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8.EE.A-Work
with radicals
and intergerexponents.
8 . E E , B - U n d e r s t at n
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8,EE.C-Analyze
andsolve
linearequations
andpairs
linear
of simutaneous
equations
8.F.A-Defi
ne,evaluatp,
and '<+,t'cLlla1 a-r, (
compare
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8.F.B-Use
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modelrelationships
betweenquantities.
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congruence
andsimilarity
usingphysical
models,
transparencies,
or
geometrvsoftware.
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? 9 hat'('cor.ul
Family ReunionPicture
Assessment
Task
Franceswent to her family reunion. They took a picture of the family.
i3
IA
ruffi
I|rtt
R
:imt
;TW
r 6
/\"bs ri ..
pr'\.
'
tl
>r'
i
J
cE
Francesdrew a graphof the family memberscomparingtheir agesto their heights.
Familv Reunion Picture
A
o
b
e
Height
Performance
Task
Family ReunionPictureTest 8
PI
O Sificon Valley MathematicsInitiative2013. To reproducethis document,permissionmustbe grantedby the
SVMI [email protected]
1. Underthepictureis a placeto write eachfamily member'sname.Matchthe
nameof the family membersto eachof the peoplein the family picturein
orderfrom left to rieht.
2. Dana is five times as old as Alex. Write an expressionto show the
relationshipbetweenDana and Alex.
3. Two yearsago, Elam was half as old as Dana. Write an equationto show
the relationshipbetweenElam and Dana.
4. Elam is currently 31 yearsold. How old is Alex?
Show how you figured it out.
tr
Performance
Task
Family ReunionPictureTest 8
P2
O SiliconValley MathematicsInitiative2013. To reproducethis document,permissionmustbe grantedby the
SVMI [email protected]
2073 MACRubricsGradeB
Family Reunion
Rubric
The coreelementsof performancerequiredby this taskare:
Expressions
andEquations
Analyzeand solvelinearequationsandpairsof simultaneous
linearequations.
8.EE.7.Solvelinearequations
in onevariable.
8.EE.8.Analyzeandsolvepairsof simultaneous
linearequations.
8.EE.8.c.
Solvereal-worldand mathematicalproblemsleadingto tvvolinear equationsin two
variables.
Functions
Define,evaluate,andcomparefunctions.
8.F.2.Comparepropertiesof two functionseachrepresented
in a differentway (algebraically,
graphically,
numericallyin tables,or by verbaldescriptions).
MathematicalPractice:MP2 Reasonabstractlyand quantitatively.
MathematicalPractice:MP5 Use appropriate
tools strategically.
polnts
sectron
points
Based on these. credit for specific aspectsof performance should be assigned as follows
l.
Givescorrectanswers: Bo, Chris, Dana,Alex, EIam, Glyn, Frances
All sevencorrectlyplaced
3
Six or Five correctlyplaced
(2)
Fourcorrectlyplaced
(l)
2 . Givescorrectanswer:
I
D=5A
a
-).
J
I
Givescorrectanswer:
E-2=Yz(D-2)
2
2
4. Givescorrectanswer:12 yearsold
I
Showshow theyfiguredit out suchas:
3 1- 2 = V z ( 5 A - 2 ) , 2 9 = V z ( 5 A - 2 ) , 5 8 = 5 4 - 2 , 6 0 = 5 . A , A= 1 2
I
2
Total Points
8
(c) SiliconValley MathematicsInitiative2013. To reproducethis document,permissionmustbe grantedby the
SVMI [email protected]
MACTest8
2073 NIACRubricsGrade8
Family Reunion
Rubric
The coreelementsof performancerequiredby this taskare:
Expressions
andEquations
Analyzeand solvelinearequationsandpairsof simultaneous
linearequations.
8.E8.7.Solvelinearequations
in onevariable.
8.EE.8.Analyzeandsolvepairsof simultaneous
linearequations.
8.EE.8.c.
Solvereal-worldand mathematicalproblemsleadingto tvvolinear equationsin tvvo
variables.
Functions
Define,evaluate,andcomparefunctions.
8.F.2.Comparepropertiesof two functionseachrepresented
in a differentway (algebraically,
graphically,
numericallyin tables,or by verbaldescriptions).
MathematicalPractice:MP2 Reasonabstractlyand quantitatively.
