Smarter Balanced Assessment Consortium:

Transcription

1 Smarter Balanced Assessment Consortium: High School Mathematics Smarter Balanced Assessment Consortium, 2017

2 Interim Comprehensive Assessment (ICA) No Calculator Session 1 C 1 I 2 The student selects These points might be on the graph of a function for the second, third, and fourth tables selects These points cannot be on the graph of a function for the first table. 3 The student selects Yes for the third expression selects No for the first, second, and fourth expressions. 1 K 1 A 4 15x 5 y 7 1 F 5 A 1 H 6 D 1 D Calculator Session 1 C 1 P 2 C 1 L 3 A 3 F 4 C 1 L 5 C and D 4 C 6 2 points: 6s + 5 = 221, or equivalent equation s = 36 OR 36 6s + 5 = 221, or equivalent equation OR s = 36 OR 36 2 A 7 C 3 A 8 c = rt 1 G 9 B 3 A 10 A 1 J Smarter Balanced Mathematics High School 2

3 11 B 1 C 12 t = 1200/480, or an equivalent equation 1 G 13 A 1 P 14 C 3 C 15 The student receives full credit by selecting: The maximum amount of gas in the gas tank was 60 ounces: False The amount of gas in the gas tank is at a maximum at 0 minutes: True The gas tank will be empty after 60 minutes: True 1 L C 17 B 1 J 18 The student receives full credit by selecting: sin(f) = 4.5/7.5: No cos(f) = 6/7.5: No sin(g) = 4.5/7.5: Yes cos(g) = 6/7.5: Yes 19 The student receives full credit by selecting: hour 0 to hour 1: Positive hour 5 to hour 9: Equal to 0 hour 9 to hour 12: Positive hour 11 to hour 14: Negative 1 O 4 D 20 D 3 C 21 2 points: Student clearly identifies an additional piece of information that Thomas could obtain to better determine which road is more dangerous. Student describes an appropriate calculation using that information that can help to make that determination. Sample responses (2 points): Thomas can try to estimate the number of people who use each street in 4 B Smarter Balanced Mathematics High School 3

4 a year. He can divide the number of accidents by the number of drivers on that street to find out the likelihood of being involved in an accident on that street. For example, if Maple Street had 2000 drivers, 97/2000 would tell how likely an accident was on Maple Street. There may be more accidents on Elm Street simply because it is a much longer street, and there are more places to get into accidents. He would need to find out the length of both streets, then divide the amount of accidents each street had by the length of the street. Then he could use that to compare the accident rate and figure out which was more dangerous. Student clearly identifies an additional piece of information that Thomas could obtain to better determine which road is more dangerous. BUT Student does not describe a calculation that can be used to help make that determination. 0 points: Student does not identify an additional piece of information that Thomas could obtain to better determine which road is more dangerous , or any value in the range of 49 to 50 1 O = v, or an equivalent equation 1 G 24 C 1 N 25 The student receives full credit by selecting: The line of symmetry of g(x) is x = 1: False The maximum of g(x) is less than the maximum of f(x): False The value of x when f(x) is at its maximum is less than the value of x when g(x) is at its maximum: True 1 M 26 A and D 3 B PT 1 B 2 C PT 2 2 points: The student disagrees with Kelly presents evidence to justify his/her conclusion. Evidence should include a comparison in the percentage of drivers that get in an accident for another age level. Sample response (2 points): I disagree with Kelly. 16-year-olds do have the least number of accidents but only because the number of drivers is much fewer than the other ages. 19- year-old drivers are much safer with an accident rate of 25% opposed to 37% for 16-year-old drivers. The student disagrees with Kelly presents partial evidence to justify his/her conclusion. Evidence should include a partial comparison in the 3 E Smarter Balanced Mathematics High School 4

