Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.

Students collect and analyze data for their unit project.Students are given class time to work on their project. Some students may choose to use the time to collect data (if their project is an experiment based on experimental probability), while others will use the tools (spinners, coin toss, number cube, etc.) to collect their data. Students should use the time to analyze their data, finding the theoretical (if possible) probability and comparing it to the experimental results.Key ConceptsStudents will apply what they have learned about probability to work on their project, including likelihood of events, determining theoretical and experimental probability, comparing results to calculations, and using simulations to establish probability.Students may also use data analysis tools to discuss their results.Goals and Learning ObjectivesComplete the project, or progress far enough to complete it outside of class.Review concepts of probability (simple probability, compound events, experimental vs. theoretical probability, simulations).

Lesson OverviewStudents will extend their understanding of probability by continuing to conduct experiments, this time with four-colored spinners. They will compare experimental results to expected results by first conducting an experiment, then calculating the probability of an event.Key ConceptsThis lesson takes an informal look at the Law of Large Numbers, comparing experimental results to expected results.Goals and Learning ObjectivesLearn about experimental probability.Compare theoretical probability to experimental probability and show that experimental probability approaches theoretical probability with more trials.Use proportions to predict results for a number of trials.

Students will extend their understanding of probability by continuing to conduct experiments with outcomes that do not have a theoretical probability. They will make predictions on the number of outcomes from a series of trials, and compare their predictions with the experimental probability calculated from an experiment.Key ConceptsStudents continue to investigate the Law of Large Numbers.Goals and Learning ObjectivesDeepen understanding of experimental probability.Use proportions to predict results for a number of trials and to calculate experimental probability.Understand that some events do not have theoretical probability.Understand that there are often many factors involved in determining probability (e.g., human error, randomness).

This lesson is designed to develop students' understanding of probability in real life situations. Students will also be introduced to running experiments, experimental probability, and theoretical probability. This lesson provides links to discussions and activities related to probability as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Students explore the relationship between theoretical and experimental probabilitiesin this student interactive, from Illuminations. Students use this "box model" as a statistical device to simulate standard probability experiments such as flipping a coin or rolling a die.