Sandwich Mass

Draw Best-Fit Line. Display the Graphing Mistakes: What's Wrong Here? Master to discuss correct graphing technique. This master shows errors in scaling, labeling, and drawing a best-fit line.

Ask students to draw a line or curve for the data on their graphs (Question 7). If the size of the bites are fairly regular, the data should suggest a decreasing line as shown in Figure 3. In general, irregularities in the data and graphs will be caused by irregularities in the consumption of the sandwich and variations in the size of the bite.

Use Graph to Estimate. Have students use their data tables and graphs to answer Questions 8–16 in pairs.

Questions 8–9 ask students to use the data on their graphs to make predictions. Students should be able to use their data table or graph for Question 8, but they may have to extend their line to find a point for Question 9. In Figure 3, the mass of the sandwich is approximately 50 grams after three bites. Some students may not have a solution for Question 9 if their data shows that they would have finished eating their sandwich in less than six bites. The sample data in Figure 3 shows a sandwich with a mass of approximately 27 grams after six bites.

Question 10 explores the relationship between the variables. (See the Content Note.) Have students discuss them with their partners, then discuss them with the class. For Question 10A, students will notice that as they look down the first column of the data table, the number of bites increases in a doubling pattern (1, 2, and 4 bites). For Question 10B, they will notice that the mass decreases as they look down the column. However, patterns in the data may be hard to see, particularly if there is measurement error or if students did not take the same size bites. For example, in the data table in Figure 2, the difference in the mass of the sandwich and the first bite is 8 grams and the difference between the first and second bites is 5 grams. The difference between the second and fourth bites is 14 grams, or about 7 grams per bite. If students took the same size bites, the difference between each bite should be about the same.

Question 10C asks students to use the graph to find the change in the mass each time one bite is taken. This is easier to do on the graph than in the data table because the best-fit line essentially averages out the data. On the sample graph in Figure 3, taking one bite is the same as moving one unit to the right. When you move one unit to the right, the mass goes down about 8 grams on the vertical scale. Students can more easily see this change if they first find points on the graph where the best-fit line crosses grid lines. They can then look at what happens to the line exactly one unit to the right. Using this information from the sample graph, an estimate for the mass of one bite is 8 grams (Question 10D).

Question 11 asks students to predict the number of bites it will take them to finish the whole sandwich. Encourage students to find more than one way to make their predictions. Students can extend the line on the graph until it crosses the horizontal axis. The graph in Figure 3 shows that when the Mass (M) is 0 grams, the Number of Bites (N) is between 9 and 10. Students can also use their answer to Question 10D. The total mass of the sandwich in the sample data is 72 grams and the estimate for the mass of one bite from Question 10D is 8 grams. Dividing the total mass of the sandwich by the mass of one bite will give an estimate for the total number of bites in the sandwich (72 g ÷ 8 g = 9 bites).