Enagage Ensure that students understand the connection between the Essential Question and the video.]]>ExploreS.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. S.ID.9 Distinguish between correlation and causation. ]]>x and y, the relationship in each of the three graphs showing correlation, for example, For a positive correlation, as x gets larger, the value of y also gets larger. ]]>Explore Notes Stress that the term correlation is concerned with whether or not there is a relationship, not the nature of the relationship. A strong correlation can be positive or negative. In a positive correlation both data sets increase in value. In a negative correlation one set decreases while the other increases. No correlation means the sets do not affect one another. ]]>Explainr value of 1 or –1 would indicate a perfect correlation with all the points exactly on the line. Explain that correlation between x and y can be perfect and still fail to be an example of causation if other factors are influencing the situation. For example, there is a very strong correlation between the number of fire trucks at a fire and the damage done by the fire. That does not mean that fire trucks cause fire damage. Additional fire trucks come to a more serious fire precisely because it is likely to cause more damage.]]>Math Talk In Explain 2, if the point (19.4, 60.8) for Mexico City is added to the scatter plot, how would the correlation coefficient change? Answer:The correlation coefficient would not be as close to 1 as it was for the original scatter plot, because the set of points would not lie as close to the best fitting line.
Explain Notes In Example 1, discuss the scatter plot. Have students try various lines to fit the data and then choose the best-fitting line. Students should recognize that for this data, a downward slope is the best fit, showing a negative correlation. Discuss changing the graph to compare Hours Spent Studying and Test Scores, and the kind of correlation you might expect. Help students see that this might be a positive correlation; usually the more one studies for a test, the better one does on it. In Example 2, discuss that the key difference between a strong correlation and a weak correlation is that a strong correlation shows points that are close together in what appears to be a linear pattern, while a weak correlation has points that are spread out and a pattern that is not as clear.]]>r values with slope. Stress that slope should be considered only to determine whether a correlation is positive or negative. Once that is determined, r values describe only how closely the points approximate a straight line. ]]>ElaboratePersonal Math Trainerwith your students, pointing out the variety of learning aids to help them to not only work through the problems, but to better understand the concepts of the lesson and build their skills.
If a student needs visual support to help solve a problem, View Example will provide a sample problem and solution.
Some students may need more structured help. Step-by-Step provides a guided approach. This solves the problem one step at a time, and students can input answers and check their understanding. Try Another provides more practice opportunities, with similar problems.
Some students may prefer to watch a video before trying the problem on their own. For these students, suggest the Math On the Spot video tutorials. In this video, an author models the problem with a detailed explanation.
As students complete the problems in Elaborate, their work is graded with immediate feedback and targeted instruction to set them on the right course for success. All student work is captured and can be reviewed in Reports. You may want to look at Reports to determine if a student needs specific help or if there is a trend that you should address with the class before students move to the Evaluate section.]]>EvaluateEvaluate section, students get immediate feedback as their skills are assessed. Students do not have access to the learning aids. Teachers get prescriptive information to provide targeted intervention.]]>