Embed Size (px)
Citation preview
ARMTAlabama Reading and Mathematics Test
Alabama Department of EducationStudent Assessment
Presentors: Judy Pugh Nannette Pence
Student AssessmentContact Information: [email protected]
Content Standards for Reading and MathContent Standards for Reading and Math
• Reading - Addendum to English Language Arts Course of Study
• Reading and Math were adopted in 2003• Reading and Math are required for compliance with No
Child Left Behind
– Standards developed for All students – Standards measurable on State assessments– Standards aligned with assessments and initiatives – No repetition of standards– Math – mastery is expected at each grade level
•Stanford 10 Word Study Skills (Grade 3 only)•Stanford 10 Reading Vocabulary•Stanford 10 Reading Comprehension•ARMT Part 2 Reading
•Items designed to specifically address standards from the Alabama Course of Study: Reading Addendum that are not addressed in the Stanford 10
Alabama Reading and MathematicsAlabama Reading and Mathematics TestTest (ARMT) (ARMT) for Reading:for Reading:
• Three types of reading are assessed– Literary/recreational– Textual/informational– Functional
• Reading is assessed in a variety of genres– Stories– Poetry– Subject texts– Manuals, brochures, pamphlets, etc.
ARMT - Numbers and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability
Stanford 10 – Mathematical Procedures
Mathematical Problem-
Solving
Alabama Reading and Mathematics Test Alabama Reading and Mathematics Test (ARMT) (ARMT) for Math:for Math:
Types of Items (Reading and Math)Types of Items (Reading and Math)
Multiple-Choice items Item stem (question) 4 or 5 answer choices One point each
Gridded Response (math only – none for 3rd grade) Item stem (questions) No answer choices (students must reason and solve the
problem) Students write the answer in the boxes at the top of the
answer grid and fill in the circle under each box used. (Responses are gridded differently according to grade level)
One point each
44thth Grade Gridded Response Sample Grade Gridded Response Sample
3• 2 2$
55thth Grade Gridded Response Grade Gridded Response SampleSample
3. 2 + 2 = 9 6
Mark your answer in the answer grid.
3 0 5 4
ARMT Grade 6 Gridded SampleARMT Grade 6 Gridded Sample
2 %5
77thth Grade Grid Grade Grid88thth Grade Grid Grade Grid
0 7 9
8 7 4 5
Open-Ended FormatOpen-Ended Format
READING:
• Question (Item Stem)
• No answer choices – student must read passage and formulate an answer based on question
• Three points each
MATH
• Question (Item Stem)
• No answer choices
• Problem may have multiple parts or steps that require student reasoning
• Student either:
– Shows all work (by using drawings, symbols and numbers) and/or writes a narrative
– If use calculator, must show all steps or explain how problem was worked
– Three points each
Specified time and 30 additional minutes for each subtest
Reading passages – nine on Stanford 10 and two or three on augmented portion
Reading passages are one to one and one-half pages long
Approximately 70% reading objectives are covered in Stanford 10
Responses do not have to be in complete sentences or grammatically correct.
ARMT Facts You Should KnowARMT Facts You Should Know About ReadingAbout Reading
Students MUST take all parts of Stanford 10 and ARMT Part 2 to count in participation
ARMT Facts - MathARMT Facts - Math• Students MUST take all parts of Stanford 10 and ARMT Part 2 to count in participation
• Approximately 30% of Math objectives are covered in the Stanford 10
• Standards are tested because that is what is expected to be mastered
• Bullets are not tested but must be taught
• In 4th grade, if objective is money or decimals then must have $ or decimal point in answer to receive credit. However, if testing something else and problem happens to involve money, the student may leave off $ and still receive credit.
• Calculator usage: 4 function calculators may be used on the problem-solving portion of the Stanford 10 and the math portion of the ARMT Part 2. (4th through 8th grades only)
• Gridded responses do NOT have to be right justified!!
Response Attributes
3
The response should demonstrate a thorough understanding of the reason von Humboldt went mountain climbing and include complete details for what he discovered for support. Examples may include, but are not limited to, the following:WHY:He dreamed of exploring the world when he was a young boy.As he explored north, he had to cross various terrains, including mountains and volcanoes.He made maps of parts of his explorations and set a worlds record for it.WHAT DISCOVERED:As he climbed higher, there was less oxygen, leading to mountain sickness.He discovered unique cultures of the Amazon such as poison arrows for hunting.Humboldt discovered that a plant used to treat malaria was in danger of dying out.Any other defensibly feasible answer.
2The response should demonstrate a general understanding of the reason von Humboldt went mountain climbing and includes some detail about what he discovered for support. The response is not as complete or organized as a score point 3 response.
1The response should demonstrate a limited understanding of the reason and/or discovery von Humboldt went while mountain climbing and includes bare or no support.
0 There may be an attempt to address the prompt, but it is inaccurate, insufficient, or off task.
Rubric
The response demonstrates a limited understanding of the reason why von Humboldt went mountain climbing (“He want exploer the world”) and includes no support for what he discovered; this is a minimal score point 1 answer.
Sample Resonse
Score Point 1
Sample Response
Score Point 2
The response demonstrates a general understanding of the reason why (“… to learn about the world around him”) von Humboldt went mountain climbing. This answer includes some detail of what he discovered (“…that the higher you climb the more oxygen you run out of”); therefore, meeting the standard for a score point of 2.
The response demonstrates a thorough understanding of the reasons (“… to explore and discover new things” “…enjoyed his trips… wanted to learn more science…”) why he went mountain climbing. It also includes complete details in support of what he discovered (“…that you get mountain sickness the higher you go with less oxygen” and “…native people use plants in their lives many times”). This response satisfies the requirements for a solid score point of 3.
Sample Response
Score Point 3
The response demonstrates a general understanding of the reason why (“… he clinbed for discovery”) von Humboldt went mountain climbing. There is some detail of what he discovered (“… if you climb hight you lose oxigen…”) making this answer a score point of 2.
