8
Introduction For 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

Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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Page 1: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 2: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 3: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 4: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 5: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 6: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 7: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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

Page 8: Introduction - Amazon S3...Introduction For Parents and Teachers Mathematics 6 combines proven teaching methods with colorful pictures and illustrations to teach students basic math

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?