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IntroductionFor Parents and Teachers
Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach
students basic math facts and concepts. Its use of practical applications helps students relate to math in
the real world. Its incremental approach and spiral review (teaching concepts in small increments and
continuous review) make Mathematics 6 an effective math course. The consistent, systematic review helps
students retain what they have learned. The goal is mastery, not just exposure.
How to Use Mathematics 6
Each unit follows a theme, introduced by a story and photographs relating to the theme. Many nuggets of
information follow this theme.
The header in each lesson tells what unit and lesson is taught that day. It also tells which speed or mastery
drill to administer.
The colored teaching box beginning each lesson teaches the new concept, followed by exercises
to reinforce the concept. This concept is reviewed again just before Sharpening Your Skills.
We Remember follows the teaching lesson and its reviews. It also reviews concepts taught in earlier
lessons. Students should be able to work through these exercises independently. A small reference
number after each exercise indicates the page number where the concept was taught.
Sharpening Your Skills drills students in basic computation (using any of the four math operations), mental
math, and fact focus. Fact Focus drills basic math facts and measurement equivalents.
Lessons 5, 10, and 16 of each unit are quiz or test lessons.
Most material has been reviewed five times before it is quizzed
or tested. Quiz and test lessons include optional enrichment
activities. They are neither reviewed nor tested. They are
optional and just for fun.
The Glossary, Reference Charts, and Index are reference
materials to help students work independently.
Mathematics 6 will equip students with tools that will
enable them to apply principles to math in everyday life. It
enables students to see the beauty in numbers and to learn
to appreciate math. We believe that mathematics should help
students achieve the ultimate goal—loving, serving, and
bringing glory to God.
Course Materials
› Mathematics 6 Textbook
› Student Packet Worksheets
Tests
Quizzes
Speed/Mastery Drills
› Teacher’s Guide Resource CD
› Full Solution Answer Key
Lesson 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 134Dividing by a Three-Digit Divisor
Lesson 2 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 137Finding a Fraction of a Number Mentally
Lesson 3 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 140Revising an Estimate With a Three-Digit Divisor
Lesson 4 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 143Writing Ratios as Percents
Lesson 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 146Quiz 1
Lesson 6 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 147Simplifying Expressions by Substituting Variables With Numbers
Lesson 7 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 150Finding Reciprocals and Dividing Fractions
Lesson 8 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 153Finding the Circumference With Fractions
Lesson 9 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 156Identifying Prime and Composite Numbers
Lesson 10 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 159Quiz 2
Lesson 11 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 160Solving Two-Step Word Problems
Lesson 12 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 163The Sum of Angles Formed by Intersecting Lines
Lesson 13 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 166Common Ways to Show Division
Lesson 14 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 169Finding a Percent of a Number
Lesson 15 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 172Multiplying and Dividing by Moving the Decimal Point
Lesson 16 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 175Test 4
Unit
4
86 ,6 18 24 , 59 7 7 4
+504 ,93 1 4596 , 1 46 4
Lesson 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 222Repeating Decimals
Lesson 2 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 225Finding the Area of a Circle
Lesson 3 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 228Finding Prime Factors Using Division
Lesson 4 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 231Naming and Plotting Points on a Grid
Lesson 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 234Quiz 1
Lesson 6 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 235Converting Decimals and Percents to Fractions
Lesson 7 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 238Using Proportions to Convert U.S. Measures
Lesson 8 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 241Computing Sales Tax
Lesson 9 � � � � � � � � � � � � � � � � � � � � � � � � � 244Finding Distance Using the Formula
Lesson 10 � � � � � � � � � � � � � � � � � � 247Quiz 2
Lesson 11 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 248Solving Word Problems With Remainders
Lesson 12 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 251Writing Negative Integers; Classifying Triangles by Their Angles
Lesson 13 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 254Reading Circle Graphs
Lesson 14 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 257Combining More Than Two Integers
Lesson 15 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 260Reading Tables
Lesson 16 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 263Test 6
Unit
6
Lesson 1 � � � � � � � � � � � � � � � � � 398The Associative
Property of Addition and Multiplication
Lesson 2 � � � � � � � � � � � � � � 401Calculating Simple
Interest on Savings Accounts and Loans
Lesson 3 � � � � � � � � � � � � � � � � � � � � � 404Using Place Value to
Expand Numbers
Lesson 4 � � � � � � � � � � � � � � � � � � � � � � � � � 407Counting Weeks
Lesson 5 � � � � � � � � � � � � � � � � � � � � � 410Quiz 1
Lesson 6 � � � � � � � � � � � � � � � � � � � � � 411Changing Amounts on a Recipe
Lesson 7 � � � � � � � � � � � � � � � � � � � � � 414Using Decimal Equivalents to Compare Fractions; Lines of Symmetry
Lesson 8 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 417Buying From a Menu
Lesson 9 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 420Using a Budget
Lesson 10 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 423Quiz 2
Lesson 11 � � � � � � � 424Comparing Unit Prices
Lesson 12 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 427Scale Drawings
Lesson 13 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 430Reading Double Bar Graphs
Lesson 14 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 433Map Scales
Lesson 15 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 436Organizing and Solving Word Problems Using Charts; Why We Don’t Divide by Zero
Lesson 16 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 439Test 10
Glossary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 440
Reference Charts � � � � � � � � � � � � � � � � � � � � � � 447
Index � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 451
Credits � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 469
Unit
10
Unit 1
Lesson 16 – Test 1 43
16
Use a calculator to do this exercise. Follow the directions carefully.
