G6 U8 Constructed Response Rubric
Grade 6 Unit 8 Constructed Response Statistics and Probability Description Task
Common Core State Standard for Mathematical Content (MC) 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
1. Line Plots
6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
2. Histograms
3. Box Plots
6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Standards for Mathematical Practice (MP) MP.1 MP.2 MP.4 MP.5 MP.6 MP.7 MP.8 MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8 MP.1 MP.2 MP.4 MP.5 MP.6 MP.7 MP.8
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked. Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 1
Scoring Rubric Question 1. a. Student gives the correct answer and accurately rewrites the question. Responses will vary. Sample responses: How many full years has each sixth grader attended our school? How many full years has each sixth grader in our class attended our school?
Points 1
b. Student gives the correct answer and accurately rewrites the question. Responses will vary. Sample responses: What is the favorite cafeteria lunch of all sixth graders in our school? How many times a week do the sixth graders in our school eat pizza?
1
c. Student gives the correct answer and accurately rewrites the question. Responses will vary. Sample responses: How many times has each sixth grader received a certificate of achievement from the principal since Kindergarten? How many certificates of achievement has each sixth grader received from the principal this year?
1
1 1
d. Student gives the correct answer. Yes 2. a. Student gives the correct answer. 32 b. Student gives the correct answer. Skewed to the right
1
c. Student gives the correct answer. 9
1
d. Student gives the correct answer and shows work. Mean is 2.75; Median is 3 3. Student accurately X X displays the data in a X X line plot. Sample response: X X X X
X
X
X
X
1
2
3
1 2
X
X
X
X
X
X
X
4
5
6
7
Number of Years in the After-School Program
4. Student gives accurate advice. Responses will vary. Sample response: I would advise Snow to ask a question that anticipates variability. As it is written, Snow’s question can be answered by asking students to raise their hands if they have perfect attendance and counting them. There would be no variation in responses – either “yes” a student has had perfect attendance or “no” they haven’t. Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 2
2
Total
5. Student gives an accurate explanation. Wording may vary. Sample response: A histogram is a better choice than a line plot or a box plot to display Snow’s data because there is a large amount of data over a wide range with many unique numbers. It would be more informative to view the data in intervals on the number line. 6. a. Student creates an accurate histogram. Intervals may vary. Sample histogram:
2
2
Title: Mr. Melo's Class Attendance 10
Number of Students
9 8 7 6 5 4 3 2 1 0 0-4
5-9
10-14
15-19
20-24
24-29
Number of Days Absent
b. Student gives the correct answer. 29
1
c. Student gives the correct answer and shows work. Mean is 11; Median is 8.5
1
d. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: No, without the data, the measures of variability and center could not be calculated. To find the range, mean, and median, we need to know the lowest and highest value, and in a histogram those are “hidden” within the ranges. Without the data set, we cannot find precise numbers to calculate any of the measures of variability and center.
2
Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 3
7. Student gives the correct values and accurate descriptions of their meanings. Wording may vary. Sample responses. Value
Meaning The shortest
Minimum
48 in
6th
grade student is 48 inches
tall. 48 inches is the smallest data point in the set. 52 inches marks the height of the student who is taller than 25% of all 6th graders
Q1
52 in
and shorter than 75% of all 6th graders. Within the middle 50% of all sixth grade heights (IQR), 52 inches is the shortest. 53 inches is the median height, the height that is found in the middle of the data set when the values have been listed in order.
Median
53 in
In this case, since there are an even number of data points, the median is the average of the middle two heights in the list. 60 inches marks the height of the student who is taller than 75% of all the 6 th
Q3
60 in
graders and shorter than 25% of the sixth graders. Within the middle 50% (the IQR), 60 inches is the tallest.
Maximum
72 in
The tallest 6th grader is 72 inches tall. 72 inches is the largest data point in the set. The IQR is calculated by subtracting Q1
IQR
8 in
from Q3. The value is the middle 50% of all heights measured. Half of the students’ heights are between 52 and 60 inches.
Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 4
6
8. a. Student gives the correct answers.
