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When Math Meets Main Street
Why should I shop locally if I can buy the same things for less money at national chains?
Students select a locally-owned business they wish to support and use quadratic modeling to better understand the challenges that these businesses face and why members of their community, when possible, should seek to shop locally. Students synthesize their high-level research, modeling and analysis on a poster that they will then present at a small business fair.
Students will hold a small business fair in which they use their findings to make the case for supporting their chosen business. They will do this by showing how pricing structures, revenue streams and profit margins compare to those of a larger, nationally-owned retail chain. Additionally, students will seek to differentiate their chosen business from other, potentially less expensive options and the overall value that “shopping local” brings to the community.
Financial Literacy
Math
This TLE assumes baseline understanding of modeling with functions.
A unit within an Algebra 1 course – could be used as an application-based unit alongside a more traditional unit on quadratic functions or as a full quadratic functions replacement unit.
HSA-CED.A.2 – Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
HS.A-REI.B.4.b – Solve quadratic equations by inspection, taking square roots, the quadratic formula, and factoring, as appropriate to the initial form of the equation.
HS.F-LE.A.2 – Construct linear functions given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
HS.F-LE.B.5 – Interpret the parameters in a linear or exponential function in terms of a context.
HS.F-IF.B.4 – For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
HS.F-IF.C.7.a – Graph linear and quadratic functions and show intercepts, maxima, and minima.
HS.F-BF.A.1.b – Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
HS.A-APR.B.3 – Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
HS.F-BF.B.3 – Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Written Commentary
In preparing to create their posters, students will capture their questions, assumptions, models and analysis of these models in a written “Market Analysis” report. Each section of the report is organized around the driving question and mathematical concepts within the 4 phases of the unit.