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Math

Fundamental Skills 2nd Edition

Fundamental Skills2nd Edition

Review, Remediation, and Reinforcement of Basic Skills Reading - Language & Writing - Mathematics

Many adult learners need to review basic skills before they can tackle high-school equivalency exams and/or seek meaningful employment. Fundamental Skills, 2nd Edition, offers targeted skill development so learners can build a strong skills foundation on which to grow. Literacy (NRS ABE Level 1)Beginning (NRS ABE Level 2)Intermediate (NRS ABE Level 3)

FEATURES AND BENEFITS

• Developed especially for adult learners• Content is chunked into manageable units to ensure step-by-step skills development• Controlled readability and vocabulary gives learners a comfortable structure in which to grow• Positive reinforcement builds learner’s confidence and enables steady progress to successive levels• Aligned to CASAS learning objectives and TABE 11/12• Instructor Editions available • Digital courses available on Paxen Focus

Review, Remediation, and Reinforcement of Basic Skills Reading - Language & Writing - Mathematics

MATH

UNIT 1: NUMBER SENSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

LESSON 1: Numbers and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3LESSON 2: Counting by 10s, 5s, and 2s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9LESSON 3: Even and Odd Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15UNIT 1 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19LESSON 4: Fractions in Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21LESSON 5: Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27UNIT 1 SECTION 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33LESSON 6: Adding Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34LESSON 7: Subtracting Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40UNIT 1 SECTION 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46LESSON 8: Adding Larger Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47LESSON 9: Subtracting Larger Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53UNIT 1 SECTION 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59LESSON 10: Problem Solving with Addition or Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61LESSON 11: Inverse Operations — Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65UNIT 1 SECTION 5 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71LESSON 12: Doubles and Halves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73LESSON 13: Multiplying Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79LESSON 14: Dividing Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87UNIT 1 SECTION 6 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

UNIT 2: ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

LESSON 1: The Identity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99LESSON 2 : The Commutative Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103LESSON 3 : The Associative Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109LESSON 4 : The Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115LESSON 5 : Equations with Unknowns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121UNIT 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

UNIT 3: MEASUREMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

LESSON 1 : Measurement — Linear Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133LESSON 2: Measurement — Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137LESSON 3 : Measurement — Digital Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143LESSON 4: Measurement — Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149LESSON 5: Non-Standard Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153UNIT 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

UNIT 4: DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

LESSON 1: Extracting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167LESSON 2: Collecting and Labeling Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173LESSON 3: Using a Tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181LESSON 4 : Data and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185UNIT 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

TABLE OF CONTENTS

FUNDAMENTAL SKILLS FOR MATH LITERACY LEVEL L

Fundamental Skills for Math Number Sense 3

L

Example:

The figure below shows a group of flashlights. Count to find the number of flashlights.

Count: 1, 2, 3, 4, 5, 6, 7.

The last number counted is 7. There are 7 flashlights in all.

The last number counted is 10. There are 10 cans in the group above.

Digit: One of the number symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Number: A group of one or more digits that tell a quantity. Examples: 4, 15

Counting numbers: The whole numbers used to count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …

1-digit number: A number with exactly one digit. Examples: 2, 9

2-digit number: A number with exactly two digits. Examples: 15, 28, 76

The figure below shows counting numbers used to find the number of objects in a group.

LESSON 1: Numbers and Quantities

one two three four five six seven eight nine ten

1 2 3 4 5 6 7 8 9 10

4 Number Sense Fundamental Skills for Math

Examples:

Group 2 and Group 4 both contain 14 clips. Group 1 contains 12 clips. Group 3 contains 15 clips. Notice that all these numbers are 2-digit numbers.

In a 2-digit number, the first digit represents the amount of tens. The second digit represents the amount of ones.

