Timeline

Title: Technology - Timeline

Author: Andrew Renaud

Grade Level: 9

Subject/Content: Integrated/Applied Mathematics

Summary of Lesson: Through the application of math concepts, the purpose of the investigation is to examine similarity, scale drawing, scale factor and conversion factor in order to develop an understanding of how these concepts apply to a timeline of evolutionary history.

Focus Question: How will an understanding of similarity, scale drawing, scale factor and conversion factor play an important role in the synthesis of an evolutionary timeline?

Databases(s): Academic ASAP, Student Resource Center

Procedures:

Materials needed:  Timeline handouts, Scientific Calculator, meter sticks, large pieces of rolled paper (at least four meters in length ruler), pictures from old magazines/news papers/internet, clip board, loose leaf paper, pencils

• After our general review of the prerequisites: similarity, scale drawing, scale factor and conversion factor, students are asked to participate in the activity in pairs.
• Each person in the pair will participate in the Timeline handout activities.
• Students will participate in a research and creation of the visual portions of the final draft timeline.
• Students will explain answers to follow-up questions appropriately.

Steps/Activities by student(s):

1. Anticipatory Set:  Students will view a video on similarity and how this concept relates to scale drawings.  If an appropriate video cannot be obtained, clips to show can be found at http://school.discovery.com/ontv/videoclips/math1.html 
2. Key terms/skills:  Students will review the prerequisites including these math ideas:  similarity, scale drawing, scale factor and conversion factor.
3. Timeline worksheets can be duplicated by using the following information:
   1. Practice Timeline.  The following activity should help in the preparation of creating a Timeline of Evolutionary History.
      1. On an 8 1/2 by 11 inch paper create a timeline that fills the page in landscape position.  Please include the following years (dates) on your timeline: 0  50,000  100,000  200,000  250,000  500,000  750,000  and 1.0 million.  Indicate the scale for conversion at the bottom in the appropriate spot.  Make sure that the increments that you use in the timeline are appropriate.
      2. If you had a large amount of information to write in between the years 100,000 and 200,000, please display how you would show this.  Create another timeline for this and state your scale for this "blown up" portion.  Please use this notation ___:___ for the scales.
   2. Timeline of Evolutionary History.  In pairs you will be creating a timeline that will include historical and biological data.  Please complete the following.
      1. a. Using the long roll paper, draw out a timeline that goes from 0 (present day) and dates back to 5 billion years ago.  Your timeline should be in increments of "millions of years."
      2. b. Indicate the scale ___:___ at the bottom of the timeline in the appropriate spot.
      3. c. Coming off the scale please "balloon" out, above the original timeline, a miniature timeline showing the time period between 0 (present day) and 3,000 years ago.  Break this timeline into 50 year increments or smaller.
      4. d. Indicate the scale you used ___:___ directly below this smaller timeline.  This section of your timeline will have a lot of information to write in, so make sure to make it large enough to stretch across most of the paper.  
   3. The following items should be added to the scaled timeline created with your partner.
      1. a. Label all eras, epochs, and periods, drawings and names of species which appeared during each period.
      2. b. By highlighting intervals of the timeline, include the following major historical events and eras.  Provide several sentences to describe each.  For items that span several years, provide an estimate of the time period.
         1. Watson & Crick publish the structure of DNA
         2. Darwin travels to the Galapagos Islands
         3. Lamark provides his theory of evolution
         4. Mendel uses peas plants to show patterns of inheritance
         5. Several other items that you've learned so far (your choice)
4. Students should view and discuss information obtained at the Thomas Gale website in order to complete this lesson:
   1. Academic ASAP:  Keyword search "similarity (geometry)."  Under Magazines & Journals, Teaching mathematics with technology: scale drawings by Robert J. Jensen,  Using self-similarity to find length, area and dimension by James T. Sandefur, and Similarity in the middle grades by Glenda Lappan, "engineering drawings"  Checklist for a complete drawing (drafting standards) by Sastry K. Gantri
   2. Student Resource Center:  Keyword search "similarity." Under the Multimedia tab, Similar right triangles, "map drawing"  Maps in a snap (Skills) Backpacker,  "geometrical drawing" Escher, M.C. (1898 – 1972) Math & Mathematicians: The History of Math Discoveries around the World  and, under the Magazines and Journals tab,  Transformations in art and math (ArtEd Online) School Arts   
5. Modeling:  Students listen to teacher describe the lesson.  Students take notes. Teachers can generate the needed handout from the information provided below.
6. Student Test for Understanding:  Students will follow this list of procedures with teacher support.
   1. Practice Timeline.
   2. Timeline of Evolutionary History.
   3. Students insert historical items.  These should be labeled.  Several sentences should be given to describe each item.  Photographs/pictures should be attached appropriately also.
7. Recap –What did we learn?  Explain verbally the important math skills that you utilized.  What are ideas/skills needed in order to create an accurate timeline?
8. Home link –Students answer these basic questions:  Why is a sounds understanding of similarity, scale drawing, scale factor and conversion factor important for this lesson?  What is the major significance of one-dimensional similar figures utilized?  Why would you consider this to be an applied mathematics lesson?  What does math have to do with human evolution? How does this relate to evolution of anything? 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 lesson 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 similarity, scale drawing, scale factor and conversion factor that exists in the context of a historical evolutionary timeline.

Related Activities: H.O.T.S. (Higher Order Thinking Skills)  -- Stresses Bloom's Syntheses and Evaluation levels. Students create 3-D timeline of the future.  They could pick a particular topic (to narrow the scope) like the evolution of music, automobiles or fashion. They could research historical information on the internet, in books, magazines, journals, and newspapers. They could use these sources as rationale for what things will be like in the future. They could present all that they learned (and the math utilized during the process.)  They could evaluate their own and others' timelines for credibility. 

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 or two- and three- dimensional geometric objects
• 3.4 Use visualization and spatial reasoning to solve problems both within and outside mathematics
• 4.1 Understands attributes, units, and systems of measurement
• 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
• 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 similarity, scale drawing, scale factor and conversion factor as these relate to the construction of a timeline of evolutionary history.

Performance Indicators:

At Level 1, the student is able to:

• Write (show basic knowledge for) about the meaning of these:  similarity, scale drawing, scale factor and conversion factor.

At Level 2, the student is able to:

• Comprehend and Apply these concepts: similarity, scale drawing, scale factor and conversion factor.

At Level 3, the student is able to:

• Synthesize  new ideas related to and Evaluate concepts: similarity, scale drawing, scale factor and conversion factor.

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