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Predicting the Future

On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.

Estimated Time:  90 minutes

Lesson Objectives:

  • The students will collect simple random samples from surveys.
  • The students will make predictions from a sample.

Key Common Core State Standards:
S.IC.1:   Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Supporting Common Core State Standards:
7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.2: 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.

Standards for Mathematical Practice Emphasized:

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
8. Look for and express regularity in repeated reasoning.

Instructional Notes:

This lesson in the module focuses on the Common Core Standard S.IC.1, which states “Understand statistics as a process for making inferences about population parameters based on a random sample from that population.” The lesson has the students continue to work with gathering random samples, as they did in the first lesson, Simply Surveying. Here in the second lesson, the students will begin to make predictions based on the sample data collected. They will make conclusions and draw inferences about the samples, comparing the results to the hypotheses they form.

Take time to read pp. 8 – 12 of the Progressions for the Common Core State Standards in Mathematics opens in new window. This document describes the progression of knowledge and understanding the students should experience as they work with Standard S.IC.1. According to this document, “Students now move beyond analyzing data to making sound statistical decisions based on probability models” (p. 8). The authors of this document identify the reasoning process as follows:

  • Develop a statistical question in the form of a hypothesis (supposition) about a population parameter.
  • Choose a probability model for collecting data relevant to that parameter.
  • Collect data.
  • Compare the results seen in the data with what is expected under the hypothesis.
It is important to note how the Progression Documents expect the students to make inferences about population parameters. It states: “That determination is left to the investigator and the circumstances surrounding the decision to be made. Statistics and probability weigh the chances; the person in charge of the investigation makes the final choice.” Thus, the students should experience many probability situations in which the inferences are left to the student, and the analysis of the data is left to the opinion of the student. This does not mean incorrect analysis of data should be accepted. It means that no formal hypothesis testing is to be done at this point. The students should not be expected to conduct t-tests or chi square testing, or any other such statistical tests.

> Go to Predicting the Future lesson

Sample Responses

For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in the Teacher Resources.

Predicting the Future - Page 4

Note that each student or group of students will need a coin, a large sheet of paper and a marker to simulate the lighting strike experiment.

Allow the student to determine if the results of the experiment are “close” to the population parameter, or “far away” from the population parameter. If the students decide the results are far enough away from the population parameter, then the students have evidence to reject their hypothesis. The more experience students have with simple situations like the lightning experiment and the dice experiment that follows, the better understanding they will have of how statistical decisions are made based on sample data that are related to probability. This decision-making process does not guarantee a correct answer to the underlying statistical question. It does, however, help the students develop their understanding of statistics as a process for making inferences about population parameters based on a random sample from that population.

> Go to lesson, page 4

Predicting the Future - Page 6

For the Algebra II Journal Reflection, each pair of students will need a coin (penny), two printouts of the die net from their journals, and tape and scissors to assemble the nets into dice.

> Go to lesson, page 6

UDL Opportunities:

Principle 1: Provide Multiple Means of Representation
Checkpoint 1.1 Offer ways of customizing the display of information
Checkpoint 1.3 Offer alternatives for visual information
Checkpoint 2.1 Clarify vocabulary and symbols
Checkpoint 2.3 Support decoding text, mathematical notation, and symbols
Checkpoint 2.5 Illustrate through multiple media
Checkpoint 3.1 Activate or supply background knowledge
Checkpoint 3.2 Highlight patterns, critical features, big ideas, and relationships
Checkpoint 3.3 Guide information processing, visualization, and manipulation
Checkpoint 3.4 Maximize transfer and generalization

Principle 2: Provide Multiple Means of Action and Expression
Checkpoint 4.1 Vary the methods for response and navigation
Checkpoint 5.1 Use multiple media for communication
Checkpoint 6.2 Support planning and strategy development
Checkpoint 6.3 Facilitate managing information and resources

Principle 3: Provide Multiple Means of Engagement
Checkpoint 7.2 Optimize relevance, value, and authenticity
Checkpoint 7.3 Minimize threats and distractions
Checkpoint 8.1 Heighten salience of goals and objectives
Checkpoint 8.4 Increase mastery-oriented feedback
Checkpoint 9.3 Develop self-assessment and reflection