In this performance assessment, students apply their knowledge and skills related to random sampling, population inferences, and comparative inferences within the context of a school ordering new graduation caps and gowns. Students critique a provided sampling approach and explain how they would revise the approach so that they could draw inferences about the population’s desired cap and gown colors. Additionally, students are provided data on the height of male and female students and asked to examine whether there are meaningful height differences between the two groups that should be considered when ordering new gowns. Students will explain their mathematical reasoning, create, interpret, and use data from a graph, and use what they know about random sampling to generalize.
Specifically, students will be asked to engage in two activities. The first has the students respond to a classmate who designs a sampling approach to gather data regarding cap and gown future graduation color preferences for grades 7-12 students in the district. Students taking the assessment will explain if the sampling approach leads to accurate inferences and what, if any, might lead to its improvement. In addition, students will have to create a mathematical model to use to display the cap and gown data and explain it to the principal. The second activity has male and female student height randomly collected data to determine the most appropriate sizes of the new cap and gowns. Several questions are raised from the data collected.
Students will respond to a total of six questions from the two parts of this performance assessment. The questions include sampling, inferencing, mathematical model from the data, random sampling, and analyzing graphs.
This performance assessment would be ideal for completing after instruction on statistics and probability--specifically, content related to using random sampling to make inferences about a population and drawing informal comparative inferences about two populations using measures of central tendency and variability.
Students should be able to recognize and explain the differences between random and non-random sampling approaches and the implications of the sampling approach for making inferences about a population. Students should also be able to create a mathematical model for survey data, read a simple line plot/histogram, interpret mean and mean absolute deviation (MAD), which is one measure of variability.
Students do not need to compute any formal comparative inferences (e.g., t-tests) using the mean and SD, or interpret p-values. Actual computations related to mean and MAD are beyond the expectations for this assessment. Students are expected to apply informal comparative inferences gleaned from interpreting the visual distributions and provided means and measures of variability. The task also includes two questions involving proportional relationships.
In this performance assessment, students apply their knowledge and skills related to random sampling, population inferences, and comparative inferences within the context of a school ordering new graduation caps and gowns. Students critique a provided sampling approach and explain how they would revise the approach so that they could draw inferences about the population’s desired cap and gown colors. Additionally, students are provided data on the height of male and female students and asked to examine whether there are meaningful height differences between the two groups that should be considered when ordering new gowns. Students will explain their mathematical reasoning, create, interpret, and use data from a graph, and use what they know about random sampling to generalize.
Specifically, students will be asked to engage in two activities. The first has the students respond to a classmate who designs a sampling approach to gather data regarding cap and gown future graduation color preferences for grades 7-12 students in the district. Students taking the assessment will explain if the sampling approach leads to accurate inferences and what, if any, might lead to its improvement. In addition, students will have to create a mathematical model to use to display the cap and gown data and explain it to the principal. The second activity has male and female student height randomly collected data to determine the most appropriate sizes of the new cap and gowns. Several questions are raised from the data collected.
Students will respond to a total of six questions from the two parts of this performance assessment. The questions include sampling, inferencing, mathematical model from the data, random sampling, and analyzing graphs.
This performance assessment would be ideal for completing after instruction on statistics and probability--specifically, content related to using random sampling to make inferences about a population and drawing informal comparative inferences about two populations using measures of central tendency and variability.
Students should be able to recognize and explain the differences between random and non-random sampling approaches and the implications of the sampling approach for making inferences about a population. Students should also be able to create a mathematical model for survey data, read a simple line plot/histogram, interpret mean and mean absolute deviation (MAD), which is one measure of variability.
Students do not need to compute any formal comparative inferences (e.g., t-tests) using the mean and SD, or interpret p-values. Actual computations related to mean and MAD are beyond the expectations for this assessment. Students are expected to apply informal comparative inferences gleaned from interpreting the visual distributions and provided means and measures of variability. The task also includes two questions involving proportional relationships.
| Big Ideas | Competencies |
|---|---|
B. Operations and Algebraic ThinkingStudents can use mathematics to analyze and evaluate historical, political, economic, scientific, and social problems and make conjectures about possible solutions. |
Compute with Rational Numbers 1Students can solve real-world and mathematical problems involving the four operations with rational numbers, using tools strategically. |
C. Measurement and Data AnalysisStudents can collect and organize data to interpret, model, and investigate issues connected to their communities, lived experiences, and cultural identities. |
Using Data 1Students can use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. |
Below are analytic teacher rubrics. The column on the left shows the dimension that is being measured in the student’s performance. The levels across the top row indicate the performance level in the dimensions. Occasionally all dimensions and performance levels are exemplified by multiple students in a single recording.
| Dimensions | Not Yet Meeting Expectations | Meeting Expectations | Exceeding Expectations |
|---|---|---|---|
Concepts/ProceduresWhat is the evidence that the student can apply correct computational processes and strategies to solve mathematical problems? |
No exemplars at this time.
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No exemplars at this time.
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No exemplars at this time.
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Reasoning/ExplainingWhat is the evidence that the student can defend a solution or critique another person's solution using mathematical language? |
No exemplars at this time.
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No exemplars at this time.
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No exemplars at this time.
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Modeling and Using Tools |
No exemplars at this time.
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No exemplars at this time.
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No exemplars at this time.
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