Two of the groups below have the same number of clips. Count to identify the two groups.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

10 eggs in all

1 group of ten

0 ones

1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12

12 eggs in all

1 group of ten

2 ones

1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20

20 eggs in all

2 groups of ten

0 ones

Group 1 Group 2 Group 3 Group 4

1 2

3 4

5 6

7 8

9 10

12

34

56

78

910

1112

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

17 18 19 20

L


Examples:

Group 2 and Group 4 both contain 14 clips. Group 1 contains 12 clips. Group 3 contains 15 clips. Notice that all these numbers are 2-digit numbers.

In a 2-digit number, the first digit represents the amount of tens. The second digit represents the amount of ones.

Two of the groups below have the same number of clips. Count to identify the two groups.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

10 eggs in all

1 group of ten

0 ones

1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12

12 eggs in all

1 group of ten

2 ones

1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20

20 eggs in all

2 groups of ten

0 ones

Group 1 Group 2 Group 3 Group 4

1 2

3 4

5 6

7 8

9 10

12

34

56

78

910

1112

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

17 18 19 20

L


PRACTICE

Count the number of birds in each group . Write your answer on the line below the group .

1 . 2 .

birds birds

3 . 4 .

birds birds

Sometimes a list of numbers has missing numbers. Count to find missing numbers.

Example:

1, 2, , , 5, , 7, 8, ,

Count starting with 1: 1, 2, 3 …

Write the missing 3 and the missing 4. 1, 2, 3, 4, 5, , 7, 8, ,

Say 5. Write the missing 6. 1, 2, 3, 4, 5, 6, 7, 8, ,

Say 7 and 8. Writing the missing 9 and 10. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

The missing numbers are 3, 4, 6, 9, and 10.

L


Count the number of objects in each group . Write your answer on the line below the group .

5 . 6 .

7 . 8 .

9 . 10 .

L


Write your answer on the line below .

11 . How many chairs? 12 . How many jars?

13 . Circle the groups that have the same number of items.

Group 1 Group 2

Group 3 Group 4

14 . Circle two tiles that have 6 dots in all.

L


15 . Fill in the missing numbers.

1, 2, 3, 4, , 6, 7, 8, , 10, , , 13


17, 18, , 20, 21, , 23, 24, , 26,

PROBLEM SOLVING

Each bar has 10 cubes . Write how many groups of 10 . Write how many ones . Write how many in all .

17 . 18 . 19 .

groups of ten groups of ten groups of ten

ones ones ones

cubes in all cubes in all cubes in all

20 . Mr. Wilson needs 6 cupcakes for a party. Which group would be best for him to buy? Explain your answer.

L



1, 2, 3, 4, , 6, 7, 8, , 10, , , 13


17, 18, , 20, 21, , 23, 24, , 26,

PROBLEM SOLVING

Each bar has 10 cubes . Write how many groups of 10 . Write how many ones . Write how many in all .

17 . 18 . 19 .

groups of ten groups of ten groups of ten

ones ones ones

cubes in all cubes in all cubes in all

20 . Mr. Wilson needs 6 cupcakes for a party. Which group would be best for him to buy? Explain your answer.

L

ii Table of Contents Fundamental Skills for Math

TABLE OF CONTENTS

UNIT 1: NUMBER SENSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

LESSON 1: Even and Odd Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3LESSON 2: The Decimal Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5LESSON 3: Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7LESSON 4: Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9LESSON 5: Estimating with Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11LESSON 6: Adding Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13LESSON 7: Subtracting Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15UNIT 1 SECTION 1: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17LESSON 8: Adding Multi-digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18LESSON 9: Subtracting Multi-digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20LESSON 10: Problem Solving with Addition or Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22LESSON 11: Inverse Operations — Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24LESSON 12: Adding Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26LESSON 13: Subtracting Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28LESSON 14: The Commutative Property of Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30UNIT 1 SECTION 2: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32LESSON 15: Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33LESSON 16: Multiplying and Dividing by 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35LESSON 17: Multiplication and Perfect Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37LESSON 18: Multiplying and Dividing by Multiples of 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39LESSON 19: Multiples of Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41LESSON 20: Factors of Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43LESSON 21: Multiplying Positive Multi-digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45UNIT 1 SECTION 3: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47LESSON 22: Dividing Positive Multi-digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48LESSON 23: Inverse Operations — Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50LESSON 24: Precision in Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52LESSON 25: Rounding Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54LESSON 26: Fractional Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56LESSON 27: The Commutative Property of Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58LESSON 28: Percents, Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60LESSON 29: Percent Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62UNIT 1 SECTION 4: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