1. Enter the first three digits of your telephone number (not the area code).
2. Multiply by 80 and press = .
3. Add 1 and press = .
4. Multiply by 250 and press = .
5. Add the last four digits of your telephone number and press
= .
6. Add the last four digits of your telephone number again and press = .
7. Subtract 250 and press = .
8. Divide by 2 and press = .
9. Write the answer.
Do you recognize the answer?
It should be your telephone number.
Calculator Exercise
Test 1
FascinatingDiscoveries
Lesson 14 – Canceling Twice to Multiply Fractions; Finding the Average 127
Sharpening Your Skills
Copy and solve. Cancel as often as possible.
34. 337 × 78 × 32
3 35. 312 × 4 × 18 × 67 36. 31
6 × 337 × 78
p. 125 p. 125 p. 125
37. 214 × 51
3 × 13 38. 313 × 14
5 × 112 39. 33
7 × 212 × 31
2 p. 125 p. 125 p. 125
Find the averages.
40. In 8 months Nellie’s father flies his light plane 128 hours. p. 125
What is his average flying time for per month?
41. The chart shows the normal snowfall in Dayton, Ohio. p. 125
What is the average monthly snowfall from November through April?
42. Find the average of Cynthia’s math scores. p. 125
100% 94% 92% 86%
43. The total cost of the sweater, coat, and boots is $66.99. p. 125
What is the average cost of each of these 3 items?
Normal Snowfall in Dayton, Ohio
Month Inches
November 0.4
December 2.9
January 5.3
February 2.2
March 1.7
April 0.1
Computation Copy and solve.
44. 34 × 79 × 27 45. 3
4 × 7 × 49 46. 12 × 56 × 35 47. 22
3 × 14 × 127
48. 35 × 15 49. 3
7 × 19 50. 35 × 23 51. 3
14 × 27
52. 53. 54. 55.
Fact Focus Write the answers.
56. 6,000 ÷ 3,000 57. 2,400 ÷ 600 58. 440 ÷ 110 59. 25,000 ÷ 5,000
60. 800 ÷ 200 61. 54,000 ÷ 6,000 62. 4,000 ÷ 500 63. 18,000 ÷ 2,000
8,104+ 190
4,532+ 3,789
7,281– 6,186
608– 309
Lesson 16 – Test 9 395
Making a Theodolite
Test 9Unit 9
16
Surveyors use an instrument called a theodolite
(thē ä’ dƏ līt’) to measure angles and directions for road-building
and other kinds of construction. You may have seen road surveyors
with their instruments mounted on a tripod for sighting faraway slopes and corners.
Materials Needed To Make a Theodolite
• drinking straw • piece of string
• square of cardboard • screw
• tape measure • tape
Directions To Make a Theodolite
1 Cut a 6 × 6 inch square from a piece of cardboard.
2 Cut the square in half diagonally.
3 Tape the straw to the diagonal side of one of the pieces of cardboard.
4 Cut a 10-inch piece of string and tie the screw on one end.
5 Tape the other end of the string to the triangle so that it hangs straight down along one of the 6-inch edges.
How To Use a Theodolite
1 Find a tall object to measure, such as a tree or a house.
2 Raise the theodolite to eye level and look through the straw.
3 Move backward or forward to find the top of the object through the straw.
4 Make sure the string stays straight along the edge of the triangle.
5 Mark your standing position on the ground.
6 Measure the distance from your standing position to the base of the object.
7 Measure your own height.
8 Add the distance to the base of the object to your height.
9 This should be the height of your object.
FascinatingDiscoveries
Changing Amounts on a Recipe
Lesson 6 – Changing Amounts on a Recipe 411
Solve the word problems.
1. The biscuit recipe calls for 34 cup of milk. Grandmother wants to make half the recipe. How much milk does she need for the biscuits?
2. Joseph likes to make chocolate chip cookies. He wants to double the recipe to have enough to share with the whole family. If the recipe calls for 34 cup of chocolate chips, how many chocolate chips does Joseph need?
Changing Amounts on a Recipe
Mastery Drill 6Unit 10
6
A recipe often tells how many
people it serves. To make half
a recipe, divide by 2. To make
a recipe larger, multiply by the
number of recipes needed.
Grandmother plans to make strawberry shortcake for her guests. The recipe makes enough for 8 people.
Grandmother wants to serve
4 people. She uses half the
amount of each ingredient.
This makes enough to serve
4 people.
Later Grandmother wants to
serve 16 people. She doubles
the amount of each ingredient.
This makes enough to serve
16 people.
Recipe for: Strawberry Shortcake
2 c flour 1 c sugar
3 tsp baking powder 1 c milk
tsp salt c butter
2 eggs 1 tsp vanilla
Mix the ingredients and pour into a 9″ × 13″ cake pan. Bake at 375° for 25
minutes. Cut cooled cake into 8 pieces. Crush 2 cups of strawberries. Whip 1 cup
of cream; add sugar to sweeten. For each serving, place a square of cake on a
saucer, spoon strawberries onto the cake, and top with whipped cream. Serves 8.
12
12
14
212 ÷ 2 = n
52 ÷
21 = n
52 ×
12 =
54 = 1
14
14 × 2 = n14 ×
21 =
24 =
12
2 12 ÷ 2 = n
n = 114 cups flour
14 × 2 = n
n = 12 cup of butter
How much flour does she need to make enough to serve 4 people?
How much butter does she need to make enough to serve 16 people?