Cluster 2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. (Algebra 2 - Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information
Number: MAFS.912.S-IC.2
Title: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. (Algebra 2 - Major Cluster)
Type: Cluster
Subject: Mathematics
Grade: 912
Domain-Subdomain: Statistics & Probability: Making Inferences & Justifying Conclusions

Related Standards

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MAFS.912.S-IC.2.AP.3a
Understand that statistics can be used to gain information about a population by examining a random sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
MAFS.912.S-IC.2.AP.3b
Identify the purpose of sample surveys, experiments and observational studies.
MAFS.912.S-IC.2.AP.3c
Use measures of center tendency (mean, median, mode) 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.
MAFS.912.S-IC.2.AP.3d
Identify the differences between sample surveys, experiments and observational studies.
MAFS.912.S-IC.2.AP.4a
Understand that the margin of error produces a range of values.
MAFS.912.S-IC.2.AP.4b
Use the sample data to create a proportional relationship to find the population data. For example, if there are 10 squirrels living in a 200 square foot area, how many squirrels are in a 2000 square foot area?
MAFS.912.S-IC.2.AP.4c
Use the sample data to estimate the population mean.
MAFS.912.S-IC.2.AP.5a
Use measures of center tendency (mean, median, mode) and measures of variability (range and standard deviation) for numerical data from random experiment to compare two treatments.
MAFS.912.S-IC.2.AP.6a
Make or select an appropriate statement(s) about findings.
MAFS.912.S-IC.2.AP.6b
Describe the data collection process. Describe potential biases or flaws in simple scenarios.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Assessments

Sample 4 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 2 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 3 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 1 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Lesson Plans

Gr 9-12 Adaptations in Everglades Ecosystems, Lesson 3: Crossing Lines:

Students will be able to explain the concepts of ecotone and edge effect and describe how the edge effect relates to biological diversity in a watershed.

Type: Lesson Plan

Gr 9-12. Water Use and Society, Lesson 3: A Question of Quality :

Students will learn about water quality management for the Everglades and will analyze sample data from a Stormwater Treatment Area. 

Type: Lesson Plan

Sea Otter Spotter - A Population Growth Curve Using Southern Sea Otter Census Data:

Students explore the world of population biology using the sea otter as a case study. The lesson involves reading technical reports from the US Fish and Wildlife Service as well as reading information about the sea otter from non-governmental organizations. Students are introduced to a specialized wildlife capture technique and monitoring of the endangered population through annual census data. Using that data students explore the limiting factors affecting sea otter growth and apply mathematical knowledge to analyze population growth curves. Students also produce an argument on whether the sea otter has met criteria and should be removed from the endangered species list.

Type: Lesson Plan

Hot Coffee Coming Through:

In this lesson, students will explore data collection using the temperature probe sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation to determine which coffee mug is the best. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a problem based STEM challenge. Due to the multiple skills there are many standards that are covered.

There are two options for this lab. The first student handout is for students at an average high school statistics level (Algebra 1) and will allow for standard deviation and graphical analyses of the data. The second option is for advanced students that have been exposed to hypothesis testing of claims (Algebra 2 or AP Stats).

Type: Lesson Plan

The Cereal Prize Estimation:

How many boxes of cereal would you have to purchase in order win all six prizes?

This lesson uses class data collected through simulations to allow students to answer this question. Students simulate purchasing cereal boxes and create a t-confidence interval with their data to determine how many boxes they can expect to buy.

Type: Lesson Plan

Changing World Oceans - An Ocean Acidification Simulation:

This 5-day lesson introduces students to the phenomenon of ocean acidification, including processes involved and the importance it has on earth ecosystems. It focuses on the atmosphere / hydrosphere interaction with respect to carbon dioxide. The lesson progresses from the introductory first day where student preconceptions and misconceptions are identified and addressed in an introductory lesson. The lab on the second day can be accomplished using non-specialized, inexpensive equipment or more sophisticated probeware. Day 3 is for data analysis and reflecting on the lab results and building process diagrams, and days 4 and 5 are time for writing the lab report.