5 percentage of drivers that get in an accident for another age level. OR The student agrees with Kelly but includes some indication of process knowledge. 0 points: The student has demonstrated merely an acquaintance with the topic, or provided a completely incorrect or uninterpretable response. The student s response may be associated with the task, but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. PT 3 PT 4 2 points: Student finds the average rate of change (0.2% or 0.002) interprets it in the context of the situation. Sample response (2 points): The average rate of change is The percent of drivers that are in an accident decreases 0.2% for every additional practice hour driven. Student finds the average rate of change. OR Student finds the incorrect rate of change but interprets it in the context of the situation. 0 points: The student has demonstrated merely an acquaintance with the topic, or a completely incorrect or uninterpretable response. The student s response may be associated with the task in the item but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. 2 points: Student states that 17-year-old drivers are not least likely, provides an explanation, and includes all calculations associated with determining answer. Sample response (2 points): 17-year-old drivers are not least likely. Drivers who receive their licenses at age 16 years, 6 months are the least likely to commit a moving violation in their first 8 months of driving with a license. The probability that they commit a moving violation over the first 8 months is 0.12 or 12%, as opposed to 14% for 17 year olds and 15% for 16 year olds. Student states that 17-year-old drivers are not least likely and provides partial mathematical justification or otherwise demonstrates a partial understanding of the mathematical content and practices essential to the task. 4 D 3 E Smarter Balanced Mathematics High School 5

6 0 points: The student has demonstrated merely an acquaintance with the topic, or provided a completely incorrect or uninterpretable response. The student s response may be associated with the task, but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. PT or = A PT 6 3 points: The student has demonstrated a full and complete understanding of all mathematical content and practices essential to this task. The student has addressed the task in a mathematically sound manner. The response contains evidence of the student s competence in problem solving, reasoning, and/or modeling to the full extent that these processes relate to the specified task. The response may, however, contain minor flaws that do not detract from a demonstration of full understanding. Award 3 points if the student makes a recommendation including all 4 requirements and offers full and complete mathematical justification for this recommendation. The times for the requirements must also fall sequentially (i.e., permit age of 15, holding their permit time for 18 months, and licensing age 16 years and 6 months). Sample response (3 points): I recommend that drivers can receive their learner s permits at age 15 and hold them for 18 months. The drivers should be required to practice for 100 hours and may receive their driver s licenses at 16 years and 6 months old. I decided on 16 years and 6 months because they have the lowest probability of committing a moving violation. Holding their permits for 18 months gives them a probability of 0.03 of getting in an accident, which is the second lowest total. Only 4% of the drivers who drive 100 practice hours get into an accident, which is very low. Age 15 is the age that drivers could get their permits and hold them for 18 months before they can receive their licenses. 2 points: The student has demonstrated a reasonable understanding of the mathematical content and practices essential to this task. The student has addressed most of the task in a mathematically sound manner. The response contains sufficient evidence of the student s competence in problem solving, reasoning, and/or modeling, but not enough evidence to demonstrate a full understanding of the processes he/she applies to the specified task. The response may contain errors that can be attributed to misinterpretation of the prompt; errors attributed to insufficient, non-mathematical knowledge; and errors attributed to careless execution of mathematical processes or algorithms. Award 2 points if the student makes a recommendation including all 4 requirements and offers reasonable mathematical justification for this recommendation. The times for the requirements must also fall sequentially. The student has demonstrated a partial understanding of the mathematical 4 A Smarter Balanced Mathematics High School 6

7 content and practices essential to this task. The student s response contains some of the attributes of an appropriate response but lacks convincing evidence that the student fully comprehends the essential mathematical ideas addressed by this task. Such deficits include evidence of insufficient mathematical knowledge; errors in fundamental mathematical procedures; and other omissions or irregularities that bring into question the student s competence in problem solving, reasoning, and/or modeling related to the specified task. Award 1 point if the student makes a recommendation including all 4 requirements and offers partial or no mathematical justification for this recommendation. The times for the requirements must also fall sequentially. OR Award 1 point if the student gives a partial recommendation and offers some mathematical justification for this recommendation. Note: A partial recommendation involves 2 or 3 valid requirements (i.e. valid requirements include times that fall sequentially and increase: the age to obtain a permit, the length of the permit time, the amount of practice time, and the age to obtain a license). 0 points: The student has demonstrated merely an acquaintance with the topic, or a completely incorrect or uninterpretable response. The student s response may be associated with the task in the item but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. Smarter Balanced Mathematics High School 7