MathematicalPractice:MP5 Use appropriate
tools strategically.
points
scctlon
points
Based on these. credit for specific aspccts of performance should be assigned as follows
1. Givescorrectanswers: Bo, Chris, Dana,Alex, EIam, Glyn, Frances
All sevencorrectlyplaced
-t
Six or Five correctlyplaced
(2)
Fourcorrectlvolaced
(l)
2 . Givescorrectanswer:
I
D=5A
a
J.
J
I
Givescorrectanswer:
E-2 = Yz(D-2)
2
2
4. Givescorrectanswer:12 yearsold
I
Showshow theyfiguredit out suchas:
3 l - 2 = V z ( 5 A - 2 ) , 2 9 = V z ( 5 A - 2 ) ,5 8 = 5 4 - 2 , 6 0 = 5 A , A = 1 2
I
2
Total Points
I
(c) SificonValleyMathematics
permission
Initiative2013.To reproduce
thisdocument,
mustbe grantedby the
SVMI [email protected]
MACTest B
Bell Peppers
g i ve syo uth ech a n ceto:
T h i sp r o b le m
. workwithnumbersand graphsin an everyday
situation
Hereis a recipefor stuffedbell peppers
fbr 2 people.
Stuffed Bell Peppers
Servestvto
1 red bell pepper
6 cherrytomatoes
I arlichoke,cut into quafters
- teaspooncapers
I
1 tablespoor-r
olive oil
Method
" Cut the pcpperin half andtake out seeds
. Put threecherrytontatoesand two quartersof
artichokein eachhalf of the pepper
. Sprinklethe capersover
. Dnzzle with olive oil
. Bake for 45 rninutes
l . Michellervantsto cook stulfedbell peppcrs
tbr 6 people.
Completeher Iist of ingredients.
red bell peppers
cherrytomatoes
arlichokes
teaspoons capers
tablespoons olive oil
Michelle cuts the artichokesinto quarters.
How many quartersare there?
O 2010by l\,,lathematics
Copyright
Assessment
ResoufceSeruiceAll rightsreseryed.
^t
Y^NF
4
Bell Peppers
2. Jin is havinga par1y.
l l o w m a n yb e l l peppersi,vill he needfor 40 people?
Explain liow to figure out the nurnbelof bell peppersneededfor any number of people.
3. Wliich line, A, B or C in this graph showsthe number of cherrytornatoesrrccdedlor
dil'ferentnumbersof people?
a
c)
c'1
fi
c)
()
-)
ti
a)
-)
(-
z
u
10
40
50
Numberof people
Explainhor,vyou figuredit or-rt.
Copyright
O 2010 by Mathematics
Assessment
ResourceSeryiceAil rightsreserued.
P:nc
5
Bell Peppers
Bell Peppers
Rubric
The coreelementsof performance
requiredby thistaskare:
. useratioin an everydaysituation
. interpret
a graph
section
points points
Eased on these, credit for specificaspects of performanceshould be assignedas follows
2
Givesfive correctaltswcrs
I
; r i t ' t i ,1 ' , , ' , , i '
l(rll\
L (rll
Partiul credit:
Four ol tlrreecorrectanswers
(l )
I
(lives correctansrver:l2
2.
3
Givescorrcctansrvcr:20
Givcs correctcxplauatiorr
srrchas: Dividc tlrenunrberol'peotrlle
by 2.
2
.1. Givcs correctansrver:A
I
(iives a correctcxplanationsrrchas:
You neecl-l tornatoesIor each persor.t
or 30 tontatocsfor l0 pcople:thesc
v a l u e sa r eo n l i n e A .
I
7
I otal tsoints
8'hGrade- 2010
C o p y r i g h@
t 2 0 1 0S V M I
All rightsreserved.
')
25
Name
Date
E|Partv
You invited17peopleto your housefor a par1y.You want
to spenda $50 gifi
cardcornpletely
on the itemsshown.You alsowantto haveexactlytwo servinss
of fbod for eachpersoli.
GIOIt[NNr'
lliril;lt)I'ilza
$6.00
4 Servings
$7.00
5 Servings
1. Write a systemof linear equationsthal represents
this situation
2' How'rany pizzasshourdyor.rbuy? How many bags
of wings shourd
you buy?
3.
