Mathematics Benchmarks & Indicators

Mathematics Benchmarks & Indicators

with Ohio Achievement Test Questions

Grade 8

Includes questions from the released

2008, 2007, 2006 and 2005 Ohio Achievement Tests

and the 2005 Practice Test

Far East Regional Partnership

for Conceptually Based Mathematics

YoungstownStateUniversity

Compiled by A. Crabtree, 2006

Revised by A. Crabtree and L. Holovatick, 2007

Revised by A. Crabtree, J. Lucas, and T. Cameron, 2008

Geometry and Spatial SenseGrade 8

1. Formally define geometric figures.

Grade 8 – 2008 OAT – Problem # 9

The locations of Andy’s house, school and local park form a triangle, as shown.

Which is a possible distance from the local park to Andy’s school?
A. 4 miles
B. 8 miles
C. 10 miles
D. 16 miles

Grade 8 – 2007 OAT – Problem #8

Triangle XYZ is shown.

Angles X and Z are congruent.
Which statement is always true? /

1. Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

8.1. Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

8.3. Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).

Grade 8 – 2008 OAT – Problem # 19

On a scale drawing of a house, a rectangular bedroom has a length of 8 inches and a perimeter of 30 inches. The scale is 0.5 inch = 1 foot. What is the actual width in feet of the bedroom? / A. 7 feet
B. 14 feet
C. 15 feet
D. 22 feet

Grade 8 – 2006 OAT – Problem # 31

In the figures, mPQR = mEFD.

In your Answer Document, identify what else must be true about the sides or the angles of the triangle in order for ΔPQR and ΔEFD to be similar triangles. Provide specific examples for these two triangles.

Grade 8 – 2005 OAT – Problem #6

Jason constructed the figure shown.

He knows ∆ERS is similar to ∆EFG and thatRS ||FG.
Jason claims 
.
In your Answer Document, identify two geometric properties that can be used to justify Jason’s claim.

Grade 8 – 2005 OAT – Problem #15

∆PQRis similar to ∆XYZ.

What is the perimeter of ∆XYZ? / A. 21 cm
B. 63 cm
C. 105 cm
D. 126 cm

Grade 8 – 2005 Practice Test – Problem #6

Pentagon JKLMN is similar to pentagon VWXYZ.

What is the measurement of angle X? / A. 30°
B. 60°
C. 150°
D. 120°

1. Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.

8.2. Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.

Grade 8 – 2008 OAT – Problem # 5

A parallelogram is shown.

What is the measure of angle F? / A. 45 degrees
B. 65 degrees
C. 90 degrees
D. 135 degrees

Grade 8 – 2007 OAT – Problem #32

A map of downtown Centerville shows North Street parallel to Canal Street.

Main Street is perpendicular to both North and Canal streets. The angle between Central Avenue and Main Street is 45º.
What is the measure of angle X? / A. 45°
B. 120°
C. 135°
D. 150°

Grade 8 – 2006 OAT – Problem # 39

In the diagram below, line m is parallel to line n.

What is the measure of PTR? / A. 72°
B. 76°
C. 108°
D. 118°

Grade 8 – 2005 OAT – Problem #35

In the figure, lines j and k are parallel.

Which angle is congruent to? /

Grade 8 – 2005 Practice Test – Problem #2

What is the sum of the measures of Kand L?
/ A. 47°
B. 94°
C. 133°
D. 227°

1. Use coordinate geometry to represent and examine the properties of geometric figures.

8.1. Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

8.4. Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex.

Grade 8 – 2006 OAT – Problem # 40

Right triangle XYZ and points J and K are shown below.

Triangle XYZ is similar to triangle JKL. What could be the location of point L so that triangle JKL is similar to triangle XYZ? / A. (–4, 4)
B. (–4, 1)
C. (–2, 2)
D. (–2, 0)

Grade 8 – 2005 OAT – Problem #4

Three vertices of a trapezoid are located atpoints (2, 3), (–2, –2) and (5, –2).

Which point could represent the fourth vertexof the figure? / A. (5, 0)
B. (5, 4)
C. (–1, 3)
D. (–1, 5)

1. Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.

8.6. Draw nets for a variety of prisms, pyramids, cylinders and cones.

Grade 8 – 2005 OAT – Problem #17

Ray found the paper cut-out shown.

Which 3-dimensional object is formed whenthe cut-out is assembled? / A. cone
B. cylinder
C. prism
D. sphere

Grade 8 – 2005 Practice Test – Problem #11

Which illustration represents the net of a cylinder?

1. Represent and model transformations in a coordinate plane and describe the results.

8.5. Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations.

Grade 8 – 2007 OAT – Problem # 11

Rectangle PQRS is shown on the coordinate plane.

In your Answer Document, sketch rectangle ABCD centered at the origin to represent a dilation of rectangle PQRS by a scale factor of 1.5.
Then, state one characteristic of rectangle PQRS that does not change as a result of the dilation.

Grade 8 – 2005 OAT – Problem #39

The parallelogram shown is translated 4 units to the left and 2 units down.

Which property will remain the same?
A. length of the sides
B. coordinates of the vertices
C. coordinates of the y-intercept
D. distance from the vertices to the origin

Grade 8 – 2005 Practice Test – Problem #18

A flag is drawn on a coordinate plane.

In your Answer Document, sketch this flag on a coordinate plane. Then rotate the flag 180º about the origin and sketch the flag in its new position.

G. Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.

