> KMJ` bjbj .6J4&$. pVL$&h*SSS.SSSSJ?M=S@0pSxMdxSSxg"Sp. . . . . . 4$"FRealLife Proportions
Activity Summary: In this activity students will use proportions to determine the relationship between similar figures. Then, they are taught to apply those proportions to real life problems. The students will calculate the height of their school building using similar triangles. They can also check their accuracy by calculating their own height and comparing it to their measured height.
Subject:
Math:
6th Grade:
6.1 (C) Represent reallife situations with integers
6.2 (C) Use multiplication and division in problems with equal ratios and rates
6.2 (C) Use multiplication and division in problems with equal ratios and rates
6.2 (D) Estimate and round to approximate results
6.3 (A) Describe proportions using ratios
6.3 (B) Represent ratios and percents with models, fractions, decimals
6.3 (C) Use ratios to make predictions
6.5 Formulate an equation from a problem situation using letters as unknowns
6.6 (A) Use angle measurements to classify angles as acute, obtuse, or right
6.6 (B) Identify relationships involving angles in triangles and quadrilaterals
6.8 (D) Convert measures within the same measurement system
6.11 (A) Identify and apply mathematics to everyday experiences
6.11 (B) Use problemsolving model to answer questions
6.11 (C) Select or develop an appropriate problem solving strategy
6.11 (D) Select appropriate tools to solve problems
7th Grade:
7.2 (A) Represent multiplication and division with fractions and decimals
7.2 (B) Add, subtract, multiply, and divide fractions and decimals to find answers
7.2 (D) Use division to find unit rates and ratios in proportional relationships
7.2 (F) Select and use appropriate operations to solve problems
7.3 (B) Estimate and find solutions to application problems involving proportions
7.5 (B) Formulate a possible problem situation when given a simple equation
7.6 (A) Use angle measurements to classify pairs of angles
7.6 (D) Use critical attributes to define similarity
7.9 Estimate measurements and solve problems involving length
8th Grade:
8.2 (A) Use appropriate operations to solve problems
8.2 (B) Add, subtract, multiply, and divide rational numbers in problems
8.2 (D) Use multiplication by a unit rate to represent proportional relationships
8.3 (A) Compare and contrast proportional and nonproportional relationships
8.3 (B) Find solutions to problems involving percents and rates
8.6 (A) Generate similar shapes using dilations
8.9 (B) Use proportions in similar shapes to find missing measurements
8.14 (A) Identify/apply mathematics to everyday experiences
8.14 (B) Use problemsolving model
8.14 (C) Select an appropriate problem solving strategy
8.14 (D) Select from among various tools to solve problems
Grade Level:
Target Grade: 8
Upper Bound: 8
Lower Bound: 6
Time Required: 12 Class periods Activity Team/Group Size: 13Reusable Activity Cost Per Group [in dollars]:
The only cost of this activity is the cost of the yardstick/meterstick, which can be reused, and the paper for printouts to the students. A tape measure is also required to measure the shadows. The tape measure is reusable as well. SI units are preferable, in order to get students more familiar with the metric system, but materials can be adjusted according to availability.
Authors: Undergraduate Fellow Name: Andrew Shuff, Victoria McCallum
Graduate Fellow Name: Bruce NgoTeacher Mentor Name: Mrs. Stallings Date Submitted: Jan. 2, 2006 Date Last Edited: Jan. 9, 2006Activity Introduction / Motivation: Ask the students how they would go about measuring the height of their school building.Activity Plan: To lead this activity follow the HYPERLINK "Proportions.ppt"PowerPoint associated with this activity. Follow the notes and slides in the PowerPoint. In the part where the students go outside to measure the shadows of the building, the yardstick, and themselves bring a tape measure for measuring. When picking a time to measure the shadow, remember the longer the shadow is the more accurate the result will be, but the harder it will be to measure. Also remember that the length of the shadow can change as the sun moves so the students will have a limited amount of time to measure. Have the students complete the attached HYPERLINK "Proportions%20Worksheet.doc"worksheet. The students can record their data and calculations on this page.
An alternative to the outdoor activity with building measurement is to use a spotlamp indoors. Mount the lamp as high as possible and use it to cast shadows of students and other objects. Students can then measure the length of the shadows and the height of a known object in order to calculate the height of other objects. This way, it will be easier to obtain the actual measurements and compare them to the calculated measurements in order to discuss concepts like measurement error and so on.Activity Closure:
What are some possible reasons for inaccuracies for measuring your height?
Do the triangles created by the shadows stay similar for a long period of time?
Why not?Assessment:
Do a couple more problems with similar shapes.
