 Mathematics Grade 7

Strand: STATISTICS AND PROBABILITY (7.SP)

Use random sampling to draw inferences about a population (Standards 7.SP.1�2). Draw informal comparative inferences about two populations (Standards 7.SP.3�4). Investigate chance processes and develop, use, and evaluate probability models (Standards 7.SP.5�8).
• Beat the Odds
Students will develop and use models of probability in this online game interactive. The classroom activity has them explore the experimental side of probability and probability and randomness. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Chapter 1 - Mathematical Foundation (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Probability, Percent, Rational Number Equivalence.
• Chapter 1 - Student Workbook (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 7 student workbook. It covers the following topics: Probability, Percent, Rational Number Equivalence.
• Chapter 7 - Mathematical Foundation (UMSMP)
This is Chapter 7 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities.
• Chapter 7 - Student Workbook (UMSMP)
This is Chapter 7 of the Utah Middle School Math: Grade 7 student workbook. It focuses on Probability and Statistics.
• College Athletes
In this task, students are able to conjecture about the differences in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability.
• Compound Probability
This video shows students how to calculate the probability of drawing a particular card from a deck of cards. The students continue to work with cards in the classroom activity where they calculate the probability of drawing specific cards and explain their strategy for the calculation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Conditional Probability and Probability of Simultaneous Events
This lesson plan is designed to help students understand and use the formula for probability of simultaneous independent events.
• Create a Graph
This applet allows students to create bar, line, area, pie, and XY graphs.
• Designing Experiments: Physicians' Health Study
How do scientists and doctors use data to deal with and control disease? This video from Annenberg's Learners Learning Math show how data was used to design an trial dealing with epidemiology. Students then apply their new understanding to take part in an experiment and design a trial of their own. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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).
• 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).
• 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).
• 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.
• Estimating: Counting Trees
This lesson unit is intended to help educators assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, and collect discrete data and record them using a frequency table.
• Estimation from Random Sampling
By taking random samples of the number of penguins in a sub-region in this interactive students understand how those samples can be used to estimate the total penguin population in the region. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
This lesson unit addresses common misconceptions relating to probability of simple and compound events. The lesson will help educators assess how well students understand concepts of equally likely events, randomness, and sample sizes.
• Events and Outcomes (Counting) video
This video introduces and explains the topic.
• Experimental Probability
Using devices such as spinners and dice, students can conduct probability experiments in this lesson plan's applet.
• Fire: Modeling Probability
This lesson is designed to help students understand probability and chance and understand it in real life situations.
• Gathering Data for a Line Plot
Two interactives are used in this lesson and both involve counting raisins in boxes and then plotting a graph. Students extend their understanding of mean, median, mode, and range after creating line plots in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Grade 7 Math Module 5: Statistics and Probability (EngageNY)
In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• Grade 7 Unit 5: Inferences (Georgia Standards)
The units in this instructional framework emphasize key standards that assist students in developing a deeper understanding of numbers. They have learned to recognize and express different representations of rational numbers. Now they will learn how to apply the statistical aspect of mathematics to the measures of center, variability and population. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.
• Grade 7 Unit 6: Statistics (Georgia Standards)
In this unit students will: Analyze data from many different sources such as organized lists, box-plots, bar graphs, histograms and dot plots. Understand that responses to statistical questions may vary. Understand that data can be described by a single number. Determine quantitative measures of center (median and/or mean). Determine quantitative measures of variability (interquartile range and range).
This task asks students to think about how the distribution of observed outcomes from a chance experiment might differ from the theoretical distribution and to use observed data to estimate a probability.
• How Many Buttons?
This task uses student generated data to assess standard 7.SP.7. This task could also be extended to address Standard 7.SP.1 by adding a small or whole class discussion of whether the class could be considered as a representative sample of all students at your school.
• Introduction to the Concept of Probability
The goals of this lesson are that students will understand the definition of probability, outcomes in probability, and know how to calculate experimental probability.
• Line Plot Representation of Deviation from the Mean
The concepts of means and deviations are the focus of this interactive from Annenberg. Students manipulate dots on a line graph to experiments with deviation. The classroom activity helps them understand positive and negative deviation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Making Random Samples
Students learn about population samples in this interactive by comparing various circles. They are then given a statistical population and have to decide what would make a random sample in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Marbles
This activity helps the student understand randomness and probability by pulling marbles out of a bag.
• Mr. Briggs'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.
• Offensive Linemen
In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability.
• Probability
Students learn about probability in this lesson by predicting the outcome of experiments and playing racing games.
• Probability and Geometry (elementary)
This lesson asks students to practice calculating probability and understand how probability problems can be solved with the help of geometry.
• Probability of Dependent and Independent Events
This Teaching Channel video shows how students can identify and create examples of independent and dependent events. (Common Core Standards Math.7.SP.8a) (5 minutes)
• Probability of Dependent Events video
This is a video introduction and explanation of the topic.
