one~eighth fraction pieces to form a "curvy" parallelogram,Arrange the 12, one~twelfth fraction pieces to form a different "curvy" parallelogram,

Jessie recalls that the area of a parallelogram is (base x height),

She considers the arrangement of fraction pieces to be a parallelogram and she reasons thatthe height of the parallelogram is the radius (r) of the full circle,

She further reasons that the base of the parallelogram is half the circumference of the circle,(2m.;. 2), which is TTl: With all of this information, Jessie concludes that the area of the

"parallelogram" is

Jessie concludes that the area of a full circle is

Do you agree or disagree

Give reasons for your answer.

Jessie's reasoning?

Section' ,. Queen's Printer for Ontario. 2004 (modified by HeDSEl) Page 83

18.3: Estimating the Area of a Circle {continued)

Activity 3: Circ'. on Grid Paper

Trace the circle below onto centimeter grid paper.Colour the squares it completely covers,Estimate the area of the circle, remembering to think about the partially covered squares,

How could you use a similar method to get a more accurate answer?

TIPS Section:3 - Grade 8 Queen's Printer for Ontario, 2004 (modified by HeDSEl) 84

area in problem

GradeSI1ttti1I8• overhead (> f BtJv1

10.1• BLM2(),2

Auessment

WboJ! elm -+ Data <;gIfectionSome students record their data from 19 on an overhead of Bl..M 2<)JModel severa! to emlVert from to em.

Add some#!maginarY' pizzaprices,necessary.

IS5S <e'Ui X

x 2.54 em 1 inch 45.72 ern2.54 cm 21.65 inches

To consolidateconversionsbetween fradions.decimals. andpercents. stUdentscould Wile

geometry sldillil tothe sedor

of eachexpress sizepiece as a

fraction of thewhole a.nd thenconvert the fractionto a decimal and/orpercent

area.

whenI,;W;;;C:;:>C. inclusion of

based on

the information ga!there{1

least t"vrn>n"iVf''rl""'tih' the most

&mall GroU" -+ AdvbStudents complete BLM 20.1 onfrom the oreVIOlllS

Who" Groul! -+D*_Facilitate a discussion on thedete'l'mil1ing "best .. e,g.. thickness

Individual ~ QuaStudents complete qUiz: \rndVI

ClInifltlam E~tioulQld7JMarldJlIKey: Circulate to deterl11dneditlferentitrted needs tt)r home activitv.

• Actionl

• ConsolidateDebrief

Individual ~ BMQOf!U JournalStudents choose a company from which

their choices,would their and

Home ActMtx or Further Clg.room Con80lildon1 Pepperoni covers a fraction of the surface ofa pepperoni and

Describe how you would determine percentage area covered

The crust of a is like a rim aroundthe centre If this "rim" is 2 em wideand ifthe has a of30 cm then how would you tlnd thesurtace area of the "rim" Describethe you would take in yoursolution,

omwklt

TIPS Section :3 ~ Grade 8 Queen's Printer for Ontario, 2004 (modified by HeeSB) 87

20.1: Pizza Prices

ItemNumber

SlmotLarge Pizza(diametel)

Number ofSlic•• Cost Areaot

PizzaCost per1000cm2

Rank forLowest

Price perUnit Area

Write a concluding statement about marketing strategies and the best value for your money.

TIPS ~ Section 3·- Grade Queen's Printer for OntariO, 2004 (modified by HeeSB) 88

20.2: Developing Proficiency(from TIPS Section 2)

Grade 8

Nama:Date:

emficitnm:Target Met.[Practise occasionally to maintain or improve your proficiency leveL] 0Still Developing[Search out extra help and practise until you are ready for df IVlIlt:/1 0opportunity to demonstrate proficiency>1

1 Determine the area of each shape, Showyour wot*

'/~

~"'.Jcm

Answer: .......;=--..;;;;~;..;;..:...f.

b)

l1ldiult .. 3.3 em

Answer:"l....

2, Determine the perimater of each shape. Showyour work

a)

C7t1ldkIlI .. 2.7 em Answer: • , '" •

Answer: • '-" • . v ,~,-

b)

Section:3 Grade 8 Queen's Printer for Ontario, 2004 (modified by 89

in ",..",hi",,,

Gradel

MaWftII• eLM 2l!, 21

2U,21A• graph paper

~t

Mathemati~ for

Think

differentiating by

eXllfm~)les fromto know the

Students one or twocreate a circular llin,ln\lp.

their possibly an outdoor $\C'livl'lv

that lands closest to them. Students read the hidden question and thinkabout a Volunteers share and responses to the qu~~sti(ms.

stuJdents to estimate the them and location thelanded. Then ask students to the area

est:imllrted distance is the distance their

Wb9tt CluJ o71raiDIfQrmBrainstorm a tist of shapes that have circular

e.g. Lead a discussi<marea or oorimeter of the

ImliYkllI8t~ ...QUMtiQD'.

• Action!

areadiness.

GSP2USkateboard Parlegsp can be used tocreate similarcomposite shapes,

Wh. CluJ 7 Mwvring NflIn preparation for the next day's activity, the school field or

area. Tell that area is: now to become amini-track and races:. Measure the dimensions of the area atrundle

in fbrtbe

• CormofidateDebrief

Moll Clue 7 Di$!tYHionDiscuss the connection between the circumferencea trundle to measure distances.Lead a on the de(:on1!x)sltionhome activitv lBLM 21

wheel and

Home AdYUY or Ful1btl CIMSf'!i!9!D ConsolidationDetemline the area of the model of the skateboard park on worksheet 2! A.

