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This task addresses many standards regarding the description and analysis of bivariate quantitative data, including regression and correlation. Students should recognize that the pattern shown is one of a strong, positive, linear association, and thus a correlation coefficient value near +1 is plausible. Students should also be able to interpret the slope of the least-squares line as an estimated increase in y per unit change in x (and thus for a 3 unit increase in x, students should expect an estimated increase in y that equals 3 times the model's slope value).
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating. This task addresses a very important issue about precision in reporting and understanding statements in a realistic scientific context.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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In this task, output is given from a computer-generated simulation, generating size-100 samples of data from an assumed school population of 2000 students under hypotheses about the true distribution of yes/no voters.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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The purpose of this task is to assess a student's ability to compute and interpret an expected value. Notice that interpreting expected value requires thinking in terms of a long-run average.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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Using this lesson worksheet, computers and a simple programming interface, students step through and build a simple program to sequentially calculate all of the variables in the Hardy Weinberg equations. By building the program in sequence it is hoped that students will learn the sequence to solve a Hardy Weinberg problem and appreciate the value and power of computer number crunching capabilities as well as sequential programming considerations.
- Subject:
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Science and Technology
- Grade Level:
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Secondary,
Post-secondary
- Collection:
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Individual Authors
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By building a program to determine the valence of ANY element on the first three rows of the Periodic table, students learn the steps to solve the problem while learning how to program logic and think about processing data in sequence. NOTE: The worksheet includes the option of letting students create a bug that they have to fix.
- Subject:
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Science and Technology
- Grade Level:
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Primary,
Secondary,
Post-secondary
- Collection:
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Individual Authors
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This task lets students explore the concept of independence of events. There are two alternative ways of solving the problem.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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The lessons posted on this site were designed to engage students with real-world data relevant to content taught in middle school and high school science courses, and to foster an understanding of ways in which they might gather organize, analyze and interpret the data in order to draw scientifically valid inferences, interpretations and conclusions. Most of the labs use computer-based technology of spreadsheet programs or the Python programming interface. The Python lessons guide students in computational thinking to create simple programs to manipulate data. The lessons also provide students (and teachers) with instructions and guidance in the use of these technologies. Teacher and Student worksheets, as well as any supporting files, are linked to from links at the top of each lesson webpage as well as from the downloads page ("downloads" link on the scrolling menu to the left).
- Subject:
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Science and Technology
- Grade Level:
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Secondary
- Collection:
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Individual Authors
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In this segment from Curious, learn about creating energy from solar rays to meet the growing energy needs of the world.
- Subject:
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Science and Technology,
Social Sciences
- Grade Level:
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Primary,
Secondary
- Collection:
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Teachers' Domain
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Read the Fine Print
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This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages. There are several ways (tables, graphing calculators, or statistical software) that students might calculate the required normal percentages. Depending on the method used, answers might vary somewhat from those shown in the solution.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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Students create a spreadsheet (or use the one provided) to gather planet data and put in categories. They massage spreadsheet to tease out relationship between distance from sun and revolution speed. They use data to predict speed and/or distance for Ceres, the new dwarf planet between Mars and Jupiter.
- Subject:
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Science and Technology
- Grade Level:
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Primary,
Secondary
- Collection:
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Individual Authors
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This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred. The task would be well-suited either as an introduction to this distinction, or as an assessment item.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting. More generally, the idea of the lesson could be used as a template for a project where students develop a questionnaire, sample students at their school and report on their findings.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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"Pre" extension - The first extension creates programming to ask the user for values that are needed to figure out the frequency of individuals showing the recessive trait. This is THE one number needed to calculate all the other frequencies. The frequency of individuals showing the recessive trait is the only one that can be observed in a population BUT it is not always given in the word problem.
"Post" extension - The second will take the frequencies and apply them to an actual population number to generate actual numbers of individuals of the 3 genotypes and numbers of each allele … in that population.
- Subject:
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Science and Technology
- Grade Level:
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Secondary,
Post-secondary
- Collection:
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Individual Authors
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The purpose of this task is to assess understanding of how study design dictates whether a conclusion of causation is warranted. This study was observational and not an experiment, which means that it is not possible to reach a cause-and-effect conclusion.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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This task is designed as an assessment item. It requires students to use information in a two-way table to calculate a probability and a conditional probability. Although the item is written in multiple choice format, the answer choices could be omitted to create a short-answer task.
- Subject:
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Mathematics and Statistics
- Grade Level:
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Secondary
- Collection:
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Illustrative Mathematics
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Students massage (by sorts) spreadsheet data to tease out the relationships between latitude, angle of the sun, surface area of light beam and temperature. Also introduces possible confounding variable of elevation and the need to control for elevation.
• Uses data in a spreadsheet (provided) and flashlight beam lab or Sketchup file to see light surface area increase or decrease with angle change.
- Subject:
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Science and Technology
- Grade Level:
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Secondary
- SubTopics:
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Energy
- Collection:
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Individual Authors
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