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3. I think neither of these variables causes the other to change. Most likely a very good team may feel they have the ability to give up a few penalties and still win, so they don’t worry as much about getting penalized.
Activity Synthesis
The purpose of this discussion is for students to communicate how they used mathematics to justify their ndings.
If students are able to research their own data, tell the groups to create a visual display to present their ndings. Some questions for discussion are listed here:
• “If there is a negative correlation, do you think the penalties would cause the fewer number of wins?” (Although is may be part of the cause, it is generally not the main reason a team loses several games.)
• “Were there any interesting data points you would like to research more about?” (Some points were very far away from the rest of the data and might be interesting to look at more closely.)
• “How did you reach a conclusion? Explain your reasoning.” (I created a scatter plot from data that I collected. I then plotted the residuals to verify that a linear model would be appropriate. I computed a line of best t and a correlation coe cient and found that there was a weak relationship between penalties and wins because the correlation coe cient was between 0 and 0.5. )
Lesson Synthesis
Here are some questions for discussion.
• “What did you nd important, challenging, or otherwise notable about today’s lesson?” (It was really interesting to collect data to answer a question. I really felt like I was guring something out.)
• “What mathematical work from this unit did you use in today’s activity?” (I used scatter plots, lines of best t, and the correlation coe cient. I also had to determine whether or not the two variables showed a causal relationship.)
• “How might the mathematical tools that you have learned in this unit help you outside of mathematics class?” (I could use these tools to think about graphs or claims that I see being made in the media. It would help me to determine what to believe and what not to believe.)
Student Lesson Summary
Scatter plots can be useful to display possible relationships between two variables. Once a pattern is recognized, tting a function to the data and then recognizing how well the function represents the relationship in the data can quantify your intuition about relationships between variables. The best t line, for example, can be used to predict the value of one variable based on the value of a second variable. Although technology can aid in
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Teacher Guide Algebra