westest 2 mathematics - west virginia department of...
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Changes to the WESTEST 2 Math Section
Types of Questions on Mathematics Test
Multiple Choice
Gridded Response items – 2 per test
Format of Mathematics Tests
More reading because of the 21st century context.
Graphic organizers when appropriate.
Opportunity for multiple strategies to be used.
Student engagement encouraged.
Content of Mathematics Test
Objectives as per CSOs
Rigor based on the DOK of the CSO
Content relevant to the student
Mathematical Tools
Rulers
Calculators are permitted on all sections of the mathematics
test for all grade levels.
M.O.3.1.9 Demonstrate and model multiplication (repeatedaddition, arrays) and division (repeated subtraction,portioning)DOK2
ManyunusualanimalsliveontheplanetHtml.
Someofthemhavebodiesthataremadeofcubeshapes.
Theseanimalsgrowbygettingnewcubeshapesoneachbirthday.
WhenBabyBoxapedeisbornitlookslikethis.
Itis1cubelongandhas2legs.
Onitsfirstbirthdayithasgrown.
Itis4cubeslongandhaseightlegs.
TheBoxapedecontinuestogrowinthisway.Oneachbirthdayitgetsmore3cubeshapesand6morelegs.
1. How long is a Boxapede when it is 10 years old?
a. 10 b. 18 c. 31 d. 80
2. Scientists are studying how Boxapedes grow. One of the Boxapedes is 16
cubes long. How old is this Boxapede?
a. 4 b. 5 c. 8 d. 16
3. Another Boxapede that the scientist is studying has 20 legs. How old is this
Boxapede?
a. 2
b. 3
c. 4
d. 5
4. When Boxapede was 7 years old he had an accident. As a result of the
accident, he lost 4 of his cubes. How long was he after his accident?
a. 3
b. 11
c. 18
d. 28
M.O.3.2.1 Analyze and extend geometric and numeric
patterns (DOK 2)
1) Find the missing piece of the pattern shown below:
_________
a: b: c: d:
2) Look at the number pattern below.
2, 5, 8, 11, ____, ____, ____, ____, ____, ____
Determine the pattern.
What number will be the tenth number in the pattern?
M.O.4.3.1 Identify, classify, compare and contrast two‐dimensional (including quadrilateral shapes) and three‐dimensionalgeometricfiguresaccordingtoattributesDOK1
Aspartofyourpreparationformathfieldday,completethefollowingchartindicatingwhentheattributeisalwaystrueforthefigureandthenanswerthequestionsbyfillinginthecirclenexttothebestanswer.
1. Which polygon has more of the featured properties?
a. Rectangle
b. Quadrilateral
c. Rhombus
d. Square
2. Which attribute(s) is/are not shared by both the square and the rhombus?
a. Equilateral
b. Equiangular
c. 4‐sided
d. None
Attributes
Types of Polygons Equilateral Equiangular 4‐sided
Rectangle
Quadrilateral
Rhombus
Square
3. Which attribute is shared by all four of the shapes?
a. Equilateral
b. Equiangular
c. 4‐sided
d. None
4. Which shape(s) are equilateral?
a. Quadrilateral only
b. Quadrilateral and rectangle
c. Rhombus and square
d. Square only
5. Which shapes are equiangular?
a. Quadrilateral and square
b. Square and rectangle
c. Rectangle and rhombus
d. All of the shapes
M.O.5.4.7Collect,record,estimateandcalculateelapsedtimesfromreal‐worldsituations(withandwithouttechnology)DOK2
Theclasswentonafieldtrip.Thestudentsleftschoolat9:00a.m.Theyreturnedtoschoolat1:30p.m.Howlongweretheygone?
a. 8hours30minutesb. 8hoursc. 4hours30minutesd. 4hours
M.O.6.1.4Analyzeandsolverealworldproblemsinvolving:addition,subtraction,multiplicationanddivisionofwholenumbers,fractions,mixednumbers,decimalsandintegersandjustifythereasonablenessbyestimation.DOK3
OnBill’sfootballsquad,1/3oftheplayerswalktopracticeand25%aredrivenbytheirparents.Theremaining15playerstakethebus.Howmanymembersareonthefootballsquad?
a. 48b. 24c. 36d. 30
M.O.6.4.4Developstrategiestodeterminevolumeofcylinders:solvereal‐worldproblemsinvolvingvolumeofcylinders,justifytheresults.DOK2
Afarmhasaverticalcylindricaloiltankthathasaninsidediameterof2.5feet.Thedepthoftheoilinthetankis2feet.Ifacubicfootofspaceholds7.48gallons,abouthowmanygallonsofoilareinthetank?
a. 59gallonsb. 75gallonsc. 230gallonsd. 294gallons
M.O.6.4.4Developstrategiestodeterminevolumeofcylinders;solvereal‐worldproblemsinvolvingvolumeofcylinders,justifytheresults.DOK2
A water tank has the shape and dimensions as shown above.