UNIT 2: ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

LESSON 1: The Identity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67LESSON 2: The Commutative Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72LESSON 3: The Associative Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77LESSON 4: The Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82LESSON 5: Equations with Unknowns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87UNIT 2: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

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FUNDAMENTAL SKILLS FOR MATH BEGINNING LEVEL B

Fundamental Skills for Math Table of Contents iii

UNIT 3: DATA ANALYSIS AND PROBABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . 93

LESSON 1: Collecting and Labeling Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95LESSON 2: Using a Tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99LESSON 3: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103UNIT 3 SECTION 1: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109LESSON 4: Data and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111LESSON 5: Information from Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117LESSON 6: Observations and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121LESSON 7: Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125UNIT 3 SECTION 2: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

UNIT 4: GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

LESSON 1: Lines of Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133LESSON 2: Two-Dimensional Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137LESSON 3: Three-Dimensional Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141LESSON 4: Manipulating Two-Dimensional Figures — Building Up and Breaking Apart . . . . . . . . . . . . . . . . 145LESSON 5: Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148LESSON 6: The Compass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151UNIT 4: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155


LESSON 1: Units and Linear Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159LESSON 2: Units of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162LESSON 3: Units and Analog Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165LESSON 4: Measurement of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168UNIT 5 SECTION 1: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171LESSON 5: Using Non-Standard Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172LESSON 6: Comparing Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175LESSON 7: Approximation of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178LESSON 8: Accuracy and Precision of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181LESSON 9: Units of Length — US Customary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184UNIT 5 SECTION 2: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186LESSON 10: Units of Length — Metric System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187LESSON 11: Units of Weight — US Customary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189LESSON 12: Units of Capacity — US Customary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191LESSON 13: Comparing Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193LESSON 14: Units of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195UNIT 5 SECTION 3: REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197


FUNDAMENTAL SKILLS FOR MATH BEGINNING LEVEL B

Fundamental Skills for Math Unit 1: Number Sense 9

BLESSON 4: Fractions

Fractions are a type of number. Fractions show a part of a whole. Fractions can also show a part of a group of objects.

The denominator is the bottom number of the fraction. It shows the total number of equal parts.The numerator is the top number in the fraction. It shows the number of parts considered.

Sometimes, the numerator and the denominator are the same number. When this happens the fraction means 1 whole.

The fraction 4 __ 4 represents 4 out of 4 parts shaded, or 1 whole.

Part of a Whole Part of a Group

numerator ____________ denominator

→ ___ →    1 __ 4    ← ___ ←  number of parts shaded

______________________ total number of parts

numerator ____________ denominator

→ ___ →    2__4 ←___ ←

number of objects shaded_____________________________total number of objects in group

Example:

Elton opened the refrigerator and saw this pizza.

How many parts (slices) was the whole pizza cut into?What fraction names the original (whole) pizza?What fraction of the pizza is missing?What fraction of the pizza is left?

The whole pizza was cut into 6 slices. The fraction 6 __ 6 means 6 parts out of 6 parts. It represents the whole pizza.

1 __ 6    ← ___ ←  slices missing

_____________ total slices

5 __ 6    ← ___ ←  slices left__________

total slices

1 __ 6 of the pizza is missing. 5 __

6 of the pizza is left.

Example:

Petra has a carton of 8 bottles of water. She drank 2 bottles of water. She puts the others on the counter.

What fraction names all of the bottles in the carton?What fraction of the 8 bottles did she drink?

There are 8 bottles of water in the carton. The fraction 8 __ 8 represents all the bottles in the whole carton.

2 __ 8    ← ___ ←  bottles Petra drank____________________

total bottles in cartonPetra drank 2 __ 8 of the bottles.


10 Unit 1: Number Sense Fundamental Skills for Math

PRACTICE

1 . Write a fraction that shows what part of the group of glasses is circled. Use one of the given numerators and denominators.

_____

Numerators: 1 2 3 5

Denominators: 3 4 5 6

2 . Match each fraction with the image that best shows it.

1 __ 3 3 __

4 2 __

6 4 __

5

Write a fraction to show the part of the figure or group shaded or circled .

3 .

_____

4 .

_____

PROBLEM SOLVING 5 . There are 25 players on the baseball team. Six of the players are pitchers. What fraction shows the

number of pitchers?

←         pitchers on team

___________________________

←  total players on team

Of the 25 players, _____ are pitchers.

6 . Nelson painted 5 __ 8 of the exterior of his house. What fraction of the exterior of his house does he still needto paint? Shade the circle to show the answer. Write the answer in the space provided.

Nelson still needs to paint _____ of the exterior of his house.


B

ii Fundamental Skills for Math

UNIT 1: WHOLE NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

LESSON 1: Estimation Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3LESSON 2: Precision in Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5UNIT 1 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7LESSON 3: Multiplication Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8LESSON 4: Multiplying and Dividing by 10, 100, and 1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10UNIT 1 SECTION 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12LESSON 5: Factors of Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13LESSON 6: Multiplying Positive Multi-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15UNIT 1 SECTION 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17LESSON 7: Dividing Positive Multi-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18LESSON 8: Inverse Operations — Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20UNIT 1 SECTION 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22LESSON 9: Precision in Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23LESSON 10: Inverse Operations — Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25UNIT 1 SECTION 5 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27LESSON 11: The Commutative Property of Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28LESSON 12: The Commutative Property of Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30UNIT 1 SECTION 6 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34LESSON 13: The Distributive Property — Multiplication and Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35LESSON 14: The Identity Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39UNIT 1 SECTION 7 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43LESSON 15: The Commutative Property — Multiplication and Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44LESSON 16: The Associative Property — Multiplication and Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48LESSON 17: More on the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52UNIT 1 SECTION 8 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

UNIT 2: FRACTIONS, DECIMALS, PERCENTS, AND RATIOS . . . . . . . . . . . . . . . 57

LESSON 1: The Decimal Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59LESSON 2: Rounding Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61LESSON 3: Using the Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63UNIT 2 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65LESSON 4: Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66LESSON 5: Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68LESSON 6: Mixed Numbers and Improper Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70UNIT 2 SECTION 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72LESSON 7: Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73LESSON 8: Solving Problems with Addition or Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75UNIT 2 SECTION 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77LESSON 9: Adding Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78LESSON 10: Subtracting Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80UNIT 2 SECTION 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82LESSON 11: Fractions and Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83LESSON 12: Fractional Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85LESSON 13: Parts of Whole Numbers and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87UNIT 2 SECTION 5 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89LESSON 14: Multiplying and Dividing with Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90LESSON 15: Reasonable Multiplication and Division Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94LESSON 16: Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96UNIT 2 SECTION 6 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

TABLE OF CONTENTS

FUNDAMENTAL SKILLS FOR MATH INTERMEDIATE LEVEL I

ii Fundamental Skills for Math


. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99101

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103105106108110

LESSON 17: Percents, Fractions, and Decimals LESSON 18: Percents and Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 19: Finding 10% and 1% of a Number UNIT 2 SECTION 7 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 20: Common Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 21: Percent Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 22: Percent of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 2 SECTION 8 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

UNIT 3: ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

115 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

123127131133137141145149151155159163

LESSON 1: Exponential Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 2: Dividing a Problem into Simple Parts LESSON 3: Strategies for Simplifying Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 4: Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 3 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 5: Recurring Numeric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 6: Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 7: Symbols for Number Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 8: Expressions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 3 SECTION 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 9: Substitution in Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 10: Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 11: Distance, Time, and Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 12: Applying Technical Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 3 SECTION 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

