Download A. Mathematical Processes and E. Statistics and Probability Grade 8

Grade 8
Classroom Assessments Based on State Standards
(CABS)
A. Mathematical Processes and E. Statistics and Probability
(From the WKCE-CRT Mathematics Assessment Framework, Beginning of Grade 10)
A. Mathematical Processes
• Use reasoning and logic to: Perceive patterns, Identify relationships, formulate questions, pose
problems, make conjectures, justify strategies and test reasonableness of results.
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of
ways, e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
E. Statistics and Probability
E.a Subskill: Data Analysis and Statistics
• Organize, display, compare and interpret data in a variety of ways in mathematical and real-world
contexts e.g., histograms, line graphs, stem-and-leaf plots, scatter plots, box-and whiskers, bar charts,
Venn diagrams, tables, circle graphs.
• Interpret, analyze and make predictions from organized and displayed data e.g. mean, median, mode.
and measures of variation such as range. *
• Analyze, evaluate and critique methods and conclusions of statistical experiments e.g., randomness,
sampling, techniques, surveys.
E.b Subskill: Probability
• Determine the likelihood of occurrence of simple and complex events e.g., experimental versus
theoretical probability. *
* Slightly modified to reflect “Sharing the 10th Grade Descriptors”
Note:
While both Grade 8 learning targets for statistics and probability are given for each of the following
CABS, it is the target in BOLD font which aligns with that particular CABS.
Examining the 10th Gr. Descriptors: What’s “New” for 8th Graders?
The 8th Grade Classroom Assessments Based on State Standards were created to reflect the 10th grade
state descriptors and the MPS learning targets for 8th grade. The 10th grade state descriptors should be
used by both 8th and 9th grade math teachers. See your MTL for the document, “Sharing the 10th Grade
Descriptors”, or visit the Portal (math page, inside the teacher community), for the delineated shared
responsibilities.
The 10th grade state descriptors contain both previously introduced and new concepts. It is the intent of
the 8th - 9th Grades Math Assessment Pilot, after considerable feedback from Kevin McLeod, UWM
Mathematics Professor and Co-Investigator, MMP, to emphasize the new concepts. Alerting teachers to
what is new for 8th graders should have classroom implications.
The 8th grade math CABS are therefore split into two categories. First, a series of “Power CABS” which
can be used to assess student understanding of concepts not found in earlier grade level state descriptors.
Second, a series of CABS not denoted with “Power” which can be used to assess student understanding
of concepts found in both earlier state descriptors and in the 10th grade descriptors.
The chart below identifies the descriptors that are new to 8th grade as determined by the 8th - 9th Grades
Math Assessment Pilot, 2006-2007.
E. Statistics and Probability
Objective/Subskill 10th Gr. Descriptor Piece that
is “New”
E.a
“Organize, display, compare
and interpret data in a variety
of ways in mathematical and
real-world contexts e.g.
histograms, scatterplots, and
box and whiskers plot”
E.a
“Interpret, analyze, and make
predictions from organized and
displayed data e.g. mean,
median, mode and measures of
variation such as range”
E.a
“Analyze, evaluate, and
critique methods and
conclusions of statistical
experiments, e.g. randomness,
sampling techniques, surveys”
E. b
“Determine the likelihood of
occurrence of complex events”
Notes
While earlier grades are asked to organize,
display and interpret data, it has not been with
histograms, scatterplots, and box plots.
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
CABS Identifier: “Reading Survey”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptors:
• Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
• Interpret, analyze and make predictions from organized and displayed data e.g. mean, median, mode, and measures of
variation such as range.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
A survey was done to find out how many books students had read during the first semester. These are
the responses from twenty students.
5, 11, 8, 1, 5, 3, 4, 1, 7, 9, 3, 5, 6, 2, 1, 10, 5, 6, 5, 12
Create a line plot to display the data.
