By Dr. Dorothea EberzWagner, Math Teacher
During the week before Thanksgiving, the students in Algebra 2 worked on a math problem that fit right into the theme of Thanksgiving.
It is about a group of caring people who plan a Thanksgiving dinner for the homeless. The menu includes pumpkin pie and fruit salad for dessert. As people are preparing for the dinner, they need to make sure that they will have enough desserts for the vast number of people that they are expecting and that the volunteers will be able to prepare the sweets in a given amount of time. Also, at least five pies and a certain number of bowls of fruit salad must be made.
All of these requirements can be modeled by setting up suitable linear inequalities. The goal now is to choose the number of pies and bowls of fruit salad which will minimize the cost for the dessert.
Mathematically speaking, this is a problem in linear programming, the cost function being a linear function in the variables x (number of pies) and y (number of bowls of fruit salad). As the students were working on this puzzle, they learned about:
• Mathematical modeling
• How to use a graph to represent the possible pairs (x,y) which satisfy all the given inequalities
• How to find the vertices of that region by solving systems of linear equations and
• The vertex principle of linear programming
It is a math problem involving many steps, building on topics from Algebra 1. Yet, it is concrete and presented in an everyday context that the students can relate to.
The problem can be adjusted to find other ‘best outcomes.' For instance, how do we maximize total sales or profit given a system of linear constraints?
By using a relevant, easy to understand problem, the students were highly motivated to dive right in. It also helped them better appreciate mathematical concepts. As a result, I believe our students are now more confident to use math for other reallife applications.
Below: Left to right: Esti Toban, Rachel Eisenstein, Shifra Wren
Further below: Standing left to right: Yael Genauer, Kaden Balkany, Shifra Wren, Aliza Margolese, Rachel Eisenstein. Seated: Esti Toban
