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The
Maryland State |
Below are sample test items from the prototype assessment for Geometry.
Sample selected response items:
Directions: An artist will reflect triangle ABC across the dotted line on the computer screen shown below.
What will be the coordinates of the image of vertex A?
(25,72)
(35,72)
(85,72)
(95,72)
Answer: c Mathematics Goal, Expectation, Learning Indicator: 2.1.3 The student will use transformations to move figures, create designs,
and/or demonstrate geometric properties.Instructional Implications: The Geometry assessment for the State will emphasize students' ability to solve mathematical and real-world problems using measurement and geometric models. Students should receive ongoing instruction and encouragement related to justifying solutions and explaining processes used. Instruction should assist them to understand key concepts in mathematics such as coordinate points and the skill of manipulating geometric shapes according to pre-determined coordinates. Once again, instruction should continually reinforce the application of mathematical concepts, principles, and algorithms to the world beyond the classroom.
Directions: Both rectangular solids shown below have the same volume.
What is the value of x?
4
8
12
16
Answer: b Mathematics Goal, Expectation, Learning Indicator: 2.3.2 The student will use techniques of measurement and will estimate,
calculate, and/or compare perimeter, circumference, area, volume and/or
surface area of two and three dimensional figures and their parts. The
results will be expressed with appropriate precision.Instructional Implications: Students need ongoing instruction to enable them to apply geometric equations to solve for volume, perimeter, area, and related measurements. They should also be able to examine pictorial representations, models, and graphic structures to solve geometric equations. Additionally, students should have extensive experience in solving word problems or other real-life scenarios involving geometric equations and their application. As is true in all areas of mathematics instruction, students need ongoing experiences in justifying and providing evidence to support their problem-solving approach(es).
Sample extended constructed response item:
Time limit - 10 minutes
Directions: A person is stacking six cylindrical pipes as shown below. Each pipe is 30 inches in diameter. Look at the drawing and answer the question that follows.
What is the height (h) of the stack of pipes?
Explain how you determined the height of the stack. Use words, symbols, and/or diagrams in your explanation.
Justify your answer.
Solution: Approximately 82 inches.. For an extended constructed response, the student will be graded in a rubric
scale of 0-4. The criteria includes:
- Analysis - Did the student show understanding of the problem?
- Representation - Did the student appropriately display and
identify information?- Application - Did the student use appropriate concepts and
strategies to solve the problem?- Explanation - Did the student use words and/or symbols to
explain the process used to solve the problem?- Justification - Did the student use definitions, postulates,
theorems of mathematics to verify the solution to
the problem?Scoring Rubric:
- A score of 4 indicates application of a reasonable strategy that
leads to a correct solution in the context of the problem. The
representations are correct. The explanation and/or justification are
logically sound, clearly presented, fully developed, support the
solution, and do not contain significant mathematical errors. The
response demonstrates a complete understanding and analysis
of the problem.- A score of 3 indicates application of a reasonable strategy that
may or may not lead to a correct solution. The representations
are essentially correct. The explanation and/or justification
are generally well developed, feasible, and support the solution.
The response demonstrates a clear understanding and analysis
of the problem.- A score of 2 indicates incomplete application of a reasonable
strategy that may or may not lead to a correct solution.
The representations are fundamentally correct. The explanation
and/or justification may not be well developed, are plausible,
and/or may be incomplete. The response demonstrates a
conceptual understanding and analysis of the problem.- A score of 1 indicates little or no attempt to apply a reasonable
strategy that may be incomplete or underdeveloped. It may or
may not have the correct answer. The representations are
partially correct. The explanation and/or justification reveal
serious flaws in reasoning. The response demonstrates a minimal
understanding and analysis of the problem.- A score of 0 indicates the work is completely incorrect or
irrelevant. There may be no response or the response may
state "I don't know."Mathematics Goal, Expectation, Learning Indicator: 1.2.3 The student will solve and describe if and where two straight lines
intersect using numbers, symbols, and/or graphs.
1.2.5 The student will apply formulas and/or use matrices(arrays of
numbers) to solve real-world problems.Instructional Implications: The experience of preparing students for the Maryland School Performance Assessment Program (MSPAP) confirms the critical value of students' having direct and ongoing experience in defending and supporting conclusions with concrete evidence. Real-life applications and problem solving should be a fundamental and ongoing part of students' experience in their mathematics classrooms. Additionally, as this question emphasizes, students need to master the operational language of Algebra, Geometry, and Probability/Statistics, including accurate and elaborated use of words, symbols, and diagrams associated with the explanation of solutions to mathematical problems. To ensure that all students acquire and integrate these skills, students should have extended opportunities for timed and untimed writing activities in their mathematics classrooms. Teachers must become familiar with the scoring rubric used and practice using the rubric when grading teacher-designed classroom-based tests.
