Discovery & Exploration: Spaghetti Models
Students will determine if there is a relationship between fat grams and the total calories in fast food. Students will be paired in groups of two.
Sandwich / Fat Grams (x) / Calories (y)BK Hamburger / 12 / 290
BK Whopper / 37 / 650
BK Chicken Sandwich / 36 / 640
McD Hamburger / 9 / 250
McDQuarter Pounder / 26 / 520
McD Chicken Sandwich / 33 / 510
5 Guys Little Burger / 26 / 480
5 Guys Burger / 43 / 700
Wendy's Jr. Hamburger / 8 / 230
Wendy's 1/4 Pound Burger / 31 / 580
Wendy's Chicken Sandwich / 19 / 350
Chick-fila Chicken Sandwich / 18 / 440
Step 1: Given the following data set, students will copy the table and create a scatterplot using graph paper and pencil. Students should include a title for the graph and label all axes.
Step Two: Students will position a piece of spaghetti so that the plotted points are as close to the spaghetti as possible. This will accurately reflect the line of best fit for the data set.
Step Three: Students will find two points that lie on their line of best fit that most accurately reflect the data, Students may choose different points.
Step Four: Students will calculate the slope of their two points, rounding to the nearest hundredths place.
Step Five: Students will use the slope and choose a point from the data. They will then use point-slope form to find the equation of the line in slope intercept-form. Some students may choose to use a point and the slope to find the y-intercept and then rewrite the equation in slope-intercept form.
Step 6: Students will compare their equation with other groups and answer the following questions. Did you obtain similar results? Is there a correlation between fat grams and number of calories? If so, what is the correlation? What does the slope of your line represent in terms of the relationship between fat grams and calories?
(Student results should be similar. Students should also state the positive correlation and mention that the slope is representative of the fact that as fat grams increase, calories also increase)
When students are finished comparing, ask students the following questions:
What general shape did your scatterplots make? (In general, the data points were linear and showed a positive correlation)
Is there a constant rate of change? (No)
How do you know? (Calculating different pairs of points would produce different slopes)
How did you determine one slope that best described the data? (Answers will vary but students should mention that they chose points based on how closely they fell to the spaghetti line of best fit)
Use the graph and the equation to make a prediction about how many calories sandwiches with 7 and 45 fat grams would have. (Answers will vary. Ask students to share their answers. Write them on the board and discuss as a class whether or not the answers are reasonable)
Explain to students that different people may choose different points and arrive at different equations. All of these equations are "correct”, but in order to arrive at the “BEST” answer a graphing calculator would be a better tool.
Answer Key
Student models should resemble the following graph. The linear regression equation is 13.48x + 135.26.
Extension:
If time permits, students may use graphing calculators to find the line of best fit as an extension activity. Teachers may also choose to use Geogebra to model the linear regression to the class.