Type: Lesson Plan

Interpreting Statistics: A Case of Muddying the Waters:

This lesson is intended to help you assess how well students are able to:

  • Interpret data and evaluate statistical summaries.
  • Critique someone else's interpretations of data and evaluations of statistical summaries.
The lesson also introduces students to the dangers of misapplying simple statistics in real-world contexts, and illustrates some of the common abuses of statistics and charts found in the media.

Type: Lesson Plan

CollegeReview.com:

This is a model-eliciting activity where students have been asked by a new website, CollegeReview.com, to come up with a system to rank various colleges based on five categories; tuition cost, social life, athletics, education, city population and starting salary upon graduation.

Type: Lesson Plan

5K and No More - Producing Data:

Can your school use $5000? What school doesn't?! Well, the money is available, but the student body must decide how the money will be spent!

5K and No More - Producing Data will enable students to fantasize about what they would do to improve their school if given the opportunity to answer the question, "How would $5000 best be spent at your school?" The activity begins with students distinguishing the differences between a sample survey, an experiment, and an observational study through a pre-activity. After which, the students are given five (5) scenarios in which they must discuss the pros and cons of each. In life we want things to be fair, so students must constantly think about bias. The company in this MEA desires the most efficient and effective way to collect information from the students without having to talk to everyone ... who has that kind of time!

Now, just when the students have found the most efficient and effective way to get students to share their thoughts on where the money should go, more information is revealed about the High School. How do we account for the brains and the brawn, the perfect attendee and the most missed days, or for the goth or skater?

Your Savvy Statisticians in the making will figure it out and tell you ALL about it.

Type: Lesson Plan

Preserving Our Marine Ecosystems:

The focus of this MEA is oil spills and their effect on the environment. In this activity, students from a fictitious class are studying about the effects of an oil spill on marine ecosystems and have performed an experiment in which they were asked to try to rid a teaspoon of corn oil from a baking pan filled with two liters of water as thoroughly as possible in a limited timeframe and with limited resources. By examining, analyzing, and evaluating experimental data related to resource usage, disposal, and labor costs, students must face the tradeoffs that are involved in trying to preserve an ecosystem when time, money, and resources are limited.

Type: Lesson Plan

Got You Covered!:

Students will develop a procedure for selecting car covers to protect the fleet of vehicles used by the Everywhere Sales Corporation. They will use a given data table to consider the attributes of several different brands of car covers, analyze their strengths and weaknesses, and then rank and weight the attributes according to their level of importance. The procedure will be written out in detail and a rationale provided to advise the company which car cover(s) should be used.

Type: Lesson Plan

The Video Game:

This activity can be used with students in statistics, algebra 2, or a precalculus course who have a good understanding of the statistical methods that are used in describing a given data set.

Type: Lesson Plan

Efficient Storage:

The topic of this MEA is work and power. Students will be assigned the task of hiring workers to complete a given task. In order to make a decision as to which workers to hire, the students initially must calculate the required work. The power each worker can exert, the days each worker is available to work each week, the number of sick days each worker has taken over the past 12 months, and the salary each worker commands will then be provided. Full- and/or part-time positions are available. Through data analysis, the students will need to evaluate which factors are most significant in the hiring process. For instance, some groups may select the most efficient workers; other groups may select the group of workers that will cost the company the least amount of money; still other groups may choose the workers that can complete the job in the shortest amount of time. Each group will also be required to provide the rationale that justifies the selection of which workers to hire.

Type: Lesson Plan

A TASTEFUL Experiment:

This purpose of this lesson is to enhance students' understanding of the research question that is really being addressed by experiments, observational studies and research. Through the use of a very simple question about which brand of soda that students prefer, the discussion allows the teacher and students to dig deeper into the idea that what you think a study is asking may not really be what is being found. Students will actually do an experiment, observational study and survey with only a superficial examination of the research question. (They are doing a quick TASTE TEST.) It is only after the activity that the students will try to decide precisely what they were researching and to whom this study can be generalized.