'l'he
priceof a bagof wingsincreases
to $7.50.Now how manyof.each
iternsliouldyou buy?Explain.
4. Assumea bagof wingscosts$7.50.your friendtellsyou
thal by spending
just .ne dollarin additionto thegift
card.vo. rviil hauemorelbod options.
FIowdoesthis changethe systenrof rinearequationsthatyou
wrotein
Exercise1? Ilxplainwhy your friendis rieht.
C o p y r i g h tO B i g l d e a s L e a r n i n g ,L L C
All rights reserved.
Big ldeas Math
PerformanceTasks
15
CommonCoreStateStandard
tlffI
E
8.EE.8 Analyzeandsolvepairsof simultaneous
linearequations.
a. Understandthat solutionsto a systenrof two linearequationsin two
variablescorrespondto pointsof intersectionof their graphs,because
pointsof intersectionsatisfyboth equationssimultaneously.
b. Solvesystemsof two linearequationsin two variablesalgebraically,
and estimatesolutionsby graphingthe equations.Solvesimplecases
by inspection.
c. Solvereal-worldand mathematical
problemsleadingto two linear
equationsin two variables.
GradingRubric
Answers
Score
1. 6x'r 7y : JQ
z
4x+5y=J4
2 . 6 p i z z a s , 2 b a go f w i n g s
2
3. Thereis no combinationof itcmsthat meetsthe requirements
becausethe systemof ecluations
that represents
thissituationhas
no solution.
4. The first equationchanges
to 6x + 7.5y = 51.'fhe two equations
now representthe sameline, so any point on that linc will be a
solutionof the system.
z
z
Precision
1. Studentunderstands
how to usethe given infbrmationto write a
systemof linearequations.
2
2. Studentsolvesthe systemof linearequationsalgebraically.
I
3 . Studentrecognizesthat the systemhasno solutionand
understands
how that appliesto the situation.
4. Studentappropriatelysubstitutes
new valuesinto the equation
from Exercise1. Studentrecognizes
thatthe two linescoincide
and understands'uvhat
thatmeansin this situation.
Total Points
16
Big ldeas Math
PerformanceTasks
2
2
15
C o p y r i g h@
t B i g l d e a sL e a r n i n gL,L C
All rightsreserved.
Parallel and Perpendicular
MAC Assessment
Task
You are helpingyour friend graph lines on the coordinateplane.
II
l-i-
tl
tl
II
l-l-l
ltl
t_t_
t_t_l-rli
-t-I
li
l_t_l
_i_t _l_
_i_t I
_i_l
_i_l
_t_l
Ill
tl
t-tII
I
-t-ltl
_t_
_t_
I
_t_t_
_l
I
-t-l
tl
-i-l t l
tl
tl
Draw a line on the coordinateaxesthroughthe points (-3,4) and(-I , -2).
Label the line J.
2. What is the slopeof line J?
MAC Test8
Paralleland Perpendicular
P9
O Silicon Valley MathematicsInitiative 2011. To reproducethis document,permissionmust be grantedby the
SVMI [email protected]
3. Write the equationfor the line J.
4. Draw a line K on the graphparallelto J that passesthroughpoint (3, 1).
Explain how you drew it to ensurethat it was parallel.
5. Determinethe equationof line L perpendicularto J that passesthrough
p o i n t( - 3 , 4 ) .
Show how you figured it out.
6. Explain how the slopesof lines K and L arerelated.
Where do thesetwo lines intersect?
Show how you figured it out.
MAC Test8
ParallelandPerpendicular
P 10
permission
O SiliconValleyMathematics
Initiative2011. To reproduce
thisdocument.
mustbe grantedby the
SVMI [email protected]
Rubric
Parallel and Pernendicular
The coreelementsof performancerequiredby this task are:
Functions 8.F
Define, evaluate, and compare functions.
3. lnterpret the equation y = mx + b as defining a linear function, whose graph is a straight
line; give sxamples of functions that are not linear.
Expressions and Equations 8.EE
Understand the connections between proportional relationships, lines, and linear
equations.
5. Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Analyze and solve linear equationsand pairs of simultancouslinear equations.
points
8. Analyze and solve pairs of simuhaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables
correspond to points of intersection of their graphs, becausepoints of intersection satisfy
both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate
solutions by graphing the equations. Solve simple casesby inspection.
