Mathematics

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Mathematics

• What does mathematics mean in the elementary
  school today?
• What skills will a fifth grader develop and learn
  in each of the five content standards?
• What will a fifth grader be doing in a
  mathematics classroom?

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What is mathematics?
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Mathematics Today

• Mathematics today means more than just
  memorizing basic facts and completing assigned
  computational tasks.
• Students are provided with opportunities to learn
  concepts in five different content standards.

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The Five Content Math Standards

• The five NCTM content standards are number and
  operations, algebra, geometry, measurement, and
  data analysis and probability.
• The following slide depicts a graph developed by
  the National Council of Teachers of Mathematics
  to reflect the amount of time, or emphasis, that
  should be placed on each of the five content
  standards during a students years in Pre-K-grade
  2, grades 3-5, grades 6-8, and grades 9-12.
• The graph shows how the emphasis placed on each
  of the content standards is transformed as the
  student grows older.
• Concentrate on the vertical line placed at the
  end of the grade 3-5 band. Notice that the
  amount of time placed on each of the five areas
  is approximately the same with number and
  operations, algebra, and geometry receiving the
  greatest, and equal, emphasis.

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Emphasis Given the Five Content Standards

• NCTMs Principles and Standards for School
  Mathematics, 2000, p. 30.

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What skills will a fifth grader develop and learn
in each of these content standard areas?
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Number and Operations

• Understand numbers, ways of representing numbers,
  relationships among numbers, and number systems
• Understand meanings of operations and how they
  relate to one another
• Compute fluently and make reasonable estimates

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Algebra

• Understand patterns, relations, and functions
• Represent and analyze mathematical situations and
  structures using algebraic symbols
• Use mathematical models to represent and
  understand quantitative relationships
• Analyze change in various contexts

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Geometry

• Analyze characteristics and properties of two-
  and three- dimensional geometric shapes and
  develop mathematical arguments about geometric
  relationships
• Specify locations and describe spatial
  relationships using coordinate geometry and other
  representational systems
• Analyze transformations and use symmetry to
  analyze mathematical situations
• Use visualization, spatial reasoning, and
  geometric modeling to solve problems

10
Measurement

• Understand measurable attributes of objects and
  the units, systems, and processes of measurement
  (including time and money)
• Apply appropriate techniques, tools, and formulas
  to determine measurements

11
Data Analysis and Probability

• Formulate questions that can be addressed with
  data and collect, organize, and display relevant
  data to answer them
• Select and use appropriate statistical methods to
  analyze data
• Develop and evaluate inferences and predictions
  that are based on data
• Understand and apply basic concepts of probability

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What do you do when you are doing mathematics?
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Doing mathematics includes

• Using higher order thinking skills to analyze and
  solve problems
• Collaboratively sharing ideas and discovering
  solutions to problems
• Communicating ideas, strategies, and solutions
  both orally and in writing

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Doing mathematics includes (cont.)

• Using manipulatives (including calculators) for
  exploration and discovery
• Making connections to other mathematical concepts
  and academic disciplines
• Developing an understanding of concepts being
  studied

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Doing Math with Process Standards

• The goals of NCTMs process standards are
  integrated throughout the teaching/learning of
  the five content standards.
• The five process standards are
• Problem solving
• Reasoning and proof
• Communication
• Connections
• Representation

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Where can I find more information about the NCTM
Math Standards and the HCSDs fifth grade
benchmarks?

• NCTM Standards
• http//standards.nctm.org/document/index.htm
• HCSDs Fifth Grade Benchmarks
• http//www.harlan.k12.ia.us/mrsc/fifth_grade_mat
  hematics.htm

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• I hear and it helps a little,
• I see and the ideas begin to form,
• I do and the ideas becomes real to me,
• I do, see, and hear, and I
  understand,
• I talk about it and I
  understand more,
• I apply it and I see its
  value.
• - Dr. Phares G. ODaffer