WESTEST 2
MATHEMATICS
Changes to the WESTEST 2 Math Section
Types of Questions on Mathematics Test
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
Multiple Choice
Gridded Response items – 2 per test
Format of Mathematics Tests
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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
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Objectives as per CSOs
Rigor based on the DOK of the CSO
Content relevant to the student
Mathematical Tools
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
Rulers
Calculators are permitted on all sections of the mathematics
test for all grade levels.
SAMPLE ITEMS
Answers are provided at the end of the
sample items.
M.O.3.1.9 Demonstrate and model multiplication (repeated
addition, arrays) and division (repeated subtraction,
portioning) DOK 2
Many unusual animals live on the planet Html.
Some of them have bodies that are made of cube shapes.
These animals grow by getting new cube shapes on each birthday.
When Baby Boxapede is born it looks like this.
It is 1 cube long and has 2 legs.
On its first birthday it has grown.
It is 4 cubes long and has eight legs.
The Boxapede continues to grow in this way. On each birthday it gets
more 3 cube shapes and 6 more legs.
1. How long is a Boxapede when it is 10 years old?
a.
b.
c.
d.
10
18
31
80
2. Scientists are studying how Boxapedes grow. One of the Boxapedes is 16
cubes long. How old is this Boxapede?
a.
b.
c.
d.
4
5
8
16
3. Another Boxapede that the scientist is studying has 20 legs. How old is this
Boxapede?
a.
b.
c.
d.
2
3
4
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.
b.
c.
d.
3
11
18
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 twodimensional (including quadrilateral shapes) and threedimensional geometric figures according to attributes DOK 1
As part of your preparation for math field day, complete the following chart
indicating when the attribute is always true for the figure and then answer the
questions by filling in the circle next to the best answer.
Attributes
Types of Polygons
Equilateral
Equiangular
4-sided
Rectangle
Quadrilateral
Rhombus
Square
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
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.5.4.7 Collect, record, estimate and calculate elapsed times
from real-world situations (with and without technology)
DOK 2
The class went on a field trip. The students left school at 9:00 a.m. They
returned to school at 1:30 p.m. How long were they gone?
a.
b.
c.
d.
8 hours 30 minutes
8 hours
4 hours 30 minutes
4 hours
M.O.6.1.4 Analyze and solve real world problems involving:
addition, subtraction, multiplication and division of whole
numbers, fractions, mixed numbers, decimals and integers and
justify the reasonableness by estimation. DOK 3
On Bill’s football squad, 1/3 of the players walk to practice and 25% are
driven by their parents. The remaining 15 players take the bus. How
many members are on the football squad?
a.
b.
c.
d.
48
24
36
30
M.O.6.4.4 Develop strategies to determine volume of cylinders:
solve real-world problems involving volume of cylinders,
justify the results. DOK 2
A farm has a vertical cylindrical oil tank that has an inside diameter of
2.5 feet. The depth of the oil in the tank is 2 feet. If a cubic foot of space
holds 7.48 gallons, about how many gallons of oil are in the tank?
a.
b.
c.
d.
59 gallons
75 gallons
230 gallons
294 gallons
M.O.6.4.4 Develop strategies to determine volume of cylinders;
solve real-world problems involving volume of cylinders,
justify the results. DOK 2
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.
b.
c.
d.
(3, 4)
(3, -4)
(-3, -4)
(-3,4)
M.O.7.4.1 Select and apply an appropriate method to solve
(including, but not limited to, formula) justify the method and
the reasonableness of the solution, given a real-world problem
solving situation involving: perimeter, circumference, area,
surface area of prisms (rectangular and triangular), volume of
prisms and cylinders, distance and temperature (Celsius,
Fahrenheit). DOK 3
Jimmy wants to know how much fencing he should buy to fence his
yard. What does he need to calculate?
a.
b.
c.
d.
e.
The perimeter of his yard
The area of his yard
The height of the new fence
Both a and b above
All of the above
M.O.7.4.1 Select and apply an appropriate method to solve
(including, but not limited to, formulas) justify the method and
the reasonableness of the solution, given a real-world problem
solving situation involving perimeter, circumference, area,
surface area of prisms (rectangular and triangular), volume of
prisms and cylinders, distance and temperature (Celsius,
Fahrenheit). DOK 2
Which net best represents the triangular prism shown below?
