# MAFS.7.SP.1.1

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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use random sampling to draw inferences about a population. (Supporting 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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Assessed with: MAFS.7.SP.1.2
Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

A company has three sales departments (local, regional, and national) at each of several locations across the United States. Each local sales department has 120 employees. The company wants to survey its employees to determine the most effective sales method.

Which sample should the company use to arrive at the most reliable conclusion?

• Difficulty: N/A
• Type: MC: Multiple Choice

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0800010: M/J Health Grade 7 Year (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
0800015: M/J Health & Career Planning Grade 7 Year (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022 (current), 2022 and beyond)
0800040: M/J Health Grade 7 Semester (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)
2003030: M/J STEM Physical Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2002200: M/J STEM Environmental Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2001025: M/J STEM Astronomy and Space Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2104040: M/J Emerging Leaders (Specifically in versions: 2015 - 2022 (current), 2022 - 2023, 2023 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.SP.1.AP.1a: Survey a sample population to generate data that represents the total population.

## Related Resources

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

## Assessments

Sample 3 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 2 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

## Formative Assessments

Ice Cream Survey:

Students are asked to choose a sampling method that would be most representative of a population and justify their selection.

Type: Formative Assessment

Height Research:

Students are asked to describe a method for collecting data in order to estimate the average height of 12 year old boys in the U.S.

Type: Formative Assessment

Favorite Sport Survey:

Students are asked to evaluate an inference made using a biased sampling method.

Type: Formative Assessment

Estimating: Counting Trees:

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

• Solve simple problems involving ratio and direct proportion.
• Choose an appropriate sampling method.
• Collect discrete data and record them using a frequency table.

Includes worksheets and student work examples, including specific feedback and analysis of misconceptions

Type: Formative Assessment

## Lesson Plans

Analyze Data:

This lesson uses statistical analysis to evaluate data. The data used is from the app created by the students in lesson 2 of the Data Set and Statistics Unit. This lesson also guides students in recognizing the different types of data collected and how the distribution's shape can be affected when graphed at different intervals in histograms. This is the final lesson in the unit.

Type: Lesson Plan

Gather Data For Distribution by Programming an App:

This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet.

Type: Lesson Plan

Data Sets Represented in Computers:

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Type: Lesson Plan

Students will learn about the importance of using multiple radioactive dating methods to date an artifact as well as learn about the if programming control structure. This is Lesson 2 in the Radioactive Dating Unit and will begin the experience in coding a program to illustrate student understanding of radioactive dating.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

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

Is My Backpack Too Massive?:

This lesson combines many objectives for seventh grade students. Its goal is for students to create and carry out an investigation about student backpack mass. Students will develop a conclusion based on statistical and graphical analysis.

Type: Lesson Plan

Cricket Songs:

Using a guided-inquiry model, students in a math or science class will use an experiment testing the effect of temperature on cricket chirping frequency to teach the concepts of representative vs random sampling, identifying directly proportional relationships, and highlight the differences between scientific theory and scientific law.

Type: Lesson Plan

Populations and Samples:

In this lesson students work through class discussions and activities to identify populations and samples, as well as gain an understanding of the importance of selecting reliable random samples to gain information about a population. Students work in pairs to gather information using a biased sample and random sample to compare data and reflect on possible misconceptions that a biased sample could produce.

Type: Lesson Plan

Statistically Speaking…..:

This lesson will demonstrate how data in a real-world situation can be used to make predictions or inferences. The lesson also will help students become familiar with randomly selecting samples, biased, and unbiased information.

Type: Lesson Plan

And the survey says...:

This short and fun lesson connects random sampling and generalizations to students' real-life situations. The lesson is interactive, participative, and allows for easy modification(s) to meet your class' interests.

Type: Lesson Plan

How Old Are My Employees?:

This lesson provides activities for students to conceptually understand how to estimate an unknown characteristic of a population, the effect of sample size, the effect of multiple samples in same sizes on estimations, and the representativeness of the random sampling. The lesson consists of three tasks followed by group discussion sessions and a whole class discussion session at the end. Teachers use formative assessment by giving feedback after each task.

