This hardcover textbook has 170 lessons that review and extend skills taught in previous grades. Review in each lesson keeps previous skills current. New concepts include the following areas.

*Numbers*—Greatest common factor, lowest common multiple, mental shortcuts in calculation.
*Fractions*—Decimal-fraction equivalents.
*Decimals*—Multiplying and dividing.
*Percents*—Discounts, commissions, interest.
*Measures*—Conversions between English and metric measures, time zones.
*Geometry*—Perimeter and area of triangles and parallelograms, circumference and area of circles, measuring angles with a protractor.
*Graphs*—Constructing circle grafts.

Quizzes and Speed Tests are provided in a separate booklet with tear-out sheets.

Chapter tests are also in a separate booklet.

The teacher's manual comes in two volumes. Each lesson shown the pupil's pages full size with answers filled in. Extra pages guide the teacher in lesson preparation. Answer keys for quizzes, speed tests, and chapter tests are included.

### Contents of the Teacher's Manuals

- Materials for This Course

#### To The Teacher

- Basic Philosophy
- Plan of the Course
- Pupil's Book
- Teacher's Manual
- General Class Procedure
- Quizzes and Speed Tests
- Chapter Tests

#### Chapter 1: Working With Numbers

- 1. Working With Large Numbers
- 2. The Place-Value System
- 3. Rounding Numbers
- 4. Roman Numerals
- 5. Column Addition
- 6. Horizontal Addition
- 7. Mental Addition
- 8. Subtraction
- 9. Horizontal Subtraction
- 10. Mental Subtraction
- 11. Working With Graphs: The Picture Graph
- 12. Reading Problems: Finding the Needed Information
- 13. Chapter 1 Review
- 14. Chapter 1 Test (in test booklet)

#### Chapter 2: Multiplication and Division

- 15. Multiplication With One-Digit Multipliers
- 16. Multiplication With Two- and Three-Digit Multipliers
- 17. Checking Multiplication by Casting Out Nines
- 18. Multiplication With Four-Digit Multipliers
- 19. Multiplying by Multiples of Ten
- 20. The Double-and-Divide Shortcut
- 21. Working With Division
- 22. Short Division
- 23. Working With Two-Digit Divisors
- 24. Working With Three-Digit Divisors
- 25. More Challenging Three-Digit Divisors
- 26. Division Shortcuts
- 27. Finding Averages
- 28. Reading Problems: Choosing the Correct Operation
- 29. Chapter 2 Review
- 30. Chapter 2 Test (in test booklet)

#### Chapter 3: Working With Measures

- 31. Introduction to Measures
- 32. Units of Linear Measure
- 33. Units of Weight
- 34. Units of Capacity
- 35. Converting Measures Mentally
- 36. Units of Area
- 37. Units of Time
- 38. Time Zones
- 39. Adding and Subtracting Compound English Measures
- 40. Multiplying Compound English Measures
- 41. Dividing Compound English Measures
- 42. Reading Problems: Finding the Needed Information
- 43. Chapter 3 Review
- 44. Chapter 3 Test (in test booklet)

#### Chapter 4: Working With Fractions

- 45. Prime and Composite Numbers
- 46. Finding the Prime Factors of Composite Numbers
- 47. Greatest Common Factors
- 48. Lowest Common Multiples
- 49. Introduction to Fractions
- 50. Improper Fractions and Mixed Numbers
- 51. Comparing Fractions
- 52. Adding Proper Fractions
- 53. Subtracting Proper Fractions
- 54. Adding Mixed Numbers
- 55. Adding Three or More Mixed Numbers
- 56. Subtracting Mixed Numbers
- 57. Chapter 4 Review
- 58. Chapter 4 Test (in test booklet)

#### Chapter 5: Multiplying and Dividing With Fractions

- 59. Finding Fractional Parts by Division and Multiplication
- 60. Multiplying a Whole Number by a Fraction
- 61. Multiplying a Fraction by a Fraction
- 62. Multiplying a Fraction by a Mixed Number
- 63. Multiplying a Whole Number by a Mixed Number
- 64. Multiplying Mixed Numbers
- 65. Dividing a Whole Number by a Proper Fraction
- 66. Dividing a Fraction by a Fraction
- 67. Dividing Mixed Numbers
- 68. Multiplying Compound Measures as Mixed Numbers
- 69. Reading Problems: Estimating in Everyday Life
- 70. Chapter 5 Review
- 71. Chapter 5 Test (in test booklet)

#### Chapter 6: Working With Decimals

- 72. Learning About Decimals
- 73. Changing Fractions to Decimals
- 74. Changing Decimals to Fractions
- 75. Comparing Decimals
- 76. Adding and Subtracting Decimals
- 77. Subtracting More Challenging Decimals
- 78. Multiplying Decimals by 10, by 100, and by 1,000
- 79. Multiplying Decimals
- 80. Multiplying More Challenging Decimals
- 81. Semester Review I
- 82. Semester Review II
- 83. Semester Test (in test booklet)