Sample Response
Score Point 2
This response demonstrates a limited understanding of what von Humboldt discovered (“…there was less oxegen in the air up in the mountains. Plus new plants and animals”). It does not address the reason why he went mountain climbing, keeping this answer at the score point 1 level.
Sample Response
Score Point 1
The response demonstrates a thorough understanding of why (“…finish the map of South America…” and “…set the world record…”) von Humboldt went mountain climbing. In addition, this answer also includes the discovery that (“… the higher you climb the harder it is to breath because there is less oxagen is in the air”), resulting in a solid score point 3 response.
Sample Response
Score Point 3
8187168 168132300
A---The logic (subtraction of correct numbers) is correct, and the answer (168) is correct. The student selected 300 (total student population) and subtracted 132 (students who wear blue shirts), and found the correct answer of 168 (students not wearing blue shirts).B---The logic is incorrect because 87 is added, not subtracted, and the answer is incorrect.
According to the rubric, this response earned a score point of 1 because one answer is correct OR 1 logic is correct.
RESPONSE ATTRIBUTES
3 All correct.
2 Both logics are correct. OROne logic and both answers are correct.
1 One or both answers are correct. OROne logic is correct.
0 None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)
Score Point 1Sample Response
A--- The logic (subtraction of correct numbers) is correct, and the answer is incorrect. The student selected 300 (total student population) and subtracted 132 (students who wear blue shirts). The resulting answer is incorrect.B---The logic (subtraction of “correct” numbers, based on error in part A) is correct. Subtracting 87 from 268 was the next correct step, even though 268 was an incorrect answer to Part A. The student subtracted the correct number, and the subtraction was completed correctly.According to the rubric, this work earns a score point of 2 because both logics are correct.
Note: The student is not penalized twice in Part B after making a computational error in Part A.
Score Point 2
Sample Response
Score Point 3
A--- The logic (subtraction of correct numbers) is correct, and the answer (168) is correct. The student selected 300 (total student population) and subtracted 132 (students who wear blue shirts), and found the correct answer of 168 (students not wearing blue shirts).B--- The logic (subtraction of correct numbers) is correct, and the answer (213) is correct. This alternate answer is accepted because the question’s wording in part B states, “There are 87 students wearing red shirts, and all the other students are wearing white shirts”, and the student is allowed to interpret “all the other students” to mean out of the total of 300. According to the rubric, all logics and answers correct meets the requirements for a score point of 3.
Sample Response
A---The logic (subtraction of correct numbers) is correct, and the answer is not determined. The student selected 300 (total student population) and subtracted 132 (students who wear blue shirts). The correct answer is not calculated.B---This is not attempted.
According to the rubric, this response earned a score point of 1 because one logic is correct.
Score Point 1
Sample Response
Score Point 3
A--- The logic (subtraction of correct numbers) is correct, and the answer (168) is correct. The student selected 300 (total student population) and subtracted 132 (students who wear blue shirts), and found the correct answer of 168 (students not wearing blue shirts).B--- The logic (subtraction of correct numbers) is correct, and the answer (213) is correct. This alternate answer is accepted because the question’s wording in part B states, “There are 87 students wearing red shirts, and all the other students are wearing white shirts”, and the student is allowed to interpret “all the other students” to mean out of the total of 300.
According to the rubric, all logics and answers correct meets the requirements for a score point of 3.
Sample Response
Score Point 2
A--- The logic (subtraction of correct numbers) is correct, and the answer (168) is correct. The student selected 300 (total student population) and subtracted 132 (students who wear blue shirts), and found the correct answer of 168 (students not wearing blue shirts).B--- The logic is not shown, but the correct answer (81) is found.
According to the rubric, two correct answers with one correct logic meets the requirements for a score point of 2.
Sample Response
• Standard 2: Solve addition and subtraction problems, including word problems, involving two- and three-digit numbers with and without regrouping.
Item Type Additional InformationMultiple-choice • Word problems may be usedOpen-ended • Tables and charts for organization • Multiple steps • Time • NH
Response Attributes
3 The response should thoroughly tell about a time the student lost or misplaced an item and use well-chosen examples from the story to draw comparisons and contrasts between the student’s experience and the events of the story.
2 The response should demonstrate a general understanding of the prompt by addressing only two of the three required tasks.
1 The response should demonstrate a limited understanding of the prompt by attempting to address one of the three tasks using bare or no detail for support.
0 There may be an attempt to address the prompt, but it is inaccurate, insufficient, or off task.
This response demonstrates a limited understanding of the prompt with only one of the three tasks addressed. In this response, the student tells us about losing something (“…I lost a brown ball…”), but the reader does not know how the experience was either similar or different from the main character in the story. There is no tie back into the prompt, which keeps this at a score of 1.
Score Point 1
Sample Response
This response demonstrates a general understanding of the prompt by partially addressing required tasks. The student lost an item (“I lost my gameboy…”). This response tells of a difference (“…I found it on a table and her dog took hers…”). It fails to use an example from the text to explain how their experiences were the same (“…and the way it was the same was that we had something lost”) and is not sufficient for a higher score, keeping it at the score point 2 level.
Score Point 2
Sample Response
This student’s response accomplishes all three tasks required by this prompt. It thoroughly tells how the student lost and couldn’t find something (“… I lost one of my Junie B. Jones books”). It uses well-chosen examples from the story to draw comparisons and contrasts between the student’s experience and events in the story. It explains why it was like Lisa’s in the story (“I was just like Lisa, I had put it somewher and now it was gone!”). Also, the response explains their experience was different because (“…that my pet didn’t take it”). This response earns a score of 3.
Sample Response
Score Point 3
The response demonstrates a general understanding of the prompt by addressing only two out of the three required tasks. The student lost an item, (“I lost my coin …”). How the student’s experience was different (“…is it was a spider not a dog”). This response meets the standard for a score of 2.
Score Point 2
Sample Response
The response demonstrates a limited understanding of the prompt by addressing only one of the required tasks (“Along time ago I lost my linze to my glasses”) and provides no textual support. This meets the basic criteria for a score of 1.