Concepts for Teachers:
 right triangles
 right angles
 similar shapes
Vocabulary / Definitions:
right angle an angle measuring 90o
similar two things which are not the same size, but have the same relative dimensions
Materials List:  yardstick/meterstick
 tape measure
 tall building
Activity Extensions:
Try more examples with similar triangles. There is also another activity under the Teacher Requested Resources at peer.tamu.edu called Scaling the Statue of Liberty (or other buildings) which deals with scaling.Multimedia Support and Attachments:
HYPERLINK "Proportions.ppt"Proportions PowerPoint file (proportions.ppt)
HYPERLINK "Proportions%20Worksheet.doc"Proportions Worksheet
)*+I@ T t v
w
y
̹yncVcOcVchNhchNhcB*H*phhNhcB*phhNhB*phhB*phhnhhZHhhhhvymhvymB*phhvym5B*\phh%5B*\ph$jhGWh%5B*U\ph#h%hvym5B*CJ0\aJ0ph#h%h($5B*CJ0\aJ0phhN5B*CJ0\aJ0ph B
7^IA
u
v
1$7$8$H$^`gdcH$gdvym$xH$a$gd%
pN
?(h>vH$^`gd*H$gdvym1$7$8$H$^`gd*
./24Rbļļ~ļwoewawhZHhhvym5\hvymB*phhhh!p8B*phh!p8h!p8hz5B*\ph#hB*CJOJQJ^JaJph#hvymB*CJOJQJ^JaJphhvymB*phhvym5B*\phhNh*B*phhNhcB*H*phhNhcB*phhNh*hNhc%c%$+v
&8GXYu+;<ROH$gdvym6K$%;DZhxz$&46WXstuݻݴݭݔ}tph.C`hh0Jjh!p8Uh!p8jhUhhh!p8hvymB*phhZHhhZHhvymhZHhZHh*h*h*B*phhB*phhvym5B*\phhvymB*phhhhZHh*h&;hh,"6*
$%&XYru·¨·¡}vn] h'8h'8CJOJQJ^JaJh'8B*phh'8h'8hvymB*phh'85B*\ph hp1hp1CJOJQJ^JaJhp1hvymh\7B*phh\7h\7hvym5B*\phhvymB*phh=Xh\7h\7h.C`0J
h*0Jjh!p8Uh!p8jh\7Uh.C`h*!*;<PQR')LOPklmƾƾƾpfYh'8h'8B*\phh'8h'80J\'jh!p8h!p8B*U\phh!p8B*\phjh'8B*U\phh'8B*phh'8B*phh'8hvymhZHh'8h'8hvymB*phhvym5B*\phh'85B*\ph h'8h'8CJOJQJ^JaJ#h'8h'8CJH*OJQJ^JaJݿhaL%h+zB*\ph
h=X0J\h'8h'80J\jh'8B*U\ph'jqh!p8h!p8B*U\phH$gd,1h/ =!"#$%Dd
0
#Ab_둧z!9uDnm_둧z!9PNG
IHDR@@%sRGBIDAThCZI#Gvȝ$3dUuWuFx6i$7>?w6؇1
=izQwګY%bI֨x `{ŋIʲm>Jؠ5IjTU
ih5K"Nh^YcH""LD'RWV^}G4dD=KA'%?hOQ,hJ+Js&a~KjE5_օZcza("?J#`z=O U&
R2~7ϾjB(ў!: e&TA0LGcsoNYe?_\HOaHͳ/[\nmW5eAΆo_oF}QrUTyfD6 0zXx,)1Iiq.Iͮݹp!ivn_/^vjcEC =r,KcyU!y/4XQi1̚j~?ä6,Q(4.T]D՟nZ3"A,u+/4WN;~x81[g"FOQ'ժkKXeQ0%4EٍZs{VtY4JqkѺbkujN *4bBU4{muڣ=U}bemv^';%[yz֥0?m_([f}gR<'zt{"B.1EQ!>
n]
RA"="9J;hkSW=OWQEJS(&Ҋ&\ǂ#(U
{]+&I T8b>ľ3IRʺ¢N`*S84 *"8A!AU%[>gF} Ap^b>0;08U6~0(0 n~W@}̅C~<,`s"/iUWgx@00pk;vf;Xu(͑XϹro^EOA{!~pftO`S".V7CelS^oG+zLA K(2pMKqw0.1~
lp*h'^~C}$a2!i1*m9kS0ɩ%w:.K~Ww(ҭfQR0b *[q WLS6nKĜ&[/c`vܝ^>xX+j䷀
נʘ
^=a1!ߒ<@'~*$&;=S'
zQܿѭQ
xqf:HxfC/vX r*`Q04'b8qT FqA8.9
&1?2YLaV4s NEg˽89NTonͩ~Bܜfۜ_;vw2RFC0sFٯA*zzCyno]}m8_ܞa &4mufunX˶
BpnW)~$Tc@QXbZi90'ñxpFiQzv;]/ɒLDT`10~3=8 >S'7`Q;