Type: Lesson Plan

The Election Resource:

This lesson is designed for students who enrolled in an elementary statistics or math for college readiness class who are at the stage of collecting and analyzing data. In their algebra 1 class, they were introduced to statistical topics such as line of best-fit and equation of a line as they relate to real-world meaning.

Type: Lesson Plan

Which Brand of Chocolate Chip Cookie Would You Buy?:

In this activity, students will utilize measurement data provided in a chart to calculate areas, volumes, and densities of cookies. They will then analyze their data and determine how these values can be used to market a fictitious brand of chocolate chip cookie. Finally, they will integrate cost and taste into their analyses and generate a marketing campaign for a cookie brand of their choosing based upon a set sample data which has been provided to them.

Type: Lesson Plan

Corn Conundrum:

The Corn Conundrum MEA provides students with an agricultural problem in which they must work as a team to develop a procedure to select the best variety of corn to grow under drier conditions predicted by models of global climate change. Students must determine the most important factors that make planting crops sustainable in restricted climate conditions for the client. The main focus of this MEA is manipulating factors relating to plant biology, including transpiration and photosynthesis.

Type: Lesson Plan

Perspectives Video: Experts

Statistical Sampling Results in setting Legal Catch RateĀ :

Fish Ecologist, Dean Grubbs, discusses how using statistical sampling can help determine legal catch rates for fish that may be endangered.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Mathematically Modeling Hurricanes:

Entrepreneur and meteorologist Mark Powell discusses the need for statistics in his mathematical modeling program to help better understand hurricanes.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Statistical Inferences and Confidence Intervals :

Florida State University Counseling Psychologist discusses how he uses confidence intervals to make inferences on college students' experiences on campus based on a sample of students.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Let's Make a Math Deal:

Should I keep my choice or switch?  Learn more about the origins and probability behind the Monty Hall door picking dilemma and how Game Theory and strategy effect the probability.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Carbon Foam and Geometry:

Carbon can take many forms, including foam! Learn more about how geometry and the Monte Carlo Method is important in understanding it.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

Hydrogeologist from Nestle Waters discusses the importance of statistical tests in monitoring sustainability and in maintaining consistent water quality in bottled water.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Fishery Independent vs Dependent Sampling Methods for Fishery Management:

NOAA Scientist Doug Devries discusses the differences between fishery independent surveys and fishery independent surveys.  Discussion includes trap sampling as well as camera sampling. Using graphs to show changes in population of red snapper.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Sample Size and Shark Research:

Deep sea shark researcher, Chip Cotton, discusses the need for a Power Analysis to determine the critical sample size in order to make inferences on how oil spills affect shark populations.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

Underwater sampling with cameras has made fishery management more accurate for NOAA scientists.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Sampling Strategies for Ecology Research in the Intertidal Zone:

Will Ryan describes methods for collecting multiple random samples of anemones in coastal marine environments.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

How to Build a Research Study on Education:

This researcher explains common methods behind randomized studies in the social sciences, specifically in education.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Filtering Noise from a Data Sample:

Safe water? Safe soil? How can we calibrate our equipment to detect small levels of pollutants and ignore other substances in the sample?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Ideas

Pitfall Trap Classroom Activity:

Patrick Milligan shares a teaching idea for collecting insect samples.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Ecological Sampling Methods and Population Density:

Dr. David McNutt explains how a simple do-it-yourself quadrat and a transect can be used for ecological sampling to estimate population density in a given area.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Strict Parents:

This task challenges students to describe parameter of interest for the given context, and design a sample survey.

Type: Problem-Solving Task

Words and Music II:

The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.

Type: Problem-Solving Task

Teaching Idea

Conditional Probability and Probability of Simultaneous Events:

This lesson is designed to further students' practice with probability as well as introduce them to conditional probability and probabilities of simultaneous independent events. The lesson provides links to discussions and activities related to conditional and simultaneous probabilities as well as suggested ways to integrate them into the lesson. Finally, this lesson provides links to follow-up lessons designed for use in succession with this one.

