Mathematics Grade 7
Educational Links

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).

Standard 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.

• 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.
• Create a Graph
  This applet allows students to create bar, line, area, pie, and XY graphs.
• 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.
• Events and Outcomes (Counting) video
  This video introduces and explains the topic.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Student Task: Candy Bars
  In this task, students analyze a survey to decide how many candy bars students typically eat in a week.
• 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.

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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.