Test Information Guide
Field 51: Mathematics/Science (Middle School)
Sample Open-Response Items
The following materials contain:
- Sample test directions for the open-response items
- Sample open-response items
- Examples of strong responses to the open-response items
- The scoring rubric
Sample Test Directions for Open-Response Items
This section of the test consists of two open-response item assignments. You will be asked to prepare a written response of approximately 150–300 words, or 1–2 pages, for each assignment.
Read the assignments carefully before you begin your responses. Think about how you will organize your responses. You may use the erasable sheet(s) to make notes, write an outline, or otherwise prepare your responses. However, your final response to each assignment must be either:
- typed into the on-screen response box,
- written on a response sheet and scanned using the scanner provided at your workstation, or
- provided using both the on-screen response box (for typed text) and a response sheet (for calculations or drawings) that you will scan using the scanner provided at your workstation.
Instructions for scanning your response sheet(s) are available by clicking the "Scanning Help" button at the top of the screen.
As a whole, your response to each assignment must demonstrate an understanding of the knowledge of the field. In your response to each assignment, you are expected to demonstrate the depth of your understanding of the subject area by applying your knowledge rather than by merely reciting factual information.
Your responses to the assignments will be evaluated based on the following criteria.
- PURPOSE: the extent to which the response achieves the purpose of the assignment
- SUBJECT KNOWLEDGE: appropriateness and accuracy in the application of subject knowledge
- SUPPORT: quality and relevance of supporting evidence
- RATIONALE: soundness of argument and degree of understanding of the subject area
The open-response item assignments are intended to assess subject knowledge. Your responses must be communicated clearly enough to permit valid judgment of the evaluation criteria by scorers. Your responses should be written for an audience of educators in this field. The final version of each response should conform to the conventions of edited American English. Your responses should be your original work, written in your own words, and not copied or paraphrased from some other work.
Be sure to write about the assigned topics. Remember to review your work and make any changes you think will improve your responses.
Any time spent responding to an assignment, including scanning the response sheet(s), is part of your testing time. Monitor your time carefully. When your testing time expires, a pop-up message will appear on-screen indicating the conclusion of your test session. Only response sheets that are scanned before you end your test or before time has expired will be scored. Any response sheet that is not scanned before testing ends will NOT be scored.
Sample Open-Response Item #1
Objective 0041
Prepare an organized, developed analysis on a topic related to one or more of the following: number sense and operations; patterns, relations, and algebra; geometry and measurement; data analysis, statistics, and probability; and trigonometry, calculus, and discrete mathematics.
Use the information below to complete the exercise that follows.
A company is considering two bonus-plan options for its employees for the next 20 years. The two options are explained in the following chart.
Option 1: Receive $2 the first year. Every year thereafter receive twice the bonus amount of the previous year.
Option 2: Receive $200 the first year. Every year thereafter receive $200 more than the bonus amount of the previous year.
Use your knowledge of exponential and linear functions to develop a response in which you analyze the bonus received each year during a 20-year period under each option. In your response:
- create a data table representing the bonus received each year over a 12-year period for each option;
- graph the data from both tables on the same coordinate grid and connect the data with the line or curve that best fits the data;
- compare the bonus plans over the 12-year period, including a discussion of the significance of the point of intersection of the two graphs;
- explain what type of function, exponential or linear, models each option;
- find equations that describe each option; and
- identify an expression that represents the difference between the bonuses received under the two options in the twentieth year.
Be sure to show your work and explain the reasoning you use in analyzing and solving this problem.
Sample Strong Response to Open-Response Item #1
The sample response below reflects a strong knowledge and understanding of the subject matter.
The data tables representing the bonuses received each year over a 12-year period for the two options are shown below.
Option 1
Year 1 2 3 4 5 6 7 8 9 10 11 12 Bonus (dollars) 2 4 8 16 32 64 128 256 512 1024 2048 4096 Option 2
Year 1 2 3 4 5 6 7 8 9 10 11 12 Bonus
(dollars)200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 The data from the tables can be graphed on a coordinate grid as shown below.
