Extrapolation and Interpolation With Spaghetti

Students measure the mass and length of broken pieces of dry spaghetti, plot the data on a graph, and use a line of best fit to predict the mass of unmeasured lengths. This activity introduces the use of graphs for making predictions and demonstrates proportional relationships between variables.

1. Break spaghetti sticks into various random lengths.
2. Measure the length of each piece with a ruler (in millimeters).
3. Measure the mass of each piece using a beam or electronic balance.
4. Plot the data on a graph with length on the x-axis and mass on the y-axis.
5. Draw a straight line of best fit through the data points.
6. Select a length not directly measured (within the range of the graph for interpolation, or outside of the range of the graph for extrapolation), mark it on the x-axis, and use the graph to predict its mass.
7. Break a fourth spaghetti stick to that length, measure its mass, and compare the actual value with your prediction.

Graphing Data from Spaghetti Mass vs Length Investigation - Suzie “Fedsie” Feodoroff:

📄 Spaghetti Graphing Activity - mychemistryclass.net: https://www.mychemistryclass.net/Files/1%20Interactive%20Notebook%202011%202012/Unit%200%20Foundations%20in%20Chemistry%20DONE/Graphing/Spaghetti%20Graphing%20Activity%20with%20graph%20paper.pdf

• Test different brands or types of spaghetti to see if they follow the same mass–length relationship.
• Extend the experiment by comparing thin versus thick pasta shapes (e.g., spaghetti vs. linguine).
• Instead of snapping randomly, cut precise lengths and compare predictions with actual data.

• Be cautious when snapping spaghetti as small pieces may fly off.

• Why is a line of best fit better than joining the points dot-to-dot? (It smooths out small measurement errors and shows the overall trend more clearly.)
• What is the relationship between length and mass of spaghetti? (They are directly proportional—the longer the piece, the greater the mass.)
• Why might your prediction not match the measured value exactly? (Experimental error, uneven density, or slight inconsistencies in breaking the spaghetti.)
• How could this method be applied to other real-world measurements? (Predicting weight from height, estimating costs from quantities, or scaling recipes.)