Take The Plunge: Linear Equations

Published On: November 2nd, 2023 | Categories: Food for Thought |

This hands-on math Design Challenge in Mr. Hagerty’s Algebra I class was a blast!

Algebra I students have been studying Linear Equations in class, so Mr. Hagerty gave them a design challenge as a culminating activity called the Barbie Doll Drop.

After breaking up into small collaborative teams, the class was outfitted with a measuring tape, a bag of rubber bands and a Barbie doll. Students measured Barbie’s height, as each doll was slightly different in size, without rubber bands. Each team placed a measuring tape on the wall and set up their station. Then each group added the rubber bands and dropped Barbie from the top of a meter stick in a very controlled environment. They measured the lowest point that the doll’s head reached. Students continued this process multiple times, adding a rubber band each time.

The more bands we add, the lower Barbie would drop. Each team then recorded the data in a chart and began tinkering with the number of rubber bands and the estimated outcome. There were, of course, different variables involved. Each doll was a slightly different height or weight than the next, the size of each rubber band was not uniform, and these differences made for interesting conversations and problem solving along the way.

It got dangerous for Barbie during the next class period.



Mr. Hagerty took the class outside into the breezeway between the two buildings facing the athletic fields. This drop was just more than 14 feet in height. Using their test data from the previous day, Mr. Hagerty tasked each team to make their prediction of how many rubber bands they would need to safely drop Barbie from the breezeway.

Mr. Hagerty allowed each group to perform two separate bungee drops. Most of the teams were either not close enough to the sidewalk or Barbie smashed head first into the concrete on the initial effort. Teams readjusted and tinkered with the line of best fit, knowing they either needed to take rubber bands away or add to the original estimate. There was plenty of learning through failure and some emergency triage after the first jump.

One drop was so close that Barbie’s hair brushed the sidewalk but the head did not hit. In the end, the students had a blast and an experience that really connected them to the concept of linear equations.

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Linear Equations:

In Algebra I, linear equations are fundamental mathematical expressions that describe the relationship between two variables in a straight line. These equations are typically written in the form of y = mx + b, where ‘y’ represents the dependent variable, ‘x’ represents the independent variable, ‘m’ is the slope of the line, and ‘b’ is the y-intercept. Linear equations help us represent and analyze various real-world scenarios, such as the cost of an item based on the number of units purchased or the distance traveled as a function of time. They serve as a foundational concept in algebra, and understanding them is crucial for more advanced mathematical and scientific studies.

Final Thoughts:

This activity provides a tangible, real-world context for the mathematical concept. As students manipulate the rubber bands and dolls, they can directly observe how the height of the drop affects the time it takes for the dolls to reach the ground. By collecting data and plotting it on a graph, they can visually grasp the linear relationship between time and height, helping them internalize the key components of a linear equation, such as the slope and y-intercept. This hands-on experience not only makes the concept more engaging but also aids in the retention and application of algebraic principles in practical situations, which is essential for students’ overall mathematical education.

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