At the beginning the tank is empty. Then it is filled with water at the rate of one
liter per second.
Which of the following graphs shows how the height of the water surface changes
over time?
M.O.7.3.3 DOK 2 Apply rotations, reflections and transformations to plane figures and determine the coordinates of its transformation.
Triangle DEF is reflected on the y‐axis to create another triangle, what are the coordinates of point D in the reflected triangle?
a. (3, 4) b. (3, -4) c. (-3, -4) d. (-3,4)
M.O.7.4.1Selectandapplyanappropriatemethodtosolve(including,butnotlimitedto,formula)justifythemethodandthereasonablenessofthesolution,givenareal‐worldproblemsolvingsituationinvolving:perimeter,circumference,area,surfaceareaofprisms(rectangularandtriangular),volumeofprismsandcylinders,distanceandtemperature(Celsius,Fahrenheit).DOK3
Jimmywantstoknowhowmuchfencingheshouldbuytofencehisyard.Whatdoesheneedtocalculate?
a. Theperimeterofhisyardb. Theareaofhisyardc. Theheightofthenewfenced. Bothaandbabovee. Alloftheabove
M.O.7.4.1Selectandapplyanappropriatemethodtosolve(including,butnotlimitedto,formulas)justifythemethodandthereasonablenessofthesolution,givenareal‐worldproblemsolvingsituationinvolvingperimeter,circumference,area,surfaceareaofprisms(rectangularandtriangular),volumeofprismsandcylinders,distanceandtemperature(Celsius,Fahrenheit).DOK2 Which net best represents the triangular prism shown below?
A C
B D
M.O.7.4.2 Use the Pythagorean Theorem to find the length of
any side of a right triangle and apply to problem solving
situations. (DOK 2)
Jim needs a ladder to be able to climb onto the roof of his house. His
house is 15 feet tall and he sets the ladder 5 feet from the house. What
is the minimum length ladder (to the nearest tenth) he will need to use
to reach the top of his house?
M.O.8.2.3Addandsubtractpolynomialslimitedtotwovariablesandpositiveexponents.DOK1
Simplify:(x2‐5x+4)–(5x2+3x‐1)
a. ‐5x2‐2x+3b. ‐4x2‐8x+3c. ‐4x2‐8x+5d. ‐5x2‐8x+5
M.O.8.4.3SolverighttriangleproblemswheretheexistenceoftrianglesisnotobvioususingthePythagoreanTheoremandindirectmeasurementinreal‐worldproblemsolvingsituations.DOK3
Twostudentsareusingameasuringtapetomeasurethelengthofaroom.Theymeasureittobe13feet6inches.However,thestudentatoneendisholdingthetape9incheshigherthanthestudentattheotherend.Whatisthedifferencebetweentheirmeasurementandthetruelength?
a. About9feetb. About3.5feetc. About½footd. Nodifference
M.O.8.5.5Drawinferences,makeconjecturesandconstructconvincingargumentsinvolving:differenteffectsthatchangesindatavalueshaveonmeasuresofcentraltendencyandmisusesofstatisticalornumericinformation,basedondataanalysisofsameanddifferentsetsofdata.DOK3
Ifeachdatapointinadatasetismultipliedbythesamenumber,whichofthefollowingstatementswillbetrue?
a. Therangeisunaffected.b. Themedianisdoubledregardlessofthenumberused.c. Themeanisequaltotheconstanttimestheoriginalmean.d. Theinterquartilerangeremainsthesame.
M.O.8.5.4Analyzeproblemsituations,gamesofchance,andconsumerapplicationsusingrandomandnon‐randomsamplingstodetermineprobability,makepredictions,andidentifysourcesofbias.DOK3
PlayersAandBareplayingagame.Onatablebetweenthemisastackofpennies.FirstplayerAremoveseitheroneortwopenniesfromthestack.ThenPlayerBremoveseitheroneortwopenniesfromthestack.Theyalternatethiswayuntilnopenniesremain.Theloseristheplayerwhoremovesthelastpennyfromthestack.
Ifyoustartthegamewith7penniesinthestackandyouwanttobethewinner,whichPlayerwouldyouprefertobe?
a. PlayerAb. PlayerBc. EitherAorBd. Notenoughinformationtomakeachoice.
MA.8.5.2Investigatetheexperimentalandtheoreticalprobability,includingcompoundprobabilityofaneventDOK1
M.0.8.5.3 Create and extrapolate information from multiple‐bar graphs, box and whisker plots and other data displays using appropriate technology. DOK 2 Twenty‐five people watched a movie showing at the Empire Theaters. Of them,
fifteen order a drink, eight order popcorn and seven order candy. Two people
order all three items, three order drinks and candy, five order drink and popcorn
and three order popcorn and candy. Organize the information in a Venn diagram
and use your display to find the probability that a moviegoer chose not to eat
popcorn or candy and only ordered a drink.
a. 6/15 or 2/5
b. 9/15 or 3/5
c. 6/25
d. 9/25
M.O.A1.2.2 Create and solve multi‐step linear equations, absolute value equations, and inequalities in one variable, (with or without technology): apply skills toward solving practical problems such as distance, mixtures, or motion and judge the reasonableness of solutions DOK 2 The spreadsheet below contains 20 cells. A cell in a spreadsheet can be identified first by the column letter and then by the row number. For example, the number 10 is found in Cell C4.
