Myrna Manly

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Myrna Manly
August 2224, 2006 Washington, DC
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What is Algebra?

• Functions and Relations
• Modeling
• Language and Representations
• Structure
• (NRC 1998)

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What is Algebra?Functions and Relations

• GEDTS
• Analyze and use functional relationships to
  explain how a change in one quantity results in
  change in the other quantity, including linear,
  quadratic, and exponential functions.
• Recognize and use direct and indirect variation.

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What is Algebra?Modeling

• GEDTS
• Analyze and represent situations involving
  variable quantities with tables, graphs, verbal
  descriptions, and equations.
• Create and use algebraic expressions and
  equations to model situations and solve problems.

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What is Algebra?Language and Representations

• GEDTS
• Convert between different representations such as
  tables, graphs, verbal descriptions, and
  equations.
• Analyze tables and graphs to identify and
  generalize patterns and relationships.

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What is Algebra?Structure

• GEDTS
• Create and use algebraic expressions and
  equations to solve problems.
• Evaluate formulas.

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Other Relevant GED Specifications

• Measurement and Geometry
• Find, use, and interpret the slope of a line, the
  y-intercept of a line, and the intersection of
  two lines.
• Number, Number Sense, Operations
• Select the appropriate operation to represent
  problem situations (e.g., when do you divide?).

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Examples from Practice Tests

• Form PA 19 Write an equation from a verbal
  description of the situation. Note the fixed cost
  and the cost that varies.
• Form PD 11 What element of the equation
  changes when the starting distance increases?

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Comparing Vehicle Costs

• A dynamic activity that
• Requires the use of high school math.
• Reflects the kinds of problems that are prevalent
  on the GED practice tests.
• Builds on a context that concerns students today.
• Is rich with possibilities for extensions.

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Comparing Vehicle Costs

• Situation
• High Gas Prices demand that we try to cut back
  on our use.
• Hybrid Vehicles use a combination of gas and
  electricity to save fuel.
• Hybrid Vehicles are more expensive to buy than
  standard vehicles.

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Comparing Vehicle Costs
Data for Cost Comparison
Costs include available incentives and are
rounded to the nearest hundred. Sources
http//www.fueleconomy.gov
http//www.autos.yahoo.com
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Comparing Vehicle Costs
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Comparing Vehicle Costs

• Imagine that the graph and table make up the
  stimulus for an item set on the GED Math Test.
  What questions could be asked?
• Discuss with a partner.
• Share with your table.
• Write one question per table on a transparency
  and select a presenter.
• (5 minutes)

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Comparing Vehicle Costs

• Imagine that the table and graph appeared in a
  newspaper article that you brought to class.
• What questions can you ask that will encourage
  the students to explore the mathematics of the
  situation further?
• How did they get
• What if
• How would that affect

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Comparing Vehicle Costs

• Focus on Annual Fuel Costs. How did they get
  that number? How would you figure your own costs?
  A ??
• General Strategy
• What elements are involved?
• What operations apply? How do you know?

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Comparing Vehicle Costs

• In your groups
• Analyze the process of arriving at the formula
  for annual fuel cost.
• Share techniques and questions that can be used
  to foster understanding of modeling this
  situation.

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Comparing Vehicle Costs

• Variations and Extensions
• Go to the websites referenced.
• Explore a personal scenario vary the parameters
  to fit own habits or compare costs when selling
  own vehicle.
• Reverse the order build up to the equation and
  graph.
• ??

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Comparing Vehicle Costs

• Reflect
• What are the prerequisite skills that students
  should have in advance of participating in this
  activity?
• What reservations do you have about implementing
  an activity like this in your classrooms?
• How does this activity embody the ANN Principles
  of Teaching and Learning?
• Did we address both test preparation and deep
  understanding?

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References

• Pendleton, Kenn, Item Writers Manual, Test 5,
  Mathematics. 1999, GED Testing Service,
  Washington, DC
• National Research Council, The Nature and Role of
  Algebra in the K-14 Curriculum Proceeds of a
  National Symposium, 1998, National Council of
  Teachers of Mathematics and Mathematical Sciences
  Education Board, http//www.nap.edu/catalog/6286.
• http//www.fueleconomy.gov
• httpwww.autos.yahoo.com