2
Minimum
Q1
Median
Q3
Maximum
IQR
.5
3
5
6.5
9.5
3.5
2
b. Student displays an accurate box plot. Sample response:
Total
Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 5
30
Common Core State Standard for Mathematical Content (MC) 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
1. Line Plots
6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
2. Histograms
3. Box Plots
6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Standards for Mathematical Practice (MP) MP.1 MP.2 MP.4 MP.5 MP.6 MP.7 MP.8 MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8 MP.1 MP.2 MP.4 MP.5 MP.6 MP.7 MP.8
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked. Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 1
Scoring Rubric Question 1. a. Student gives the correct answer and accurately rewrites the question. Responses will vary. Sample responses: How many full years has each sixth grader attended our school? How many full years has each sixth grader in our class attended our school?
Points 1
b. Student gives the correct answer and accurately rewrites the question. Responses will vary. Sample responses: What is the favorite cafeteria lunch of all sixth graders in our school? How many times a week do the sixth graders in our school eat pizza?
1
c. Student gives the correct answer and accurately rewrites the question. Responses will vary. Sample responses: How many times has each sixth grader received a certificate of achievement from the principal since Kindergarten? How many certificates of achievement has each sixth grader received from the principal this year?
1
1 1
d. Student gives the correct answer. Yes 2. a. Student gives the correct answer. 32 b. Student gives the correct answer. Skewed to the right
1
c. Student gives the correct answer. 9
1
d. Student gives the correct answer and shows work. Mean is 2.75; Median is 3 3. Student accurately X X displays the data in a X X line plot. Sample response: X X X X
X
X
X
X
1
2
3
1 2
X
X
X
X
X
X
X
4
5
6
7
Number of Years in the After-School Program
4. Student gives accurate advice. Responses will vary. Sample response: I would advise Snow to ask a question that anticipates variability. As it is written, Snow’s question can be answered by asking students to raise their hands if they have perfect attendance and counting them. There would be no variation in responses – either “yes” a student has had perfect attendance or “no” they haven’t. Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 2
2
Total
5. Student gives an accurate explanation. Wording may vary. Sample response: A histogram is a better choice than a line plot or a box plot to display Snow’s data because there is a large amount of data over a wide range with many unique numbers. It would be more informative to view the data in intervals on the number line. 6. a. Student creates an accurate histogram. Intervals may vary. Sample histogram:
2
2
Title: Mr. Melo's Class Attendance 10
Number of Students
9 8 7 6 5 4 3 2 1 0 0-4
5-9
10-14
15-19
20-24
24-29
Number of Days Absent
b. Student gives the correct answer. 29
1
c. Student gives the correct answer and shows work. Mean is 11; Median is 8.5
1
d. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: No, without the data, the measures of variability and center could not be calculated. To find the range, mean, and median, we need to know the lowest and highest value, and in a histogram those are “hidden” within the ranges. Without the data set, we cannot find precise numbers to calculate any of the measures of variability and center.
2
Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 3
7. Student gives the correct values and accurate descriptions of their meanings. Wording may vary. Sample responses. Value
Meaning The shortest
Minimum
48 in
6th
grade student is 48 inches
tall. 48 inches is the smallest data point in the set. 52 inches marks the height of the student who is taller than 25% of all 6th graders
Q1
52 in
and shorter than 75% of all 6th graders. Within the middle 50% of all sixth grade heights (IQR), 52 inches is the shortest. 53 inches is the median height, the height that is found in the middle of the data set when the values have been listed in order.
Median
53 in
In this case, since there are an even number of data points, the median is the average of the middle two heights in the list. 60 inches marks the height of the student who is taller than 75% of all the 6 th
Q3
60 in
graders and shorter than 25% of the sixth graders. Within the middle 50% (the IQR), 60 inches is the tallest.
Maximum
72 in
The tallest 6th grader is 72 inches tall. 72 inches is the largest data point in the set. The IQR is calculated by subtracting Q1
IQR
8 in
from Q3. The value is the middle 50% of all heights measured. Half of the students’ heights are between 52 and 60 inches.
Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 4
6
8. a. Student gives the correct answers.
2
Minimum
Q1
Median
Q3
Maximum
IQR
.5
3
5
6.5
9.5
3.5
2
b. Student displays an accurate box plot. Sample response:
Total
Copyright © Swun Math Grade 6 Unit 8 Constructed Response Rubric, Page 5
30