Score Point 1
Sample
Response
The response tells about a time the student lost an item (“A few weeks ago, I lost my favorite pair of shoes”). The student provides details from the text to show comparisons (“My experience was simular to Lisa because we both thought we had something but they disapered”), and contrasts, (“My story is different to Lisa’s because my dog didn’t steal my soccer shorts and put them in his bed”) between the student’s experience and events from the story. This satisfies the requirement for a score point of 3.
Score Point 3
Sample Response
ARMT Grade 4 Mathematics
Accurate Response
This bar graph contains 4 errors: 1--- The x- axis, Country, is not labeled.2--- The y-axis, Area in thousands of square miles, is not labeled.3--- Although there is a scale present on the y-axis, it doesn’t start at 0.4--- The bar for Luxembourg doesn’t match the scale.All other countries’ bars match the scale and are considered correct.Note: 1) It doesn’t matter in what order the bars are drawn. 2) The bars do not need to be of equal width, or evenly spaced on the x-axis.According to the rubric, this response earns a score point of 1: “graph has more than three errors.”
RESPONSE ATTRIBUTES
3 Table or graph is completely correct.
2 Table has one to three errors.
1 Table has more than three errors.
0 No table or graph, or none correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)
Score Point 1
Sample Response
This bar graph contains 3 errors: 1--- The x-axis, Country, is not labeled.2--- The y-axis, Area in thousands of square miles, is not labeled.3--- The bar for Swaziland should be 7, not 12.All other bars fit the scale.Note: 1) The placement of the scale on the right side of the graph is acceptable.2) Letters in place of the full names of the countries areacceptable.
According to the rubric, this response earns a score point of 2: “graph has one to three errors.”
Score Point 2
Sample Response
Score Point 3
Sample Response
This bar graph is completely correct: 2 acceptable labels, acceptable scale on y-axis, and bars drawn correctly.
According to the rubric, this response earns a score point of 3. The bars do not need to be of equal width.
This bar graph contains 3 errors: 1--- The x-axis, Country, is not labeled.2--- The y-axis, Area in thousands of square miles, is not labeled.3--- There is a scale present but each bar is off by one square. Instead of counting this as 5 errors, it’s counted as one scaling error.
According to the rubric, this response earns a score point of 2: “graph has one to three errors.”
Score Point 2
Sample Response
This bar graph contains 4 errors: 1--- The x-axis, Country, is not labeled.2--- The y-axis, Area in thousands of square miles, is not labeled.3--- Although there is a scale present on the y-axis, it is not a consistent scale.4--- The bar for Armenia is missing.
Note: It doesn’t matter in what order the bars are drawn.
According to the rubric, this response earns a score point of 1: “graph has more than three errors.”
Score Point 1
Sample Response
This bar graph is completely correct: uses horizontal bars drawn correctly, acceptable labels for both axes, and acceptable scale on the “Area in square miles” axis.
According to the rubric, this response earns a score point of 3.
Score Point 3
Sample Response
ARMT Grade 5 Reading The Eagle
Response Attributes
3 The response should demonstrate that the student thoroughly comprehends the relationship between the eagle and his environment. It should be suggested that a mutual respect and/or communication exists between the eagle and the environment. Examples may include, but are not limited to, the following:• The eagle is able to “feel the power” of the mountains.• The eagle listens to trees “exhale.”• The eagle dives near a river to hear it “sing.”• The eagle “waits” for message from the fields.• The eagle “dances” near a waterfall and “welcomes its rumble.”• The eagle “answers” the environment over which it flew.
2 The response should demonstrate a general comprehension of the eagle’s relationship with the environment. Response is not as complete or organized as a score point 3 response.
1 The response should demonstrate a limited comprehension of a relationship between the eagle and the environment. Response contains little or no support from the text.
0 There may be an attempt to address the prompt, but it is inaccurate, insufficient, or off task.
The response demonstrates a limited comprehension of a relationship between the eagle and the environment (“…is very nice”). It contains little support from the text (“Cause as he passes by the mountains, oceans, and grassy feilds, evrything is calm”), meeting the standard for a score point of 1.
Score Point 1
Sample Response
This response demonstrates a general comprehension of the eagle’s relationship with the environment (“he has a good relationship…”). The response cites two parts of the poem (“…he welcomed the rumble of the watterfall and he likes the silfy flowers”) which support that relationship and results in a lower score of 2 answer.
Score Point 2
Sample Response
The response demonstrates a thorough comprehension of the relationship between the eagle and his environment (“The eagle has a good relationship with its enviroment.”) The textual evidence (“He loves to fly over the many scenes and carefully listens for thier songs” through the closing thought “Then, after all of his visits, adds is own call to the sound of nature”) suggests that a mutual respect and communication exists between the eagle and the environment. This response is a very good example of some of the higher level score 3 responses.
Score Point 3
Sample Response
The response demonstrates that the student thoroughly comprehends the relationship between the eagle and his environment. It suggests that a mutual respect and communication exists between the two (“The eagle flies through the breeze, knowing where to go, gently flowing to his destination. He understands why the clouds sigh, why the oceans roar, even why the flowers are silent.”) The support from the text passage show that the eagle knows where to go to (“…smell the scented treetops, or to hear the rumble of the waterfall”). This response meets the standard for a score of 3.
Score Point 3
Sample Response
The response demonstrates a limited comprehension of a relationship between the eagle and the environment (“The eagle thinks it’s an enjoyable environment”) because he (“…enjoys life and nature”). It provides vague support from the text (“He likes all the sounds that his environment makes and the way it acts”), resulting in a solid score point 1 answer.
Score Point 1
Sample Response
The response demonstrates a general comprehension of the eagle’s relationship with the environment: (“…the animal likes the environment around him…”). The support (“…he like’s passing through the clouds … relaxes to the sounds of his inviroment”) is not as complete or organized as a score point 3 response, but is sufficient for a score of 2.