8 Interim Assessment Block: Algebra and Functions I Linear Functions, Equations, and Inequalities , or an equivalent value 1 I 2 17 < n or n > 17 1 I 3 C 1 I 4 2 points: 6s + 5 = 221, or equivalent equation s = 36 OR 36 6s + 5 = 221, or equivalent equation OR s = 36 OR 36 2 A 5 B 1 J 6 A 1 J 7 A 1 J 8 The student receives full credit by selecting: 9 2 points: The maximum amount of gas in the gas tank was 60 ounces: False The amount of gas in the gas tank is at a maximum at 0 minutes: True The gas tank will be empty after 60 minutes: True 3.5t + 4t = 60, or equivalent equation t = 8 OR 8 3.5t + 4t = 60, or equivalent equation OR t = 8 OR 8 10 The student receives full credit by selecting: f(x) = 4x ( 1/4): Table B f(x) = 4x + ( 1/4): Table C f(x) = 4x + (3/4): Table A 1 L 2 A 1 M Smarter Balanced Mathematics High School 8

9 11 C 3 E 12 The student matches all of the following: the first recursive function and f(n) = 2n + 6 the second recursive function and f(n) = 2n + 10 the third recursive function and f(n) = 3n N = v, or equivalent equation 1 G 14 B 1 J 15 D 4 E Interim Assessment Block: Algebra and Functions II Quadratic Functions, Equations, and Inequalities 1 The student receives full credit by selecting: x = 2: Yes x = 1/2: No x = 2: Yes 1 H 2 A 3 A 3 A 1 I 4 26/15, or equivalent value 1 H 5 The student receives full credit by selecting: x 13 = 4: One Real Solution 2 x + 10 = 8: No Real Solution 2/(x 1) = 3/(x + 2): One Real Solution 1 H 6 D 1 J 7 b = d wn, or equivalent equation 1 G 8 A 1 N 9 The student receives full credit by selecting: The height of the ball decreased from when the ball was at a distance of 2.5 feet from the starting point to a distance of 5 feet from the starting point: False 1 L Smarter Balanced Mathematics High School 9

10 The starting and ending heights are equivalent: True The highest point reached by the ball was 6.8 feet: False 10 The student receives full credit by selecting: The line of symmetry of g(x) is x = 1: False The maximum of g(x) is less than the maximum of f(x): False The value of x when f(x) is at its maximum is less than the value of x when g(x) is at its maximum: True 1 M 11 B 1 J 12 A 4 D 13 D and F 1 J 14 The student receives full credit by selecting: The length (longest side) of the rectangle created by the living space and the observation decks is 22 feet: Yes The width (shortest side) of the rectangle created by the living space and the observation decks is 20 feet: No The area of each observation deck is 128 square feet: No The perimeter of the rectangle created by the living space and the observation decks is equal to the perimeter of the indoor living space: Yes 15 The student selects Growth for the second, fourth, and fifth functions selects Decay for the first and third functions. 4 A 1 M Interim Assessment Block: Geometry and Right Triangle Trigonometry 1 A 3 F 2 The student receives full credit by selecting: sin (A) = 4/5: Yes cos (A) = 5/3: No sin (B) = 3/4: No 1 O Smarter Balanced Mathematics High School 10