Page 1 of 2
A. Identify the mean, median, mode, and range for this data.
Mean: ________
Median: ________
Mode:
________
Range: ________
B. What observations can you make about the distribution of this data?
C. Formulate a question that this data raises for you.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
CABS Identifier: “Marissa’s Bike Trip”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
Speed (miles per hour)
MARISA’S BIKE TRIP
16
12
8
4
0
20
40
60
Time in Minutes
Page 1 of 2
80
Using the information in the graph, describe what could have happened during each of the four
segments of the trip, including her speed throughout the trip.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “New Show Survey”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptors:
• Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
• Interpret, analyze and make predictions from organized and displayed data e.g. mean, median, mode, and measures of
variation such as range.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
These are the results of a class survey on whether students liked a new television show:
25 students liked the new show.
15 students disliked the new show.
10 students had no opinion on the new show.
A. Create a graph to display the data.
Page 1 of 2
B. What do you think the future of this show will be? Use the data to support your answer.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
CABS Identifier: “Cuddly Critters”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze and
summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of
outcomes, and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Probability
Descriptor:
Determine the likelihood of occurrence of simple and complex events e.g. experimental versus theoretical probability.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
A. Draw bars on the graph below so that the number of dogs is twice the number of cats, and the
number of hamsters is one-fourth the number of dogs.
How Many Pets?
Number of pets
12
10
8
6
4
2
Dogs
Cats
Type of Pets
Page 1 of 2
Hamsters
B. The data from the graph in Part A came from the animals that were for sale at the Cuddly Critter Pet
Shop. Last night, Jerell got a pet from this shop. Use the data from Part A to find the probability that the
pet he took home was a certain type.
P (Hamster) =
P (Cat) =
P (Dog) =
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
CABS Identifier: “Pat’s Pie Chart”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
Objective: A. Mathematical Processes
Descriptors:
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
The pie chart below shows the portion of time Pat spent on homework in each subject last week.
Pat’s Homework
.
If Pat spent 2 hours on mathematics, about how much longer did he spend on science than on history?
Answer: _________________________
Page 1 of 2
Show all your work, and explain your thinking using words, numbers, symbols, and/or
pictures.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Venn Diagram”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
Place the numbers 1 through 30 in the correct categories in the Venn diagram below.
Even Numbers
Numbers Divisible by 3
Page 1 of 2
Make two observations about your results.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 031489\
Page 2 of 2
Name __________________________________________________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Date _______________________
CABS Identifier: “School Supplies”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Solve and analyze routine and non-routine problems.
The graph below shows the number of pens, pencils, rulers, and erasers sold by a store in one week.
160
School Supplies
Number of Items
140
120
100
80
60
40
20
Items Sold by Store
The names of the items are missing from the graph. Pens were the item most often sold. Fewer erasers
than any other item were sold. More pencils than rulers were sold. How many pencils were sold?
Answer: ________________
Reproduced and adapted with permission from the TIMSS and PIRLS International Study Center, Lynch Education, Boston
College.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Mary’s Mean”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Interpret, analyze and make predictions from organized and displayed data e.g. mean, median, mode, and measures of
variation such as range.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Solve and analyze routine and non-routine problems.
Joe had three test scores of 78, 76, and 74, while Mary had scores of 73, 83, and 75.
What is the minimum score Joe would have needed on his third test to have a higher mean than Mary’s
mean?
________________
How do you know?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Representative?”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Analyze, evaluate and critique methods and conclusions of statistical experiments e.g. randomness, sampling, techniques,
surveys.
Objective: A. Mathematical Processes
Descriptors:
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Solve and analyze routine and non-routine problems.
A poll is being taken at John Audubon Middle School to determine whether to change the school
mascot. Which of the following would be the best place to find a sample of students to interview?
A.
B.
C.
D.
E.
A school bus
The cafeteria
A foreign language class
The faculty room
Name another place: ____________________________________
Explain why your choice?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Chip Pairs”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze and
summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of
outcomes, and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Probability
Descriptor:
Determine the likelihood of occurrence of simple and complex events e.g. experimental versus theoretical probability.
Objective: A. Mathematical Processes
Descriptors:
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
A box contains 3 chips numbered 1 through 3. One chip will be taken at random from the box and then
put back into the box. Then a second chip will be taken from the box.
In the space provided below, list all possible pairs of chips.
