Page 218 - IM_Algebra1_FL Print Sample.pdf

coe cients. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Instructional Routines
• Fit it
Plot It indicates activities where students have an opportunity to use a table of points to produce a graph to see patterns and make predictions. Also when appropriate, nd a function that best ts the data.
Launch
If students have access to graphing technology, suggest that it might be a helpful tool in this activity.
Arrange students in groups of 2 to 4. Present the task to students and ask students to brainstorm di erent ways that they could answer the question. After 2 minutes of quiet think time, ask student to share their ideas with the class. The remaining time should be used by students collecting, analyzing, summarizing, and interpreting the data.
Student Task Statement
An anthropologist nds a fossil humerus bone of an ancient human ancestor. The humerus is an arm bone running from the shoulder to the elbow. This fossil bone is 24 centimeters in length. Use data from your classmates to estimate the height of this ancient human.
Student Response
Sample response: About 123 centimeters (around 4 feet). I measured the humerus and height of several classmates and created a scatter plot. I used a plot of the residuals and found that a linear model seemed to be appropriate. I then found the line of best t to be about where
is the height in centimeters and is the length of the humerus in centimeters. Using 24 centimeters for , I found that which I rounded since this is a rough estimate.
Activity Synthesis
The purpose of this discussion is for students to communicate how they used mathematics to justify their ndings.
Ask students:
• “How con dent are you in your answer? What information helped you determine your con dence?” (Not very con dent. Since the correlation coe cient is near 0.6, there is only a moderate relationship between height and humerus length. Additionally, this ancient human ancestor may have a di erent anatomy, for example apes tend to have proportionally longer arms than humans do.)
• “How did you use mathematics to estimate the height of the ancient human?” (First, I collected data on the height and the approximate length of the humerus of my classmates. I then made a scatter plot to determine whether or not a linear model was appropriate, and then
Unit 3
Lesson 10: Estimating Lengths 151