1. Anticipatory Set: Students visit the following Web site and discuss its relevance relative to population dynamics http://www.worldometers.info/
2. Key terms/skills: Students will review the prerequisites including these math ideas: matrices, inequalities, population graphs, frequency tables, histograms, stem-and leaf plots, areas of polygons and volumes 3-D Space figures.
3. Teachers can obtain data for student use on the following Web site: http://www.prb.org/Content/NavigationMenu/PRB/Educators/LessonPlans
   /Pyramid_Building__Data_Table_Key1.htm
4. Students should view and discuss information obtained from Gale databases in order to complete this lesson:
   1. Academic ASAP: Keyword search population pyramid. (evaluation) Kavita Pandit. The Professional Geographer
   2. Infotrac Student Edition: Keyword search matrices. View two Encyclopedia excerpts, one periodical reference, see also five related subjects, inequalities. View two encyclopedia excerpts, volume. View four encyclopedia excerpts.
   3. Student Resource Center: Keyword search "histogram." Under the Magazines and Journals tab select Harnessing histograms. these little charts can help ensue that your digital photos are properly exposed (Statistical Data Included) The American Statistician and The normal distribution (medical statistics) (Statistics Notes, part 11) British Medical Journal, Volume and surface area, area and polygon Math & Mathematicians: The History of Math Discoveries Around the World, volume U·X·L Encyclopedia of Science and, under the Multimedia tab, volume.
5. Modeling: Students listen to teacher describe the lab. Students take notes.
6. Student Test for Understanding: Students will follow this list of procedures with teacher support:
   1. On the handout, students are told to accomplish the following:
      1. Create a matrix for the given data. What are the dimensions of the matrix in proper format?
      2. Construct a population pyramid for the country using the data provided on the graph paper provided.
      3. Show an inequality for each age range.
      4. Use you data to create a frequency table, stem-and-leaf plot, and a histogram.
      5. What type of population graph does this best represent?
   2. Some follow-up questions can include these: In the United States, what are some of the likely impacts baby boomers will have on American society when they retire and achieve senior citizen status? In China, why would the 2025 pyramid look so markedly different from the 200 pyramid? In Germany, is Germany's total population expected to decline between 200 and 2025? If so, what impact will this decline have on the world? Why is Bangladesh's 2000 pyramid so different from U.S. and Genrmany?
   3. A Web site that shows how to make a 3-D pyramid is http://www.enchantedlearning.com/crafts/Pyramid.shtml. A square-based pyramid works well for this lesson. Students can transfer their two-dimensional data onto one of the triangle faces. The other faces can be sued for labels, pictures or other relevant data. The base can have students' names and/or surface area and volume calculations.
   4. The 3-D pyramids can be converted to a classroom ceiling or flat world population pyramid model.
7. Recap – What did we learn? Explain verbally the important math skills that you utilized. What are important group skills (communication, cooperation, collaboration) used?
8. Home link – Students answer these basic questions: Why is a sound understanding of Population Dynamics important for this lab? What is the significance of frequency tables, stem-and-leaf plots and histograms? How are these three concepts related to each other, be specific? What do matrices have to do with population pyramids? How do two and three dimensional models help in the understanding of the significance of population dynamics? Why is this stuff important for you and your life?
9. Follow-up – Class presentation of the results. Students type a three paragraph summary in proper (Type III format – proper grammar, punctuation, spelling, 5-7 sentences per paragraph, at least ten word per sentence, no sentence starts with the same word in a paragraph.) Paragraph One explains what the lab was about. Paragraph Two describes what the student learned. Paragraph Three explains how this applied to the individual's own current or future life. The highlights of paragraph three are verbally shared with the class by each student.

Outcome: Through the application of math concepts (listed above), the students gain at least an application level understanding of Population Dynamics (in particular overpopulation) that exists in the world.

Related Activities: H.O.T.S. (Higher Order Thinking Skills) – Stresses Bloom's Syntheses and Evaluation levels. Students participate in My high school pyramid. Students can collect data about students within the school. Statistical techniques for data collection starting with a questionnaire design can be explained. The data can be analyzed and modeled as with the Population Pyramid Lab. Students can be presented to the class. Students connect this data to world data during this presentation. Microsoft Excel can be used in the presentation.