Score Point 2
Sample Response
ARMT Grade 5 Mathematics
Accurate Response(s): •Chocolate stars, jawbreakers, licorice sticks: 1.082 + 1.004 + 0.998 = 3.084
•Peppermints, licorice sticks, chocolate stars: 0.921 + 0.998 + 1.082 = 3.001Any other correct answers will be accepted.
A---The logic (addition of 3 feasible numbers) is correct and one answer (the total) is correct, but no list is given. The student selected three candy weights (chocolate stars-1.092, jaw breakers- 1.004, and peppermints- 0.921) that when added together weigh 3.017, which is over 3 pounds. There is a transcription error - the chocolate stars weigh 1.082, not 1.092 pounds - but the answer is consistent with that mistake.
B--- The logic and answer are missing. The student states “There is no other way.”
According to the rubric, this response earned a score point of 1 because “One logic and one answer are correct.”
RESPONSE ATTRIBUTES
3 All correct.
2
All logics are correct. OR All of part A or all of part B is correct.
1
One logic is correct. OR One or more answers are correct.OROne logic and one answer are correct.
0 None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)
Score Point 1
Sample Response
A---The logic (addition of 3 feasible numbers) is correct and one answer (total) is correct. The student selected three candy weights (chocolate stars-1.082, licorice sticks-.998, and peppermints-0.921) that when added together weigh 3.001, which is over 3 pounds. No list is given.
B--- The logic (addition of 3 feasible numbers) is correct and one answer (total) is correct. The student selected three candy weights (licorice sticks-.998, jaw breakers-1.004, and chocolate stars-1.082) that when added together weigh 3.084, which is over 3 pounds. Again, no list is given.
According to the rubric, this response earned a score point of 2 because “All logics are correct.”
Score Point 2
Sample Response
A--- The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student selected three candy weights (chocolate stars- 1.082, licorice sticks-.0998, and jaw breakers-1.004,) that when added together weigh 3.084, which is over 3 pounds.
B--- The logic is correct and the answers are correct. The student selected three candy weights (peppermints 0.921, chocolate stars- 1.082, and jaw breakers-1.004,) that when added together weigh 3.007, which is over 3 pounds.
According to the rubric, this response earned a score point of 3 because all logics and answers are correct.
Note: Crossed out portions signify a “guess-and-check” method and are ignored.
Score Point 3
Sample Response
A--- The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student selected three candy weights (chocolate stars-1.082, licorice sticks-.998, and jaw breakers-1.004,) that when added together weigh 3.084, which is over 3 pounds.
B--- The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are partially correct. The student selected three candy weights (chocolate stars-1.082, peppermints-0.921, and jaw breakers-1.004,) that when added together weigh 3.007, which is over 3 pounds. The answer is missing the decimal point and therefore wrong.
According to the rubric, this response earned a score point of 2 because “All of part A or all of part B is correct.”
Score Point 2
Sample Response
A--- The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student selected three candy weights (chocolate stars- 1.082, licorice sticks-.0998, and jaw breakers-1.004,) that when added together weigh 3.084, which is over 3 pounds.
B--- The logic is correct and the answers are correct. The student selected three candy weights (chocolate stars- 1.082, jaw breakers-1.004, and peppermints -0.921) that when added together weigh 3.007, which is over 3 pounds.
According to the rubric, this response earned a score point of 3 because all logics and answers are correct.
Score Point 3
Sample Response
A---The logic (addition of 3 feasible numbers) is partially correct and the answers (total and list) are partially correct. The student listed three candies and three candy weights (chocolate stars-1.082, licorice sticks-0.998, and peppermints- 0.921) that when added together weigh 3.001, which is over 3 pounds. However, no decimals are evident in either the 3 numbers or the total.
B--- The logic (addition of 3 feasible numbers) is partially correct and the answers are not correct. The list of candies has Peanut brittle, but the student actually added the weights of chocolate stars, jaw breakers, and licorice sticks. No decimals are evident in either the 3 numbers or the total.
According to the rubric, this response earned a score point of 1 because “One or more answers are correct.” The absence of decimal points is a major flaw, keeping this response at a score point of 1.
Score Point 1Sample Response
Response Attributes
3
The response should demonstrate a thorough understanding of the passage and question, state that the passage is more about the birds and include at least three details for support. tells about the birds’ flight, tells about the birds’ colors, tells about the birds’ sounds tells about how they hide tells what is being done to protect them, etc. It might mention that only the island’s location is given, but the basis for the score is the choice of birds over island and the subsequent three supports.
2The response should demonstrate a general understanding of the passage and question, state that the passage is more about the birds and include at least two details for support.
1
The response should demonstrate a limited understanding of the passage and question, state that the passage is more about the birds and may include at least one detail for support ORstates that the passage is more about .
0There may be an attempt to address the prompt, but it is
inaccurate, insufficient, or off task.
ARMT Grade 6 ReadingAdventure on the Wing
This response demonstrates limited understanding of the passage and question by mentioning the correct answer (“… more about birds…”) and offers only minimal support (“And because why would birders be in a story all about Dauphin Island”). This answer represents the typical or standard score point 1 response.
Score Point 1
Sample Response
This response demonstrates a general understanding of the passage and question by selecting the correct answer (“…more about the birds”). It gives the reader two supporting details (“… gives spacific detail, about the birds, such as thier sounds and visable appearance …”), from the passage. This answer is sufficient for a score point 2 response.
Score Point 2
Sample Response
This response demonstrates a clear understanding of the prompt and the question by selecting the correct answer (…”more about the birds than Dauphin Island”). It provides sufficient supporting details (“… is devoted to explaining the who, what, where, when, why, and how of the birds. It also talks about the conservation of them and the birders that give up being in their cozy beds to watch and help the winged creatures”) from the story, and satisfies a minimal requirement for a score point 3 response.
Score Point 3Sample Response
The response demonstrates a general understanding of the passage and question by selecting the correct answer (“…more about the birds”). Even though it provides three supporting details (“…how birds migrate, that there are bird watchers, and that the birds need to be counted”) from the story, they were not specific enough to raise this score point 2 response to the higher score point of 3.
