Table of Contents

CONTENTS

INTRODUCTION

 1

DIAGNOSTIC TEST

 3

MILESTONES

 4

MATH KEY WORDS AND SYMBOLS

 5

SECTION 1 - THE NUMBERING SYSTEM

TIP # 1.1: MATHEMATICS AND COUNTING

 1-1

TIP # 1.2: THE NUMBER SENSE

 1-2

TIP # 1.3: THE NUMBERING SYSTEM

 1-3

TIP # 1.4: LARGE NUMBERS

 1-5

TIP # 1.5: WRITING NUMBERS

1-6

TIP # 1.6: DIGITS AND PLACE VALUE

 1-8

TIP # 1.7: THE ROMAN NOTATION

 1-10

TIP # 1.8: NATURAL AND WHOLE NUMBERS

 1-11

TIP # 1.9: CARDINAL AND ORDINAL NUMBERS

 1-13

TIP # 1.10: CONCRETE AND ABSTRACT NUMBERS

 1-14

TIP # 1.11: NUMBERS AND UNITS

 1-15

ANSWERS TO EXERCISES

 1-17

SECTION 2 ADDITION

TIP # 2.1: BASIC ADDITION

 2-1

TIP # 2.2: SYMBOLS FOR ADDITION

 2-3

TIP # 2.3: THE INTERMEDIATE SUM OF TEN

 2-3

TIP # 2.4: THE NUMBER LINE

 2-5

TIP # 2.5: PATTERNS IN ADDITION

 2-7

TIP # 2.6: PROPERTIES OF ADDITION

 2-9

TIP # 2.7: MENTAL ADDITION

 2-10

TIP # 2.8: ADDING BY COLUMNS

 2-13

TIP # 2.9: ROUNDING NUMBERS

 2-15

TIP # 2.10: ADDITION WITH ROUNDING

 2-16

ANSWERS TO EXERCISES

 2-17

SECTION 3 SUBTRACTION

TIP # 3.1: BASIC SUBTRACTION

 3-1

TIP # 3.2: SYMBOLS FOR SUBTRACTION

 3-3

TIP # 3.3: INVERSE OF ADDITION

 3-3

TIP # 3.4: MENTAL SUBTRACTION

 3-5

TIP # 3.5: SUBTRACTING BY COLUMNS

 3-6

TIP # 3.6: POSITIVE & NEGATIVE NUMBERS

 3-8

TIP # 3.7: MIXED OPERATIONS

 3-10

TIP # 3.8: VERIFICATION

 3-11

TIP # 3.9: PROBLEM SOLVING

 3-13

ANSWERS TO EXERCISES

 3-15

SECTION 4 MULTIPLICATION

TIP # 4.1: BASIC MULTIPLICATION

 4-1

TIP # 4.2: SYMBOLS FOR MULTIPLICATION

 4-2

TIP # 4.3: THE FACTOR OF TEN

 4-3

TIP # 4.4: "REPEATED ADDITION"

 4-5

TIP # 4.5: MULTIPLICATION TABLES

 4-7

TIP # 4.6: PROPERTIES OF MULTIPLICATION

 4-8

TIP # 4.7: MENTAL MULTIPLICATION

 4-10

TIP # 4.8: MULTIPLYING BY COLUMNS

 4-12

TIP # 4.9: MULTIPLYING LARGE NUMBERS

 4-14

TIP # 4.10: MIXED OPERATIONS

 4-16

ANSWERS TO EXERCISES

 4-18

SECTION 5 DIVISION

TIP # 5.1: BASIC DIVISION

 5-1

TIP # 5.2: RULES FOR DIVISION

 5-2

TIP # 5.3: INVERSE OF MULTIPLICATION

 5-4

TIP # 5.4: DIVISION BY COLUMNS

 5-6

TIP # 5.5: MORE ON DIVISION BY COLUMNS

 5-8

TIP # 5.6: VERIFICATION

 5-10

TIP # 5.7: MIXED OPERATIONS

 5-12

TIP # 5.8: PROBLEM SOLVING

 5-14

ANSWERS TO EXERCISES

 5-16

SECTION 6 FACTORS 

TIP # 6.1: THE FACTORS

 6-1

TIP # 6.2: FACTORING A NUMBER

 6-2

TIP # 6.3: THE PRIME NUMBER

 6-4

TIP # 6.4: RULES OF DIVISIBILITY

 6-6

TIP # 6.5: HIGHEST COMMON FACTOR

 6-8

TIP # 6.6: DIVISION BY FACTORING

 6-10

TIP # 6.7: DIVISION AND FRACTION

 6-13

ANSWERS TO EXERCISES

 6-14

APPENDIX

ORGANIZING A MATH CLUB

 A-1

MATH CLUB GOAL, PURPOSES AND POLICIES

 A-2

INDEX

 A-4