UNIT 4: STATISTICS, DATA ANALYSIS, AND PROBABILITY . . . . . . . . . . . . . . . 169

171173175176178182183187191192196200204206208212213217219220222

LESSON 1: Independent and Dependent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 2: Collecting and Labeling Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 3: Using a Tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 4: Tables with Numerical Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 5: Tables for Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 6: Constructing a Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 7: Different Representations of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 8: Data and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 9: Statistics of a Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 10: The Mean and the Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 11: Ratios, Fractions, and Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 5 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 12: Causation and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 13: Combinations and Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 6 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 14: Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LESSON 15: Compound Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UNIT 4 SECTION 7 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

iv Fundamental Skills for Math


LESSON 1: Instruments for Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227LESSON 2: Measurements of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229LESSON 3: Measurement and Analog Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231UNIT 5 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233LESSON 4: Comparing Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235LESSON 5: Estimate of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237LESSON 6: Accuracy of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239UNIT 5 SECTION 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241LESSON 7: Units of Length in the U .S . Customary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243LESSON 8: Units of Length in the Metric System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245LESSON 9: Units of Weight in the U .S . Customary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247UNIT 5 SECTION 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249LESSON 10: Units of Capacity in the U .S . Customary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250LESSON 11: Comparing Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252LESSON 12: Units of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254UNIT 5 SECTION 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256LESSON 13: Measuring Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257LESSON 14: Compass Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261LESSON 15: Maps with Coordinate Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263UNIT 5 SECTION 5 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

UNIT 6: GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

LESSON 1: Lines of Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269LESSON 2: Two-Dimensional Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271UNIT 6 SECTION 1 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273LESSON 3: Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274LESSON 4: Angles in a Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276UNIT 6 SECTION 2 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278LESSON 5: Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279LESSON 6: Angles in a Quadrilateral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281UNIT 6 SECTION 3 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283LESSON 7: Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284LESSON 8: Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286LESSON 9: Three-Dimensional Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288UNIT 6 SECTION 4 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290LESSON 10: Perimeter of Common Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291LESSON 11: Area of Rectangles and Parallelograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295LESSON 12: Area of Triangles and Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299UNIT 6 SECTION 5 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303LESSON 13: Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305LESSON 14: Intersecting Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307UNIT 6 SECTION 6 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309LESSON 15: Measurements of Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310LESSON 16: Common Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312UNIT 6 SECTION 7 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314LESSON 17: Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315LESSON 18: Classification of Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317LESSON 19: The Protractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319UNIT 6 SECTION 8 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323LESSON 20: Determining the Size of Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324LESSON 21: Manipulating Two-Dimensional Figures — Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 328LESSON 22: From Two-Dimensional to Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332UNIT 6 SECTION 9 REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336


I

8 Whole Numbers Fundamental Skills for Math

Example:

Write the same number in both boxes to make the sentence true.

4

25

49

Check and correct your answers if needed: 2 2 4; 5 5 25; 7 7 49.

Examples:

Write the word Yes or No.

Is 4 a perfect square? Is 25 a perfect square? Is 49 a perfect square?

Check and correct your answers if needed: Yes; Yes; Yes.

4 is the square of 2. 25 is the square of 5. 49 is the square of 7.

LESSON 3: Multiplication Facts

Making squares Is it possible to arrange 9 pennies in a square, without open spaces?Yes. 9 pennies can be arranged in 3 rows of 3 pennies each.

Is it possible to arrange 12 pennies in a square, without open spaces?

No. 12 pennies can be arranged in a rectangle or an open square but NOT in a square without open spaces.

Perfect squaresA perfect square is a number that can be written as the product of 2 equal counting numbers. Since 9 3 3, 9 is a perfect square. 9 is the square of 3.Can you write the SAME number in both boxes so the product is 12?

12

No. Since there is no number that multiplies by itself to give a product of 12, 12 is NOT a perfect square.

Fundamental Skills for Math Whole Numbers 9

Perfect squares in the multiplication table

Use the multiplication table to learn all the multiplication facts up to 12 12. You will use these facts often as you do mental math problems.

Notice the diagonal pattern made by the perfect squares in the multiplication table.

