Students continue to extend their understanding of compound events by comparing independent and dependent events. This includes drawing the sample space to understand how the first event does or does not affect the second event. Students will solve problems with dependent compound events.Key ConceptsStudents will learn about the differences between dependent and independent events.Events are independent if the outcome of an event does not influence the outcome of the others.Events are dependent if the outcome of an event does influence the outcome of the others.The difference can be observed by drawing a diagram to represent the sample space. For dependent events, the sample space is smaller.Goals and Learning ObjectivesUnderstand the difference between independent and dependent compound events.Draw diagrams for dependent compound events.Solve compound event problems.

Students will compare expected results to actual results by first calculating the probability of an event, then conducting an experiment to generate data. They will use an interactive to simulate a familiar event—rolling a number cube. Students will also be introduced to terminology.Key ConceptsThis lesson takes an informal look at the Law of Large Numbers through comparing experimental results to expected results.There is variability in actual results.Probability terminology is introduced:theoretical probability: the ratio of favorable outcomes to the total number of possible equally-likely outcomes, often simply called probabilityexpected results: the results based on theoretical probabilityexperimental probability: the ratio of favorable outcomes to the total number of trials in an experimentactual results: the results based on experimental probabilityoutcome: a single possible resultsample space: the set of all possible outcomesexperiment: a controlled, repeated process, such as repeatedly tossing a cointrial: each repetition in an experiment, such as one coin tossevent: a set of outcomes to which a probability is assignedGoals and Learning ObjectivesPredict results using ratio and proportion.Compare expected results to actual results.Understand that the actual results get closer to the expected results as the number of trials increase.

Students will begin to think about probability by considering how likely it is that their house will be struck by lightning. They will consider the relative likelihood of familiar events (e.g., outdoor temperature, test scores) on the continuum between impossible and certain. Students will discuss where on the continuum "likely," "unlikely," and "equally likely as unlikely" are.Key ConceptsAs students begin their study of probability, they look at the likelihood of events. Students have an intuitive sense of likelihood, even if no numbers or ratios are attached to the events. For example, there is clearly a better chance that a specific student will be chosen at random from a class than from the entire school.Goals and Learning ObjectivesThink about the concept of likelihood.Understand that probability is a measure of likelihood.Informally estimate the likelihood of certain events.Begin to think about why one event is more likely than another.SWD: Students with disabilities may need additional support seeing the relationships among problems and strategies. Throughout this unit, keep anchor charts available and visible to assist them in making connections and working toward mastery. Provide explicit think alouds comparing strategies and making connections. In addition, ask probing questions to get students to articulate how a peer solved the problem or how one strategy or visual representation is connected or related to another.

Students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes and whether increasing the sample size improves the results.Key ConceptsSampling is a way to discover unknown characteristics about a population. The size of the sample is important in determining the accuracy of the results. Ratio and proportion are used to compare the sample to the population.Goals and Learning ObjectivesStudents will use sampling to determine the number of different color marbles in a jar.Students will explore sample size compared to population size.

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 of methods for randomly sampling a population to ensure that it is representative.The idea of sampling is connected to probability; a relatively small set of data (a random sample/number of trials) can be used to generalize about a population (or determine probability). A larger sample (more trials) will give more confidence in the conclusions, but how large of a sample is needed?Students also discuss what random means and how to generate a random sample. Random samples are compared to biased samples and give insight into how statistics can be misleading (intentionally or otherwise).Key ConceptsRandom samples are related to probability. In probability, the number of trials is a sample used to generalize about the probability of an event. The results in probability are random if we are looking at equally likely outcomes. If a data sample is not random, the conclusions about the population will not reflect it.Terminology introduced in this lesson:population: the entire set of objects that can be considered when asking a statistical questionsample: a subset of a population; can be random, where each object in the population is equally likely to be in the sample, or biased, where not every object in the population is equally likely to be in the sampleGoals and Learning ObjectivesIntroduce sampling as a method to generalize about a population.Discuss the concept of a random sample versus a biased sample.Determine methods to generate random samples.Understand that biased samples are sometimes used to mislead.SWD: Some students with disabilities will benefit from a preview of the goals in this lesson. Students can highlight the critical features and/or concepts and will help them to pay close attention to salient information.

Students critique and improve their work on the Self Check, then work on additional problems. Students revise the Self Check problem from the previous lesson and discuss their strategies.Key ConceptsStudents apply what they have learned to date to solve the problems in this lesson.Goals and Learning ObjectivesApply knowledge of sampling and data analysis to solve problems.Determine a random, representative sample that is nonbiased and of adequate sample size.Generalize about a population based on sampling.Compare data sets.

Students critique and improve their work on the Self Check, then work on additional problems.Key ConceptsStudents apply what they have learned to date to solve the problems in this lesson.Goals and Learning ObjectivesApply knowledge of probability to solve problems.Determine theoretical probability.Predict expected results.

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).

Students estimate the length of 50 seconds by starting an unseen timer and stopping it when they think 50 seconds has elapsed. The third attempt is recorded and compiled into a data set, which students then compare to the third attempt from the previous lesson when they estimated the length of 20 seconds. Students analyze the data to make conclusions about how well seventh grade students can estimate lengths of time.Students repeat the timing activity for 50 seconds, but only the third trial is recorded. The task today is to compare this set of data with the third trial for 20 seconds. Students will need to deal with the difference in the spread of data, as well as how to compare the data sets. Students will be reminded of Mean Absolute Deviation (MAD), which will be a useful tool in this situation.Key ConceptsStudents apply the tools learned in Unit 6.8:Measures of center and spreadMean absolute deviation (MAD)Goals and Learning ObjectivesApply knowledge of statistics to compare different sets of data.Use measures of center and spread to analyze data.

This is designed as an introductory lab for hydrogeology or other upper-level courses that are quantitative in nature in order to review key mathematical concepts that will be used throughout the semester.

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Today we’re going to talk about numeracy - that is understanding numbers. From really really big numbers to really small numbers, it's difficult to comprehend information at this scale, but these are often the types of numbers we see most in statistics. So understanding how these numbers work, how to best visualize them, and how they affect our world can help us become better decision makers - from deciding if we should really worry about Ebola to helping improve fighter jets during World War II!

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).

This is a visual demonstration of the effects of aquifer parameters and stresses on the size and shape of zones of contribution. With these simple Matlab routines, students can rapidly observe zones of contributions for different sets of input parameters.

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Uses 3 points of entry to introduce students to viscoelastic rheology: A hands-on exercise with cake as the deformable material, an accessible example of an artificial material, and using literature to apply the concepts to post-glacial rebound in the British Isles.

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Today we’re going to talk about measures of central tendency - those are the numbers that tend to hang out in the middle of our data: the mean, the median, and mode. All of these numbers can be called “averages” and they’re the numbers we tend to see most often - whether it’s in politics when talking about polling or income equality to batting averages in baseball (and cricket) and Amazon reviews. Averages are everywhere so today we’re going to discuss how these measures differ, how their relationship with one another can tell us a lot about the underlying data, and how they are sometimes used to mislead.

An example that demonstrates how to calculate the mean of a frequency distribution step by step.  

This hands-on demonstration illustrates how GPS can be used to measure the inflation and deflation of a volcano. Volcanoes may inflate when magma rises closer to the surface and deflate when the pressure dissipates or after an eruption.

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This lesson will be a fun way for students to be create and use the collected data to find the measures of central tendency.