• Probability Space
In this video students learn the meaning of the phrase "probability space for random events." They learn about the origin of the idea in the 16th century and then apply their understanding via a dice game in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Probability with Dice
Given 2 dice students learn how to find the probability of rolling a specific number in this video. They then use 2 dice in the classroom activities to apply their understanding of probability. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Probability: Playing with Fire
This lesson is designed to help students understand possible outcomes of a probability experiment.
• Probability: Tell the Future
A Flocabulary hip-hop song explains and demonstrates ways to express probability in this lesson. To expand their understanding students toss coins and record the results in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Racing Game with One Die
Students can simulate a race between two cars with the roll of a die and learn about probability through this activity.
• Racing Game with Two Dice
By using the applet embedded in this lesson plan, students can simulate a race and learn about probability.
• Random Coin Toss
In this interactive from Annenberg students use a tree diagram to record the results of coin tosses to help them understand probability. The classroom activity extends this understanding to compare theoretical and experimental probability. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Random Sampling and Estimation: Lake Victoria
An Annenberg Learner's Learning Math video shows students a real-life application of random sampling by scientists studying fish in Lake Victoria. Students then apply their understanding by designing their own study using random sampling to make predictions and draw conclusions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Random Sampling: How Many Fish?
Goldfish crackers stand in for real fish as this video demonstrates the use of random sampling by scientists to make predictions and inferences about wildlife populations. The classroom activity has students make calculations related to the capture-recapture process used by scientists. They also explore other research methods using random sampling.
• Recognize and Represent Proportional Relationships Between Quantities: Ratio, Proportion, Cross Mult
Four videos are included in this lesson explaining ratio, proportion and how to use the shortcut of cross multiply and divide. Students then play the game "Pom-Pom Nose Push" to collect data and determine the ratio of time to distance. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Red, Green, or Blue?
The purpose of this task is for students to find the probability of compound events using organized lists, tables, or tree diagrams.
• Replacement and Probability
This lesson will help students learn the difference between sampling with and without replacement.
• Responses to a Court Verdict: Analyzing Samples to Gain Understanding
The infographic basis of this activity pulls the Trayvon Martin case out of the headlines to examine the data collected from a poll about the case. The students need to analyze the responses to conclude whether the results fall along racial lines. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Rolling Dice
This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.
• Rolling Twice
The purpose of this task is for students to compute the theoretical probability of a compound event.
• Scatter Plot
An understanding of how a scatter plot works is the focus of this interactive. Students interpret a scatter plot representing the relationship of height to arm length. They then create their own plot by measuring foot and forearm lengths. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Sitting across from Each Other
The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.
• Spinner
By manipulating a spinner and its pointer students will learn about probability in this activity.
• Statistics and Probability (7.SP) - 7th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - Statistics and Probability.
• Stay or Switch?
The purpose of this task is for students to find the theoretical probability of an event by systematically recording all of the possible outcomes in the sample space and identifying those that correspond to the event.
• Storage Shed - student task
Students are going to build storage sheds as a fund raising project, but before they can start they must determine the best dimensions for the shed, make scale drawings and decide on how much to charge for each shed.
In this task, students analyze a survey to decide how many candy bars students typically eat in a week.
In this task, students will use probability to make predictions about a card game.
Ann is in charge of a "Lucky Dip" game to raise money for charities. In this task, students use the rules of probability to advise Ann on how to improve the game so that it raises more money.
In this task, students must use math to figure out the best way to play a number bingo game.
In this task, students will use graphs and box diagrams to compare temperatures in California and Washington
In this task, students must use math to decide whether a lottery idea will make money.
• Tetrahedral Dice
The purpose of this task is to have students develop an organized list, table, etc. to determine all possible outcomes of a chance experiment and then to use this information to calculate various probabilities.
• The Hunger Games
By analyzing the lottery system used in the novel Hunger Games students will learn about probability. Students then create their own lottery system based on criteria from the novel in the accompanying classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• The Number System (7.NS) - 7th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System
• Tossing Cylinders
The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data.
• Valentine Marbles
For this task, Minitab software was used to generate 100 random samples of size 16 from a population where the probability of obtaining a success in one draw is 33.6% (Bernoulli). Given that multiple samples of the same size have been generated, students should note that there can be quite a bit of variability among the estimates from random samples and that on average, the center of the distribution of such estimates is at the actual population value and most of the estimates themselves tend to cluster around the actual population value.
• Variation About the Mean: The Boston Harbor Project
The use and statistical analysis of data in the efforts to improve the water quality in Boston Harbor is the subject of this video. Students then apply an understanding of mean absolute deviation to examine data. They also use data about bacteria found in a river in an analysis of what that data set tells. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Waiting Times
As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions.
• Your Odds of Winning Powerball: Probabilities of Compound Events Using Visuals
The sobering odds of winning at Powerball are made clear in this video. Students then create their own models of lotteries to help them understand the probability of compound events. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.