- Quizzes and Speed Tests
- Chapter Tests
- Index
- Symbols
- Formulas
- Tables of Measure

#### Chapter 7: Decimals and Proportions

- 84. Dividing Decimals by 10, by 100, and by 1,000
- 85. Dividing a Decimal by a Whole Number
- 86. Dividing by a Decimal
- 87. More Challenging Decimal Divisors
- 88. Rounding Decimals
- 89. Working With Non-terminating Decimals
- 90. Using Fractional Equivalents to Multiply Mentally
- 91. Choosing the Reasonable Decimal Answer
- 92. Using Ratios to Compare Numbers
- 93. Writing Proportions
- 94. Reading Problems: Using Proportions
- 95. Chapter 7 Review
- 96. Chapter 7 Test (in test booklet)

#### Chapter 8: Using the Metric System

- 97. Using the Metric Ruler
- 98. Metric Units of Linear Measure
- 99. Metric Units of Weight
- 100. Metric Units of Capacity
- 101. Metric Units of Area
- 102. Metric Measures in Reading Problems
- 103. Conversions Between Metric and English Units: Linear Measure and Weight
- 104. Conversions Between Metric and English Units: Capacity and Area
- 105. Working With Distance, Rate, and Time
- 106. Distance, Rate, and Time in Reading Problems
- 107. Using a Scale of Miles
- 108. Reading a Blueprint
- 109. Working With Bar Graphs
- 110. Chapter 8 Review
- 111. Chapter 8 Test (in test booklet)

#### Chapter 9: Working With Percents

- 112. Introduction to Percents
- 113. Expressing Decimals and Fractions as Percents
- 114. Expressing Fractions as Percents
- 115. Expressing Percents as Decimals and Fractions
- 116. Subtracting Percents From 100%
- 117. Finding a Percentage of a Number
- 118. Solving More Challenging Percent Problems
- 119. Finding a Percent More or Less Than a Number
- 120. Calculating Discount Prices
- 121. Finding Sales Commissions
- 122. Finding What Percent One Number Is of Another
- 123. Finding What Percent One Number Is of Another
- 124. Multiplying Mentally by Changing a Percent to a Fraction
- 125. Chapter 9 Review
- 126. Chapter 9 Test (in test booklet)

#### Chapter 10: Working With Money

- 127. Counting Change
- 128. Keeping an Expense Record
- 129. Income, Expense, and Profit
- 130. Calculating Unit Prices
- 131. Calculating Interest
- 132. Calculating Interest for Part of a Year
- 133. Review of Interest
- 134. Reading Problems: Solving Multi-step Problems
- 135. Chapter 10 Review
- 136. Chapter 10 Test (in test booklet)

#### Chapter 11: Geometry: Perimeter and Area

- 137. Introduction to Geometry
- 138. Working With Perimeter
- 139. Finding the Perimeter of Rectangles and Triangles
- 140. Working With Area
- 141. Finding the Area of a Square
- 142. Finding the Area of a Parallelogram
- 143. Finding the Area of a Triangle
- 144. Working With Graphs: The Line Graph
- 145. Reading Problems: Using Parallel Problems
- 146. Chapter 11 Review
- 147. Chapter 11 Test (in test booklet)

#### Chapter 12: Geometry: Circles, Angles, and Volume

- 148. Working With Circles
- 149. Finding the Circumference of a Circle
- 150. Finding the Area of a Circle
- 151. Introduction to Volume
- 152. Finding the Volume of a cube
- 153. Metric Units of volume
- 154. Working With Angles
- 155. Using Protractors to Measure Angles
- 156. Working With Triangles
- 157. Working With Graphs: The Circle Graph
- 158. Working With Graphs: Constructing Circle Graphs
- 159. Reading Problems: Using Sketches
- 160. Chapter 12 Review
- 161. Chapter 12 Test (in test booklet)

#### Chapter 13: Number Sentences and Year-End Review

- 162. Working With Number Sentences
- 163. Using Number Sentences to Solve Reading Problems
- 164. Review of Chapters 1 and 2
- 165. Review of Chapters 3 and 8
- 166. Review of Chapters 4 and 5
- 167. Review of Chapters 6 and 7
- 168. Review of Chapters 9 and 10
- 169. Review of Chapters 11 and 12
- 170. Final Test (in test booklet)

- Quizzes and Speed Tests
- ...
- 89. Quiz: Multiplying and Dividing Decimals
- ...
- 148. Speed Test: Finding Areas
- ...

- Chapter Tests
- Index
- Symbols
- Formulas
- Tables of Measure