UNIT
1
UNIT 1 MIXED REVIEW
Assessment Readiness
MIXED REVIEW
Assessment Readiness
1. Consider each expression. if x = -2, is the value of the expression
a positive number? Select Yes or No.
2
A. -2(x - 2)
Yes
No
ASSESSMENT AND INTERVENTION
B. -3x(5 - 4x)
C. x 3 + 6x
No
No
2. A bedroom is shaped like a rectangular prism. The floor has a length of
4.57 meters and a width of 4.04 meters. The height of the room is 2.3 meters.
Choose True or False for each statement.
A. The perimeter of the floor with
the correct number of significant
digits is 17.22 meters.
True
False
B. The area of the floor with the
correct number of significant digits
is 18.46 square meters.
True
False
C. The volume of the room with the
correct number of significant digits
is 42 cubic meters.
True
False
Assign ready-made or customized practice tests to
prepare students for high-stakes tests.
ADDITIONAL RESOURCES
Assessment Resources
• Leveled Unit Tests: Modified, A, B, C
3. Does the ray BD bisect ∠ABC?
Select Yes or No for each pair of angles.
A. m∠ABC = 60°, m∠ABD = 30°
B. m∠ABC = 96°, m∠ABD = 47°
C. m∠ABC = 124°, m∠ABD = 62°
• Performance Assessment
© Houghton Mifflin Harcourt Publishing Company
AVOID COMMON ERRORS
Item 7 Some students will attempt this problem
without plotting the transformations. Encourage
students to use a sheet of graph paper and test each
transformation.
Yes
Yes
• Online Homework
• Hints and Help
• Extra Practice
Yes
Yes
No
No
Yes
No
Yes
Yes
Yes
No
No
No
―
4. Is the point C the midpoint of the line AB?
Select Yes or No for each statement.
A. A(1, 2), B(3, 4), and C(2, 3)
B. A(-1, 2), B(3, -1), and C(1, 0)
C. A(-3, 0), B(-1, 5), and C(-2, 2)
―
―
5. Is RS a translation of DF?
Select Yes or No for each statement.
A. R(2, 2), S(5, 2), and D(3, 3), F(5, 3)
B. R(-1, 3), S(2, -2), and D(-4, 2), F(-1, -3)
C. R(5, -3), S(2, 2), and D(1, -4), F(-1, -3)
Unit 1
COMMON
CORE
GE_MNLESE385795_U1UC 155
Yes
No
Yes
Yes
No
No
155
Common Core Standards
Content Standards
Mathematical Practices
1
A-REI.B.3
MP.2
2
G-GMD.B.4
MP.6
3
G-CO.D.12
MP.6
4
G-CO.A.1
MP.6
5
N-CN.B.6
MP.5
Items
* Item integrates mixed review concepts from previous modules or a previous course.
155
Unit 1
29/03/14 3:19 AM
6. Does the shape have rotational symmetry?
Select Yes or No for each statement.
A. A square
B. A trapezoid
C. A right triangle
Yes
Yes
Yes
PERFORMANCE TASKS
No
No
No
There are three different levels of performance tasks:
* Novice: These are short word problems that
require students to apply the math they have learned
in straightforward, real-world situations.
7. Determine whether each image of △ABC, with A(1, 3), B(2, 3), C(4, 5), can
be formed with only the given transformation. Select True or False for each
statement.
A. A′(2, 4), B′(3, 4), C′(5, 6) is formed
by translation.
True
False
B. A′(-1, 3), B′(-2, 3), C′(-4, 5) is formed
by rotation.
True
False
C. A′(1, -5), B′(2, -3), C′(4, -1) is formed
by reflection.
True
False
** Apprentice: These are more involved problems
that guide students step-by-step through more
complex tasks. These exercises include more
complicated reasoning, writing, and open ended
elements.
8. For △DEF, with D(2, 2), E(3, 5), F(4, 3), and △D′E′F′, with D′(4, 2), E′(3, 5),
F′(2, 3), determine whether the image can be formed with the sequence of
transformations. Select True or False for each statement.
A. The image is formed by a reflection
followed by a translation.
True
False
B. The image is formed by a rotation
followed by a reflection.
True
False
C. The image is formed by two consecutive
reflections.
True
False
9. Use the figure to answer the questions below.
A. What is a specific series of rigid transformations
that maps △ABC to △DEF?
B. List all congruent pairs of angles and sides for the
two figures.
――
―
――
―
y
2
-4
A 0
-2
B
C
F
E
D
2
x
4
-4
AB ≅ DE, BC ≅ EF, CA ≅ FD
∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F
Unit 1
© Houghton Mifflin Harcourt Publishing Company
Answers may vary. Sample: Reflect across the
x-axis and translate to the right 5 units and
up 1 unit.
