# MAFS.7.SP.1.2Archived Standard

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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability
Cluster: Level 3: Strategic Thinking & Complex Reasoning
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 Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
Also Assesses: 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.
• Assessment Limits :

Context must be grade appropriate

• Calculator :

Netural

• Context :

Required

Sample Test Items (4)
• Test Item #: Sample Item 1
• Question: A middle school has
• 220 students in grade 6;
• 170 students in grade 7; and
• 100 students in grade 8.

The media specialist wants to know which books are the most popular among the students in her school. Since she cannot ask all the students, she will survey a group of them.

Which sample can best help the media specialist draw conclusions about the preferences of all the students in the school?

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

• Test Item #: Sample Item 2
• Question:

A company plans to ship 2,000 packages of chocolate. The company randomly selects 100 packages and finds that five packages have an incorrect weight.

Based on this data, how many packages out of the 2,000 should be predicted to have an incorrect weight?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question: A chocolate company produces 2 types of chocolate: type A and type B. The company selects 25 random packages of each type to check their weight and finds that one package of type A has an incorrect weight and 3 packages of type B have an incorrect weight.

How many packages should the company predict have an incorrect weight when it checks 2000 of each type?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 4
• Question: A chocolate company selects 50 random packages and checks their weight. It finds that 2 packages have an incorrect weight.

How many packages out of 2000 should the company predict have an incorrect weight?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

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

## Formative Assessments

Prediction Predicament:

Students are asked to use sample data to make and assess a prediction.

Type: Formative Assessment

School Days:

Students are asked to use data from a random sample to estimate a population parameter and explain what might be done to increase confidence in the estimate.

Type: Formative Assessment

Movie Genre:

Students are asked to use data from a random sample to draw an inference about a population.

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

Using Box Plots and the Mean Absolute Deviation to Interpret Data:

This lesson explores the use of box plots and the mean absolute deviation to compare two data sets and draw inferences.

Type: Lesson Plan

Radioactive Dating Lesson 2:

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

Sea Ice Analysis Grade 7:

The changing climate is an important topic for both scientific analysis and worldly knowledge. This lesson uses data collected by the National Snow and Ice Data Center to create and use statistical analysis as a tool to evaluate the sea ice loss. Students will use technology to quickly generate graphs for each month looking for trends, patterns, or deviations over time.

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

Measurement and Data Collection:

In this interdisciplinary lesson, students will practice the skill of data collection with a variety of tools and by statistically analyzing the class data sets will begin to understand that error is inherent in all data.

This lesson uses the Hip Sciences Sensor Wand and Temperature Probe. Please refer to the corresponding Hip Science Sensor Guide(s) for information on using the sensor.

Type: Lesson Plan

Measurement Data Error:

In this interdisciplinary lesson, students will practice the skill of data collection with a variety of tools and by statistically analyzing the class data sets will begin to understand that error is inherent in all data.

Type: Lesson Plan

Measurement and Data Collection:

In this interdisciplinary lesson, students will practice the skill of data collection with a variety of tools and by statistically analyzing the class data sets will begin to understand that error is inherent in all data.

This lesson uses the Hip Sciences Sensor Wand and Temperature Probe. Please refer to the corresponding Hip Science Sensor Guide(s) for information on using the sensor.

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

Pick Me! Pick Me!:

This lesson focuses on both parts of standard MAFS.7.SP.1.2. Students are provided with an opportunity to create multiple samples of the same size based on a population (which is the classroom.) Then students will analyze these different samples to determine whether the samples are accurate representations of the population. Also, students will make predictions about a population based on a representative sample.

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

Generating Multiple Samples to Gauge Variation:

Students explore variation in random samples and use random samples to make generalizations about the population.

Type: Lesson Plan

Using Box Plots to Interpret Data:

This lesson explores the creation of box plots to compare two data sets and draw inferences.

Type: Lesson Plan

## Original Student Tutorial

Exploring Mean Absolute Deviation: Lionfish:

Compare multiple samples of lionfish to make generalizations about the population by analyzing the samples’ mean absolute deviations (MAD) and their distributions in this interactive tutorial.

Type: Original Student Tutorial

## 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.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Mathematically Modeling Hurricanes:

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

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

<p>How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!</p>

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Field Sampling with the Point-centered Quarter Method:

In this video, Jim Cox describes a sampling method for estimating the density of dead trees in a forest ecosystem.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Fishery Independent vs Dependent Sampling Methods for Fishery Management:

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

Type: Perspectives Video: Professional/Enthusiast

Sample Size and Shark Research:

<p>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.</p>

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

<p>Underwater sampling with cameras has made fishery management more accurate for NOAA&nbsp;scientists.</p>

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

Pitfall Trap Classroom Activity:

<p>Patrick&nbsp;Milligan&nbsp;shares a teaching idea for collecting insect samples.</p>

Type: Perspectives Video: Teaching Idea

Quadrat Sampling M&M Lesson:

<p>This teacher explains how a 3D-printed quadrat can be used with an M&amp;M sampling lesson to engage students when they explore how to use data from a random sample to draw inferences about a population.</p>

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.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Election Poll, Variation 3:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 3 introduces technology and encourages students to use a random number generator or statistics software to generate a random sample of student responses and to simulate a distribution of sample proportions from a population with 50% successes.

Estimating the Mean State Area:

The task is designed to show that random samples produce distributions of sample means that center at the population mean, and that the variation in the sample means will decrease noticeably as the sample size increases.

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Election Poll, Variation 1:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). There are two important goals in this task: seeing the need for random sampling and using randomization to investigate the behavior of a sample statistic. These introduce the basic ideas of statistical inference and can be accomplished with minimal knowledge of probability.

## 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

## MFAS Formative Assessments

Movie Genre:

Students are asked to use data from a random sample to draw an inference about a population.

Prediction Predicament:

Students are asked to use sample data to make and assess a prediction.

School Days:

Students are asked to use data from a random sample to estimate a population parameter and explain what might be done to increase confidence in the estimate.

## Original Student Tutorials Mathematics - Grades 6-8

Exploring Mean Absolute Deviation: Lionfish:

Compare multiple samples of lionfish to make generalizations about the population by analyzing the samples’ mean absolute deviations (MAD) and their distributions in this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Exploring Mean Absolute Deviation: Lionfish:

Compare multiple samples of lionfish to make generalizations about the population by analyzing the samples’ mean absolute deviations (MAD) and their distributions in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

<p>How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!</p>

Type: Perspectives Video: Expert

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Election Poll, Variation 1:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). There are two important goals in this task: seeing the need for random sampling and using randomization to investigate the behavior of a sample statistic. These introduce the basic ideas of statistical inference and can be accomplished with minimal knowledge of probability.

## Parent Resources

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

## Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

<p>How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!</p>

Type: Perspectives Video: Expert