Estimando con fuego

Introducción a varios métodos de estimación mediante la simulación de un incendio forestal

Grados 3-5

• Medición 
  • Aplicar técnicas, herramientas y fórmulas apropiadas, para determinar medidas

Grados 6-8

• Medición 
• Aplicar técnicas, herramientas y fórmulas apropiadas, para determinar medidas

• Aritmética: Los estudiantes deben ser capaces de:
  • convertir entre porcentajes, fracciones y decimales
  • calcular y entender probabilidad usando porcentajes, fracciones y decimales.
• Tecnológicos Los estudiantes deben ser capaces de:
  • hacer movimientos básicos con el ratón, como apuntar, hacer click y arrastrar.
  • utilizar un navegador para experimentar con las actividades

• Acceso a un navegador
• Copias de Preguntas de exploración y Taller

algoritmo,caos,decimal,fracción,porcentaje,probabilidad

• Enfoque y repaso

  Recuerde a los estudiantes lo que han aprendido anteriormente que sea relevante para el tema de esta lección. Haga estas preguntas:

  • ¿Qué significa estimar la respuesta a un problema?
  • ¿En qué difiere estimar de hallar la respuesta exacta?
  • Levante la mano quien cumpla años entre el 1 de enero y el 31 de junio
    • ¿Cuántas personas de este colegio creen ustedes que cumplan años en la primera mitad del año? 
    • Si usted fuera a estimar la respuesta a la pregunta anterior, ¿cuáles son algunas formas en las que podría enunciar la respuesta? ¿Podría usar un número, una fracción, un porcentaje? 

   

• Objetivo

  Let the students know what it is they will be doing and learning today. Say something like this:

  • Today we are going to investigate the relative merits of using fractions, percents, and decimals to estimate trees burned in a fire. Then, we will discuss how different algorithms can be used to make estimating easier, faster, and more accurate in certain situations.
  • We will be using a computer to simulate burning down a forest and check our estimations, but please do not turn your computers on until I tell you to do so.

   

• Aportes del maestro

  Discuss the concept and utility of estimation. Ask the following questions:

  • What are some situations in which estimation would be more useful than actually counting out an exact number?
  • There are three main ways to express estimated results - numbers, fractions, and percents
    • Can anyone describe how to estimate the number of objects with a certain property if the objects are difficult to count?
    • What about the fraction of some objects with a certain property?
    • What about the percent of some objects with a certain property?
    • Can we convert between these three measures? How?

   

• Práctica guiada

  Show the students the Fire Assessment applet. Set one of the trees on fire and watch the fire spread. Pose the following questions to the students:

  • About how many trees do you think burned?
  • About what proportion of the trees do you think burned, as a fraction?
  • About what proportion of the trees do you think burned, as a percent?
  • Which type of estimation was easiest - number, fraction, or percent?
  • How close do you think your estimation was?

   

  Put the class's estimate into the "Guess the Burn" box after first specifying whether you are entering numbers, percents, or fractions. Submit to check how close the class actually was.

  Demonstrate the different controls of the applet to students, including the following:

  • How to change the percentage chance that a fire will spread
  • How to change the forest size
  • How to change between estimating percents, fractions, and numbers

   

• Recolección independiente de datos

  Have students work in groups of 2-4 to fill out the worksheet. Assign each group a certain burn probability and forest size, then have them fill out the worksheet, estimating fractions, percents, and numbers of trees burned. As they work, instruct students to think about which type of estimation was easier/more accurate and why.

  When groups finish with the worksheet, have them write responses to the exploration questions to reflect on their work.

• Discusión

  Bring the class back together and discuss their responses to each of the exploration questions. Have students write their average error in estimation for percents, fractions, and numbers on the board. Based on those results, come to a conclusion as a class as to which type of estimation is the most accurate.

  Discuss with students the different methods of estimation and reasons why each may or may not have worked well in this exercise.

  Discuss other contexts for estimation and how the requirements can be different. Ask each group to come up with a situation in which their estimation algorithm would be most appropriate and discuss the various situations.

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