OREGON MATH STANDARDS (2021): [7.DR]
Overview
The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.
Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.
2021 Oregon Math Guidance: 7.DR.A.1
Cluster: 7.DR.A - Formulate Statistical Investigative Questions.
STANDARD: 7.DR.A.1
Standards Statement (2021):
Formulate summary, comparative investigative questions to gain information about a population and that a sample is valid only if the sample is representative of that population.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.DR.A.1 | 8.DR.A.1 | N/A | 7.SP.A.1 7.DR.A Crosswalk |
Standards Guidance:
Clarification
- Students can generate questions about things they notice and wonder from an authentic situation.
- Understand that statistics can be used to gain information about a population and that a sample is valid only if the sample is representative of that population. (7.SP.A.1)
- Understand that random sampling tends to produce representative samples and support valid inferences.
Terminology
- A statistical investigative question is one that requires data that will vary.
- Understand that random sampling tends to produce representative samples and support valid inferences.
- Potential limitations may include how the sample was selected and/or how the questions were asked.
Teaching Strategies
- Students should have opportunities to answer statistical investigative questions about a population by collecting data from a representative sample, using random sampling techniques to collect the data.
Progressions
- A statistic computed from a random sample, such as the mean of the sample, can be used as an estimate of that same characteristic of the population from which the sample was selected. This estimate must be viewed with some degree of caution because of the variability in both the population and sample data. A basic tenet of statistical reasoning, then, is that random sampling allows results from a sample to be generalized to a much larger body of data, namely, the population from which the sample was selected. (Please reference page 8 in the Progression document).
Examples
- “How old are the students in my class?” is a statistical investigative question because it anticipates variability in students’ ages. “How old am I?” is a question used to collect data to answer the investigative question.
- Illustrative Mathematics:
- Student Achievement Partners:
- Smarter Balanced Assessment Item Illustrating 7.DR.A.1
2021 Oregon Math Guidance: 7.DR.B.2
Cluster: 7.DR.B - Collect and Consider Data.
STANDARD: 7.DR.B.2
Standards Statement (2021):
Collect or consider data from a random sample to compare and draw inferences about a population with an unknown characteristic of interest.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.DR.B.2 | 8.DR.B.2 | N/A | 7.SP.A.2 7.DR.B Crosswalk |
Standards Guidance:
Clarifications
- Use data from a random sample to gauge how far off the estimate or prediction might be.
- Students should use sample data collected to draw inferences.
Terminology
- A statistical investigative question is one that requires data that will vary.
- Potential limitations may include how the sample was selected and/or how the questions were asked.
Teaching Strategies
- Students should have opportunities to answer statistical investigative questions about a population by collecting data from a representative sample, using random sampling techniques to collect the data.
- Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
- Students should have opportunities to critique examples of sampling techniques.
- Students should conclude when conditions of sampling methods may be biased, random, and not representative of the population.
Progressions
- In short, students realize that conclusions drawn from random samples generalize beyond the sample to the population from which the sample was selected, but a sample statistic is only an estimate of a corresponding population parameter and there will be some discrepancy between the two. Understanding the variability in sampling allows the investigator to gauge the expected size of that discrepancy. (Please reference page 9 in the Progression document).
Examples
- Estimate the mean word length in a book by randomly sampling words from the book. Gauge how far off the estimate is from the actual mean.
- Predict the winner of a school election based on randomly sampled survey data. Gauge how far off the prediction might be.
- Illustrative Mathematics:
2021 Oregon Math Guidance: 7.DR.C.3
Cluster: 7.DR.C - Analyze, summarize, and describe data.
STANDARD: 7.DR.C.3
Standards Statement (2021):
Analyze two data distributions visually to compare multiple measures of center and variability.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.DR.C.3 | 8.DR.C.3 | N/A | 7.SP.B.3 7.DR.C Crosswalk |
Standards Guidance:
Teaching Strategies
- Given visual representations of data from dot plots, line graphs, histograms and box-plots, create statements that compare the measures of center and variability between two data sets.
- Students should use side by side bar graphs or segmented bar graphs to compare categorical data distributions of samples from two populations.
- Students should compare data of two samples or populations displayed in box plots and dot plots to make inferences.
- Students should be able to draw inferences using measures of central tendency (mean, median, mode) and/or variability (range, mean absolute deviation and interquartile range) from random samples.
- Students should be given multiple opportunities to compare quantitative data distributions of samples from two populations.
Progressions
- If all measurements in a population are known, no sampling is necessary and data comparisons involve the calculated measures of center. Even then, students should consider variability.
- Conclusions should be made related to a population, using a random sample, by describing a distribution using measures of central tendency (mean, median, mode) and/or variability (range, mean absolute deviation, and interquartile range). (Please reference page 10 in the Progression document).
Examples
- By comparing distributions, investigate whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
- The mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
- Illustrative Mathematics:
2021 Oregon Math Guidance: 7.DR.D.4
Cluster: 7.DR.D - Interpret data and answer investigative questions.
STANDARD: 7.DR.D.4
Standards Statement (2021):
Interpret measures of center and measures of variability for numerical data from random samples to compare between two populations, and to answer investigative questions.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.DR.D.4 | 8.DR.D.4 | N/A | 7.SP.B.4 7.DR.D Crosswalk |
Standards Guidance:
Clarification
- Students should use sample data collected to draw inferences.
Teaching Strategies
- Students should have opportunities to critique examples of sampling techniques.
- Students should conclude when conditions of sampling methods may be biased, random, and not representative of the population.
Progressions
- For random samples, students should understand that medians and means computed from samples will vary from sample to sample and that making informed decisions based on such sample statistics requires some knowledge of the amount of variation to expect. Just as for proportions, a good way to gain this knowledge is through simulation, beginning with a population of known structure. (Please reference page 10 in the Progression document).
Examples
- Decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
- Estimate the mean word length in a book by randomly sampling words from the book. Gauge how far off the estimate is from the actual mean.
- Predict the winner of a school election based on randomly sampled survey data. Gauge how far off the prediction might be.
- Illustrative Mathematics:
- Student Achievement Partners: