enVision Mathematics Topic 6
7th Grade; March – April (2 weeks); 4th Quarter
Embedded Files
Topic Title(s):
Use Sampling to Draw Inferences About Populations
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
Standard(s):
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
7.SP.A. Statistics & Probability: Use random sampling to draw inferences about a population.
Understand that statistics can be used to gain information about a population by examining a sample of the population; explain that generalizations about a population from a sample are valid only if the sample is representative of that population. Explain that random sampling tends to produce representative samples and support valid inferences. (CCSS: 7.SP.A.1)
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. (CCSS: 7.SP.A.2)
7.SP.B. Statistics & Probability: Draw informal comparative inferences about two populations.
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, 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. (CCSS: 7.SP.B.3)
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, 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. (CCSS: 7.SP.B.4)
Infer about a population using a random sample. (Entrepreneurial Skills: Inquiry/Analysis)
Make conjectures about population parameters and support arguments with sample data. (MP3)
Use multiple samples to informally model the variability of sample statistics like the mean. (MP4)
Interpret variability in statistical distributions and draw conclusions about the distance between their centers using units of mean absolute deviation. (Entrepreneurial Skills: Inquiry/Analysis)
Base arguments about the difference between two distributions on the relative variability of the distributions, not just the difference between the two distribution means. (MP3)
Model real-world populations with statistical distributions and compare the distributions using measures of center and variability. (MP4)
Inquiry Questions
Why would a researcher use sampling for a study or survey?
Why does random sampling give more trustworthy results than nonrandom sampling in a study or survey? How might methods for obtaining a sample for a study or survey affect the results of the survey?
How can a winner be concluded in an election, from a sample, before counting all the ballots?
How do measures of center (such as mean) and variability (such as mean absolute deviation) work together to describe comparisons of data?
How can we use measures of center and variability to compare two data sets? Why is it not wise to compare two data sets using only measures of center?
Coherence Connections
This expectation (7.SP.A) supports the major work of the grade.
This expectation (7.SP.B) is in addition to the major work of the grade.
In Grade 6, students study measures of center and variability to describe, compare, and contrast data sets.
In Grade 7, this expectation connects with drawing informal comparative inferences about two populations, investigating chance processes, and with developing, using, and evaluating probability models.
In Grade 7, this expectation connects with using random sampling to draw inferences about a population.
In high school, students understand and evaluate random processes underlying statistical experiments and also make inferences and justify conclusions from sample surveys, experiments, and observational studies.
In high school, students summarize, represent, and interpret data on a single count or measurement variable and also make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Academic Vocabulary & Language Expectations:
Random sample, representative sample, valid inference
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 6
Let's Investigate! Tasks
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: None since this Unit Plan supports the major work of the grade
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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