Number on First Chip
Number on Second Chip
Page 1 of 2
How likely is it that the two chips will have the same number? Give your reasoning.
Adapted from the U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Box Plot”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptors:
• Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
• Interpret, analyze and make predictions from organized and displayed data e.g. mean, median, mode, and measures of
variation such as range.
Objective: A. Mathematical Processes
Descriptors:
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
Samples of seventh and eighth grade students were asked how much time they spent doing homework
last Wednesday night. The results are show below.
Time (in minutes) Spent on Wednesday Night Homework
8th Graders
7th Graders
0
10
20
30
40
50
60
70
Minutes
Page 1 of 2
80
90
100
110
Fill in the following data for the 7th graders based on the box plot on page 1:
Range
Median
Lower quartile
Upper quartile
Use the following data to construct a box plot for the 8th graders on page 1:
Range
Median
Lower quartile
Upper quartile
0 to 110
40
20
70
Describe some similarities and differences between the distribution of study times for the 7th and 8th
graders.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Probability Candy”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze and
summarize data using measures of central tendency and variation, and evaluate methods and conclusions.
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of
outcomes, and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Probability
Descriptor:
Determine the likelihood of occurrence of simple and complex events e.g. experimental versus theoretical probability.
Objective: A. Mathematical Processes
Descriptors:
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Solve and analyze routine and non-routine problems.
A package of candies contained 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the
package, opened it, took out one candy at a time and ate it. The first two candies he took out and ate
were blue. Bill thinks the probability of getting a blue candy on his third try is 10 or 1 .
30
3
Is Bill correct or incorrect? _________________________
Explain your answer using words, numbers, and/or pictures.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National
Assessment of Educational Progress (NAEP)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Math Girls”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze and
summarize data using measures of central tendency and variation, and evaluate methods and conclusions.
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of
outcomes, and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Probability
Descriptor:
Determine the likelihood of occurrence of simple and complex events e.g. experimental versus theoretical probability.
Objective: A. Mathematical Processes
Descriptors:
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Solve and analyze routine and non-routine problems.
In a math class of 30 students, the probability that a student chosen at random will be a girl is 2 . How
5
many girls are in the class?
Answer: __________
Show all your work.
Reproduced and adapted with permission from the TIMSS and PIRLS International Study Center, Lynch Education, Boston
College.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Scatter Plot”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures,
justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g. using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
Your teacher has asked everyone in the class to measure their heights and arm spans. That data is shown
in the table below.
Height (inches)
67
61
68
61
63
66
62
64
69
72
68
71
66
60
65
63
67
65
64
66
67
Arm Span (inches)
65
60
69
63
60
64
59
64
70
70
66
72
65
59
66
64
67
63
65
67
68
Page 1 of 2
Construct a scatter plot using the data from the table.
Identify a relationship between the two variables.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2
Name __________________________________________________________
Date _______________________
Mathematics Grade 8
Classroom Assessment Based on Standards
Power CABS Identifier: “Histogram”
MPS Learning Target: Statistics and Probability
MPS Learning Target #4: Design and conduct investigations, display data using appropriate representations, analyze
and summarize data using measures of central tendency and variation, and evaluate methods and conclusions
MPS Learning Target #5: Design and analyze experiments with simple and complex events, predict likelihood of outcomes,
and justify strategies based on theoretical and experimental probabilities.
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Data Analysis and Statistics
Descriptor:
Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts e.g. histograms,
line graphs, stem-and-leaf plots, scatter plots, box plots, bar graphs, Venn diagrams, tables, circle graphs.
Objective: A. Mathematical Processes
Descriptors:
• Connect mathematics to the real world as well as within mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Solve and analyze routine and non-routine problems.
A survey was taken by Mary outside her town’s local movie theater on a Friday night. She asked the
first 90 people going into the theater their ages and recorded their responses in a frequency table.
Place the following 10 ages into the table below:
22 24 29 30 8 47 48 31 29 51
Age Group
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
Frequency
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Using the information from the frequency table on page 1, construct a histogram.
Most of the movie goers are between what ages: _________________________
How could this information be useful to the theater’s management to make a profit?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant
No. 0314898.
Page 2 of 2