Score Point 2
Sample Response
The response demonstrates a thorough understanding of the passage and question by stating that the passage is (“…more about Birds…”) and including more than three details for support (“… ‘cause its talking about how they fly 600 mls without stoping and how they don’t care about people watching them and taking pictures. Also how some are shy and how they hide and how you can hear their soft chreps”). This answer is typical of a solid score point 3 response.
Score Point 3
Sample Response
The response shows a limited understanding of the passage and question. Either “birds” or “Dauphin Island” alone is enough for a minimal score point 1 response.
Score Point 1
Sample Response
ARMT Grade 6 Mathematics
Accurate Response(s):
1.As the editor of the school newspaper, I would not accept this graphic because it is visually misleading. The vertical axis does not start at zero and the difference between classes appears to be more substantial than it actually is.
2.A better representation would include a bar graph (histogram) or a circle graph drawn to scale.
Band Members by Class
0
5
10
15
20
Band Members by Class
20%
22%
26%
32% Freshman
Sophomore
Junior
Senior
A---The logic is not acceptable: “No, it makes it look like there are a lot of senior members and no freshman.” B---The graph contains one error: 1---The x-axis, Class, is not labeled.The y-axis, Number of members, is labeled.All bars are correct. The scale starts at 0.The logic for B is not given.
According to the rubric, this response earns a score point of 1 for a graph that has no more than three errors.
Sample Response
Score Point 1
RESPONSE ATTRIBUTES
3 All is correct.
2 All logics or explanations are correct.
OR
One logic or explanation and the graph are correct.
1 One logic is correct.
OR
The graph has no more than three errors.
0 None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)
A--- The logic is correct: “No, because there aren’t 4 times as many seniors as there are freshmen.”B--- The graph is correct. The percentages of freshman (20%), sophomores (22%), juniors (26%), and seniors (32%) displayed in the circle graph are correct. The logic for B is not given.
According to the rubric, this response earns a score point of 2 for one correct logic and a correct graph.
Sample Response
Score Point 2
A--- The logic is correct: “No, because the senior don’t have 4 times as many band members than freshman.”B--- The graph is correct. The percentages of freshman (20%), sophomores (22%), juniors (26%), and seniors (32%) displayed in the circle graph are correct. The lack of a title doesn’t detract from the score. The logic for choosing the new graph is acceptable: “…It’s easier to see which grade is the biggest and how it compares with the other grades.”
According to the rubric, this response earns a score point of 3 for all correct.
Sample Response
Score Point 3
Sample Response
Score Point 1
A---The logic is incorrect: “yes because it shows how many people are in each band class.”
B---The graph contains two errors:
1---The x-axis, Class, is not labeled.
2---The y-axis, Number of Band Members, is not labeled.
All bars are correct.
The scale starts at 0.
Note: no title is required for the graph at any score point level.
The logic for choosing the graph, “I like this one because it has a key”, is not acceptable.
According to the rubric, this response earns a score point of 1 for a graph that has no more than three errors.
A--- The logic is correct: “I would not accept it because the data is wrong. The number of seniors should be 40, or the number of freshmans is wrong. It should be 4.”B--- The graph contains no errors. The graph is drawn to show what the relationship of freshman and seniors would be if the article were true and there were four times as many seniors as freshman. Both the x-axis and y-axis are labeled.The scale begins at 0 and is evenly distributed.All bars are correct.The lack of a title is not considered an error.The logic for choosing the graph in B is valid and correct.
According to the rubric, this response earns a score point of 3 for all correct.
Sample Response
Score Point 3
A--- The logic is correct: “No, if there were four times as many seniors then freshmen there would have to be 40 seniors, or only 4 freshman.”B---The graph contains two errors: 1--- The x-axis, Class, is not labeled.2--- The junior bar is off. (Note: this change in height does not affect the freshman/senior proportions.)The graph is drawn to show what the relationship of freshman and seniors would be if the article were true and there were four times as many seniors as freshman.The logic in B is acceptable: “I chose this graph because you can show the information clearly on it.”
According to the rubric, this response earns a score point of 2 for all correct logics.
Sample Response
Score Point 2
6th gradeData Analysis and Probability
• Standard 10: Interpret information from bar graphs, line graphs, and circle graphs.
Item Type
• Multiple-choice• Gridded• Open-ended
Additional Information
• Word problems may be used• Comparing types of graphs• Determining percents• Money Values
Response Attributes
3
The response should demonstrate a thorough understanding of the information provided by the graph and recognize that the 1940s was the most significant decade for Cole. The response includes complete details for support. Examples may include, but are not limited to, the following: 1943- Capital Record deal.1944 – “Straighten Up and Fly Right” hit.1946 – National radio show.
2
The response should demonstrate a general understanding of the graph and include some of the significant dates of the 1940s, but the support is not as accurate or thorough as a point 3 score.
1The response should demonstrate a limited understanding of the graph and include inaccurate dates and bare or no support.
0There may be an attempt to address the prompt, but it is inaccurate, insufficient, or off task.
ARMT Grade 7 ReadingThe Life of Nat King Cole
This response shows limited understanding of the graph. It only mentions one event from the correct decade (“The National Radio Show was more events because he have more significance”) and results in the minimum score point of 1.
Sample Response
Score Point 1
This response demonstrates a general understanding of the graph by selecting the correct data (“The 1940’s was his biggest decade…”) and includes the most significant career events during that decade (“…his big music deal with Capital records. Also he had his best hit in this decade. Finally, he started his very popular Radio show”). Without listing the dates of those events and not identifying the name of the “hit”; this answer fails to go beyond this high score point of 2.
