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Full Description
This text was written in response to the recommendations of A Call to Change, and the vision of the NCTM Standards. Its goals are to present important, challenging mathematics relevant to a Standards-based K-8 curriculum, and to prepare prospective elementary teachers to implement the Standards in their own classrooms. Students acquire an understanding of mathematics that is considerably broader than that which they will be required to teach. They develop number sense, spatial sense, and mathematical intuition, and are able to explain mathematical concepts, relationships, and processes, clearly and correctly. This text helps the future teacher to see elementary school mathematics as a "Big Picture," in which important, interconnected ideas are developed and applied from K through 8. They learn from experience that mathematical understanding begins with concrete models, and then progresses through verbal, numerical, and, finally, abstract stages. As a result, they become confident, successful problem-solvers, and develop an appreciation for the power and beauty of mathematics, and an enthusiasm for teaching it.
Contents
Meaning, Representation, and Relationships of Rational Numbers. Numeration.Bases other than Ten.Divisibility of Whole Numbers.Factorization.Building Numbers with Primes (Group Activity).Divisibility Tests and Generalizations (Group Exploration - Discussion).Meaning of Fractions.Equivalent Fractions.Mixed Numbers and Comparison of Fractions.Fractions Which Represent Probabilities.Fractions Which Represent Ratios.Fractions Which Represent Rates.Meaning of Decimals.Meaning of Percent.Opposites.Chapter Review.Concrete, Verbal, and Numerical Understanding of the Arithmetic Operations and How They Are Related. Understanding Addition.Understanding Subtraction.Understanding Multiplication.Properties of Multiplication.Product of Two Negative Numbers.Meaning of Division.Making Sense of How We "Do" Division.Cumulative Review.Attributes, Units, and Measurement. What Is Measurement?Measurements on Labels.Measurement of Length.More about Circumference.Measurement of Weight.Measurement of Area.Measurement of Volume.Measurement of Temperature.Chapter Review.Geometric Features. Straightness, Flatness, Dimension.Angles and Parallels.Sum of Measures of Angles of a Triangle.Polygons.Centers and Lines of Symmetry.Discovery Activities with Patty Paper.Recap.Congruent Figures.Similarity.Chapter Review.Area and Volume. Area of Triangles.Area of Other Figures.The Pythagorean Theorem.Surface Area.Surface Area II.Volume.Data Collection and Interpretation. Collecting a Set of Data.Methods of Organizing Data.The "Center" of the Data - Part I.The "Center" of the Data - Part II.The "Spread" of Data.Standardized Scores.Sampling.Review.Probability. Probability Review.Theoretical vs. Experimental Probability.Conditional Probability.Counting Techniques.Counting Specific Orders.Counting Different Groups.Geometric Probability.The Normal Distribution.Chapter Review.Number Systems and Their Properties. Natural Numbers and Whole Numbers.The Set of Integers.Inverses.Rational Numbers.