11 cos (B) = 4/5: Yes 3 C 3 C 4 The student receives full credit by selecting: tan (D) = 5/12: Yes sin (F) = 12/13: Yes cos (F) = 13/5: No sin (D) = 13/5: No 1 O A 6 49, or any value in the range of 49 to 50, inclusive 1 O 7 The student receives full credit by selecting: 12/sin (P): Yes 12/cos (P): No 5/sin (Q): Yes 5/tan (Q): No 1 O O or O 10 The student receives full credit by selecting: 6/sin B: Yes 6/cos A: Yes 8 tan A: No 8 tan B: No 1 O O 12 A and D 1 O or O 14 75, or any number in the range of to 75 1 O 15 E and F 2 A Smarter Balanced Mathematics High School 11

12 Interim Assessment Block: Statistics and Probability 1 A 4 F 2 D 1 P 3 C 1 P 4 The student receives full credit by selecting: Mean: Decreases Median: Cannot Be Determined Standard Deviation: Increases 1 P 5 D 1 P 6 D 4 D 7 B 1 P 8 B 2 D 9 The student receives full credit by selecting: Number of Students Who Did Push-ups: Greater for Mr. Anderson s Class Maximum Number of Push-ups: Equal for Both Classes Mean Number of Push-ups: Greater for Ms. Brown s Class 10 The student selects Value A is Greater for the second pair of values selects Value B is Greater for the third pair of values selects Equal for the first pair of values. 11 The student selects True for the first and third statements selects False for the second and fourth statements. 1 P 4 C 2 A 12 any value between 10.8 and B Interim Assessment Block: Seeing Structure in Expressions/Polynomial Expressions 1 3x 2 4x OR 4x + 3x 2 1 F Smarter Balanced Mathematics High School 12

13 2 The student receives full credit by selecting: 7 3x = 3 7x : No 64 x = 4 3x : Yes 2 4x = 16 x : Yes 6 5x = 30x: No 1 D 3 C 1 E 4 x 2 + y 2 x, or equivalent expression 1 F 5 C 1 D 6 a 8 b 16 1 E 7 C 1 D 8 C 1 D 9 b 8 1 E 10 D 3 F 11 a 27 b 6 1 E 12 C 3 D D 14 A 3 E 15 C 4 D Interim Assessment Block: Geometry Congruence 1 C 3 B 2 B 3 B 3 D 3 A 4 The student receives full credit by selecting: Rotation of 180º around the origin: Supports Jessie s Claim Reflection across the line y = 2: Does Not Support Jessie s Claim 3 G Smarter Balanced Mathematics High School 13

14 Translation up 1.25 units: Supports Jessie s Claim Reflection across the x-axis: Does Not Support Jessie s Claim 5 The student receives full credit by selecting: m 1 + m 4 = 180º: Always True m 5 m 7 = 0º: Always True z y: Sometimes True 2 8: Always True m 2 m 3 = m 1 m 4: Sometimes True 3 G 6 C 3 F 7 B 3 E 8 The student enters y = x, or any line that passes through the origin, i.e., y = mx for any value of m, in the first response box. The student enters y = x + 2, or any line with a non-zero y-intercept, i.e., y = mx + b for any non-zero value of b, in the second response box. 3 F 9 A 3 F 10 D 3 F 11 C 3 B 12 A 3 B Interim Assessment Block: Geometry Measurement and Modeling A 2 68, 69, or 70 4 A 3 D 4 B 4 C 2 A A Smarter Balanced Mathematics High School 14

15 6 The student receives full credit by selecting: Square coop with side length of 10 feet: Greater than 10 Rectangular coop with width of 5 feet and perimeter of 26 feet: Equal to 10 Circular coop with diameter of 4 feet: Less than 10 4 D 7 A 2 D A 9 D 2 A A Interim Assessment Block: Interpreting Functions 1 D 1 K 2 B and F 2 C 3 The student receives full credit by selecting: f(x) = (x 5)/(x 3): x 3 f(x) = x 3/(x 5): x 5 and x 3 f(x) = x 3 : x 3 f(x) = (x 3)/(x 5): x 5 1 K 4 C 1 K 5 The student receives full credit by selecting: The temperature reached its highest point during the experiment at Hour 12: False The temperature was at its lowest when the experiment began: False The temperature was decreasing for more hours than it was increasing during the experiment: True The temperature at the end of the experiment was equal to the temperature at the beginning of the experiment: True 1 L Smarter Balanced Mathematics High School 15

