Time for numbers [1966]

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

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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.

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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
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BILHSTRIPS: NUMBER Al~D NUMERAL; SETS: Colonial Films, series by Gundlack, B. H. ADVENTURES WITH NUMBERS SERIES: Pouplar Science Films
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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.

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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

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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

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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".

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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
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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

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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.

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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.

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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
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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

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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

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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

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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<es in carrying in multiplication are pointed out and corrected.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I~ 1962

MATHEMATICS FOR ELEMENTARY TEACHERS: School Mathematics Study Group, Teachers Commentary, 1961

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LESSON 14: ETV - Math .- MiddJe Grades

TITLE:

THE OPERATlOi.~ OF DIVISION

OBJECTIVES:

1. To increase children's understanding of the nature and properties of division.

2. To help children understand that the operation ~ numbers called'~ivisiorr'canbe described as finding a missing factor when the product and ~ factor are known.

NATURE OF CONTENT:

The meaning of division is reviewed as:

1. repeated subtraction 2. an operation that operates on two numbers
and produces a third number.

Problems are worked emphasizing division as the finding of a missing factor when the product and one factor are known.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary, 1961

GREATER CLEVELAND MATHEMATICS PROGRAM TEACHER I S GUIDE FOR THIRD GRADE:
Science Research Associates, Inc., 1961

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LESSON 15: ETV - Math - Middle Grades

TITLE:

WORKING TtHTH THOUSANDS

OBJECTIVES:

1. To help children understand larger numbers.

2. To show that we add, subtract, multiply, and divide thousands the way we add, subtract, multiply, and divide ones, tens, and hundreds.

NATURE OF CONTENT:

Activities in this lesson deal with:

1. reading and writing numbers in the thousands in dollars, feet, population figures, dates, telephone numbers, automobile license plates, and house numbers.
2. working problems dealing with numbers in the thousands.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I

MATHEMATICS FOR THE ELEMENTARY TEACHER: School Mathematics Study Group, Teachers Commentary, 1961

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LESSON 16: ETV - Math - Middle Grades

TITLE:

ESTIMA'I'ING AND FINDING AVERAGES

OBJECTIVES:

1. To help children develop ability to round off numbers and estimate answers.

2. To help children gain an understanding of the meaning and method of finding averages.

NATURE OF CONTENT:

The following terms are explained: estimate, estimated answer, round off numbers, average.

The number line is used to help in rounding off numbers to the nearest hundreds and thousands.

Problems are worked to show the meaning of average and to give practice in finding averages.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS FOR GEORGIA SCHOOLS: Volume I

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LESSON 17: ETV - Math - Middle Grades

TITLE:

PROBLEM SOLVING

OBJECTIVES:

1. To make problem solving easier.

2. To teach children to solve problems scientifically.

NATURE OF CONTENT:

As word problems are worked out in this lesson, the following pattern is emphasized:

1. SAY the word problem. 2. SEE the action. 3. WRITE the number sentence 4. WORK it~

The terms, "equation" and "number sentence", are explained and used in solving the problems.

The symbols for "equal" (=) and "is not equal" (:::;b) are used.

Some problems used have hidden facts needed in solving the problem; some have facts not needed in solving the problem.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary, 1961

EXPERIMENTAL MATH~MATICS PROJECT: Teacher's Guide for Booklet 6; Scott Foresman

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LESSON 18: ETV - Math - Middle Grades

TITLE:

PROBLEM SOLVING: THE SCIENTIFIC APPROACH (Continuation of Lesson 17)

OBJECTIVES:

1. To encourage children to use the scientific approach in solving problems:

NATURE OF CONTENT:

This lesson consists of a series of problems worked out by various class groups. It shows how they have applied the scientific approach to problem solving.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary, 1961

EXPERIM~NTAL MATHEMATICS PROJECT: Teacher's Guide for Booklet 6; Scott Foresman

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LESSON 19: ETV - Math - M.iddle Grades

TITLE:

EQUATIONS AND INEQUALITIES

OBJECTIVES:

1. To teach the concept of equality and help children gain skill in solving placeholder equations.

2. To teach the concept of inequality and help children gain skill in making comparisons when one quality is less than or greater than another quality.