A B C D E
1 6 ‐3 7 1 5
2 12 ‐4 8 2
3 18 ‐5 9 3 ‐35
4 24 ‐6 10 4
If the number in Cell A3 = B4 – 3(E2 + D4), which of the following must be the number in Cell E2?
a. ‐21 b. ‐15 c. ‐4 d. ‐12
M.O.G.3.19 Create and apply concepts using transformational geometry and laws of symmetry, of a reflection, translation, rotation, glide reflection, dilation of a figure, and develop logical arguments for congruency and similarity. DOK 3
Triangle DEF is reflected on the y-axis to form triangle D’E’F’, what is the relationship of the coordinates of ΔDEF and ΔD’E’F’?
a. The x-coordinates are the same on both triangles while the y-coordinates are opposites.
b. The x-coordinate and the y coordinates are equal to each other in the triangles.
c. The y-coordinates are the same on both triangles while the x-coordinates are opposites.
d. There is no relationship between the coordinates
M.O.G.3.7Makeconjecturesandjustifycongruencerelationshipswithanemphasisontrianglesandemploytheserelationshipstosolveproblems.DOK2
Let ABC be any triangle.
Quantity D = Measure of angle 1 + Measure of angle 2
Quantity E = 90 degrees
What is the relationship between the quantities?
a. Quantity D > Quantity E
b. Quantity E > Quantity D
c. Quantity D = Quantity E
d. Relationship is indeterminate
M.O.G.3.13Investigatemeasuresofanglesformedbychords,tangents,andsecantsofacircleanddrawconclusionsfortherelationshiptoitsarcs. DOK2
ABisthediameterofthecircle.ThelinetouchingthecircleatpointDisatangenttothecircle.QuantityX=Measureofangle1+Measureofangle2QuantityY=Measureofangle3
WhatistherelationshipbetweenQuantityXandQuantityY?
a. QuantityX=QuantityYb. QuantityX>QuantityYc. QuantityX<QuantityYd. Relationshipisindeterminate
M.O.G.3.13Investigatemeasuresofanglesformedbychords,tangents,andsecantsofacircleanddrawconclusionsfortherelationshiptoitsarcs. DOK2
Quantity A = Measure of angle 2
Quantity B = Measure of angle 1
What is the relationship of the Quantities?
a. Quantity A > Quantity B
b. Quantity A < Quantity B
c. Quantity A = Quantity B
d. Relationship is indeterminate
M.O.A2.2.15
Identify a real life situation that exhibits characteristics of change that can be modeled by
a quadratic equation; pose a question; make a hypothesis as to the answer; develop,
justify, and implement a method to collect, organize, and analyze related data; extend the
nature of collected, discrete data to that of a continuous function that describes the
known data set; generalize the results to make a conclusion; compare the hypothesis and
the conclusion; present the project numerically, analytically, graphically and verbally using
predictive and analytic tools of algebra (with and without technology). (DOK 4)
Note: The following item is a DOK 3 to accompany the above CSO.
The city is constructing a skate park near your school. In order to create a parabolic ramp, at least 3 points are needed to define the exact shape. The machine that fabricates the ramp needs the information in the form of an equation in order to create the ramp. The ramp is 30 feet wide and has a depth of 15 feet. The top left side of the ramp is designated with the point (0, 0). Complete the chart and graph below in order to answer the question.
‐30
‐25
‐20
‐15
‐10
‐5
0
5
10
0 10 20 30 40
Dep
th of R
amp
Distance from Starting Point
Depth of Ramp versus Distance from Starting Point
Distance FromStarting Point
Depth of Ramp
0 0
Using the data above, determine which equation will allow the machine to create the ramp to the correct specifications.
A. B. C. D. 212
15y x x 21
2 3015
y x x 215 2y x x 215 2 30y x x
ANSWERS CSO 3.1.9 1.c 2.b 3.b 4.c
CSO 3.2.1 1.c 2.29
CSO 4.3.1 1.d 2.b 3.c 4.c 5.b
CSO 5.4.7 1.c
CSO 6.1.4 1.c
CSO 6.4.4 1.b
CSO 6.4.4 1.b
CSO 7.3.3 1.d
CSO 7.4.1 1.a
CSO 7.4.1 1.c
CSO 7.4.2 1.15.9
CSO 8.2.3 1.c
CSO 8.4.3 1.d
CSO 8.5.5 1.c
CSO 8.5.4 1.b
CSO 8.5.2 1.c
CSO 8.5.3 1.b
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