A
B
C
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.8.2.3 Add and subtract polynomials limited to two
variables and positive exponents. DOK 1
Simplify: (x2 - 5x + 4) – (5x2 +3x -1)
a.
b.
c.
d.
-5x2 -2x +3
-4x2 - 8x +3
-4x2- 8x +5
-5x2- 8x +5
M.O.8.4.3 Solve right triangle problems where the existence of
triangles is not obvious using the Pythagorean Theorem and
indirect measurement in real-world problem solving
situations. DOK 3
Two students are using a measuring tape to measure the length of a
room. They measure it to be 13 feet 6 inches. However, the student at
one end is holding the tape 9 inches higher than the student at the other
end. What is the difference between their measurement and the true
length?
a.
b.
c.
d.
About 9 feet
About 3.5 feet
About ½ foot
No difference
M.O.8.5.5 Draw inferences, make conjectures and construct
convincing arguments involving: different effects that changes
in data values have on measures of central tendency and
misuses of statistical or numeric information, based on data
analysis of same and different sets of data. DOK 3
If each data point in a data set is multiplied by the same number, which
of the following statements will be true?
a.
b.
c.
d.
The range is unaffected.
The median is doubled regardless of the number used.
The mean is equal to the constant times the original mean.
The interquartile range remains the same.
M.O.8.5.4 Analyze problem situations, games of chance, and
consumer applications using random and non-random
samplings to determine probability, make predictions, and
identify sources of bias. DOK 3
Players A and B are playing a game. On a table between them is a stack of
pennies. First player A removes either one or two pennies from the stack.
Then Player B removes either one or two pennies from the stack. They
alternate this way until no pennies remain. The loser is the player who
removes the last penny from the stack.
If you start the game with 7 pennies in the stack and you want to be the
winner, which Player would you prefer to be?
a.
b.
c.
d.
Player A
Player B
Either A or B
Not enough information to make a choice.
MA.8.5.2 Investigate the experimental and theoretical
probability, including compound probability of an event
DOK 1
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.
1
2
3
4
A
B
C
D
E
6
12
18
24
-3
-4
-5
-6
7
8
9
10
1
2
3
4
5
-35
If the number in Cell A3 = B4 – 3(E2 + D4), which of the following must be the
number in Cell E2?
a.
b.
c.
d.
-21
-15
-4
-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.3.7 Make conjectures and justify congruence
relationships with an emphasis on triangles and employ these
relationships to solve problems. DOK 2
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.
b.
c.
d.
Quantity D > Quantity E
Quantity E > Quantity D
Quantity D = Quantity E
Relationship is indeterminate
M.O.G.3.13 Investigate measures of angles formed by chords,
tangents, and secants of a circle and draw conclusions for the
relationship to its arcs. DOK 2
AB is the diameter of the circle.
The line touching the circle at point D is a tangent to the
circle.
Quantity X = Measure of angle 1 + Measure of angle 2
Quantity Y = Measure of angle 3
What is the relationship between Quantity X and Quantity Y?
a.
b.
c.
d.
Quantity X = Quantity Y
Quantity X > Quantity Y
Quantity X < Quantity Y
Relationship is indeterminate
M.O.G.3.13 Investigate measures of angles formed by chords,
tangents, and secants of a circle and draw conclusions for the
relationship to its arcs. DOK 2
Quantity A = Measure of angle 2
Quantity B = Measure of angle 1
What is the relationship of the Quantities?
a.
b.
c.
d.
Quantity A > Quantity B
Quantity A < Quantity B
Quantity A = Quantity B
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.
Depth of Ramp versus Distance from Starting Point
10
Distance From
Starting Point
0
5
Depth of
Ramp
0
Depth of Ramp
0
-5
-10
-15
-20
-25
-30
0
10
20Starting Point
Distance from
30
40
Using the data above, determine which equation will allow the machine to create the
ramp to the correct specifications.
A.
y
1 2
x  2x
15
B.
y
1 2
x  2 x  30
15
C.
y  15x 2  2 x
D.
y  15x 2  2 x  30
ANSWERS
CSO 3.1.9
1.c
2.b
CSO 3.2.1
1.c
2.29
CSO 4.3.1
1.d
2.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
3.b
4.c
3.c
4.c
5.b
CSO A1.2.2
1.d
CSO G3.19
1.c
CSO G3.7
1.d
CSO 3.13
1.a
CSO 3.13
1.a
CSO A2.2.15
1.a