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Title: Ecology - Biodiversity Lab

Author: Andrew Renaud

Grade Level: 9

Subject/Content: Integrated/Applied Mathematics

Summary of Lesson: Through the application of math concepts (listed below), the purpose of the investigation is to examine the degree of biodiversity that exists in one's everyday environment, in order to develop an understanding of how scientists classify organisms and to explain why biodiversity is important for living things.

Focus Question: What does biodiversity mean and why is this important to all life forms?

Databases(s): Student Resource Center, Opposing Viewpoints Resource Center


  • Materials needed: baggies, tape measures, ping-pong ball, cut-out polygons, graph paper (5 division/inch), basic calculator, string (2 – 10 foot pieces per group), ruler, clip board, loose leaf paper, pencils
  • After our general review of the prerequisites: discussions on sampling types (random, systematic, cluster, convenient) and similar (same shape), congruent polygons (same size and shape), transformation types and properties (translations, rotations, reflections) , Cartesian coordinate systems (quadrants, ordered pairs), coordinate geometry and areas of polygons (graph paper estimation methods), Congruency (scale factors) students are randomly placed into groups of four.
  • Students select the roles of Calculator (the person who insures that proper mathematical reasoning and calculations are accurate), Historian (the person who insures that all data is recorded correctly), Encourager (the person who acknowledges all information suggested by group members and encourages on-task behavior) and Organizer (the person who is responsible for the accountability and proper usage of all supplies).
  • Students will create a 10 foot X 10 foot model rectangular (Cartesian) coordinate axis system in sample area outside using string. Students will toss several cut-out polygons into the coordinate area. Students will collect sample species from the area where the polygon lye. All results will be sketched, labeled and recorded.

Steps/Activities by students:

  1. Anticipatory Set: Students view video clips on Biodiversity and its importance. Students listen to the short story of Rene' Descarte', the "founder" of the Cartesian Coordinate System.
  2. Key terms/skills: Students will review the prerequisites including these math ideas: transformations, properties of a rectangular coordinate system, properties of polygons, basic sampling types, scale factors and congruency and coordinate geometry and area estimates.
  3. Modeling: Students will watch the brief teacher demonstration of the lab.
  4. Student Test for Understanding: Students will follow this list of procedures with teacher support.
    1. Choose a location away from other groups, but staying within the boundary as specified by your teachers.
    2. In a random fashion, toss your ping-pong ball into the air in a specific direction. The ball should be tossed no further than 10 feet.
    3. Keeping the ball in place, it now becomes the origin marker of you rectangular coordinate system. On your graph paper the scale that you will use is that each graph paper square side = 6 inches.
    4. Carefully place the Dependent (y) and Control (x) axis with ping-pong ball origin as the focal point. You will have a four quadrant system with a five unit extension in each direction.
    5. While standing at the origin, toss your polygon in a specific direction without disturbing others in the area. Your polygon must lie within the coordinate system or you will need to implement a "do over" until this happens.
    6. Using the tape measure, record how far away from the origin you are on your graph paper. STOP for a progress check: get teachers initials______.
    7. Using the appropriate scale, sketch the polygon on the graph paper.
    8. Collect two living animal or plant specie (you must have a variety) within the boundary of the polygon shape. STOP for a progress check: get teachers initials______.
    9. Repeat steps 5-8 until you have a total of 10 samples in your baggies. Toss your shape in a different direction every time in order to avoid "overlap" sketches on your sketches. STOP for a progress check: get teachers initials______.
    10. Now collect four items from your coordinate system that you consider to be nonliving in a separate baggie labeled appropriately.
    11. Gather all items to bring inside. STOP for a progress check: get teachers initials______.
    12. Once inside, use your data to complete the following within your group:
      1. Label all polygons on your graph paper with letters at the vertices.
      2. Name the polygons.
      3. Use proper notation to state how any two polygons are congruent, corresponding vertices and sides.
      4. Compare several polygons in transformation terminology.
      5. Compare any two polygons in terms of area estimates (be specific).
    13. Complete the classification key practice exercise.
    14. Using the 10 samples that your group collected outside, create your own classification key that includes illustrations and labels.
    15. Complete the mini lab in the biology Text as assigned.
  5. Recap – What did we learn? Explain verbally the important biology and math skills that you utilized. What are important group skills (communication, cooperation, collaboration) used?
  6. Home link – Students answer these basic questions: What kind of sampling technique did you use for steps 5-8? For step 10? Why is this important to know? What does diversity means in the context of biology and math? How does this laboratory experiment illustrate the importance of Biodiversity? Why is this important for you and your life?
  7. 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 10 words per sentence, no sentence starts with the same word in a paragraph.) Paragraph One explains what the experiment 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 biodiversity that exists in one's everyday environment.

Related Activities: H.O.T.S. (Higher Order Thinking Skills) -- Stresses Bloom's Syntheses and Evaluation levels. Students participate in Geometers Sketchpad "BioDiversity Creation". Students can create their own diverse environment using the program. The sketch can be incorporated into a PowerPoint presentation. Students will evaluate their choices made and how geometry played in the role of these selections.

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
  • 3.1 Analyze characteristics and properties of two- and three- dimensional geometric objects
  • 3.2 Select and use different representational systems, including coordinate geometry and graph theory
  • 3.3 Recognize the usefulness of transformations and symmetry in analyzing mathematical situations
  • 3.4 Use visualization and spatial reasoning to solve problems both within and outside mathematics
  • 4.1 Understand attributes, units and system measurements
  • 4.2 Apply a variety of techniques, tools and formulas for determining measurements
  • 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
  • 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 coordinate geometry and polygon classification within the context of Biodiversity.

Performance Indicators:

  • At Level 1, the student is able to: Write (show basic knowledge for) about the meaning of these: translations, rotations, reflections, Cartesian Systems, polygons, coordinate geometry, area estimates using graph paper, sampling types, congruency, scale factors and scale drawings.
  • At Level 2, the student is able to: Comprehend and Apply these concepts: translations, rotations, reflections, Cartesian Systems, polygons, coordinate geometry, area estimates using graph paper, sampling types, congruency, scale factors and scale drawings.
  • At Level 3, the student is able to: Synthesize new ideas related to and Evaluate concepts: translations, rotations, reflections, Cartesian Systems, polygons, coordinate geometry, area estimates using graph paper, sampling types, congruency, scale factors and scale drawings.

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 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 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
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