Linear Equations: Stacking Cups to Solve Problems
T
his week freshman at Roberto Clemente Community Academy focused on linear inequalities and slope in their Algebra one class. Students began the week by reviewing slope and how it is used in linear equations. As students progressed through the week they began to learn more about using slope intercept form to create equations for a graph and how to manipulate the equation into standard form. As the week progressed, students wanted to see how using slope intercept equations could actually be used in real life.
Students were then given the challenge to find out how many plain white styrofoam cups they could stack in order to reach the equivalent height of their math teacher. Students were provided 10 styrofoam cups and the height of the teacher in centimeters in order to solve this problem. They also were told that they would not be permitted to stack the cups next to the teacher.
At the beginning of the activity many students noted that it was going to be an impossible task or that they needed a lot more cups to figure it out. Eventually students began to ask for specific tools to help them such as a ruler, string, and a calculator. Many groups began to create equations that showed the height of the teacher in centimeters divided by the height of one cup to show how many cups would equal the teacher’s height. When a group decided on their answer, they were allowed to test it out against the teacher. Unfortunately, when the groups used this equation it did not match up. This caused the students to go back to the drawing board and think about what they could change to get it closer to matching the teacher’s height. After trying out many different equations and stacking cups in numerous ways, student Daylynn Phillips’ group realized that the amount being added to the cup every time was equivalent to the height of the rim (and also the slope).She used this information to quickly formulate a linear equation and calculate how many cups would equal her teacher’s height. This is just one of the many ways in which our IB learners are using real world applications to make their learning interesting and meaningful!