Type: Lesson Plan

Estimating: Counting Trees:

This lesson unit is intended to help you assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, collect discrete data, and record their data using a frequency table.

Type: Lesson Plan

Computer Simulated Experiments in Genetics:

A computer simulation package called "Star Genetics" is used to generate progeny for one or two additional generations. The distribution of the phenotypes of the progeny provide data from which the parental genotypes can be inferred. The number of progeny can be chosen by the student in order to increase the student's confidence in the inference.

Type: Lesson Plan

Selecting a Sample Population:

The student explores several strategies for selecting a sample population to support making inferences about the population.

Type: Lesson Plan

## Perspectives Video: Experts

Statistical Sampling Results in setting Legal Catch Rate :

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

Type: Perspectives Video: Expert

Assessment of Antarctic Ice Sheet Movement Rate by Sediment Core Sampling:

Eugene Domack, a geological oceanographer, describes how sediment cores are collected and used to estimate rates of ice sheet movement in Antarctica. Video funded by NSF grant #: OCE-1502753.

Type: Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Type: Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

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.

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.

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.

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.

Type: Perspectives Video: Professional/Enthusiast

Making Inferences about Wetland Population Sizes:

This ecologist from the Coastal Plains Institute discusses sampling techniques that are used to gather data to make statistical inferences about amphibian populations in the wetlands of the Apalachicola National Forest.

Type: Perspectives Video: Professional/Enthusiast

Random Sampling to Estimate Wildlife Populations:

Dr. Bill McShea from the Smithsonian Institution discusses sampling and inference in the study of wildlife populations.

This video was created in collaboration with the Okaloosa County SCIENCE Partnership, including the Smithsonian Institution and Harvard University.

Type: Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

Pitfall Trap Classroom Activity:

Patrick Milligan shares a teaching idea for collecting insect samples.

Type: Perspectives Video: Teaching Idea

Collecting Population Data: "What Lives in the Wetland?":

Want an unforgettable field trip led by a real scientist where your students get hands-on experience with collecting population data? Consider the "" educational program from Remote Footprints.

Type: Perspectives Video: Teaching Idea

Don’t Spill the Beans!:

The purpose of this task is for students to make a hypothesis, and then doing an experiment to test each students hypothesis. Students will collect and record their data, use graphical methods to describe their data, and finally analyze and interpret their results in the context of the activity.

Mr. Brigg's Class Likes Math:

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.

## Text Resource

Cell Phone Ownership Hits 91% of Adults:

This informational text resource is intended to support reading in the content area. A Pew Research Center survey indicates that cell phone ownership is at an all-time high, with 91% of Americans owning a cell phone in 2013. Statistical tests show that cell phone usage is significantly higher in men, college-educated people, the wealthy, and those living in urban/suburban areas. This rise in ownership is associated with a variety of positive impacts of cell phone use, but previous research shows there are several negative impressions and impacts of cell phones as well.

Type: Text Resource

## Virtual Manipulative

The students will play a classic game from a popular show. Through this they can explore the probability that the ball will land on each of the numbers and discover that more accurate results coming from repeated testing. The simulation can be adjusted to influence fairness and randomness of the results.

Type: Virtual Manipulative

## MFAS Formative Assessments

Favorite Sport Survey:

Students are asked to evaluate an inference made using a biased sampling method.

Height Research:

Students are asked to describe a method for collecting data in order to estimate the average height of 12 year old boys in the U.S.

Ice Cream Survey:

Students are asked to choose a sampling method that would be most representative of a population and justify their selection.

## Student Resources

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

## Perspectives Video: Experts

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Type: Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast

Mr. Brigg's Class Likes Math:

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.

## Virtual Manipulative

The students will play a classic game from a popular show. Through this they can explore the probability that the ball will land on each of the numbers and discover that more accurate results coming from repeated testing. The simulation can be adjusted to influence fairness and randomness of the results.

Type: Virtual Manipulative

## Parent Resources

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

## Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast