I I pEORGIA STATE DEPARTMENT OF EDUCATION ET V NETWORK PRESENTS STATE BOARD OF EDUCATION James S. Peters, Chairman Robert Wright, Vice-Chairman Claude Purcell, Secreta~y MEMBERS FIRST CONGRESSIONAL DISTRICT J. Brantley Johnson SECOND CONGRESSIONAL DISTRICT Robert Byrd Wright THIRD CONGRESSIONAL DISTRICT Thomas Nesbitt, Jr. FOURTH CONGRESSIONAL DISTRICT James S. Peters FIFTH CONGRESSIONAL DISTRICT David Rice SIXTH CONGRESSIONAL DISTRICT Francis Shurling SEVENTH CONGRESSIONAL DISTRICT Henry Stewart EIGHTH C.NGRESSIONAL DISTRICT Lonnie E. Sweat NINTH CONGRESSIONAL DISTRICT Mrs. Bruce Schaffer* TENTH CONGRESSIONAL DISTRICT Zack Daniel *Resigned, but not replaced as yet. FOREWORD We are now providing more televised instruction that we hope will be of help to you in your classroom. YOU are the best authority on HOW it will help you, and in what ways you wish to use it. We are providing teacher guides like this one with suggestions that may be of service to you as you plan the best use of these lessons and fit them into the program you have planned. These guides were written by our television teachers. We think of the television teacher and the classroom teacher as being partners in the best creative teaching for the children. Television's dynamic power--Iong used in communicating other information--is now being made use of in education. It is making this a better educated world. None of us knows as much as we would like to know about it. It is a new medium and we are all learning together. We need your help and your suggestions as we seek to make the best use of our television facilities. Our aim is to make the school program more meaningful in Georgia. Our competent television teachers are well prepared to help you and the members of your class with lessons in science, mathematics, modern foreign languages, music, and Georgia history. They have time to gether up visuals that may not be readily available to you or that you may not have time to collect. This relieves you of much planning and preparation and leaves you with more time to devote to the actual teaching of the child in the classroom, and your personal teaching-andlearning contact with him. I hope you will find this teacher guide useful in your classroom work. We would be happy to have your suggestions about how our television teaching can be made more effective. If you have found some especially good ways to adapt'these lessons to your pupils, let us know about it. Perhaps it would help other teachers. This is a cooperative venture: it is important that we all work together to make the best use of this new power that has come into our hands in this technological age, so that we may make learning more effective in Georgia schools. ---CLAUDE PURCELL state Superintendent of Schools The material in this bulletin has been prepared to correlate with the curriculum guides, MATHEMATICS FOR GEORGIA SCHOOLS, published by the State Department of Education and with the consultative help of Gladys M. Thomason and Betty Altman, Consultants in Mathematics Education, State Department of Education. EDUCATIONAL TELEVISION UNIT GEORGIA STATE DEPARTMENT OF EDUCATION MATHEMATICS FOR MIDDLE GRADES Teacher: Lola Lauff NUMERATION SYSTEMS FUNDAMENTAL OPERATIONS with WHOLE NUMBERS 1. OUr Numeration System, How It Began 2. Number Bases 3. Zero, the Most Important Figure in Arithmetic 4. Number sequences and Patterns 5. The Number Line 6. The Nature of Addition and Subtraction 7. Properties of Addition and Subtraction 8. Expanded Notation 9. Increasing Skill in Subtraction 10. Understanding Multiplication and Division 11. Properties of Multiplication 12. Factors and Prime Numbers 13. Carrying in Multiplication 14. The Operation of Division 15. Working with Thousands 16. Estimating and Finding Averages I PROBLEM SOLVING RELATIONS SPECIAL FUNDAMENTAL OPERATIONS with FRACTIONS MEASUREMENT GEOMETRY SPECIAL 17. Problem Solving 18. Problem Solving: The Scientific Approach 19. Equations and Inequalities 20. Ratio and Proportion 21. Mathemagics 22. Fractional Numbers 23. Five Meanings of Fractions 24. Addition and Subtraction of Like Fractions 25. The Story of Measures 26. Time, a Most Important Measure 27. The Story of Money 28. Measurement 29. Linear Measure 30. Geometric Shapes 31. Finding Perimeters and Areas 32. Sets of Points 33. How to Whizz Through a Quizz II GEORGIA ::i'l'A'l'~ .u~t'AR'rMENT OF EDUCATION DR. CLAUDE L. PURCELL STATE SUPERINTENDENT OF SCHOOLS Division of Instruction Dr. H. S. Shearouse, Director Educational Television Serviceb Mr. E. A. Crudup, Administrator TEACHER Lola Lauff LESSON 1: ETV - Math - Middle Grades TITLE: OUR NUMERATION'SYSTEM, HOW IT BEGAN OBJECTIVES: 1. To show that our system of numeration is one of many systems used long ago. 2. To stress the importance of place value in our numeration system. 3. To develop a better understanding of our base ten system. NATURE OF CONTENT: This lesson tells the story of how our system of numeration began. It relates that early people "counted" on their fingers and by comparing, matching, and tallying. It shows that our numeration system is based on ten, probably because of ten fingers; that because i~ is based on ten, we call it the "base ten system" and use only ten symbols. The term, "set", is introauced. The terms, "number" and "numeral", are used with precise meaning. -1- ADDITIONAL RESOURCE INFOR1vlATION: f BASIC MATHEMATICS FOR ELEMENTARY TEACHERS: Greater Cleveland Mathematics Plan, Educational Research Council of Greater Cleveland, Cleveland, Ohio; Gundlach, B. H. EXPLORING MATHEMATICS ON YOUR OWN: Webster Publishing Company, Atlanta; 1956 1. "Understanding Numeration Systems" 2. "Sets, Sentences, and Operations" THE WONDERFUL WORLD OF MATHEMATICS: Garden City Books, Garden City, New York; Hogben, L. MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I NUMBERS AND NUMERALS: Bureau of Publications, Teachers College, Columbia University, New York, N. Y. BASIC CONCEPTS OF ELEMENTARY MATHEMATICS: John Wiley and Sons, Inc., Publishers; New York, N. Y.; 1960; Schaaf, William L. MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group Material (Units CEA - I, CEA - 2) SETS AND NUMBERS: Book Ie, Stanford University, Stanford, Calif. Suppes, Patrick SETS AND NUMBERS: Book II, Stanford University, Stanford, Calif. Suppes, Patrick ELEMENTARY CONCEPTS OF SETS: HEmry Holt and Company; 1959; Woodward, Edith J. and McLennan, Roderick C. FILMS: THE NUMBER SYSTEM: Encyclopedia Britannica Films -2- BILHSTRIPS: NUMBER Al~D NUMERAL; SETS: Colonial Films, series by Gundlack, B. H. ADVENTURES WITH NUMBERS SERIES: Pouplar Science Films -3- LESSON 2: ETV - Math -Middl.e Grades TITLE: NUMBER BASES OBJECTIVES: 1. To motivate students to experiment with number bases other than base ten. 2. To stimulate thinking. 3. To help students gain a better understanding of our base ten system. NATURE OF CONT ENT : In this lesson ancient number systems of base ten and base twenty are discussed. Examples of other bases in use today are pointed out, and children are encouraged to experiment with a new base. Lesson activities include base five, four, and three. ADDITIONAL RESOURCE INFORMATION: MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I MODERN MATHEMATICS FOR JUNIOR HIGH SCHOOL: Silver Burdett Company, Rosskopf, Morton, Hooten, and Sitomer MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group THE TEACHING OF ARITHMETIC: 1961: Spitzer, H. F. -4- LESSON 3: ETV - Math _. Middle Grades TITLE: ZERO, 'l'RE .M.OSrr lIYlPOR'rANT FIGURE IN ARITHMETIC OBJECTIVES: 1. To explain the uses of zero. 2. To help children discover, or understand more clearly, the generalizations which apply to adding, subtracting, and multiplying with zero. NATURE OF CONT ENT : This lesson points out the need for a sYmbol to show "not any". It tells of the invention of zero and how we can use zero with the digits one through nine over and over. These nine figures and zero are all that are needed to write any number. These generalizations are brought out: To add zero to a number does not change the number. To subtract zero from a number does not change the number. To multiply a number by zero gives----zero~ Many familiar objects are used as visuals. Zero is shown as just a certain point on the thermometer, as a starting point on a scale; as the smalles~ whole number on the number line. Zero is also shown as the "spaceman of arithmetic", and as a "VIP"; Very Important Placeholder. ADDITIONAL RESOURCE INFORMATION: ELEMENTARY MATHEMATICS COURSE OF STUDY: Kindergarten to Grade Six, Public Schools; Montgomery County, Maryland. BASIC CONCEPTS OF ELEMENTARY ARITHMETIC: Schaaf, William L. UNDERSTANDING ARITHMETIC: Swain, Robert L. -5- LESSON 4: ETV - Math - Hidd ]f'3.r;ades TITLE: NUMBER SEQtJ ENCES AND PAT'I'ERNS OBJECTIVES: 1. To point out underlying sequences and patterns in arithmetic. 2. To increase pupils' interest in arithmetic. 3. To prepare pupils for discoveries with mathematical patterns in later grades. NATURE OF CONT ENT : Number sequences and patterns are pointed out in the familiar addition chart, subtraction chart, and the multiplication chart. Exercises are worked in which children are asked to find the pattern and discover the missing term. ADDITIONAL RESOURCE INFORMATION: MATHEMATICS FOR THE ELEMENTARY SCHOOL, GRADE 4: School Mathematics Study Group, Revised Edition 1962 i (Part I) GREATER CLEVELAND MATHEMATICS PROGRAM TEACHER'S GUIDE FOR THIRD GRADE: Science Research Associates, Inc., Chicago MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I -6- LESSON 5: ETV - Math - Middle Grades TITLE: THE NUMBER LINE OBJECTIVES: 1. To help children understand counting, adding, and subtracting, as well as multiplying and dividing. 2. To show how the number line can be used as an aid to understanding the basic operations in arithmetic. NATURE OF CONTENT: The number line is used in establishing the concept of: a line the set of counting numbers the set of whole numbers "greater than" and "less than" addition, subtraction, multiplication, and division as operations counting on, as adding counting off, as subtracting subtracting, as the undoing of adding adding by equal groups, as multiplication subtracting by equal groups, as division division, as the undoing of mu1tiplica_ion ADDITIONAL RESOURCE INFORMATION: GREATER CLEVELAND MATHEMATICS PLAN: Educational Research Council of Greater Cleveland, Cleveland, Ohio; Gundlach, B. H., "Basic Mathematics for Elementary Teachers" MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I SCHOOL MATHEMATICS STUDY GROUP: Mathematics for the Elementary School, Teacher'R Commentary; 1961 -7- LESSON 6: ETV - Math - Mldd 'L(~ <":]""'()':8 'rITLE: THE NATURE OF AJJJJI'rION }\i.\JD SUBTRACTION OBJECTIVES: 1. To help children understand the nature of addition and subtraction; understand the meaning of addition and the meaning of subtraction. 2. To help children decide what operation to use. 3. To help children see the relation of addition and subtraction. NATURE OF CONTENT: The following concepts and generalizations are brought out in this lesson: A. Set Vocabulary 1. A "set" is a collection of things. 2. A thing that belongs to a set is a "member" of that set. 3. In set notation, the use of "curly braces" to group members of a set means "the set whose members are". 4. Capital letters are often used in naming sets. 5. A set which has no members is called the "enlpty" set; shown like this: ( ) or the "null" set; shown like this: ~. () 6. The SYmbo 1, "U", means "the union of", and is usee in set notation as "A U B", to mean the union of set A and set B. 7. Sets can be joined or s8parated; not added or subtracted. Numbers can be added or subtracted. 