• • • • • • • • # Articles

### Middle School Articles

“Rethinking Ratios, Rates, and Percentages” Mathematics Teaching (GB), 240, 26-28.  Chelst, K. R., Özgün-Koca, S. A., & Edwards, T.G. (2014).

Mathematics Level: Grade 6 and 7.

Skills: Ratio, rates, proportion and percentages, model real world situation

The calculation of ratios, rates, proportions, and percentages as critical 6th and 7th grade skills. It is relatively easy to write a short scenario, and then ask students to calculate the ratio, rate, proportion, or percentage. All that the scenario requires is two numbers. However, these scenarios rarely accurately portray the ways in which these concepts are used to make a point when used in context. This paper explores the role of ratios when numerator and denominator are non-commensurate values and contrasts this to the case when they share the same units of measurement.

“Linking Lego and Algebra.” Mathematics Teaching in the Middle School. 20(7), 400-405.  Özgün-Koca, S. A., Edwards, T.G., & Chelst, K. R. (2015)

Mathematics Level: Grade 6 and 7.

Skills: Model real world situation, interpret solution, Excel (optional)

Students are provided with a collection of small and big Lego pieces. They are provided with a description of how many blocks of each type are needed for a dog and for a duck. They are asked to build the optimal number of dogs and ducks so as to maximize total profit.

### High School Articles

“Controlling Inventory: Real World Mathematical Modeling” Mathematics Teacher, 107(1), 62-67, Edwards, T.G., Koca, S.A., and Chelst, K. (2013)

Mathematics Level: Algebra 1

Skills: Construct Algebraic Relationship, Graphing Calculator, Create and Interpret Tables, Model Real World Situation

Students explore the interaction of two costs associated with maintaining an inventory of game consoles. There is a cost for placing an order and having it delivered. There is also a cost of keeping inventory in stock. Students explore different ordering policies and graph the results to determine the optimal strategy.

“LP or IP? Why it Matters?” Edwards, T.G. and Chelst, K.R.

Mathematics Level: Algebra 2

Skills: Systems of linear equations, linear programming, model real world situation

All linear programming examples in high school text have integer decision variables and integer solutions. In this paper we explain the impact of restricting the decision variables to be only integer values. The optimal solution will not necessarily be at corner point principle of the feasible region.

“Promote Systems of Linear Inequalities with Real-World Problems” Mathematics Teacher, 92, 118-123, Edwards, T and Chelst, K. (1999)

Mathematics Level: Algebra 2

Skills: Systems of linear equations, linear programming, model real world situation

The fields of operations research offers uses mathematics to solve a wide array of real world decision contexts. Mathematical programming is the sub-specialty that involves optimizes an objective in the presence of a collection of constraints. We use a Lego example to illustrate a product mix optimization problem that is constrained by the number of different block types. This example can be used to motivate the study of systems of linear inequalities. 