Sample Response
Score Point 2
The response demonstrates a thorough understanding of the information provided by the graph by selecting the correct information (“1940 through 1950 was the most significant decade in Cole’s life”). Although the dates of the events are not given, the student has provided the correct events of the decade (“…capitol record deal…sung ‘Straighten Up and Fly Right’”; and “…radio show”). While the “TV show” did not occur in the 1940’s decade, it appears to be more of an afterthought and does not drop the score for this answer below a score point of 3
Sample Response
Score Point 3
The response demonstrates a general understanding of the graph by correctly listing two of the three events (“He got a capitol Record Deal … and He had a National Radio Show at 1946…”). This answer gave some information outside the correct decade (“…and had to go on a Network Television Show around 1958”) and an inaccurate date of “1941” for the Capital Record Deal of 1943, resulting in a score point of 2.
Sample Response
Score Point 2
The response demonstrates a limited understanding of the graph by selecting an inappropriate span of ten years (“The most significant decade of Nat King Cole’s life was between 1946 and 1956”). It includes an accurate event and date (“In 1946 the King Cole Trio was given a national radio show”) and some information outside of the requested correct decade (“In 1956, Cole had his first appearance on television”). This answer meets the standard for a score point of 1.
Sample Response
Score Point 1
The response demonstrates a thorough understanding of the information provided by the graph and recognizes that (“The 1940s were the most significant events of Nat King Cole’s great life”). It includes complete details (“It all started when he was signed by Capitol Records in 1943.”; “The next year, he recorded his first hit single, ‘Straighten Up and Fly Right.’”; “The last big event of the 40s was when he received his national radio show”) for support. This answer explains the significance of these events and results in a high score point 3 type response.
Sample Response
Score Point 3
Accurate Response(s): a. When ordered, the scores are: 97, 98, 99, 99, 100, 108, 108, 110, 110, 110, 111, 112, 118, 121, 121, 123. The 8th and 9th positions are 110. The median is 110.b. The scores total 1745. 1745 ÷ 16 = 109.06. The mean is 109.c. The bowling score that occurs the most often, 3 times, is 110. 110 is the mode.
ARMT
Grade 7
Mathematics
RESPONSE ATTRIBUTES
3 All correct.
2
The logics are correct and two answers are correct.
ORThe logics for two parts are correct and three answers are correct.
OR
All logics are correct.
OR
Parts A and B are correct.
1
The logic for one part is correct.
OR
The logics are missing or incomplete but one to three answers are correct.
0 None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)
Rubrics
A---Median-The logic, placing the numbers in order, is partially correct. The student doesn’t take into account the repeat numbers. This leads to an incorrect median.B---Mean- The response doesn’t demonstrate understanding of mean.
C---Mode-The response shows correct logic for mode and the correct selection.This response receives a score point of 1 for a correct logic and answer in part C.
Sample Response
Score Point 1
A---Median-The logic, placing the numbers in order, is partially correct. A correct answer is given but there is an error in list. There should be only two 108’s and there should be a 100 in the list.B---Mean- The logic is correct when it’s based on the copy error in part A, leading to a correct answer.C--- Mode- Correct answer for mode based on a consistent copy error.
The response is penalized only once for the copy error.
This response earns a score point of 2 because all logics are correct.
Sample Response
Score Point 2
A --- Median- The logic is correct for median (based on a set of 16 numbers), yielding a correct median of 110. For part A, the logic that the median is the middle number is correct.
B --- Mean- The logic is correct. The 16 numbers added together equal 1745. Then they are divided by 16 to reach a correct mean of 109. C --- Mode- The correct answer 110 is written. The logic “number repeated most often” is a correct definition.
This answers earns a score point of 3 because of correct answers for all three parts (110, 109, 110), with adequate logic (explanation), for determining each measure of central tendency (median, mean, and mode).
Sample Response
Score Point 3
A --- Median- The logic is correct for median (based on a set of 16 numbers), yielding a correct median of 110. B --- Mean- The logic is correct. The 16 numbers added together equal 1745. Then they are divided by 16 to reach a correct mean of 109. C --- Mode- The correct answer 110 is written. The logic “is correct.This response earns a score point of 3 because of correct answers for all three parts (110, 109.06, 110), with complete logic (work shown), for determining each measure of central tendency (median, mean, and mode).
Sample Response
Score Point 3
A --- Median-This logic is considered incomplete since the Median was found for the individual bowler and not all the entire group.B --- Mean- This logic is considered incomplete since the Mean was found for the individual bowler and not all the entire group. C --- Mode- The correct answer 110 is written. The logic is unclear.
The response receives a score point of 1 for correct answers, with incomplete logic.
Sample Response
Score Point 1
A --- Median- The logic is correct for median (based on a set of 16 numbers), yielding a correct median of 110.B --- Mean- The logic is correct. The 16 numbers added together equal 1745. Then they are divided by 16 to reach a correct mean of 109. C --- Mode- The correct answer 110 is written. No logic stated.
This response earns a score point of 2 because both parts A and B are correct or two logics and all answers correct.
Sample Response
Score Point 2
7th GradeData Analysis and Probability
• Standard 12: Determine measures of central tendency (mean, median, and mode) and the range using a given set of data or graphs, including histograms, frequency tables, and stem-and-leaf plots.
Item Type
• Multiple-choice• Open-ended
Additional Information
• Tables• Word problems• Any representation of rational numbers• Verbal description of proportions
ARMT Grade 8 ReadingTime to Pick the Spaghetti
Response Attributes
3
The response should demonstrate a thorough description of the support that is found in the passage. Examples may include but are not limited to:The report contained staged pictures.There was great detail, i.e. spaghetti weevil and weather for the harvest.The report was aired on the prestigious news show “Panorama”.Viewers called and asked for more information.Staff continued the joke by telling them how to plant and grow spaghetti.
2
The response should demonstrate a general description of the support. The response may include some elements of a score point 3 response, but is less well-rounded and complete.
1The response should demonstrate a limited description of the support and may include bare or no support or inappropriate support.
0There may be an attempt to address the prompt, but it is inaccurate, insufficient, or off task.
The response has a limited description (“After the broadcast the entire staff enjoyed a good chuckle”) that supports the author’s statement. This answer meets the basics of a score point 1 response.
