MATH

MATH

STUDENT BOOK

6th Grade | Unit 9

Unit 9 | Integers and Transformations

MATH 609 Integers and Transformations

1. INTEGERS

5

INTEGERS |6 COMPARING AND ORDERING INTEGERS |12 ABSOLUTE VALUE |16 COORDINATE PLANE |21 SELF TEST 1: INTEGERS |28

2. INTEGER OPERATIONS

31

ADDITION |31 SUBTRACTION |37 MULTIPLICATION |41 DIVISION |45 SELF TEST 2: INTEGER OPERATIONS |49

3. TRANSFORMATIONS

51

TRANSLATIONS |51 REFLECTIONS AND ROTATIONS |57 LINE SYMMETRY |63 SELF TEST 3: TRANSFORMATIONS |68

4. REVIEW

70

GLOSSARY |79

LIFEPAC Test is located in the center of the booklet. Please remove before starting the unit.

Section 1 |1

Integers and Transformations | Unit 9

Author: Glynlyon Staff Editor: Alan Christopherson, M.S.

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Unit 9 | Integers and Transformations

Integers and Transformations

Introduction

In this workbook, you will be introduced to the topic of integers and transformations. The set of numbers that you use for math will grow to include negative numbers. You will use a number line to represent and compare integers. You will learn about absolute value to show the distance of an integer from zero. You will learn the four basic operations for integers (addition, subtraction, multiplication, and division). You will find that operations with integers are similar to operations with whole numbers, but the rules made it easy to determine the sign of the result. For instance, we know that 5 ? 6 = 30, so -5 ? 6 = -30 because the signs of the factors are different. Your knowledge of the coordinate plane will expand to include all four quadrants and to include negative coordinates. You will learn about three transformations that preserve size and shape while a figure moves in the coordinate plane: translations, reflections, and rotations. You will see similarities between reflections and line symmetry. You will use integers frequently in your future math studies and learn more about transformations and the coordinate plane as you begin to see the connection between algebra and geometry.

Objectives

Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC?. When you have finished this LIFEPAC, you should be able to:

z Represent integers as points on the number line. z Compare and order integers. z Find the absolute value of a number. z Add, subtract, multiply, and divide with integers. z Know that translations, reflections, and rotations preserve size and shape. z Determine the effect of a translation or a reflection on a point in the coordinate plane. z Identify whether a figure has been rotated, and the degree of rotation. z Identify line symmetry.

Section 1 |3

Integers and Transformations | Unit 9

Survey the LIFEPAC. Ask yourself some questions about this study and write your questions here. ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________

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