Type: Teaching Idea

Text Resources

Sample Size Calculation:

This informational text resource is intended to support reading in the content area. This article describes the important process used when setting up trials for statistical investigation. The article explains each parameter that is needed to calculate the sample size, then provides examples and illustrates the process. This article will enhance an upper level math course's study of statistics after significance levels and basic inferential statistics concepts have been taught.

Type: Text Resource

Scientists See the World Differently:

This informational text resource is intended to support reading in the content area. Pew Research Center surveyed scientists and the general public on 12 science oriented issues, including genetically modified foods, vaccines, nuclear power and evolution. Results of the survey showed large discrepancies between the thoughts, causes and recommendations on the issues of the scientists and the general public. Sample sizes and margins of errors are given on the survey results which are represented in percent form. The overall survey showed that the public and the scientists see the world very differently.

Type: Text Resource

How to Win at Rock-Paper-Scissors:

This informational text resource is intended to support reading in the content area. This article describes a new study about the game rock-paper-scissors. The study reveals that people do not play randomly; there are patterns and hidden psychology players frequently use. Understanding these potential moves can help a player increase their winning edge. As part of interpreting the results of the study, the article references the Nash equilibrium and the "win-stay lose-shift" strategy.

Type: Text Resource

Tutorial

Population Demographic Lab:

This lab simulation allows you to use real demographic data, collected by the US Census Bureau, to analyze and make predictions centered around demographic trends. You will explore factors that impact the birth, death and immigration rate of a population and learn how the population transitions having taken place globally.

Type: Tutorial

Video/Audio/Animation

MIT BLOSSOMS - Is Bigger Better? A Look at a Selection Bias that Is All Around Us:

This learning video addresses a particular problem of selection bias, a statistical bias in which there is an error in choosing the individuals or groups to make broader inferences. Rather than delve into this broad topic via formal statistics, we investigate how it may appear in our everyday lives, sometimes distorting our perceptions of people, places and events, unless we are careful. When people are picked at random from two groups of different sizes, most of those selected usually come from the bigger group. That means we will hear more about the experience of the bigger group than that of the smaller one. This isn't always a bad thing, but it isn't always a good thing either. Because big groups "speak louder," we have to be careful when we write mathematical formulas about what happened in the two groups. We think about this issue in this video, with examples that involve theaters, buses, and lemons. The prerequisite for this video lesson is a familiarity with algebra. It will take about one hour to complete, and the only materials needed are a blackboard and chalk. The downloadable Teacher's Guide found on the same page as the video, provides suggestions for classroom activities during each of the breaks between video segments.

Type: Video/Audio/Animation

Virtual Manipulative

Advanced Fire Simulator - Shodor:

In this online activity, students burn a simulated forest and adjust the probability that the fire spreads from one tree to the other. This simulation also records data for each trial including the burn probability, where the fire started, the percent of trees burned, and how long the fire lasted. This activity allows students to explore the idea of chaos in a simulation of a realistic scenario. Supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet are linked to the applet.

Type: Virtual Manipulative

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Problem-Solving Task

Words and Music II:

The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.

Type: Problem-Solving Task

Tutorial

Population Demographic Lab:

This lab simulation allows you to use real demographic data, collected by the US Census Bureau, to analyze and make predictions centered around demographic trends. You will explore factors that impact the birth, death and immigration rate of a population and learn how the population transitions having taken place globally.

Type: Tutorial

Virtual Manipulative

Advanced Fire Simulator - Shodor:

In this online activity, students burn a simulated forest and adjust the probability that the fire spreads from one tree to the other. This simulation also records data for each trial including the burn probability, where the fire started, the percent of trees burned, and how long the fire lasted. This activity allows students to explore the idea of chaos in a simulation of a realistic scenario. Supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet are linked to the applet.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Task

Words and Music II:

The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.

Type: Problem-Solving Task