Grade 8 – 2005 OAT – Problem #30

Circle A has a radius that is twice the length of the radius of Circle B.
Which is an accurate statement about the relationship of the areas of Circles A and B?
A. The area of Circle A is four times the area of Circle B.
B. The area of Circle A is twice the area of Circle B.
C. The area of Circle A is one-half the area of Circle B.
D. The area of Circle A is one-fourth the area of Circle B.

H.Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

8.1. Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

I. Use right triangle trigonometric relationships to determine lengths and angle measures.

Prepared by A. Crabtree for FERPCBM, Youngstown, OhioSummer 2006 (Rev. 2008)

Benchmarks & Indicators with OAT ProblemsPage 1 of 18

Geometry and Spatial Sense – Answer KeyGrade 8

OAT – Grade 8
Geometry and Spatial Sense
Test
Year / Question # / Answer
A / 2008 / 9 / C
2007 / 8 / D
B / 2008 / 19 / B
2006 / 31 / S.A.
2005 / 6 / S.A.
2005 / 15 / D
2005* / 6 / B
C / 2008 / 5 / A
2007 / 32 / C
2006 / 39 / C
2005 / 35 / B
2005* / 2 / B
D / 2006 / 40 / B
2005 / 4 / C
E / 2005 / 17 / A
2005* / 11 / D
F / 2007 / 11 / S.A.
2005 / 39 / A
2005* / 18 / **
H / 2005 / 30 / A
* Half-Length Practice Test
** Scoring Rubric Not Released
GSS – Benchmark F
2007 OAT – Grade 8 – Problem # 11 Scoring Guidelines:
Points / Student Response
2 / The focus of this task is to draw the results of a dilation about a fixed point and to state a characteristic of the object that remains fixed following the dilation. The response provides a grid with the dilated rectangle and states a characteristic that does not change as a result of the dilation.

Exemplar Response:
All four angles still measure 90º.
OR
One characteristic that does not change is the ratio of length to width which is 2 in both rectangles.
Note:
• Vertex labels are not considered in scoring.
• Characteristics may include but are not limited to: angles are 90 degrees, ratio of sides stays the same, opposite sides are parallel, adjacent sides are perpendicular.
Unacceptable responses: it is still a rectangle, the perimeter or the area stay the same.
1 / The response shows partial evidence of drawing the results of a dilation about a fixed point and stating a characteristic of the object that remains fixed following the dilation; however, the solution may be incomplete or slightly flawed.
For example, the response may:
• Provide a correct sketch of the dilated rectangle without a description of a characteristic that does not change.
• Provide a correct statement about a characteristic of a dilation that does not change; however, the response does not provide a correctly drawn dilation of the rectangle or provides no dilation at all.
0 / The response provides inadequate evidence of drawing the results of a dilation about a fixed point and stating a characteristic of the object that remains fixed following the dilation. The response contains major flaws and errors in reasoning.
For example, the response may:
• Extend the rectangle 1.5 units in every direction.
• Dilate the rectangle but move the center off the origin.
• Incorrectly draw rectangle PQRS.
• Restate the information provided in the item.
• Be blank or give irrelevant information.
GSS – Benchmark B
2006 OAT – Grade 8 – Problem # 31 Scoring Guidelines:
Points / Student Response
2 / Sample Correct Responses:

The focus of this task is to make and test conjectures about characteristics and properties of two-dimensional figures. The response correctly identifies what else must be true about the sides or the angles of the triangles in order for ∆PQR and ∆EFD to be similar triangles. The response also provides specific examples for these two triangles. Note: P = E is acceptable or
P = E is acceptable.
1 / The response provides partial evidence of making and testing conjectures about characteristics and properties of two-dimensional figures; however, the solution is incomplete or slightly flawed. For example, the response may:
• Provide a proportional statement but reverses the ratios; e.g.,
.
• Provide the definition of similar triangles; e.g., states that sides are proportional and angles are equal.
0 / The response provides inadequate evidence of making and testing conjectures about characteristics and properties of two-dimensional figures. The response has major flaws in reasoning or irrelevant information. For example, the response may:
• State that if one pair of angles is congruent then all the angles are congruent. So, the triangles are similar.
• Be blank or state unrelated statements.
• Recopy information from the item.
GSS – Benchmark B
2005 OAT – Grade 8 – Problem # 6 Scoring Guidelines:
Points / Student Response
2 / Sample Correct Response:
• Since the triangles are similar, corresponding angles ERS and EFG are congruent. In addition, angle ERS is congruent to angle EFG, because EF intersects parallel lines (RS and FG) and creates congruent corresponding angles.
The focus of this task is to describe and apply the properties of similar triangles and parallel lines. The response explains that because the two triangles are similar, the corresponding angles of similar triangles are congruent. The response also explains that because the lines are parallel corresponding angles are congruent.
Note: Response does not need to use formal geometric notation.
1 / The response shows partial evidence of describing and applying the properties of similar triangles or parallel lines; however, the solution may be incomplete or slightly flawed.
For example, the response may:
• Suggest that angles ERS and EFG are congruent by similar triangles but fails to mention parallel lines.
• Explain that parallel lines create congruent corresponding angles but fails to use properties of similar triangles.
0 / The response shows inadequate evidence of describing and applying the properties of similar triangles and parallel lines. The response provides an explanation with major flaws and errors of reasoning.
For example, the response may:
• Restate the information provided in the item.
• Provide irrelevant information.
• Be blank.

Prepared by A. Crabtree for FERPCBM, Youngstown, OhioSummer 2006 (Rev. 2008)

Benchmarks & Indicators with OAT ProblemsPage 1 of 18