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# Predicting Bridge Strength via Data Analysis (Day 1 of 2)

Lesson 18 of 20

## Objective: SWBAT collect data of number of pennies to number of layers of paper bridges, create a scatter plot, and write a prediction equation to extrapolate the data.

## Big Idea: Students use the paper bridge and pennies as a mathematical model of loads on a structure, including dead weight and live weight.

*50 minutes*

In this lesson students use **Linear Regression** to make predictions about how many pennies can be held by the paper bridge as the layers are increased. For this activity, I create homogeneous groups of three to four students per group. I prefer homogeneous grouping for this project.

**Materials needed for each group:**

**100 pennies****one cup-small bathroom Dixie Cup****ruler****three 8.5 X 11 pieces of copy paper****Paper Bridge Activity Sheet**

It is helpful to introduce the Paper Bridge Project to students with a connection to engineering, so I refer students to this document first to help with the definitions of dead weight and live weight of a bridge. The dead weight in this activity is the paper bridge and the live weight is the pennies being placed on the bridge. I introduce this activity with the driving question: Can your bridge hold 100 pennies?

After introducing the activity, I demonstrate to students how to fold the paper for each bridge. I have students fold their first bridge layer with me while I am demonstrating. The folding of the bridge can be difficult for some students, so I quickly check each group for success on one paper bridge as we are starting the activity. However, I remind students of how important it is to be precise (MP6). Students create five bridges for this activity. Each piece of paper creates two bridges. I demonstrate how to create the paper bridge from a 8.5 in. by 11 in. paper in the video below.

As two students in each group work on creating the bridges, I have the other students set two Algebra Books 8 inches apart, again reminding them to be precise. As the picture shows on the first page of the Paper Bridge Project, the first bridge is placed with 1 inch at each end on an Algebra book. The students then place a paper cup in the center of the bridge, again being precise as possible.

Once the Bridge is properly placed, students take turns placing pennies in the cup, counting as they go. They should continue to add pennies until the bridge collapses and hits the table.

In order to investigate the effect of the variable, Bridge Thickness, students then follow the same procedure to create and test a two-layer bridge. For today's investigation students will collect data for the number of pennies held up by bridges that are 1-to-5 layers of paper thick.

Throughout the project I stress the importance of keeping our methods and materials the same. I remind students that we want our data to be comparable, so that we can model the strength of a paper bridge. I say, "This is not a competition to see who gets the most pennies. In fact, your goal is to be as close as possible to the mean!" Here are some sources of experimental error:

- Placing the books too close or too far apart.
- Failing to center the cup on the bridge.
- It also matters how students put the pennies in the cup: Students should drop the pennies carefully, from just above the rim of the cup.

#### Resources

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During today's work on the Paper Bridge activity, students will complete five bridge tests. As they work, I ask students to record their data in the chart on the first page of the Activity Sheet. If time permits, students should make a scatter plot of their data using the grid on page 2. If they do, students should see a linear pattern with a strong positive correlation. If they do not, the likely culprit is a lack of attention to precision resulting in experimental error. Observing and later discussing this is an important part of my work during the lesson. In order for students to learn to pay attention to precision, they need to experience success and failure, and receive feedback that helps them to improve.

The video below shows a group of students working on the activity:

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#### Closure (Day 1)

*5 min*

With about 10 minutes left in the period, I start motivating students to finish collecting their data by the end of the period. I also ask students try to complete their Scatter Plot. For those who manage these two steps, I encourage them to make an initial interpretation with respect to the relationship between Bridge Thickness and Bridge Strength (the # of Pennies). Students who do not complete the scatter plot in class will be asked to plot their data and label the graph for homework.

Tomorrow we will continue our work with this project.

#### Resources

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- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Sequences
- LESSON 2: The Recursive Process with Arithmetic Sequences
- LESSON 3: Recursive vs. Explicit
- LESSON 4: Increasing, Decreasing, or Constant?
- LESSON 5: Change Us and See What Happens!
- LESSON 6: Why are lines parallel?
- LESSON 7: Get Perpendicular with Geoboards!
- LESSON 8: Dueling Methods for Writing the Equation of a Line
- LESSON 9: Comparing Linear Combinations in Ax +By= C to y=mx +b
- LESSON 10: Equations for Parallel and Perpendicular Lines.
- LESSON 11: Assessment of Graphing Lines through Art!
- LESSON 12: Are x and y Directly or Inversely Proportional? (Day 1 of 2)
- LESSON 13: Are x and y Directly or Inversely Proportional? (Day 2 of 2)
- LESSON 14: Writing, Graphing, and Describing Piecewise Linear Functions
- LESSON 15: Introduction to Scatter Plots, Line of Best Fit, and the Prediction Equation
- LESSON 16: Predicting the Height of a Criminal (Day 1 of 2)
- LESSON 17: Predicting the Height of a Criminal (Day 2 of 2)
- LESSON 18: Predicting Bridge Strength via Data Analysis (Day 1 of 2)
- LESSON 19: Predicting Bridge Strength via Data Analysis (Day 2 of 2)
- LESSON 20: Linear Assessment