4
***Expert: These are open-ended, nonroutine
problems that, instead of stepping the students
through, ask them to choose their own methods for
solving and justify their answers and reasoning.
156
COMMON
CORE
GE_MNLESE385795_U1UC 156
Common Core Standards
Content Standards
Mathematical Practices
6
G-CO.A.2
MP.5
7
G-CO.A.3
MP.5
8
G-CO.A.5
MP.5
9
G-CO.A.5, G-CO.A.6
MP.2, MP.7
Items
5/14/14 7:15 PM
* Item integrates mixed review concepts from previous modules or a previous course.
Unit 1
156
Performance Tasks
SCORING GUIDES
10. A student has drawn a figure of a square PQRS with points P(-5, 5), Q(1, 5),
R(1, -1), and S(-5, -1). For the next assignment, the teacher wants students to
―
inscribe another square, but with sides of length √18 , in the square. How would a
student find the correct square? What are the vertices of the inscribed square?
Item 10 (2 points) Award the student 1 point for a
correct explanation of how to find the square, and 1
point for the correct vertices (–2, 5), (1, 2), (–2, –1),
and (–5, 2).
Note that the square’s side lengths are 6. All sides must be the same length,
so the midpoints of each square side should be found. Confirm that using
the midpoints of the square as the vertices for the inscribed square gives a
―
square with side length √18 . The vertices are (-2, 5), (1, 2), (-2, -1),
and (-5, 2).
Item 11 (6 points)
2 points for naming correct transformation type
11. A square table is set with four identical place settings, one on each side of the
table. Each setting consists of a plate and spoon. Choose one as the original place
setting. What transformation describes the location of each of the other three?
Express your answer in terms of degrees, lines of reflection, or directions from the
original place setting.
4 points for full description
Item 12 (6 points)
A. 1 point for correct answer about straight lines
1 point for correct answer about nonintersecting
lines
Possible answer: They are rotations of the first place setting with the
center of rotation in the center of the table. The second setting is a
rotation of 90 degrees, the third is 180 degrees, and the fourth is
270 degrees.
B. 1 point for correct answer about straight lines
1 point for correct answer about nonintersecting
lines
12. In spherical geometry, the plane is replaced by the surface of a sphere. In this
context, straight lines are defined as great circles, which are circles that have the
same center as the sphere. They are the largest possible circles on the surface of
the sphere.
A. On a globe, lines of longitude run north and south.
In spherical geometry, are lines of longitude straight
lines? Are any lines of longitude parallel
(nonintersecting)?
B. Lines of latitude run east and west. In spherical
geometry, are lines of latitude straight lines? Are
any lines of latitude parallel (nonintersecting)?
C. In general, in how many places does a pair of
straight lines intersect in spherical geometry?
© Houghton Mifflin Harcourt Publishing Company
C. 2 points for correct answer
A. Lines of longitude are straight lines, and no lines of longitude are
nonintersecting.
B. Most lines of latitude are not straight lines, but the equator is
straight. All lines of latitude are nonintersecting.
C. All straight lines in spherical geometry intersect in exactly two places.
Unit 1
GE_MNLESE385795_U1UC 157
157
Unit 1
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29/03/14 3:19 AM
math in careers
MATH IN CAREERS
Geomatics surveyor A geomatics surveyor is surveying a piece of land of length 400
feet and width 300 feet. Standing at one corner, he finds that the elevation of the opposite
corner is 50 feet greater than his elevation. Find the distance between the surveyor and the
middlemost point of the piece of land (ignoring elevation), the elevation of the middlemost
point in comparison to his location (assuming that the elevation increases at a constant
rate), and distance between the surveyor and the middlemost point of the piece of land
considering its elevation.
Geomatics Surveyor In this Unit Performance Task,
students can see how a geomatics surveyor uses
mathematics on the job.
For more information about careers in mathematics
as well as various mathematics appreciation topics,
visit the American Mathematical Society
http://www.ams.org
The distance, ignoring elevation, is found with the distance
formula.
―――――
300
400
√(___) + (___) = 250 feet
2
2
2
2
The elevation of the middlemost point is found by dividing the
elevation of the opposite corner by 2.
50
___
= 25 feet
SCORING GUIDES
2
―――――
formula. √(250) + (25) ≈ 251.25 feet
Task (6 points)
The final distance is found using the distance
2
2
2 points for the correct distance ignoring elevation
2 points for finding elevation
2 points for correct distance including elevation
© Houghton Mifflin Harcourt Publishing Company
Unit 1
GE_MNLESE385795_U1UC 158
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5/14/14 7:15 PM
Unit 1
158