8. The symbol, "n", means "the intersection of", and -is used in set notation as "A n B", to mean the intersection of set A and set B. Q. The term, "subset", is explained as a "set with- in a set". -8- B. The Operation of Addition and Subtraction 1. Addition and subtraction are operations on numbers. 2. Addition is a way of thinking about two numbers together and getting a number as a sum. 3. The numbers added are called "addends". 4. Subtraction can be described as finding the missing addend when the sum and one addend are known. 5. Subtraction will "undo" addition. ADDITIONAL RESOURCE INFORMATION: MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I MATHEMATICS FOR THE ELEMENTARY SCHOOL, GRADE 4: School Mathematics Study Group, Teacher's Commentary (revised edition) 1962 -9- LESSON 7: ETV - Math - Middle Grades TITLE: PROPERTIES OF ADDITION AND SUBTRACTION (CLOSURE, COMMUTATIVE, ASSOCIATIVE) OBJECTIVES: 1. To help children understand that the operation of addition is always possible within the set of whole numbers, but the operation of subtraction is not always possible within the set of whole numbers. 2. To help children understand that in addition, the order of addends may be changed without changing the results. 3. To help children understand that in addition of three addends, two addends are grouped together. NATURE OF CONTENT: The lesson includes a review of the concept of counting numbers and of whole numbers. The number line is used in explaining closure. Problems are worked showing the commutative 'property and associative property of addition. ADDITIONAL RESOURCE INFORMATION: MATHEMATICS FOR THE ELEMENTARY SCHOOL, GRADE 4: School Mathematics Study Group, Revised Edition 1962: (Part 1) SEEING THROUGH MATHEMATICS: Book I: Scott, Foresman & Co., Chicago: 1962 Henry Van Engen, et al INTRODUCTION TO MATHEMATICS: Addison-Wesley Publishing Co., Charles F. Brunfiel, Robert E. E". Shanks Inc.: 1961 Eicholz, Merrill BASIC CONCEPTS OF ELEMENTARY MATHEMATICS: John Wiley & Sons, Inc., New York: 1960 William L. Schaaf -10- LESSON 8: ETV - Math - Middle Grades TITLE: EXPANDED NOTATION OBJECTIVES: 1. To help children understand the concept of expanded notation. 2. To increase ability to use different numerals for the same number .. 3. To increase understanding of the associative property. NATURE OF CONTENT: This lesson reviews place value using the PLACE VALUE POCKET CHART, the ABACUS, and the COUNT.ING MEN. Expanded notation is explained as taking a numeral in the simplest possible form and separating it according to hundreds, tens, and ones. Practice is given in using different numerals for the same number. This "renaming" of numbers in working examples gives practice in using the associative property. ADDITIONAL RESOURCE INFORMATION: MATHEMATICS FOR THE ELEMENTARY SCHOOL, GRADE 4: School Mathematics Study Group, Revised Edition 1962 i (Part 1) GREATER CLEVELAND MATHEMATICS PROGRAM TEACHER'S GUIDE FOR THIRD GRADE: Science Research Associates, Inc., Chicago, Ill. -11- LESSON 9: ETV - Math - Middle Grades TITLE: INCREASING SKILL IN SUBTRACTION OBJECTIVES: 1. To help children have a better understanding of subtraction as the inverse of addition and as the finding of the missing addend. 2. To give practice in thinking many different names for a number. 3. To show how "different names" for a number can be used in solving equationa. 