# ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (9 - 12)
Title: Statistics: Using Sampling to Count Trees
URL: https://aptv.pbslearningmedia.org/resource/statistics-sampling-count-trees/statistics-using-sampling-to-count-trees/
Description:

This exercise was developed to complement the film The National Parks of Texas by Texas PBS & Villita Media. In this activity, students will learn about estimating the number of trees in a large area based on a smaller area.

This is one way statisticians measure forests and other wide expanses of land. It's also a great way to illustrate how polling works. Scientists will interview a smaller sample size of Americans, rather than every single American, and then make estimations based on their results. In the same way, we counted smaller samples of trees, rather than all of the trees individually to get an estimate of how many trees are in the park total.

Note: The corresponding lesson plan can be found under the "Support Materials for Teachers" link on the right side of the page.

Subject: Mathematics (9 - 12)
Title: Algebra II Module 4, Topic C: Drawing Conclusions Using Data From a Sample
URL: https://www.engageny.org/resource/algebra-ii-module-4-topic-c-overview
Description:

This topic introduces different types of statistical studies (e.g., observational studies, surveys, and experiments) (S-IC.B.3). The role of randomization (i.e., random selection in observational studies and surveys and random assignment in experiments) is addressed. A discussion of random selection (i.e., selecting a sample at random from a population of interest) shows students how selecting participants at random provides a representative sample, thereby allowing conclusions to be generalized from the sample to the population. A discussion of random assignment in experiments, which involves assigning subjects to experimental groups at random, helps students see that random assignment is designed to create comparable groups making it possible to assess the effects of an explanatory variable on a response.

The distinction between population characteristics and sample statistics (first made in Grade 7) is revisited. Scenarios are introduced in which students are asked a statistical question that involves estimating a population mean or a population proportion. For example, students are asked to define an appropriate population, population characteristic, sample, and sample statistics that might be used in a study of the time it takes students to run a quarter mile or a study of the proportion of national parks that contain bald eagle nests.

In this topic, students use data from a random sample to estimate a population mean or a population proportion. Building on what they learned about sampling variability in Grade 7, students use simulation to create an understanding of the margin of error. In Grade 7, students learned that the proportion of successes in a random sample from a population varies from sample to sample due to the random selection process. They understand that the value of the sample proportion is not exactly equal to the value of the population proportion. In Algebra II, they use margin of error to describe how different the value of the sample proportion might be from the value of the population proportion. Students begin by using a physical simulation process to carry out a simulation. Starting with a population that contains successes (using a bag with black beans and white beans), they select random samples from the population and calculate the sample proportion. By doing this many times, they are able to get a sense of what kind of differences are likely. Their understanding should then extend to include the concept of margin of error. Students then proceed to use technology to carry out a simulation. Once students understand the concept of margin of error, they go on to learn how to calculate and interpret it in context (S-IC.A.1, S-IC.B.4). Students also evaluate reports from the media in which sample data are used to estimate a population mean or proportion (S-IC.B.6).

Note: Although this module is identified as Algebra II in the EngageNY curriculum, it corresponds to the  Precalculus Alabama Course of Study.

ALEX Classroom Resources: 2