A. Mathematical Processes and E. Statistics and Probability

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” / Notes
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” / While earlier grades are asked to organize, display and interpret data, it has not been with histograms, scatterplots, and box plots.
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”

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.

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A. Identify the mean, median, mode, and range for this data.

Mean: ______

Median: ______

Mode: ______

Range: ______

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.

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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.

MARISA’S BIKE TRIP

Page 1 of 2

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.

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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

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.

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Name ______Date ______

Mathematics Grade 8

Classroom Assessment Based on Standards

CABS Identifier: “Cuddly Critters”

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.

Page 1 of 2

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.

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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.

If Pat spent 2 hours on mathematics, about how much longer did he spend on science than on history?

Answer: ______

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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

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Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 031489\

Page 2 of 2
Name ______Date ______

Mathematics Grade 8

Classroom Assessment Based on Standards

CABS Identifier: “School Supplies”

The graph below shows the number of pens, pencils, rulers, and erasers sold by a store in one week.

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.