昐sAvAu?0+ZȓtϏ+xz9`ʃW\Zx6G
GdinqYn
0{_y?lGcBx.P0K+ BvFzLI6 IcTE. ag.UDVU1L+UbaQ}_kx>Xxb
JbB=~œM 2&QT 0m)VUӆ)8҄M[Z5 ŮN冴f4]J{7ڹ)/ۻ~ф$ژ
x"ywls(V?:hriZ.,tMض7 gO9O:U_~4e'TloJ$vfeCZj2\rLݪ?Fm.,R.QEO*3)øHHԃ@_Y(gN
y
@,r`Qs41DY4{~
J(%7'AμL< ƇE#@Jd{oc/Ϩ#i>4O60Rq&hs?dY``l,6qU6L"`Ԧ9AQ}}x>/c:җVxyzo?q8[=8.dW a.ʣ5X1Doqb,m%0(#,JCр ^}Kc'bu#Ƿ7
R }VHHOpAv õSa
Zowoْ/,9age﹠MUѲzx*]SafI?xjpNHAPr~HZFt^q;`>=>wPٹڗ\4֞
]kOzh*QCC<ITbaB<מ7xn;<"M8RJ76PGsT]x
YD9;A'
7j6H299zGa)¨Mz0517%':_̃
O01/+%=4&S@եc@)'I5c AX>lXes=QR<ÃCZgW^eB
r6nyi^?bƼV Xs*":aop^"7Գ$> RRxQy[(Gx7re?Wu~s:ju:4N?N2H`xfZEf
QW$=9uam(9xRQXd0U ݳ
a2NFT<_Hx\Rk!X'1`_Eց Dt(d?,bR>duAͫ <;!^h.kّ "(yz@]iԈ"JE!%)^x]fӡ0BBpL0LQDd!7J"2^~1cvQ~Qkxb҉Wa4kb*f6wFlSE R_MaE ꓪQi\8"WbqPLYYEDVkܛ?'Z1 Ǒ=VMT̺_Dsm?L`8.c=Y仙qb%FɈdĂL=8U
V!$G1u!pV?C*B*HӪ;I%d8 OáOO!"JGqT&D՚YETRA]FڀW V7ЖVÏ1z}8BݚIX m`sR_avURIf6,MEnn6d!
@ÜJel cg[X%TsMdB]IENDB`DyKF
PROPOR~1.PPT$Proportions.pptDyKF
PROPOR~1.DOC82Proportions Worksheet.docDyKF
PROPOR~1.PPT$Proportions.pptDyKF
PROPOR~1.DOC82Proportions Worksheet.doc@@@NormalCJ_HaJmH sH tH DA@DDefault Paragraph FontRiRTable Normal4
l4a(k(No List6U@6 Hyperlink>*B*ph6 W$ W }?#B7^IAuvpN
?( h
>
v
c%
$+v
&8GXYu+;<RO!Y!4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!v:!v:!v:!!!!!!!!!!v:!!!!!!!!v:!v:!!!!!!!!!B7^IAuvpN
?( h
>
v
c%
$+v
&8GXYu+;<RO000000000000000000000000000000000000000000000000000000000000000000000000000000
WtOlXXXXVҝWҝD9*urn:schemasmicrosoftcom:office:smarttagsplace8*urn:schemasmicrosoftcom:office:smarttagsCityێ
qy+3
Ze(:?IPuz"1::::::::::::
&Yu+EIJMNYZ\]fgjkwx@EFKLTt
/6FJMOPUVYZdfhinoqruv~
#
;
@
A
D
Z
]
_
h
z
}
W
!'(+,23569:=>CDFGJKSTXY]^_`ghnoqrvwyz#*Oxy]7*($%aL%p1V4'8!p8&;ZHN.C`cc7pjvymz+zn])\7**=XwN@'3@@UnknownGz Times New Roman5Symbol3&z Arial"qh4&J&it)it)!243QKP ?72RAs you fill this out, fill in all the blanks (___) and delete the red instructionsljlab Bruce NgoOh+'0(< P\

TAs you fill this out, fill in all the blanks (___) and delete the red instructionsljlabNormal.dotBruce Ngo5Microsoft Office Word@d@@I=it՜.+,D՜.+,<hp
)SAs you fill this out, fill in all the blanks (___) and delete the red instructionsTitle 8@_PID_HLINKSA Proportions Worksheet.doch)Proportions.pptProportions Worksheet.doch)Proportions.ppt
!"#$%&'()+,./0123456789;<=>?@ACDEFGHILRoot Entry FeM=NData
E1Table*xWordDocument.6SummaryInformation(:DocumentSummaryInformation8BCompObjq
FMicrosoft Office Word Document
MSWordDocWord.Document.89q