All the numbers along this diagonal are perfect squares.

PRACTICE

1 . Circle each perfect square in the list.

12 64 30 81 144 15 121 50 28 36 25 110

2 . Is a perfect square always an even number?

Explain.

Find each product .

3 . 10 9 4 . 9 4 5 . 8 9 6 . 11 3

7 . 4 12 8 . 10 6 9 . 6 9 10 . 11 9

11 . 3 11 12 . 7 8 13 . 5 9 14 . 8 8

15 . 4 9 16 . 6 11 17 . 12 6 18 . 10 7

19 . 9 8 20 . 10 12 21 . 7 7 22 . 6 8

23 . 12 7 24 . 7 12 25 . 8 7 26 . 9 9

PROBLEM SOLVING

27 . Kathryn arranges 49 cards to form a square without open spaces. How many rows of cards are inKathryn’s array? ___________

0 1 2 3 4 5 6 7 8 9 10 11 120 0 0 0 0 0 0 0 0 0 0 0 0 01 0 1 2 3 4 5 6 7 8 9 10 11 122 0 2 4 6 8 10 12 14 16 18 20 22 243 0 3 6 9 12 15 18 21 24 27 30 33 364 0 4 8 12 16 20 24 28 32 36 40 44 485 0 5 10 15 20 25 30 35 40 45 50 55 606 0 6 12 18 24 30 36 42 48 54 60 66 727 0 7 14 21 28 35 42 49 56 63 70 77 848 0 8 16 24 32 40 48 56 64 72 80 88 969 0 9 18 27 36 45 54 63 72 81 90 99 108

10 0 10 20 30 40 50 60 70 80 90 100 110 12011 0 11 22 33 44 55 66 77 88 99 110 121 13212 0 12 24 36 48 60 72 84 96 108 120 132 144

I

Instructor Edition

MATH

Fundamental Skills for Math Instructor Edition 3

LITERAC

YLITERACY Unit 1: Number Sense

pp. 3–8 CASAS Content Standards: M1.1.1, M1.1.2 TABE Objective: 1.NBT.2

Teach the Skill

Have learners think of several groups of objects they commonly see at home or at work (groups of books on a shelf, groups of produce in a market) . Ask them to describe the objects and then draw simple sketches of the objects . Ask them to count the number of objects they have sketched for each group of objects .

Reteach the Skill

Have learners exchange the sketches they made in the Teach the Skill activity . Ask them to count the objects in these groups and to check their answers with the learner who made the sketch .

Real-World Application

Associating numbers with quantities and being able to count using whole numbers have important real-world applications . Show images of multiple objects, such as those seen in grocery store advertisements, and have learners write the correct numbers to show how many objects are in each group .

Listening/Speaking

CASAS Content Standard: S.1.1

Learners can get in groups of 3 or 4 and take turns counting objects out loud . Learners should be encouraged to provide one another feedback on accuracy .

LESSON 1: Numbers and Quantities Unit 1: Section 1

Lesson 1: Numbers and Quantities (pp. 3–8)CASAS Content Standards: M1.1.1, M1.1.2 TABE Objective: 1.NBT.2

1. 2

2. 5

3. 6

4. 8

5. 5

6. 3

7. 7

8. 9

9. 3

10. 9

11. 12

12. 10

13. Group 3 and Group 4

14. Student should circle the first tile on the left.

15. 5, 9, 11, 12

16. 19, 22, 25, 27

17. 2, 9, 29

18. 3, 4, 34

19. 4, 1, 41

20. Sample answer: Mr. Wilson should buy thesecond group of cupcakes, because thereare exactly six.

22 Instructor Edition Fundamental Skills for Math

BEG

INN

ING

pp. 9–10 CASAS Content Standard: M1.1.8 TABE Objectives: 2.G.3, 3.G.2, 3.NF.1

Teach the Skill

Count the total number of people in the room . Write this number as the denominator of a fraction on a white board or similar device . Discuss with them how to write a fraction to represent all of the people in the room . Then have learners count the number of people with dark hair . Write this number as the numerator of the fraction . Explain that this fraction tells what fraction of the class has dark hair . Continue identifying fractions such as the number of people wearing long sleeves or short sleeves, etc .