Standard Date: October, 1998

Content Standard(s):

• 1.1 Understanding numbers, ways of representing numbers
• 1.2 Understanding the meaning of operations and how they relate to each other
• 1.3 Use computational tools and strategies fluently and estimate appropriately
• 2.1 Understand various types of patterns and functional relationships
• 2.2 Use symbolic forms to represent and analyze mathematical situations and structures
• 2.3 Use mathematical models and analyze change in both real and abstract contexts
• 3.1 Analyze characteristics and properties of two- and three-dimensional geometric objects
• 3.4 Use visualization and spatial reasoning to solve problems both within and outside mathematics
• 5.2 Interpret data using methods of exploratory data analysis
• 5.3 Develop and evaluate inferences, predictions, and arguments that are based on data
• 6.1 Build new mathematical knowledge through their work with problems
• 6.2 Develop a disposition to formulate, represent, abstract, and generalize in situations within and outside mathematics
• 6.3 Apply a wide variety of strategies to solve problems and adapt the strategies to new situations
• 6.4 Monitor and reflect on their mathematical thinking in solving problems
• 7.2 Make and investigate mathematical conjectures
• 8.1 Organize and consolidate their mathematical thinking to communicate with others
• 8.2 Express mathematical ideas coherently and clearly to peers, teachers and others
• 8.3 Extend their mathematical knowledge by considering the thinking and strategies of others
• 8.4 Use the language of mathematics as a precise means of mathematical expression
• 9.1 Recognize and use connections among different mathematical ideas
• 9.2 Understand how mathematical ideas build on one another to build a coherent whole
• 9.3 Recognize, use, and learn about mathematics in contexts outside mathematics
• 10.1 Create and use representations to organize, record, and communicate mathematical ideas
• 10.2 Develop a repertoire of mathematical representations that can be used purposefully, flexibly, and appropriately,10.3 Use representations to model and interpret physical, social and mathematical phenomena

Learning Expectation: Students will apply understanding of concepts related to matrices, inequalities, population graphs, frequency tables, histograms, stem-and leaf plots, areas of polygons and volumes 3-D Space figures within the context of Populations.

Performance Indicators:

• At Level 1, the student is able to:
  • Write (show basic knowledge for) about the meaning of these: matrices, inequalities, population graphs, frequency tables, histograms, stem-and leaf plots, areas of polygons and volumes 3-D Space figures.
• At Level 2, the student is able to:
  • Comprehend and Apply these concepts: matrices, inequalities, population graphs, frequency tables, histograms, stem-and leaf plots, areas of polygons and volumes 3-D Space figures.
• At Level 3, the student is able to:
  • Synthesize new ideas related to and Evaluate concepts: matrices, inequalities, population graphs, frequency tables, histograms, stem-and leaf plots, areas of polygons and volumes 3-D Space figures.

Computer Literacy and Usage Standards 9-12:

• Students demonstrate a sound understanding of the nature and operation of technology systems
• Students are proficient in the use of technology
• Students understand the ethical, cultural, and societal issues related to technology
• Students practice responsible use of technology systems, information, and software
• Students develop positive attitudes toward technology uses that support lifelong learning, collaboration, personal pursuits, and productivity
• Students use technology tools to enhance learning, increase productivity, and promote creativity
• Students use productivity tools to collaborate in constructing technology-enhanced models, prepare publications, and produce other creative works
• Students use technology tools to process data and report results
• Students use technology resources for solving problems and making informed decisions
• Students employ technology in the development of strategies for solving problems in the real world

ISTE NETS for Students

• Identify capabilities and limitations of contemporary and emerging technology resources and assess the potential of these systems and services to address personal lifelong learning, and workplace needs
• Make informed choices among technology systems, resources, and services
• Select and apply technology tools for research, information analysis, problem solving, and decision making in content learning
• Collaborate with peers, experts, and others to contribute to a content-related knowledge base by using technology to compile, synthesize, produce, and disseminate information, models, and other creative works

Information Power; Information Literacy Standards 1-4:

• The student who is information literate accesses information efficiently and effectively
• The student who is information literate evaluates information critically and competently
• The student who is information literate uses information accurately and creatively
• The student who is an independent learner is information literate and pursues information related to personal interests
• The student who is and independent learner is information literate and strives for excellence in information seeking and knowledge generation
• The student who contributes positively to the learning community and to society is information literate and practices ethical behavior in regard to information and information technology