Sample Response
Score Point 1
The response is a general description of support (“People actually believed them” and “Some people called and asked how they could grow this spaghetti tree, It was also the best because it was on the news”). This answer provides some elements of a score point 3 response, but is less well-rounded and complete. The addition of more thorough examples would have raised this score point 2 to the higher score.
Sample Response
Score Point 2
The response includes a thorough description providing complete details for support (“Since this report was given by prestigious, serious, and studious reporters people were going to believe them”; “Also, since the report had a lot of details, viewers were going to think it is true” and “After the show, many station viewers called in and asked if it was real, the reporters whom knew from the get go it’s false told them to do something.”) This student presents a complete and well-rounded explanation for the opinion and is rewarded with a high score point 3 for this answer.
Sample Response
Score Point 3
The response has a limited description (“…people actually belived them. People though you could buy seeds of the tree. The call the station for information.”) that supports the author’s statement. This answer meets the standard of a score point 1 response.
Sample Response
Score Point 1
The response is a thorough description with complete and well-rounded examples (“…there were pictures of spaghetti growing on trees”; and “…station got lots of telephone calls because viewers really believed it and they wanted spaghetti crops also. The report was delivered with seriousness so the viewers really didn’t know what to think”) in support of the author’s opinion. This answer results in a solid score point 3 response.
Sample Response
Score Point 3
The response includes a general description by providing examples (“Spaghetti does not grow from trees”; “…Someone should have caught on” and “When they wanted to know where they could get the seeds from and they said ‘put a sprig of pasta in a can of tomato sauce and watch closely.”) While this answer includes some elements of a score point 3 response, it is less well-rounded and complete; it is clearly sufficient for a score point of 2.
Sample Response
Score Point 2
ARMT 8th Grade
Mathematics
RESPONSE ATTRIBUTES
3 All is correct.
2
Three logics or explanations are correct.OR
Two logics or explanations are correct, and all answers are correct.
1
One or more answers are correct.OR
One or two logics or explanations are correct.
0None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off task, etc.)
Accurate Response(s):
Cylinder has larger surface area. The surface area of the cylinder may range from 7536 to 7543.2 sq. cm.
)2()2( 2rrh
cm. sq. 7536251250242014.32402014.32 2
cm. sq. 2.75434.25148.502820143.324020143.32 2
Surface area of the rectangular prism
)2()2()2( lwwhlh
cm. sq. 540090015003000153025015250302
The response provides a correct answer (7536 cm) for the surface area of the cylinder and correct logic (correctly uses the surface area formula for a cylinder with the correct values substituted into the formula).
The response provides an incorrect answer (22500 cm) for the surface area of the box and incorrect logic (uses the volume formula instead of the surface area formula for a rectangular prism).
Based on the surface area error of the rectangular prism, the response provides a correct answer (“the square container has a greater surface area…”). The surface areas calculated for the cylinder and prism provide the supporting logic.
According to the rubric, if one or two logics or explanations are correct, the response earns a score point of 1.
Note: At this score point level, units are not a factor in determining the score point.
Sample Response
Score Point 1
The response provides an incorrect answer (2574.8) for the surface area of the cylinder but correct logic (chooses the correct surface area formula and substitutes the correct values into the formula, however, the student makes a mistake in calculations).
The response provides an incorrect answer (1700) for the surface area of the box but correct logic (chooses the correct surface area formula and substitutes the correct values into the formula, however, the student makes a mistake in calculations).
Sample Response
Score Point 2
The response that the basket has the greater surface area is correct.
According to the rubric this response receives a score point of 2 for three logics correct.
The response provides a correct answer (7536) for the surface area of the cylinder and correct logic (correctly uses the surface area formula for a cylinder with the correct values substituted into the formula).
The response provides a correct answer (5400) for the surface area of the box and correct logic (correctly uses the surface area formula for a rectangular prism with the correct values substituted into the formula).
The response has a correct comparison answer (“the cylinder has more surface area…”). The surface areas calculated for the cylinder and prism provide the supporting logic.
Note: The absence of units does not detract from the quality of the response.
According to the rubric, if all answers and logics are valid, the response earns a score point of 3.
Sample Response
Score Point 3
The response provides a correct answer (2400π cm2) for the surface area of the cylinder and correct logic (correctly uses the surface area formula for a cylinder with the correct intermediate products displayed beneath the formula).
The response provides an incorrect answer (2700 cm2) for the surface area of the box but correct logic (chooses the correct surface area formula and substitutes the correct values into the formula, however, the failure to multiply by 2 produces an incorrect answer).
The response has a correct comparison answer (“the cylinder container has the greater surface area.”). The surface areas calculated for the cylinder and prism provide the supporting logic.
According to the rubric, if three logics or explanations are correct, the response earns a score point of 2.
Sample Response
Score Point 2
The answers and logics for the surface areas are omitted.
The response makes a correct comparison of greater surface area through the identification of the cylinder. Supporting logic is not provided.
According to the rubric, if one or more answers are correct, the response earns a score point of 1.
Sample Response
Score Point 1
The response provides a correct answer (7536 cm2) for the surface area of the cylinder and correct logic (correctly uses the surface area formula for a cylinder with the correct values substituted into the formula).
The response provides a correct answer (5400 cm2) for the surface area of the box and correct logic (correctly uses the surface area formula for a rectangular prism with the correct values substituted into the formula).
The response has a correct comparison answer (“the cylindrical container has a greater surface area”) and correct supporting logic (7536 cm2 is greater than 5400 cm2).
According to the rubric, if all answers and logics are valid, the response earns a score point of 3.
Sample Response
Score Point 3
8th GradeMeasurement
• Standard 11: Determine the surface area and volume of rectangular prisms, cylinders, and pyramids.
Item Type
• Multiple-choice•Open-ended
Additional Information
• Word problems• Drawings• Fractions
Think-Along Sample BoxThink-Along Sample Box
What Do You Think? Why Do You Think This?