NATURE OF CONTENT:

A. Set Vocabulary

1. This lesson includes a review of the following terms included in the study of "sets":

a) set (a collection of things) b) member of a set (a thing that belongs to
a set) c) empty set (a set containing no members) d) equal sets (sets with the same members) e) equivalent sets (sets having the same
number of members)

B. Concept of Equivalence

1. The term "equivalent" is not used in the lesson; instead, the expression "sets having the same number" is used.

2. The idea of one-to-one correspondence is reviewed in emphasizing equivalence.

3. Examples of various names for the same number is used as a means of showing equivalence.

C. Concept of Equality

1. The following terms are explained:

a) equation (a special kind of number sentence which expresses equality between two quantities)

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b) placeholder equation ( an equation containing a placeholder is an open sentence which is neither true nor false)
D. Concept of Inequality 1. Inequality is explained as a number sentence which states that one quantity is less than, greater than, or not equal to, another quantity.
2. The sYmbols for greater than, :> , less than, < ,
and not equal to,~, are explained and used in number sentences worked during the lesson. 3. The number line is used in teaching inequality. ADDITIONAL RESOURCE INFORMATION: MATHEMATICS FOR THE ELEMENTARY SCHOOL, GRADE 4: School Mathematics Study Group, Teachers Commentary, (Revised Edition) 1962; Part 1 GLOSSARY: MATHEMATICAL TERMS: A Service Report for Schools from Webster Publishing Co. GREATER CLEVELAND MATHEMATICS PROGRAM TEACHER'S GUIDE FOR THIRD GRADE: Science Research Associates, Inc., Chicago; 1962
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LESSON 20: ETV - i"i21 T.b. ~diddi.e Grades

TITLE:

RATIO hND PROPORTION

OBJECTIVES:

1. To develop these understandings:

a) Comparing two numbers by division means the same as finding the ratio and two numbers.

b) Proportions are equivalent ratios.

NATURE OF CONTENT:

Illustrations are given and examples are worked showing that:

a) In finding out how much larger or smaller one number is than another, one uses subtraction.

b) In finding out how many times as large one number is as another, one uses division.

c) Comparing two numbers by :division means the same as finding the ratio of two numbers.

d) Proportions are equivalent ratios.

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LESSON 21: ETV - Math-]'vliddle C.>rades

TITLE:

MATHEMAGICS

OBJECTIVES:

1. This lesson is intended:

a) to heighten interest in arithmetic b) to stimulate good thinking in solving problems c) to show that arithmetic can be fun.

NATURE OF CONTENT:

The lesson is divided into four parts:

1. MAGIC NUMBER 9 2. ARITHMETRICKS 3. Multiplication 4. Magic Squares

ADDITIONAL RESOURCE INFORMATION:

MAGIC HOUSE OF NUMBERS: Adler, Irving

MATH IS FUN: Emerson Books, 1954; Degrazia, Joseph

FUN WITH FIGURES, EASY EXPERIMENTS FOR YOUNG PEOPLE: Random House, 1946; Freeman, Ir.a

THE MAGIC AND ODDITIES OF NUMBERS: Vantage Press, Inc., New York I, N.Y., Gilles, W. F.

THE WONDERFUL WORLD OF MATHEMATICS: Doubleday & Co., 1955; Hogben, Lancelot

MATHEMATIC~L RECREATIONS: W. W.Norton Publishing Co., 1942; Kraitchick, Maurice

ARITliMETIC CAN BE FUN: J. B. Lippincott, 1949; Leaf, Munro

MORE FUN WITH PUZZLES: J. B. Lippincott, 1947; Leeming, Joseph

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FUN WITH tlATHEMATICS: World Book Company, 1952~ Meyer, Jerome S.
MATHEMATICAL PUZZLES FOR BEGINNERS AND ENTHUSIASTS: Dover Publishing Company~ 1954~ Mott-Smith, Geoffrey
PRACTICAL CLASSROOM PROCEDURES FOR ENRICHING ARITHMETIC: Webster Publishing Company, 1956~ Spitzer-Herbert
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LESSON 22: ETV - Math - Middle Grades

TITLE:

FRACTIONAL NUMBERS

OBJECTIVES:

1. To teach these concepts:

a) fractional number b) 1/5; 1/6; 1/7; 1/8; 1/9 of a whole c) 1/5; 1/6; 1/7; 1/8; 1/9 of a group

NATURE OF CONTENT:

In this lesson the number line is used in "re-teaching" the meaning of whole numbers and "teaching" the meaning of fractional numbers.

The terms, "numerator" and "denominator", are explained and three types of fractions are discussed.

Manipulative materials are used in teaching the concept of 1/5; 1/6; 1/7; 1/8; 1/9 of a whole, and 1/5; 1/6; 1/7; 1/8; 1/9 of a group.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I

HELPING CHILDREN LEARN ARITHMETIC: Silver Burdett Company; Morton, Robert Lee

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary

FILMS:

WE DISCOVER FRACTIONS: Coronet Films

HOW TO ADD FRACTIONS: Hunt

HOW TO SUBTRACT FRACTIONS: Hunt

SIMPLE FRACTIONS: Knowledge Builders

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FILMSTRIPS: FRACTIONS: Gundlach, B. H" Colonial Films FRACTIONS SERIES: Curriculum FiL~s INTRODUCTION TO FRACTIONS: Jim Handy Organization FRACTION SERIES: SVE LEARNING NEW NUMBERS - FRACTIONS: Filmstrip House
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LESSON 23: ETV - Math - J>JJddle Grddes

TITLE:

FIVE MEANINGS OF FRACTIONS

OBJECTIVES:

1. To review the five uses and meanings of fractions as readiness for computing with fractions.

NATURE OF CONTENT:

An attempt is made to show by example the meaning of the following terms: (1) fraction (2) fractional number (3) fraction numeral (4) numerator (5) denominator

In pointing out five meanings of fractions, examples are given citing fractions used in five different ways: (1) as part of a whole (2) as part of a group (3) in measuring (4) in comparing (5) as remainders in division

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS FOR GEORGIA SCHOOLS: Volume I, 1962; State Department of Education

MATHEMATICS ?OR THE ELEMENTARY SCHOOL, GRADE 4: School Mathematics Study Group (Revised Edition) 1962i Part 1

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LESSON 24: ETV - Il.1ath - Middle Grades

TITLE:

ADDI'I'ION AND SUBTRACTION OF LIKE FRACTIONS

OBJECTIVES:
\
1. To help children understand the concept of like fractions.

2. To teach children that in addition or subtraction of like fractions the numerators are added or subtracted and the denominators remain the same.

NATURE OF CONTENT:

Concrete objects and other visuals are used in teaching the concept of like fractions as fractions having parts of equal size, or having the same denominators.

ADDITIONAL RESOURCE INFORMATION:

DISCOVERING MEANINGS IN ARITHMETIC: John C. Winston Co., Philadelphia: Grossnickle, Foster E.and Brueckner, Leo J.

MATHEMATICS FOR GEORGIA SCHOOLS: Volume I

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary

FILMS:

HOW TO ADD FRACTIONS: Hunt

HOW TO SUBTRACT FRACTIONS: Hunt

FILMSTRIPS:

ADDING FRACTIONS: Eye Gates

FRACTIONS SERIES: Curriculum Filma

FRACTIONS SERIES: Society for Visual Education

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INTRODUCTION TO FRACTIONS: Jim Handy Organization LEARNING NEW NUMBERS: FRACTIONS: Filmstrip House THE NEW ELEMENTARY MATHEMATICS: Filmstrips in Color:
Directed by Dr. Bernhard H. Gunlach (Colonial Films)
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LESSON 25: ETV - Mat:h - i'1} ddle Grades

TITLE:

THE STORY OF MEASURES

OBJECTIVES:

1. To show that without measures man would have to live a veIy simple life, like that of the caveman of long ago.

2. To show that our system of weights and measures began many, many years ago.

NATURE OF CONTENT:

This lesson tells how early man used his body as his measuring stick.

The lesson also reviews and extends understandings of the standard measures: dozen, ounce, pound, inch, foot, yard, pint, quart, gallon, peck, bushel, calendar, week, month, and year.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I

HELPING CHILDREN LEARN ARITHMETIC: Silver Burdett Company; Morton, Robe:r:t Lee

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary

FILMS :

LET'S MEASURE--OlJ.i.-ICES, POUNDS, TONS: Coronet Films

MEASUREMENT: Coronet Films

WEIGHTS AND MEASURES: E.B.F.

FIU1STRIPS:

MEASURING TIME AND THINGS: Dukane Corporation

MAN AND MEASURE SERIES: Filmstrip House

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LESSON 26: ETV - Math - ,,'iddle G1:,: <}c3S

TITLE:

TIME, A MOST IMPORTANr MEASURE

OBJECTIVES:

1. To show that the clock plays a very important part in our lives today.

2. To relate how man told time before the invention of modern clocks.

3. To explain how time is measured by the clock and by the calendar.

NATURE OF CONTENT:

This lesson shows that today many of the things we do are done "by the clock".

It tells .the story of TIME from the days of the caveman's notched stick to the present day atomic clocks, and briefly explains time zones.

It also explains how time is measured by the calendar; in weeks, months, and years.

ADDITIONAL RESOURCE INFORMATION:

ALL KINDS OF TIME: Harcourt Brace Co., 1950; Behn, Harry

TELL ME THE TIME, PLEASE: J. B. Lippincott Co., 1936; Bragdon, L. J.

THE STORY OF OUR CALENDAR: Brindze, Ruth

KEEPING TIME: Buehr, Wa 1t.er

TICK, TOCK--A STORY OF TIME: D. C. Heath Co., 1938; Flynn, Harry

SEVEN DAYS FROM SUNDAY: Galt, Tom

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WHAT TIME IS IT: Lippincot.t; 1932; Marshak, Ilin
IT I S ABOUT TIME: Scott-Foresma~ Company, 1955; Schlein, Mirim
FILMSTRIPS: MEASURING TIME AND THINGS: Dukane Corporation THE CALENDAR: DAYS I WEEKS, MONTHS: Coronet
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LESSON 27: ETV - Math -~"!Ldclle (,':::.,3",,;3

TITLE:

THE STORY OF MONEY

OBJECTIVES:

1. To show how people got things they needed before there was money in the world.

2. To show how "money", as we think of it today, began and how we use it today.

NATURE OF CONT ENT :

This lesson tells how early man traded goods or "bartered" before there was "money" in the world.

It points out man's need for some thing to use as money; something that everyone could use; something that was easy to carry about and easy to divide.

It tells of many things that have been used as money during the history of man, including a display of coins from different countries.

It shows how we use money today to pay for things we want, and to save.

ADDITIONAL RESOURCE INFORMATION:

WHAT IS MONEY: Steck Publishing Company, 1959; Wilcox and Burke

A cHILD'S BOOK OF COINS AND CURRENCY:

THE TRUE BOOK OF MONEY: Children's Press, Ziner and Thompson

MATERIAL FROM THE MUSEUM OF MONEYS OF THE WORLD:

ENCYCLOPEDIAS:

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LESSON 28: ETV ",' M<.d.n -- l'il.l<:1c'le Grades

TITLE:

MEASUREj'lll::i\j'J.'

OBJECTIVES:

1. To review and extend understandings of standard units of measure.

2. To help children understand how to change measures from one unit to another.

3. To show that like units of measure can be added and subtracted.

NATURE OF CONTENT:

Concrete objects, tables of measure, and problem solving are used in reviewing and extending understanding of: dozen, inches, feet, yards, pints, quarts, gallons, pecks, bushels, ounces, pounds, seconds, minutes, hours, weeks, months', years, degrees, penny I nickel, dime, quarter, half-dollar, dollar.

Problems are worked to show how measures are changed from one unit to another and how like units can be added or subtracted.

ADDITIONAL RESOURCE INFORMATION:

DISCOVERING MEANINGS IN ARITHMETIC: John C. Winston Co., Philadelphia; Grossnickle, Foster E. and Brueckner, Leo J.

MATHEMATICS FOR GEORGIA SCHOOLS: Volume I

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary

BOOKS FOR CHILDREN:

ALL KINDS OF TIME: Harcourt Brace Co., 1950; Behn, Harry

TIME FOR YOU: J. B. Lippincott Co., 1960; Bradley, Duane

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TELL ME THE TIME, PI,EASE: J. B. Lippincott Co., 1936; Bragdon, L. J.
THE STORY OF OUR CALENDAR: Vanguard Press, 1949; Brindze, Ruth
TICK,TOCK--A STORY OF TIME: D. C. Heath Co., 1938; Flynn, Harry
FROM BARTER TO BANKING: Appleton Century; Leemi:L.g, Joseph
IT1S ABOUT TIME: Scott Foresman Co., 1955; Schlein, Miriam
WHAT IS MONEY: Steck Publishing Co., 1959; Wilcox & Burke
WHEELS OF TIME: Crowell, 1957; Zarchy, Harry
THE TRUE BOOK OF TIME: Children1s Press, 1956; Ziner and Thompson
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LESSON 29: ETV - ~lath - l'I1Jdle Grades

TITLE:

LINEAR MEASURE

OBJECTIVES:

1. To increase children's knowledge and understanding of linear measure.

NATURE OF CONTENT:

Included in this lesson are activities which involve comparing sizes, measuring segments, using standard units of measure, using a linear scale, and using a ruler as a measuring instrument.