16 6 C 1 L 7 B 1 L 8 3, or equivalent value 1 L 9 The student receives full credit by selecting: The population is increasing throughout the time period: True The greatest growth in population was from year 5 to 15: True The population has a constant rate of change: False The population was about 9,000 when the town was founded: True 10 The student receives full credit by selecting: y = 3(x 1): Domain: All Real Numbers and Range: All Real Numbers y = 3 x 1 : Domain: All Real Numbers and Range: y 0 y = 3(x 1) 2 : Domain: All Real Numbers and Range: y 0 1 L 3 G A 12 The student receives full credit by selecting: The bird population increased the same amount each year: False The bird population is always increasing: True The greatest increase in the bird population occurred between year 2 and year 3: False 1 L 13 A 1 L 14 The student receives full credit by selecting: Hannah s orders increased by the greatest amount between weeks 7 and 8: False Hannah s orders increased at an average rate of 0. 7 orders per week from week 1 to week 10: True Hannah s orders will continue to decrease after week 10: Cannot be determined Hannah received a total of more than 60 orders in the first 10 weeks: False 4 D Smarter Balanced Mathematics High School 16

17 Interim Assessment Block: Number and Quantity 1 C 1 A 2 The student receives full credit by selecting: : Irrational 4 + 9: Rational 3 + ( 36): Rational 3 + 2: Irrational 1 B 3 B 1 A 4 B 1 A 5 C and D 1 B 6 B 1 A 7 The student receives full credit by selecting: x y: Always x y: Sometimes 3 G 8 B 1 C 9 The student receives full credit by selecting: 0 x 5 and 0 y 75: Yes 0 x 10 and 0 y 50: Yes 0 x 50 and 0 y 10: No 0 x 75 and 0 y 5: No 1 C 10 C 1 C 11 The student receives full credit by selecting: 150 x 3700 and 1 y 15: No 1 x 15 and 10 y 310: No 1 C Smarter Balanced Mathematics High School 17

18 10 x 310 and 1 y 15: No 1 x 15 and 150 y 3700: Yes 12 C 4 A 13 B 1 C 14 B 3 E 15 D 3 D Interim Assessment Block: Mathematics Performance Task 1 B 2 C 2 2 points: The student disagrees with Kelly presents evidence to justify his/her conclusion. Evidence should include a comparison in the percentage of drivers that get in an accident for another age level. Sample response (2 points): I disagree with Kelly. 16-year-olds do have the least number of accidents but only because the number of drivers is much fewer than the other ages. 19- year-old drivers are much safer with an accident rate of 25% opposed to 37% for 16-year-old drivers. The student disagrees with Kelly presents partial evidence to justify his/her conclusion. Evidence should include a partial comparison in the percentage of drivers that get in an accident for another age level. OR The student agrees with Kelly but includes some indication of process knowledge. 0 points: The student has demonstrated merely an acquaintance with the topic, or provided a completely incorrect or uninterpretable response. The student s response may be associated with the task, but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. 3 2 points: Student finds the average rate of change (0.2% or 0.002) interprets it in the context of the situation. Sample response (2 points): The average rate of change is The percent of drivers that are in an 3 E 4 D Smarter Balanced Mathematics High School 18