Supporting your facts and thinking about your facts!
Think-Along Sample BoxThink-Along Sample Box
Who(Character)
What When Where Why
Focusing on Facts
Somewhere over the rainbowSome day I'll wish upon a star
And wake up where the clouds are far behind meWhere troubles melt like lemondrops
Away above the chimney topsThat's where you'll find me
Somewhere over the rainbowBluebirds fly
Birds fly over the rainbowWhy then, oh why can't I?
Some day I'll wish upon a starAnd wake up where the clouds are far behind me
Where troubles melt like lemondropsAway above the chimney tops
That's where you'll find me Somewhere over the rainbow
Bluebirds flyBirds fly over the rainbowWhy then, oh why can't I? If happy little bluebirds fly
Beyond the rainbowWhy, oh why can't I?
Somewhere over the rainbow way up highThere's a land that I heard of once in a lullaby
Somewhere over the rainbowSkies are blue
And the dreams that you dare to dream really do come true Some day I'll wish upon a star and wake up where the clouds are far behind me
Where troubles melt like lemondrops away above the chimney topsThat's where you'll find me
Somewhere over the rainbow bluebirds flyBirds fly over the rainbowWhy then, oh why can't I?
Some day I'll wish upon a star and wake up where the clouds are far behind meWhere troubles melt like lemondrops away above the chimney tops
That's where you'll find me Somewhere over the rainbow bluebirds fly
Birds fly over the rainbowWhy then, oh why can't I? If happy little bluebirds fly
Beyond the rainbowWhy, oh why can't I?
Somewhere down past the wheat field, way, way back,
there’s some land that I heard of miles past the railroad track.Somewhere down past the wheat field,
skies are gray; and the people that trudge to work do it day by day.
Someday I want to see this spotwhere troubles grow like mildew rot ...so true.
And everything revolves around the simple life they all have found – with nothing to do.
Somewhere down past the wheat field, way, way back,
There’s a land that goes beyond the yellow shack. If happy little bluejays fly…beyond the wheat field,
why oh why can’t I?
Differentiation and Intervention Strategies: find and Differentiation and Intervention Strategies: find and focusfocus
• Highlighting tape• Focus frame• Sliding mask
ADD or Me?ADD or Me?
• Provide easily distracted students with ear protection
(Wal Mart, Hardware stores)
Familiarity Breeds AttemptFamiliarity Breeds Attempt
• Give preview of things to come
Strategies Continued: Interaction Yields ReactionStrategies Continued: Interaction Yields Reaction
• Teach in chunks
• 3 facts and a fib
• Colorful questions
• Partner pair
• Vocabulary - Act III, Scene II
Differentiation and Intervention StrategiesDifferentiation and Intervention Strategies
• “Capture Math Facts With Captive Dice”
• “What’s My Name?”
• Page Protectors
• “What’s Your Response?”
• Multiply by Graphing
Using Graphing To Multiply
21 x 32 = ?
04/21/23 124
6
2 7
Ans: 672
Multiplication continued:
123 x 312 = ?
67
1 3
7
3
+
38376
Strategies - continuedStrategies - continued
• “Howdy Partner, Factor!” 1 12
2 6
3 4
• “Cheeseburger In Paradise”
Does McDonalds Sell CheeseBurgers? Does McDonalds Sell CheeseBurgers?
• “Keep Numbers In Line”
• Make math relevant and interesting
Right Or
Wrong?
www.simpsonsmath.comhomepage.smc.edu/nestler_andrew/math2/scarecrow.htm
It must be around here someplace!
Cuddles caught a cricket, but he dropped it in the GRASS. Oh no! Even with help, this is almost as hard as finding a needle in a
haystack! Suppose 3 kittens and friend each peek under one leaf of ivy every second, and they find the cricket under the 1,000th leaf. How long will it take to find that yummy cricket? (The answer is below. Try to
solve it before you peek!)
Hints
1. With 3 kittens and 1 friend searching, they look under 4 leaves every second
2. 1000 ÷ 4 = 250; so they must look for 250 seconds to peek under 1000 leaves
3. There are 60 seconds in a minute. 250 ÷ 60 = 4 with a remainder of 10
4. … so in 4 minutes and 10 seconds they’ll look under the 1,000 leaves … and find the yummy cricket
Mathcats.com
Tips for Solving Math Open-Ended from Teachers
• Use SPEAK UP– S…State the objective– P…Provide background information– E…Explain your strategy without math– A…Add in the math– K…Key in on the results– U…Use the rubric as a guide– P…Provide the standards
Tips for Solving Open-Ended Math Problems from Teachers
• Make 2 columns– Put “work” on the left– Put “explanation” on the right
work explanation
Explanation Tips
• Encourage students to EXPLAIN their work - not DESCRIBE it– Description:
“I multiplied $1.25 and 13 and got $16.25”– Explanation
“I multiplied the price of gas per gallon and the number of gallons to get the price for the gas used.”
Use “magic words” in the explanation.These are words that gear students to ‘explain’ their
work rather than ‘describe’ it.
Ways to Use Open-Ended Items in Your Classroom
• Put a problem on every test or quiz
• Homework
• Math journal
• Open-ended portfolio…..
• DO NOT use only as extra credit
Practice, Practice, Practice
• Practice should occur the entire year
• Open-ended questions should be addressed about once a week
• Incorporate these types of questions into ALL grade levels
• Open-ended questions should be an integrated part of the math curriculum at ALL grade levels
Curriculum
• Your Goal:– Open-ended items should become
a part of your classroom instruction! • NOT just an added activity to do if
you have time at the end of the chapter or on days before vacation!
Tips for Teachers
• Insist that students use correct mathematical vocabulary in their explanations (when developmentally appropriate)
• Refer to the “Terms to Know” in the math standards (all grade levels)
• Review the formulas before taking the test
Conclusion• Teaching the adopted curriculum as
intended will not only help improve your ARMT scores, but will also help improve your students’ understanding and the ability to communicate that understanding.