Graph representing the data from the tables. The x axis is labeled Number of Years. It displays a series of fourteen tick marks equally spaced, with the labels, in numerals, of four, eight, and twelve at those tick marks. The y axis is labeled Bonus open parenthesis Dollars close parenthesis. It displays a series of eight tick marks equally placed, with the labels, in numerals, one thousand, two thousand, three thousand, and four thousand at the second, fourth, sixth, and eighth tick marks, respectively. The graph has two lines. The line labeled option one is a curved line that starts close to the x axis and increases very slowly at first then starts increasing sharply around nine years to an almost vertical increase. The line labeled option two is a straight increasing line. The two lines intersect at point p between years eleven and twelve at about two thousand four hundred dollars.
The two graphs intersect at point P, where they both pay the same bonus. For all years before this point (approximately years 1 through 11), option 2 yields a higher bonus. For all years after this point (years 12 and beyond), option 1 yields a higher bonus.
The bonus plan offered in option 1 increases by a constant factor of 2 and therefore is modeled by an exponential equation. The exponential equation that models this bonus plan is y = 2x. The bonus plan offered in option 2 increases by a constant rate of $200 each year and therefore is modeled by a linear equation. The linear equation that models this bonus plan is y = 200x.
In the 20th year, the bonus offered by option 1 exceeds that offered by option 2 by 220 – 4000 dollars.
Sample Open-Response Item #2
Objective 0042
Prepare an organized, developed analysis on a topic related to one or more of the following: history, philosophy, and methodology of science; chemistry; physics; biology; and earth and space science.
Use the information below to complete the exercise that follows.
In the lungs of mammals, including humans, the circulatory and respiratory systems are closely associated anatomically and physiologically.
Using your knowledge of the circulatory and respiratory systems, write an essay in which you:
- describe what important physiological process occurs in the lungs;
- explain how the structures of the lungs and the circulatory system facilitate this process; and
- briefly describe how pulmonary circulation differs from systemic circulation.
Sample Strong Response to Open-Response Item #2
The sample response below reflects a strong knowledge and understanding of the subject matter.
The lungs carry out the first stages of the physiological process of respiration, which carries oxygen to the cells of the body and removes carbon dioxide.
Inhaled air travels through the trachea, bronchi, bronchioles, and into the alveoli. The alveoli are air-filled sacs with walls that are only one cell thick and are surrounded by tiny capillaries filled with blood. Carbon dioxide dissolved in the blood diffuses across the walls of the alveoli into the air of the lungs and is exhaled. Oxygen diffuses from the air in the lungs across the alveolar walls and into the blood. This oxygen-rich blood travels to the heart as part of the pulmonary circulation and is then pumped to all the cells of the body as part of the systemic circulation.
The pulmonary circulation and the systemic circulation differ primarily in the relative amounts of oxygen and carbon dioxide in the arteries and veins. Blood that is low in oxygen and high in carbon dioxide is pumped through the pulmonary arteries to the capillaries surrounding the alveoli of the lungs. In the lungs, the blood loses carbon dioxide, picks up oxygen, and returns to the heart through the pulmonary veins. This blood, which is oxygen-rich and carbon dioxide-poor, is then pumped by the heart through the systemic arteries to the capillary beds of the body where it loses oxygen to the cells and picks up carbon-dioxide. The blood, which is now oxygen-poor and carbon dioxide-rich, then returns to the heart through the systemic veins and is pumped by the heart back to the lungs.
Scoring Rubric
Performance Characteristics
The following characteristics guide the scoring of responses to the open-response item(s).
| Purpose | The extent to which the response achieves the purpose of the assignment. |
|---|---|
| Subject Matter Knowledge | Accuracy and appropriateness in the application of subject matter knowledge. |
| Support | Quality and relevance of supporting details. |
| Rationale | Soundness of argument and degree of understanding of the subject matter. |
Scoring Scale
The scoring scale below, which is related to the performance characteristics for the tests, is used by scorers in assigning scores to responses to the open-response item(s).
| Score Point | Score Point Description |
|---|---|
| 4 |
The "4" response reflects a thorough knowledge and understanding of the subject matter.
|
| 3 | The "3" response reflects an adequate knowledge and understanding of the subject matter.
|
| 2 | The "2" response reflects a limited knowledge and understanding of the subject matter.
|
| 1 | The "1" response reflects a weak knowledge and understanding of the subject matter.
|
| U | The response is unrelated to the assigned topic, illegible, primarily in a language other than English, not of sufficient length to score, or merely a repetition of the assignment. |
| B | There is no response to the assignment. |