A Mathematical Power House of Ideas

By Allison Zmuda, featuring members of the American School of Tegucigalpa Math Team in Honduras: Steve McDowell, Karen Hesse, Carolina Martinez, Jacqueline Turcios, Sonia Amat, Roberto Segura and Roque Padilla.

One of the predictable challenges is how relevant and rigorous the connections are to math teachers. Many teachers I have met are reluctant to provide precious instructional minutes because the focus is typically several grade levels below what the course expects. So when I came across the American School of Tegucigalpa Math Secondary Team in Honduras, it was wonderful to see how quickly they generated powerful ideas that honor what is important in their math curriculum as well as inspire connections with other subjects.

I have featured their ideas below for inspiration.

Idea #1: The Cost of the National University’s Strike in its Budget and Community (Grade 6 Mathematics/PreAlgebra).

Subject area connections:

English Language Arts, Spanish Social Studies, Art

Goal:

To define the cost of the National University’s strike in its budget and community.

University students continue to protest and have been met by police with tear gas and water cannons with chemicals to disperse them. Learning at the University is at a standstill and the situation continues to deteriorate. Here is an article to start your research.

Product:

  • Determine university daily loss due to non-use of teacher salaries
  • Create a monthly budget for non-local University students and discuss how the strike impacts them economically
  • Develop an information report of your choice to communicate the results

Standards:

Mathematical Practice

MP. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

  • MP.1. Make sense of problems and persevere in solving them.
  • MP.2. Reason abstractly and quantitatively.
  • MP.4. Model with mathematics.
  • MP.5. Use appropriate tools strategically.
  • MP.6. Attend to precision.

Idea #2: Define the economic impact of the tolls on the CA-5 portion Tegucigalpa-San Pedro Sula (Algebra 1/Statistics).

Subject area connections:

English Language Arts, Spanish, Social Studies, Art, Science

Goal:

To define the economic impact of the tolls on the CA-5 portion Tegucigalpa-San Pedro Sula.

There is a need to rebuild the existing airport in Honduras. Toncontin International Airport is one of the most dangerous airports in the world due to its short runway and proximity to mountainous terrain. The new airport project is one of the prime initiatives taken by the Government of Honduras to increase the country’s productive infrastructure and transform it into a logistic and transport centre for the Central American region. But the challenge is that people who work at the airport have to spend more of their daily wage getting back and forth to work.

While there is a need, to what extent should local Hondurans have to pay more of their salary for the project? What’s fair? Start your research here to begin to develop the following products.

Product:

  • Impact on monthly budget of an employee traveling from Tegucigalpa to the proposed Palmerola airport and back on a daily basis
  • Create a distribution graph for the daily flow of vehicles by number of axles
  • Determine and justify a “fair” solution based on your predictions of total cost and traffic.

Standards:

Algebra 1/Statistics

Mathematical Practice

MP.The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

  • MP.1. Make sense of problems and persevere in solving them.
  • MP.2. Reason abstractly and quantitatively.
  • MP.4. Model with mathematics.
  • MP.5. Use appropriate tools strategically.
  • MP.6. Attend to precision.

HSS-ID.A. Summarize, represent, and interpret data on a single count or measurement variable

  • HSS-ID.A.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • HSS-ID.A.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • HSS-ID.A.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Idea #3: The Effects of Pollution on the Omoa’s Bay in Honduras (PreCalculus/Calculus).

Subject area connections:

English Language Arts, Spanish, Social Studies, Art, Science

Goal:

To estimate the region affected by the pollution dragged from the Motagua River into the Omoa Bay and its effects.

A shortage of infrastructure throughout the region (e.g., technically managed landfills, reliable systems for collection) means that a substantial proportion of the daily waste that is generated is not collected or contained. Municipal solid waste service in the region exists almost exclusively in urban areas and collects only about half of the domestic waste produced. Where there are no official collection services (especially in semi-rural areas), collection is occasionally done informally and waste is dumped in clandestine dumps. A substantial amount of the waste is burned, buried or deposited in rivers, creeks, lakes and the sea.

The water circulation pattern in the study area is dominated by cyclonic, counterclockwise rotating circulation gyres in a north-south direction flowing from the coast of Belize towards Guatemala and Honduras. Given those prevailing currents, it is at least as likely that, rather than originating in Guatemala and/or Honduras and being transported by the ocean currents to Belize, the bulk of the waste seen along the coastline and atolls in Belize originates in Belize.

How much of the region is affected by the pollution? Who is responsible for cleaning up the mess? How can we design a more proactive solution for the future? Click here to start your research.

Product:

  • Create a layout of the affected region using Google Maps to calculate the contaminated area
  • Create a layout of the affected region using Google Earth to calculate the contaminated volume of water
  • Calculate the rate of change (average rate of change/ instantaneous rate of change) of the contaminated region
  • Share your findings as well as take action on who should be responsible for the clean up.

Standards:

Mathematical Practice

MP.The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

  • MP.1. Make sense of problems and persevere in solving them.
  • MP.2. Reason abstractly and quantitatively.
  • MP.4. Model with mathematics.
  • MP.5. Use appropriate tools strategically.
  • MP.6. Attend to precision.

The aim of this topic is to introduce students to the basic concepts and techniques of differential and integral calculus and their applications.

  • Derivative interpreted as gradient function and as rate of change.
  • Tangents and normals, and their equations.
  • The chain rule for composite functions.
  • The second derivative.
  • Extension to higher derivatives.
  • 6.3 Local maximum and minimum points.
  • Testing for maximum or minimum.
  • Points of inflexion with zero and non-zero gradients.
  • Graphical behaviour of functions, including the relationship between the graphs of f , f’ and f” .
  • 6.5 Anti-differentiation with a boundary condition to determine the constant term.
  • Definite integrals, both analytically and using technology.
  • Areas under curves (between the curve and the x-axis).
  • Areas between curves.
  • Volumes of revolution.

 

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