![]() The results for the samples of 50 and 100 marbles are more similar to each other. For the samples of 10 marbles, the results are very different from each other (i.e., an individual sample deviates significantly from the mean).Possible responses that students will give to questions: For each part, student answers should look something like the example below: How do you know that you predicted the numbers correctly?Īnswers will vary, depending on the samples that students draw.Explain your strategy for solving the problem.Why did you approach the problem the way you did?.Student has a solution but does not provide an explanation. What was the mean for each of the colors out of 10?. ![]() How can you use this ratio to find the number of red marbles out of 500?.What was the mean number of red marbles out of 10 marbles in the sample?.What is the total for each color marble in the five samples?.How would you even them out among the five samples?.What is the total of the red marbles in the five samples?.Students will need to be able to set up proportions and solve.ĮLL: When monitoring students, pay special attention to ELLs to ascertain that they are on task and clear about what needs to be done. Students with disabilities may need direct instruction on and guided practice with the skills needed to complete this task. SWD: Consider the prerequisite skills for this task/skill. Look for students that are considering how the colors compare to each other proportionally. As the sample size increases, there is a higher probability that the same proportion of marbles is drawn.Īs students work, they will begin to conclude that there are the same number of red as green, and that yellow makes up half of the contents of the jar. ![]() Students may ask about combining the samples, which should be part of the Ways of Thinking discussion. ![]() Students will be interested to see how much or how little difference there is between the sample size of 50 and 100. As the sample size increases, the results from sample to sample will become more consistent, indicating that the results are valid. Some of the samples are likely to not include all of the colors, which would give a misleading result. MathematicsĪs students work, it will become apparent that a sample size of 10 is too small. Students will work with a partner for the Work Time problems. Give students a few minutes to become familiar with the Marble Jar interactive individually. SWD: Help students with disabilities build their mathematical vocabulary by continually modeling the use of new terms in the context of classroom work and activities. The Marble Jar has 500 marbles of 4 different colors: They will need to take samples to refine their guesses. Students will have a rough idea of the proportions of colors in the jar, since it will be clear that there aren't very many red or green marbles and that there are a lot of yellow marbles. Elicit from students that taking samples is one method they can use. There is probably some agreement about which colors have the least amount, and which have the most.Īsk students how they can determine the contents of the jar without counting and sorting all of the marbles. ![]() There are probably a range of guesses, indicating that there is not a consensus on the contents and students' estimation skills are varied. Record your students' guesses by taking an informal poll. Show the jar of marbles and give students a few minutes to speculate about its contents, and then guess the number of marbles. ![]()
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