{ tllY'Pm' Pmctkc Create a model ofthe area fiJr the track

Opti0l1al: Create a crossword puzzle with terms from this unit of

- Section:3 Grade S Queen's Printer for Ontario, 2004 (modified by 90

21.1

Instructions

How to Build a Circular Paper Airplane

1. Fold the paper in half horizontally then re-open the paper.Refer to the fold you created as the half~Une,

Fold the bottom half of the paper in half horizontally to the half line.Refer to the new fold line as the quarter-Une, Do not unfold this time.

3. Fold the top of the new "flap" to the bottom of the paper to the quarterRefer to the new fold line as the eighth~Une,

4, Hold the three layers of paper at each end, Flip the whole sheet horizontally so that the foldsare now farthest away from you,

5. Fold the new top edge to the ha!f~line, (See side view below.)Then re~fold the half line,You should now be looking at a paper with four folds in it, and should see only half of thesheet.

6. Now roll the paper lengthwise into a loop. Then, slide the folded ends into each other andoverlap approximately 5 em.

Your circular paper airplane is thrown like a football with the folds forward.

Top "unfolded" view of sheet and folds

Half line

QuarterSide "folded" view ofsheet and folds

-------Quarter line

Half line

TIPS - Sedion:3 Grade Queen's Printer for Ontario, 2004 (modified by HeDSB) 91

21 ..2: Composite Figures

1) Area (A) Circumference (C) 2) Area (A) Circumference (Cl

AS'" 3.0 emC '" 18J3cmA'" 25,()em2

CB"'4.8emC'" 15.1 emArt: 18.1 em:!

s

3) Area (A) Perimeter (P) 4) Area (A) Perimeter (P)

CB=4.0emP =18Aem

A = 22J5 cm2

DB "'6.5em

A'f£ 18.8cm2P rt: 1€L8 em

5)Area of "rim" '" 7.2 ern;:;:

~6.7ern ~

~5.2ern~

6)AS'" 7.Bem A _AC"'7.0ern .""'l'C .......

Area'" 16.2 cm2

The brokenHnes arediame~r$

c

Area (A)AS'" 3.3 emAC'" iOem

p", 285 em

A'" 61.1 em2

The brokennoes arediameters.

Perimeter (P)

c

8)

OB '" 2.7 em00'" 2.1 em

Unshaded area'" 99 cm2

TIPS Section Grade 8 Queens Printer for Ontario, 2004 (modified by HeDS8) 92

:r n o (j)

.S!:!

__, 22: Round U

Rllcr.lJ!lon.. Performance task

Grade 8

MatedIII• Bl.M22.!

~mem

PIIII -+ Dl!cuRlgnStudents share solutions to Studentsthe race area.r'\=il"".;•••".·ih" home as a whole class,

CuJTi.eumm EJ;~tlouIModellRgbrie: Circulatetrack

Ensure that eachstudent has amodel fuat wmallOW them tooorrlpfeite thepen'omlarH:Je task

asp 22,1,

can be tod'leck studentresponses or todebrleftheperformance task

IndMiMIJ -+ P,r:f2r.mI.uH rIBStudents il'ldividlUlHy do BLM 22,1,CuJTi.euJum Ex~tlouJPerformauee TukIRulnie: EVlllluliteaccuracy ofcoml'uttltiol1, al'p,ropriatene:ss oil' mathem:alica!

• Action!

• ConsolidateDebrief

WbIIt ClMf -+ DJRUHionBegin preparing students for the next unit

Home ActivItY or Further ClJHmqro Consolidation\lVhen returninggraded work tostudenl$, consIder

3and <\. responseswith studentnames removedSelect anddiscus!!, with theclass, thatshow a ofstrategies.

TIPS - Section 3 - Grade 8 Queen's Printer for Qntano, 2004 (modified by HCDSB} 94

ern

Each square is 1 cm by 1 cm.When calculating, round all values to the nearest tenth.

1. Calculate the perimeter of this figure. (Show all ofyour work.)Label all the unknown line segments and arcs.

050e\e5!l )( tt- 1r)'l.

2-:= 2Lf.

::

::

TIPS4RM: Grade 8: Unit 3 - From Powers to Circles

2. Calculate the area of this figure. (Show all of your work.)Try to find shapes that you already know, then add or subtract the area, as required.

Fi (I xl :2\

22..1: Track and Field

Your school is going to use part of its school grounds to build a two-lane track,

1, Determine the dimensions of the space available for the track,Sketch a model of the area and record dimensions on the model.

2, Add a two~lane track to the model of your school's available area,Determine appropriate dimensions for the two~lane track,Record the dimensions on your modeLRecord enough information so you can calculate perimeter and area,

v:f

3, Compare the distances for one complete lap for a runner each lane,Show all work and state any assumptions you make, e,g" the runner uses the centre part ofthe lane, or the runner uses the innermost part of the lane,

t'f'\MI'\I.:>t.:::. for alumDer of racer would haveby

4, Explain how to find thenot show calculations,

5. Your school is going to place grass sod in the middle of the trade Determine the size of thearea that needs to be covered with sod,

6, Create and solve a problem based on your two~lane track,

TIPS _. Section·~ 8 Queen"s Printer tor Ontario. 2004 (modified by HCDSEl)