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Full Description
An inquiry-based approach to this course allows future teachers to learn through exploration and group work, leading to a deeper understanding of mathematics. Known for her contributions in math education, Sybilla Beckmann writes the leading text for this approach. In Mathematics for Elementary Teachers with Activities, students engage, explore, discuss, and ultimately reach a true understanding of mathematics.The Fourth Edition provides a new full-color design, making the math come alive. For the first time, the content and activities are combined into the same text, creating a self-contained resource for this course and beyond. Common Core State Standards are integrated to complement the National Council of Teachers of Mathematics (NCTM) Focal Points and Standards that appear where appropriate. New From the Field features highlight the latest research, Integrating Mathematics and Pedagogy (IMAP) videos (available separately), children's literature, views from the classroom, and lesson planning to prepare future teachers for their teaching careers.
Contents
1. Numbers and the Base-Ten System1.1 The Counting Numbers1.2 Decimals and Negative Numbers1.3 Comparing Numbers in Base-Ten1.4 Rounding NumbersChapter Summary2. Fractions and Problem-Solving2.1 Solving Problems and Explaining Solutions2.2 Defining and Reasoning About 2.3 Equivalent Fractions 2.4 Comparing Fractions 2.5 Percent Chapter Summary3. Addition and Subtraction3.1 Interpretations of Addition and Subtraction3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts3.3 Why the Common Algorithms for Adding and Subtracting Numbers in the Base-Ten System Work3.4 Adding and Subtracting Fractions3.5 Adding and Subtracting Negative NumbersChapter Summary4. Multiplication4.1 Interpretations of Multiplication4.2 Why Multiplying by 10 is Special in Base-Ten4.3 The Commutative and Associate Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes4.4 The Distributive Property4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts4.6 Why Algorithms for Multiplying Whole Numbers WorkChapter Summary5. Multiplication of Fractions, Decimals, and Negative Numbers5.1 Multiplying Fractions5.2 Multiplying Decimals5.3 Multiplying Negative Numbers5.4 Powers and Scientific NotationChapter Summary6. Division6.1 Interpretations of Division6.2 Division and Fractions and Division with Remainder6.3 Why Division Algorithms Work6.4 Fraction Division from the "How Many Groups?" Perspective6.5 Fraction Division from the "How Many in One Group?" Perspective6.6 Dividing DecimalsChapter Summary7. Ratio and Proportional Relationships7.1 Motivating and Defining Ratio and Proportional Relationships7.2 Solving Proportion Problems by Reasoning with Multiplication and Division7.3 Unit Rates and the Values of a Ratio 7.4 Proportional Relationships Versus Inversely Proportional Relationships7.5 Percent Revisited: Percent Increase and DecreaseChapter Summary8. Number Theory8.1 Factors and Multiples8.2 Even and Odd 8.3 Divisibility Tests 8.4 Prime Numbers 8.5 Greatest Common Factor and Least Common Multiple 8.6 Rational and Irrational Numbers8.7 Looking Back at the Number SystemsChapter Summary9. Algebra9.1 Numerical Expressions 9.2 Numerical Expressions with Variables9.3 Equations for Different Purposes 9.4 Solving Equations 9.5 Solving Algebra Word Problems with Strip Diagrams and with Algebra 9.6 Sequences 9.7 Functions 9.8 Linear Functions Chapter Summary10. Geometry10.1 Visualization10.2 Angles10.3 Angles and Phenomena in the World10.4 Circles and Spheres10.5 Quadrilaterals, Triangles, and Polygons Chapter Summary11. Measurement11.1 Fundamentals of Measurement 11.2 Length, Area, Volume, and Dimension 11.3 Error and Precision in Measurements 11.4 Converting from One Unit of Measurement to Another Chapter Summary12. Area of Shapes12.1 Areas of Rectangles Revisited12.2 Moving and Additivity Principles About Area12.3 Areas of Triangles 12.4 Areas of Paralellograms and Other Polygons12.5 Shearing: Changing Shapes Without Changing Area12.6 Areas of Circles and the Number Pi12.7 Approximating Areas of Irregular Shapes12.8 Contrasting and Relating the Perimeter and Area of Shapes12.9 Using Moving and Additivity Principles to Prove the Pythagorean TheoremChapter Summary13. Solid Shapes and Their Volume and Surface Area13.1 Polyhedra and Other Solid Shapes13.2 Patterns and Surface Area13.3 Volumes of Solid Shapes13.4 Volume of Submersed Objects versus Weight of Floating ObjectsChapter Summary14. Geometry of Motion and Change14.1 Reflections, Translations, and Rotations14.2 Symmetry14.3 Congruence14.4 Constructions with Straightedge and Compass 14.5 Similarity 14.6 Areas, Volumes, and Scaling Chapter Summary15. Statistics15.1 Formulating Statistical Questions, Gathering Data, and Using Samples15.2 Displaying Data and Interpreting Data Displays15.3 The Center of Data: Mean, Median, and Mode15.4 Summarizing, Describing, and Comparing Data Distributions Chapter Summary16. Probability16.1 Basic Principles of Probability16.2 Counting the Number of Outcomes16.3 Calculating Probabilities in Multi-Stage Experiments16.4 Using Fraction Arithmetic to Calculate ProbabilitiesChapter SummaryBibliographyIndexDownloads