Reteach the Skill

Give learners eight counters that are a mix of two different colors . Have them count the total number of counters and write a fraction that represents all of the counters ( 8 __ 8 ) . Thenhave them find the fraction of counters that are one of the colors and the fraction of the counters that are the second color . Have learners say sentences to describe each fraction, such as “ 5 __ 8 of the counters are red .”


Fractions are used frequently in everyday life . For example, a teacher might say that 21__

24 of his or her students passed their spelling tests . Or a scientist may describe the number of fawns he or she counted for a woodlands survey as a fraction of the number of deer, such as 35 __ 62 meaning that of the 62 deercounted, 35 were fawns . Fractions can help us understand data .

Listening/Speaking

CASAS Content Standards: S4.17, L4.12

There are many excellent comics and cartoons that joke about fractions . (Search online for “jokes about fractions .”) Introduce learners to some of these comics and jokes . Discuss with learners the humor to ensure they all understand . Challenge them to write their own simple jokes about fractions .

LESSON 4: Fractions

BEGINNING Unit 1: Number Sense

Lesson 4: Fractions (pp. 9–10)CASAS Content Standard: M1.1.8 TABE Objectives: 2.G.3, 3.G.2, 3.NF.1

1. __23

2. Students should match: 1_3 to the circle one-

4 third shaded, 3_ to the circle three-fourths

6 shaded, 2_ to the group of motorcycles, and 4_5 to the rectangle four-fifths shaded.

3. __47

4. __109

5.

6.

__256

_3 ; Students may shade 3_ of the circle and8 8

count the unshaded sections, or they mayshade five sections.

56 Instructor Edition Fundamental Skills for Math

INTE

RMED

IATE

pp. 8–9 CASAS Content Standard: M1.3.2 TABE Objectives: 3.OA.7, 4.NBT.5

Teach the Skill

Display 16 and discuss with learners whether 16 circles can be arranged in a square and have a volunteer draw the result . Explain that since 16 can be arranged in 4 rows of 4, it is a perfect square . When two of the same number are multiplied together, the product is always a perfect square . Tell learners that learning the perfect squares along with other multiplication facts for 0 to 12 will help them to do mental math and calculations with larger numbers more quickly .

Reteach the Skill

Guide learners in how to use the multiplication table . Give them several multiplication facts and ask them to find the products using the table . Emphasize that they may use the table but should work toward the goal of knowing all of the facts up to 12 12 .


Multiplication is a short cut for repeated addition . Numerous jobs, such as finance or manufacturing jobs, require employees to multiply numbers . Understanding basic multiplication facts is a time saver . If there are 8 boxes with 9 hammers in each box, a warehouse employee can calculate the total number of hammers (72) more quickly by using multiplication than by using repeated addition .

Listening/Speaking

CASAS Standard: S2.4

Have learners work with a partner to role play the relationship of patient and pharmacist . The learner playing the pharmacist should explain to the patient that he or she needs to take new medication x number of days and x number of times per day . The learner playing the patient should confirm the total number of doses he or she will take .

LESSON 3: Multiplication Facts

INTERMEDIATE Unit 1: Whole Numbers

Unit 1: Section 2Lesson 3: Multiplication Facts (pp. 8–9)CASAS Content Standard: M1.3.2 TABE Objectives: 3.OA.7, 4.NBT.5

1. Circle 64, 81, 144, 121, 36, 25.

2. No; for example, 9, 25, and 81 are perfectsquares and odd numbers.

3. 90

4. 36

5. 72

6. 33

7. 48

8. 60

9. 54

10. 99

11. 33

12. 56

13. 45

14. 64

15. 36

16. 66

17. 72

18. 70

19. 72

20. 120

21. 49

22. 48

23. 84

24. 84

25. 56

26. 81

27. 7

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