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- Learning Math: Number and Operations
- Individual Program Descriptions
Individual Program Descriptions1. Video 1. What Is Geometry? Explore the basics of geometric thinking using rich visualization problems and mathematical language. Use your intuition and visual tools for geometric construction. Reflect on the basic objects of geometry and their representation. 2. Video 2. Triangles and Quadrilaterals Learn about the classifications of triangles, their different properties, and relationships between them. Examine concepts such as triangle inequality, triangle rigidity, and side–side–side congruence, and look at the conditions that cause them. Compare how these concepts apply to quadrilaterals. Explore properties of triangles and quadrilaterals through practical applications such as building structures. 3. Video 3. Polygons Explore the properties of polygons through puzzles and games, then proceed into a more formal classification of polygons. Look at mathematical definitions more formally, and explore how terms can have different but equivalent definitions. 4. Video 4. Parallel Lines and Circles Use dynamic geometry software to construct figures with given characteristics, such as segments that are perpendicular, parallel, or of equal length, and to examine the properties of parallel lines and circles. Look past formal definitions and discover the properties and relationships among geometric figures for yourself. 5. Video 5. Dissections and Proof Review and explore transformations such as translation, reflection, and rotation. Apply these ideas to solve more complex geometric problems. Use your knowledge of properties of figures to reason through, solve, and justify your solutions to problems. Analyze and prove the midline theorem. 6. Video 6. Pythagorean Theorem Continue to examine the idea of mathematical proof. Look at several geometric or algebraic proofs of one of the most famous theorems in mathematics: the Pythagorean theorem. Explore different applications of the Pythagorean theorem, such as the distance formula. 7. Video 7. Symmetry Investigate symmetry, one of the most important ideas in mathematics. Explore geometric notions of symmetry by creating designs and examining their properties. Investigate line symmetry and rotation symmetry; then learn about frieze patterns. 8. Video 8. Similarity Examine your intuitive notions of what makes a "good copy" and then progress toward a more formal definition of similarity. Explore similar triangles and look into some applications of similar triangles, including trigonometry. 9. Video 9. Solids Explore various aspects of solid geometry. Examine platonic solids and why there are a finite number of them. Investigate nets and cross-sections for solids as a way of establishing the relationships between two–dimensional and three–dimensional geometry. 10. Video 10. Classroom Case Studies, K-5 Watch this program in the 10th session for K–2 and 3–5 teachers. Explore how the concepts developed in this course can be applied through case studies of K–5 teachers who have adapted their new knowledge to their classrooms. 11. Video 11. Classroom Case Studies, 6-8, Part 1 Watch Videos 11 and 12 in the 10th session for grade 6–8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6–8 teachers (former course participants) who have adapted their new knowledge to their classrooms. 12. Video 12. Classroom Case Studies, 6-8, Part 2 Watch Videos 11 and 12 in the 10th session for grade 6–8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6–8 teachers (former course participants) who have adapted their new knowledge to their classrooms. Learning Math: Number and OperationsA video- and Web-based course for K-8 teachers; 12 half-hour video programs (10 per grade band), course guide, and Web site; graduate credit available Learning Math: Number and Operations, a video- and Web-based course for elementary and middle school teachers examines the three main categories in the Number and Operations strand of Principles and Standards of School Mathematics (NCTM) — understanding numbers, representations, relationships, and number systems; the meanings of operations and relationships among those operations; and reasonable estimation and fluent computation. The course covers the real number system, place value, the behavior of zero and infinity, meanings and models of basic operations, percentages, and modeling operations with fractions, often with the aid of concrete, physical models that enhance understanding. It also examines Basic Number Theory topics, such as factors and multiples, as well as divisibility tests, at both practical and abstract levels. Accordingly, parts of the Number and Operations course may be more challenging than other Learning Math courses. The course consists of 10 approximately two-and-a-half-hour sessions, each with a half hour of video programming, problem-solving activities provided online and in a print guide, and interactive activities and demonstrations on the Web. The 10th session (choose video program 10, 11, or 12, depending on your grade level) explores ways to apply the concepts of number and operations you've learned in your own classroom. Produced by WGBH Educational Foundation. 2003. ISBN: 1-57680-678-2 Individual Program Descriptions1. Video 1. What Is a Number System? Understand the nature of the real number system, the elements and operations that make up the system, and some of the rules that govern the operations. Examine a finite number system that follows some (but not all) of the same rules, and then compare this system to the real number system. Use a number line to classify the numbers we use, and examine how the numbers and operations relate to one another. 2. Video 2. Number Sets, Infinity, and Zero Continue examining the number line and the relationships among sets of numbers that make up the real number system. Explore which operations and properties hold true for each of the sets. Consider the magnitude of these infinite sets and discover that infinity comes in more than one size. Examine place value and the significance of zero in a place value system. 3. Video 3. Place Value Look at place value systems based on numbers other than 10. Examine the base two numbers and learn uses for base two numbers in computers. Explore exponents and relate them to logarithms. Examine the use of scientific notation to represent numbers with very large or very small magnitude. Interpret whole numbers, common fractions, and decimals in base four. 4. Video 4. Meanings and Models for Operations Examine the operations of addition, subtraction, multiplication, and division and their relationships to whole numbers. Work with area models for multiplication and division. Explore the use of two-color chips to model operations with positive and negative numbers. 5. Video 5. Divisibility Tests and Factors Explore number theory topics. Analyze Alpha math problems and discuss how they help with the conceptual understanding of operations. Examine various divisibility tests to see how and why they work. Begin examining factors and multiples. 6. Video 6. Number Theory Examine visual methods for finding least common multiples and greatest common factors, including Venn diagram models and area models. Explore prime numbers. Learn to locate prime numbers on a number grid and to determine whether very large numbers are prime. 7. Video 7. Fractions and Decimals Extend your understanding of fractions and decimals. Examine terminating and non-terminating decimals. Explore ways to predict the number of decimal places in a terminating decimal and the period of a non-terminating decimal. Examine which fractions terminate and which repeat as decimals, and why all rational numbers must fall into one of these categories. Explore methods to convert decimals to fractions and vice versa. Use benchmarks and intuitive methods to order fractions. 8. Video 8. Rational Numbers and Proportional Reasoning Begin examining rational numbers. Explore a model for computations with fractions. Analyze proportional reasoning and the difference between absolute and relative thinking. Explore ways to represent proportional relationships and the resulting operations with ratios. Examine how ratios can represent either part-part or part-whole comparisons, depending on how you define the unit, and explore how this affects their behavior in computations. 9. Video 9. Fractions, Percents, and Ratios Continue exploring rational numbers, working with an area model for multiplication and division with fractions, and examining operations with decimals. Explore percents and the relationships among representations using fractions, decimals, and percents. Examine benchmarks for understanding percents, especially percents less than 10 and greater than 100. Consider ways to use an elastic model, an area model, and other models to discuss percents. Explore some ratios that occur in nature. 10. Video 10. Classroom Case Studies, K-2 Watch this program in the 10th session for K-2 teachers. Explore how the concepts developed in this course can be applied through case studies of K-2 teachers (former course participants) who have adapted their new knowledge to their classrooms. 11. Video 11. Classroom Case Studies, 3-5 Watch this program in the 10th session for grade 3-5 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 3-5 teachers (former course participants) who have adapted their new knowledge to their classrooms. 12. Video 12. Classroom Case Studies, 6-8 Watch this program in the 10th session for grade 6-8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6-8 teachers (former course participants) who have adapted their new knowledge to their classrooms. 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