19 accident decreases 0.2% for every additional practice hour driven. Student finds the average rate of change. OR Student finds the incorrect rate of change but interprets it in the context of the situation. 0 points: The student has demonstrated merely an acquaintance with the topic, or a completely incorrect or uninterpretable response. The student s response may be associated with the task in the item but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. 4 2 points: Student states that 17-year-old drivers are not least likely, provides an explanation, and includes all calculations associated with determining answer. Sample response (2 points): 17-year-old drivers are not least likely. Drivers who receive their licenses at age 16 years, 6 months are the least likely to commit a moving violation in their first 8 months of driving with a license. The probability that they commit a moving violation over the first 8 months is 0.12 or 12%, as opposed to 14% for 17 year olds and 15% for 16 year olds. Student states that 17-year-old drivers are not least likely and provides partial mathematical justification or otherwise demonstrates a partial understanding of the mathematical content and practices essential to the task. 0 points: The student has demonstrated merely an acquaintance with the topic, or provided a completely incorrect or uninterpretable response. The student s response may be associated with the task, but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. 3 E or = A 6 3 points: The student has demonstrated a full and complete understanding of all mathematical content and practices essential to this task. The student has addressed the task in a mathematically sound manner. The response contains evidence of the student s competence in problem solving, reasoning, and/or modeling to the full extent that these processes relate to the specified task. The response may, however, contain minor flaws that do not detract from a demonstration of full understanding. 4 A Smarter Balanced Mathematics High School 19

20 Award 3 points if the student makes a recommendation including all 4 requirements and offers full and complete mathematical justification for this recommendation. The times for the requirements must also fall sequentially (i.e., permit age of 15, holding their permit time for 18 months, and licensing age 16 years and 6 months). Sample response (3 points): I recommend that drivers can receive their learner s permits at age 15 and hold them for 18 months. The drivers should be required to practice for 100 hours and may receive their driver s licenses at 16 years and 6 months old. I decided on 16 years and 6 months because they have the lowest probability of committing a moving violation. Holding their permits for 18 months gives them a probability of 0.03 of getting in an accident, which is the second lowest total. Only 4% of the drivers who drive 100 practice hours get into an accident, which is very low. Age 15 is the age that drivers could get their permits and hold them for 18 months before they can receive their licenses. 2 points: The student has demonstrated a reasonable understanding of the mathematical content and practices essential to this task. The student has addressed most of the task in a mathematically sound manner. The response contains sufficient evidence of the student s competence in problem solving, reasoning, and/or modeling, but not enough evidence to demonstrate a full understanding of the processes he/she applies to the specified task. The response may contain errors that can be attributed to misinterpretation of the prompt; errors attributed to insufficient, non-mathematical knowledge; and errors attributed to careless execution of mathematical processes or algorithms. Award 2 points if the student makes a recommendation including all 4 requirements and offers reasonable mathematical justification for this recommendation. The times for the requirements must also fall sequentially. The student has demonstrated a partial understanding of the mathematical content and practices essential to this task. The student s response contains some of the attributes of an appropriate response but lacks convincing evidence that the student fully comprehends the essential mathematical ideas addressed by this task. Such deficits include evidence of insufficient mathematical knowledge; errors in fundamental mathematical procedures; and other omissions or irregularities that bring into question the student s competence in problem solving, reasoning, and/or modeling related to the specified task. Award 1 point if the student makes a recommendation including all 4 requirements and offers partial or no mathematical justification for this recommendation. The times for the requirements must also fall sequentially. OR Award 1 point if the student gives a partial recommendation and offers some mathematical justification for this recommendation. Note: A partial recommendation involves 2 or 3 valid requirements (i.e. valid requirements include times that fall sequentially and increase: the age to obtain a permit, the length of the permit time, the amount of practice time, and the age to obtain a license). Smarter Balanced Mathematics High School 20

21 0 points: The student has demonstrated merely an acquaintance with the topic, or a completely incorrect or uninterpretable response. The student s response may be associated with the task in the item but contains few attributes of an appropriate response. There are significant omissions or irregularities that indicate a lack of comprehension in regard to the mathematical content and practices essential to this task. No evidence is present that demonstrates the student s competence in problem solving, reasoning, and/or modeling related to the specified task. Smarter Balanced Mathematics High School 21