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INTRODUCTION
INTRODUCTION
Have you ever checked the weather and saw that the temperature was below zero? Or noticed how money can be added to or taken from a bank account? These everyday situations may seem simple, but they actually involve an important math concept β integers!
Integers are numbers that help us describe situations involving both gains and losses, above and below, increase and decrease, and more. From tracking sports scores to measuring depth under the sea, integers are everywhere in our daily lives.
In this module, you'll explore what integers are, how to represent them on a number line, and how to work with them using basic math operations. Most importantly, you'll discover how useful they are in solving real-life problems.
So, get ready to dive into the exciting world of integers β where both positive and negative numbers have a meaningful place in how we understand the world around us!
π Lesson 1: What Are Integers?Β
Integers are a set of numbers that include:
Positive whole numbers: +1, +2, +3, β¦
Negative whole numbers: β1, β2, β3, β¦
Zero (0)
They do not include fractions or decimals.
π‘ Examples:
+5 (a β±5 deposit into your bank account)
β8 (8Β°C below zero)
0 (no gain or loss in a game)
π§ Think About It:
Why do we need numbers that are less than zero? Where do we encounter these numbers?
π§ͺ Activity:
List at least five situations where you might use integers. Identify whether the integer is positive, negative, or zero.
π Lesson 2: Representing Integers on a Number LineΒ
A number line is a visual tool to compare and order integers.
Zero (0) is at the center.
Positive integers go to the right.
Negative integers go to the left.
π Key Ideas:
The farther right a number is, the greater it is.
The farther left a number is, the smaller it is.
π§ͺ Activity:
Draw a number line from β10 to +10. Plot and label the following integers: β6, β1, 0, 3, 8.
Compare:
Which is greater: β3 or +2?
Which is farther from zero: β7 or +5?
π Lesson 3: Performing Operations on IntegersΒ
This lesson helps you master how to add, subtract, multiply, and divide integers.
β Addition of Integers
Rules:
Same signs: Add the numbers and keep the sign.
(β3) + (β2) = β5Different signs: Subtract and take the sign of the number with the larger absolute value.
(β5) + 3 = β2
Practice:
(+6) + (β8) = ___
(β7) + (β4) = ___
β Subtraction of Integers
Rule:
Change the subtraction to addition by taking the opposite of the second number.
Examples:
4 β (β3) = 4 + 3 = 7
(β6) β (+2) = β6 + (β2) = β8
Practice:
(β5) β (β2) = ___
(+10) β (+6) = ___
βοΈ Multiplication of Integers
Rules:
Same signs β Positive result
Different signs β Negative result
Examples:
(β3) Γ (β5) = +15
(+4) Γ (β6) = β24
Practice:
(+7) Γ (β3) = ___
(β2) Γ (β8) = ___
β Division of Integers
Rules:
Same signs β Positive result
Different signs β Negative result
Examples:
(β12) Γ· (+3) = β4
(+24) Γ· (+6) = +4
Practice:
(β36) Γ· (β6) = ___
(+18) Γ· (β3) = ___
π Lesson 4: Applying Integers in Real LifeΒ
π Situations Where Integers Are Used:
Banking: Deposits (+) and withdrawals (β)
Weather: Below/above zero temperatures
Games: Winning (+ points), losing (β points)
Height/Elevation: Above/below sea level
Business: Profit (positive), loss (negative)
π§ͺ Activity:
Problem 1:
Anna had β±1,200 in her wallet. She spent β±750 and later earned β±500. How much money does she have now?
Problem 2:
The temperature at 6:00 AM was β3Β°C. By noon, it increased by 8Β°C. What is the current temperature?
Challenge Problem:
A scuba diver is at β30 meters. She rises 12 meters, then dives 10 meters deeper. What is her new position?
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