4. To aid children in gaining skill in subtraction through "thinking ll expanded notation and "writing" the short form. NATURE OF CONTENT: This lesson provia.es activities which give practice in using different names for a number. In solving problems in addition and subtraction, this concept is stressed: the sets are joined or separated; the numbers are added or subtracted. Two impo~tant concepts reviewed in the lesson are: 1. subtraction as the finding of the missing addend 2. addition and subtraction as operations that will undo each other. Problems in subtraction are worked on the abacus in expanded form and in short form. ADDITIONAL RESOURCE INFORMATION: UNDERSTANDING ARITHMETIC: Holt, Rinehart and Winston; 1960; Swain, R. L. -12- MAKING ARITHMETIC MEP~INGFUL: John C. Winston Company; 1952; Brueckner, L. J. and Grossnickle, F. E. SETS AND NUMBERS: Book 1, Hawley, Newton and Suppes, Patrick SETS AND NUMBERS: Book 2, Hawley, Newton and suppes, Patrick ARITHMETIC PROJECT: Holden-Day, Inc., 1960; Suppes, Patrick MATHEMATICS FOR THE ELEMENTARY SCHOOL, GRADES 4, 5, 6: A. C. Vroman, Inc., 367 S. Pasadena Ave., Pasadena, California; School Mathematics Study Group; 1961 -13- LESSON 10: ETV - Math - Middle Grades TITLE: UNDERSTANDING MULTIPLICATION AND DIVISION OBJECTIVES: 1. To establish these concepts: a. multiplications come in pairs i divisions come in pairs b. multiplication is a short way to add the same number several times c. division is a short way to subtract the same number several times d. division is the undoing of multiplication NATURE OF CONTENT: The activities in this lesson are planned to teach or re-teach the multiplication and division facts. Methods of figuring out multiplication and. division facts are shown. (Games used as drills are shown.) ADDITIONAL RESOURCE INFORMATION: MATHEMATICS ~URRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I HELPING CHILDREN LEARN ARITHMETIC: Silver Burdett CompanYi Morton, Robert Lee MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary FILMS : MULTIPLICATION IS EASY, Coronet Films DIVISION IS EASY, Coronet Films FILMSTRIPS: MULTIPLICATION COMBINATIONS, SVE DIVISION COMBINATIONS, SVE MULTIPLICATION AND DIVISION, Young America Films -14- LESSON 11: ETV - Math - 1:1idd le Grades TITLE: PROPERTIES OF MULTIPLICATION OBJECTIVES: 1. To increase children's understanding of the meaning of multiplication. 2. To review the nature of multiplication. 3. To help children understand the" properties of multiplication. NATURE OF CONTENT: The meaning of multiplication as repeated addition is reviewed, and as a mathematical operation with certain characteristic properties. The properties of multiplication to be developed are: 1. properties of zero and one as factors 2. closure property 3. order property 4. grouping property 5. distributive property ADDITIONAL RESOURCE INFORMATION: MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I, State Department of Education MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary -15- LESSON 12: ETV - Math - Middle Grades TITLE: FACTORS AND PRIME NUMBERS OBJECTIVES: 1. To teach the meaning of the following terms: factor, prime number. NATURE OF CONTENT: The term, "factor", is explained: in multiplication the two numbers operated on are called factors and the result is called the product. The term, "prime number", is explained as a number that has nQ factors other than one and the number itself. Problems are worked to nelp children understand the ternls "factor" and "prime number". ADDITIONAL RESOURCE INFORMATION: MATHEMATICS CURRlCUWM GUIDE FOR GEORGIA SCHOOLS: Volume I -16- LESSON 13: ETV - Matn - Middle Grades TITLE: CARRYE\[C IN MULTIPLICATION OBJECTIVES: 1. To show the importance of "thinking straight". 2. To help children remember that we add the figure we carry AFTER we have multiplied the next figure. NATURE OF CONTENT: This lesson reviews basic concepts that are important in carrying in multiplication- It reviews briefly: 1. place value in our number 2. the work of zero 3. the operation of multiplication Process pockets and cards are used in explaining "carrying in multiplication". Through special effects in television, the children "see" how a number is carried to the next column. Common mista1