Integers, Positive Numbers, Negative Numbers, Absolute Value

busrabozkurtt, Jan 15, 2023

This book created for 3 objectives in [i]Turkish curriculum[/i]. These objectives are: [b]M.6.1.4.1.[/b] Recognizes integers and displays them on the number line. [b]M.6.1.4.2. [/b]Compares and sorts integers. [b]M.6.1.4.3.[/b] Determines and gives meaning to the absolute value of an integer. [b]Integer:[/b] An integer is a whole number (not a fractional number) that can be positive, negative, or zero. [b]Absolute Value:[/b] [i]The absolute value of a number is its distance from zero on the number line.[/i] To understand the absolute value, we need to understand negative and positive numbers in integers. Sorting and operations on integers help us to better understand the absolute value.

Table of Contents

  1. Remembering Part: Operations of Integers
    1. Discovering Rules in Adding Integers
    2. Adding integers with a number line
    3. Adding Integers
    4. Quiz: Adding Integers
    5. Adding Positive & Negtive Integers
  2. Integers on Number Line & Ordering
    1. 08.13 High Places, Low Places
    2. Exploring integers on a temperature scale
    3. Arrange Ascending Order
  3. Absolute Value
    1. Absolute Value and Distance
    2. Absolute Value
    3. Fun with Absolute Value
    4. Absolute Value Expedition: Acorn Adventure

1.

Remembering Part: Operations of Integers

[b]Remembering integers will help us better understand the absolute value.[/b] [i]Arithmetic operations[/i] on integers can be better explained on a number line. To begin with, one must know to locate integers on a number line. Zero is the middle point of a number line. All positive numbers occupy the right side of zero, whereas negative numbers occupy the left side of zero. [b]Addition of Integers:[/b] [i]Positive numbers:[/i] When we add two positive numbers, the result will always be a positive number. Hence, on adding positive numbers, the direction of the move will always be to the right side. For example, addition of 1 and 5 (1 + 5 = 6) Here the first number is 1, and the second number is 5; both are positive. First, locate 1 on a number line. Then moving 5 places to the right will give 6. [i]Negative numbers: [/i] When we add two negative numbers, the result will always be a negative number. Hence, on adding negative numbers, the direction of the move will always be to the left side. For example, the addition of -2 and -3 Here the first number is -2, and the second number is -3; both are negative. Locate -2 on a number line. Then moving 3 places to the left will give -5. [b]Subtraction of Integers:[/b] [i]Positive numbers:[/i] When we subtract two positive numbers, move to the left as far as the value of the second number. For example, subtract 5 from 2 Here the first number is 2, and the second number is 5; both are positive. First, locate 2 on a number line. Then moving 5 places to the left will give -3. [i]Negative numbers:[/i] When we subtract two negative numbers, move to the right as far as the value of the second number. For example, subtract -4 from -2 First, locate -2 on a number line. Then moving 4 places to the right will give 2.

  • 1. Discovering Rules in Adding Integers
  • 2. Adding integers with a number line
  • 3. Adding Integers
  • 4. Quiz: Adding Integers
  • 5. Adding Positive & Negtive Integers

1.1.

Discovering Rules in Adding Integers

Use this applet (adding integers using number line) to do the following exploration below.
Move the sliders to add the given integers.
Exploration 1: For numbers 1 & 2, perform the addition of Integers using the number line
1) 3+(-3)=[br][br][br]
2) -5+5=
Choose the best way to describe the integers we are adding in nos. 1 &2.
Observing the sums in nos. 1 & 2, what do you think is the sum of -539+539?
Try to explore more the sum opposite numbers: (a) 1+(-1) (b) -4+4 (c) -2+2
Tell whether the statement below is true or false.[br]The sum of any 2 opposite numbers is always 0.
There are two possible operations to perform in with the absolute values of the integers being added.
1) Add or[br]2) Subtract
Exploration 2: Adding different-signed integers
a) -5+3=
b) 5+(-3)=
How do you describe the direction of the integers we are adding in items a& b?
Exploration 2: Adding Integers with same signs.
Describe the sign of the sum for nos. 1 & 2.
Exploration 3: Adding integers with the same sign.
a) 5+4[br]b) -3+(-2)[br]c) -1+(-5)
What do you think happen when adding integers of the same sign.
– Shannon Bryant, TeacherBryan, Guillermo Bautista

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2.

Integers on Number Line & Ordering

We need to learn how to show whole numbers in a number line.

  • 1. 08.13 High Places, Low Places
  • 2. Exploring integers on a temperature scale
  • 3. Arrange Ascending Order

2.1.

08.13 High Places, Low Places

1. Which point in the ocean is the lowest in the world? What is its elevation?
2. Which mountain is the highest in the world? What is its elevation?
3. If you plot the elevations of the mountains and trenches on a vertical number line, what would 0 represent? What would points above 0 represent? What about points below 0?
4. Which is farther from sea level: the deepest point in the ocean, or the top of the highest mountain in the world? Explain.
– Brittany Darby, IM 6 - 8 Math

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3.

Absolute Value

The absolute value of a number is its distance from zero on the number line.

  • 1. Absolute Value and Distance
  • 2. Absolute Value
  • 3. Fun with Absolute Value
  • 4. Absolute Value Expedition: Acorn Adventure

3.1.

Absolute Value and Distance

Look at the number line below. Drag the slider to change the value of a. The distance of a from 0 on the number line will be shown, as well as the absolute value of a. Answer the following questions. [br]1. As a gets larger in the positive direction, what happens to the distance from 0? To the absolute value?[br]2. As a gets more negative, what happens to the distance from 0? To the absolute value?[br]3. Is there a value of a that creates a negative absolute value? [br]4. How are absolute value and distance from 0 related? [br]5. Give an example of two different numbers that have the same absolute value. Explain why they have the same absolute value.
Absolute Value and Distance
– Mathguru, rbwalker15

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