MPI Solve problems and perseverein solving them.
MP2 Reason abstractly and quantitatively
MP5 Usc tools strategically
section
points
Based on these,credit for specific aspectsof Derformancc should be assisned as follows
I
Draws a correct line through (-3,4) and (-1, -2)
I
2. Givescorrectanswer:-3
I
3
Write a correctequation:y = -3.x - 5
I
o"
Draws a correct line parallel to J and give a correct explanation such as: The
slopc of the line must be the sameas line J which is -3.
I
I
I
I
I
5
Write a correct equation: y = Ulx + 5
I
Shows a correct way to figure it out such as:
m= li3, 4=ll3(-3)+b, b-5
a
l
Gives a correct explanationsuch as:
The slope of line K and line L are negative reciprocals of each other.
I
Gves the correct point of intersection:(ltz,tttz)
I
Show a correct way to frgure it out such as:
The equalion of line K is y = -3 .x + l0
So -3x *10 = l/3'x + 5
x=3lzandv=11/2
I
Total Points
Coptngrno2014 by Silis Vallcy
MathcmrtB Initiatile. Afl igftts |eryed
2
3
9
Test 8
Patrick's Pattern
Assessment
Task
Patrickbuilt the following patternmade up of regularoctagons,non-regular
hexagonsand squares.
Pattern1
Pattern2
Pattern3
1. How many squareswill therebe in pattern 6?
2. Write a function that links the number of squaresto the number of nonregularhexagons.
3. If there are 27 squaresin the pattern,how many regular octagonswill there
be?
Show how you figured it out.
Performance
Task
Patrick'sPatternTest 8
P3
O SiliconValleyMathematics
Initiative2013. To reproduce
thisdocument,
permission
mustbe grantedby the
SVMI [email protected]
number of regular
4. Write a function that links the number of squaresto the
octagons.
many non-regular
5. If thereare 106 regularoctagonsin the pattern,how
hexagonswill therebe?
Show how you figured it out.
to non-regular
6. Write a function that links the number of regular octagons
hexagons.
L'l
Task
Performance
Patrick'sPatternTest 8
P4
this document,permissionmustbe grantedby the
o SiliconValley MathematicsInitiative 2013.To reproduce
SVMI [email protected]
Rubric
Patrick's Pattern
The coreelementsof performancerequiredby this taskare:
Functions
Use functionsto modelrelationships
betweenquantities.
8.F.4.Constructa functionto modela linearrelationshipbetweentwo quantities.Determinethe
rateof changeand initial valueof the functionfrom a descriptionof a relationshipor from two (x,
y) values,includingreadingthesefrom a tableor from a graph.Interpretthe rateofchangeand
initial valueof a linearfunctionin termsof the situationit models,and in termsof its graphor a
tableofvalues.
Expressions
andEquations
Analyzeand solvelinearequationsandpairsof simultaneous
linearequations.
in onevariable.
8.EE.7.Solvelinearequations
MathematicalPractice:MP7. Look for and makeuseof structure.
MathematicalPractice:MP8. Look for and expressregularityin repeatedreasoning.
pornts
section
polnts
Based on these. credit for specific aspectsof performance should be assigned as follows
I
Givescorrectanswer:6
I
2. Givescorrectfunction:
h= s- 1(accepts = h +l)
I
3 . Givescorrectanswer:56 regularoctagons
I
I
I
Showa correctway to figure it out suchas:
2(27\+2
I
y =2s+2
4. Givescorrectanswer:
(accepts = (y -2)12)
2
I
I
5 . Givescorrectanswer:51 hexagons
I
Showa correctway to figure it out suchA S :
106-4=l02andl02l2=51
6 . G i v e sc o r r e cat n s w e rJ: = 2 h + 4 ( a c c e pht = y l T - 2 )
Total Points
I
2
I
I
8
OctagonTile
Tlrisproblemgivesyouthe chanceto:
: :'Ly.ilhj*'::':1*i3:
I{ere is a designfor a tile in the shapeof a regularoctagon.
Thc designis made frorn eight squaresall the sarne
sizeplacedsymrnetrically
ror-rnd
the octagon.
I . .loineightpointsin thc cliagrarl
to make anotlrerregularoctergon.
2.The innersidesof the sqllaresform a 'star' in centreof the tile.