ADDITIONAL RESOURCE INFORMATION:

WONDERFUL WORLD OF MATHEMATICS: Newman, "World of Mathematics Encyclopedias", Hogben

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary

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LESSON 30: ETV - Math - ]\'I.i dd.le Grades

TITLE:

GEOMETRIC SHAPES

OBJECTIVES:

1. To teach the concept of plane figures (line figures) and the concept of solid figures.

2. To review the concept of these geometric forms:

a) plane figures - circle, square, triangle, rectangle, star
b) solids - cube, sphere, cone

3. To help children be able to identify the following geometric forms:

a} plane figures - ellipse, polygon" pentagon, hexagon, octagon
b} solids - cylinder

NATURE OF CONTENT:

In identifying line figures, the terms, "line", "closed line", "line segment", and "polygon", are stressed.

Manipulative objects are used in discussing solids.

By pointing out examples, children are encouraged to see the geometric forms that are all around us in the everyday world.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary, 1961

GEOMETRY FOR PRIMARY GRADES: Stanford University Project, Teacher's Manual for Bk.2; Holden-Day, Inc., 728 Montgomery St., San Francisco, Calif.; Newton Hawley and Patrick Suppes

GEOMETRY: Addison-Wesley Publishing, Inc.; Brunfiel, Eicholz, and Shanks

MODERN MATHEMATICS FOR JUNIOR HIGH SCHOOL: Silver Burdett; Rosskopf, Morton, Hooten & Sitomer
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LESSON 31: ETV - Math - Ivjidcle Grades

TITLE:

FINDING PERIMETERS AND AREAS

OBJECTIVES:

1. To help children understand that:

a) A simple, closed curve may be measured by "straightening" a model of the curve and finding the length of the model.

b) A simple, closed curve which is formed by the union of line segments is a polygon.

c) The length of a polygon is called the perimeter of the polygon.

d) The perimeter of a polygon may be. found by adding the measures of the sides.

e) ~hile perimeter measures the distance around the rim of a rectangle, ~ measures all of the flat surface that lies within this rectangle.

NATURE OF CONTENT:

The concept of a simple, closed curve, and the concept of a polygon are reviewed.

The terms, "perimeter" and "area", are explained.

The method for finding the perimeter of a polygon is shown~ and the method for finding the area of a rectangle is shown.

Problems are solved in finding perimeters and areas.

ADDITIONAL RESOURCE INFORMATION:

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary

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LESSON 32: ETV - Math - Middle GCt"j;-2S

TITLE:

SETS OF pOn,,"TS

OBJECTIVES:

1. The purpose of this lesson is to introduce some of the fundamental concepts of what might be called physical geometry.

NATURE OF CONTENT:

The following concepts are introduced:

1. point, an exact location 2. space, the set of all points 3. path or curve, a set of points connecting
one point to another 4. line segment, a part of a line; 'namely
the set of points lying between two points and including the two points 5. line, the extension of a line segment

ADDITIONAL RESOURGE INFORMATION:

GEOMETRY FOR PRIMARY GRADES: Stanford University; 1960; Hawley, Newton & Suppes, Patrick

MATHEMATICS FOR THE ELEMENTARY SCHOOL: School Mathematics Study Group, Teachers Commentary, 1961

AN ADVENTURE IN GEOMETRY: Viking Press, 1957; New York; Ravielli, A.

CREATING WITH PAPER: Seattle, University of Washington, 1958; Johnson, Pauline

FUN WITH FIGURES: New York, Random House, 1946; Freeman, Mae & Ira

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THE WONDERFUL WORLD OF MATHEMATICS: New York, Garden City Books, 1955; Hogben, Lancelot
MATHEMATICS: New York, Golden Press, 1958; Adler, Irving
MATHEMATICS CURRICULUM GUIDE FOR GEORGIA SCHOOLS: Volume I
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LESSON 33: ETV -Math - Middle GY<3(i,'s

TITLE:

HOW TO WHIZZ THROUGH A QUIZZ

OBJECTIVES:

1. To review certain principles in mathematics.

2. To show short cuts that might be used in working problems.

NATURE OF CONTENT:

The following concepts are reviewed: (1) set of counting numbers (2) set of whole numbers (3) set of even numbers (4) set of ~dd numbers.

In addition, we will review: (1) addition and multiplication of even and odd numbers (2) dividing by 2, 3, 4, 5, 6, and 9 (3) numbers called squares, and (4) factors and divisors of primes.

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