I-low many sidesdoesthe star have?
Copyright
O 2010 by l\rathematics
Assessment
ResourceSeryce All rightsreseryed
P a g e8
OctagonTile
3. Draw in all the lines of syrnmetryof the star.
I lorv urany lines of syrnrnetryclclesthe star have'?
What is thc anglebetr,veen
cachline of syrnnretryand the ncxt'i
Fixplainhow you knorv.
4.
A
A n g l e A i s 1 3 5 ' .C a l c L r l a the
t e measureof angleB.
Show your work.
['e]
O 2010by l\,4athematics
Copyright
Assessmenl
ResourceSeruice.
All rightsfeseryed
P a g e9
Octagon Tile
Rubric
OctaqonTile
.
.
The coreelementsof performance
requiredby thistaskare:
' workwithpatternand shape
seciton
points p o i n t s
Based on these, creditfor specificaspectsof performanceshould be assignedas follows
^
Draws a correctregularoctagon
2.
3.
a
L
Givescorrectansvver:l6
I
l)rarvsin all 8 correct lines of synrrnetry
I
Ciivescorrectansw'ers:
8
Ift
lfr
22.5
Givescor'fectcxplanationsuchas: -160'+ 1 6= 2 2 . 5
Partiul crctlit
Divicles360 by a nunrlrerothcr than 16.
o t ' I t t c o n t P l c tccr P l l t n t il t r t t .
2ft
(l)
5
4.
I
Givescorrectansrvcr:-15
Shorvscorrectn,ork srtchas ( 3 6 0 - 9 0 - 9 0
I
135)"
)
'I'otal
8'r'Grade- 20l0
@ 2010SVN4I
Copl'right
All rightsreserved.
Points
l0
72
Name
Date
capture
@Tank
You anclyour friendareplayinga ganrervhereyoll glressthe possiblelocations
of eachothers'tanks.
You eachplacetanksat pointson a 10-by-10coordinate
grid.Your rernaining
tanksarepositioned
as shown.
trffiffiK
CAPTURE
10
li;,r.
1. Your friendguesses
the point(5,9).Find the distancebetweenyour fiicnd's
guessand your nearesttank. Roundyour answerto the nearesttenth.
2. Your friendguesses
thepoint(7,7). Find the distancebetweenyour friend's
guessandyour nearesttank.Rour-rd
yor"rranswerto the nearesttenth.
3. Your fiiend givesyou a hint by tellingyou thata tankis located10 units
'fanks
from the origin.
can be positionedonly at whole numbercoordinates.
Whatarethe four nossiblelocationsof the tank?
4 . Y o u g u e s st h ep o i n t( 1 . 6 ) o n o n et u r na n c tl h ep o i n t( 1 . l 0 ) o n t h en e x tt u m .
Your friendsaysyollr guessesrvere3 unitsoff and 5 unitsoff, respectively,
fiom oneof thetanks.Whereshouldyou guessnext?Explain.
C o p y r i g h@
t B i g l d e a sL e a r n i n gL,L C
AIIrightsreserved.
Big ldeas Math
PerformanceTasks
15
-II
CommonCore StateStandard
IX|I
w
8.G.8
Apply the Pythagorean
Theoremto find the distancebetweentrvo
pointsin a coordinate
system.
GradingRubric
Answers
Score
1. 3.2units
2. 5. 1 units
3 . ( 0 , l 0 ) ,( 1 0 , 0 )(, 6 ,g ) ,( 9 , 6 )
4
4. ( 4 , 6 ) ; ( 4 , 6 ) i s 3 u n i t sf r o m ( 1 , 6 ) a n d5 u n i t sf r o m ( 1 , 1 0 ) .
Becauseof the grid boundary,the tank must be to the right of
( 1 , 6 ) a n db e l o w( 1 , l 0 ) .
Z
Precision
1-2. Studentusesthe Pythagorean
Theoremto find a distance.
3. Studentusesthe PythagoreanTheoremto find points that are a
given distancefrom the origin.
z
4. Studentusesreasoningto guessthe generallocationof the tank,
then usesthe Pythagorean
Theoremto find a point that fits the
givendescription.
2
Total Points
16
2
Big ldeas Math
PerformanceTasks
l4
CopyrightO Big ldeasLearning,LLC
All rightsreserved.