Mathematics · Class 1 · Number Systems and Operations · Term 1

Understanding Integers: Positive and Negative

Students will define integers and differentiate between positive and negative numbers using real-world examples like temperature and debt.

• CBSE Learning Outcomes
• NCERT: Class 7, Chapter 1, Integers

About This Topic

Integers form the backbone of number systems beyond natural and whole numbers. They include positive numbers, negative numbers, and zero. Natural numbers start from 1, whole numbers include 0, while integers extend to negatives. Use a number line to show this: positives to the right of zero, negatives to the left. Real-world examples make this clear. Temperatures below zero in hilly areas like Shimla represent negatives. Debt in a shop account shows owing money as negative rupees.

Students differentiate these by plotting on number lines and ordering integers. Key questions guide them to analyse everyday contexts, such as bank balances or floors in a building (basement as negative). Construct number lines with everyday items like sticks or floor markings.

Active learning benefits this topic because students grasp abstract negatives through physical movement and relatable scenarios, building confidence in ordering and comparing integers.

Key Questions

1. Differentiate between natural numbers, whole numbers, and integers.
2. Analyze how negative numbers are used in everyday contexts.
3. Construct a number line to represent and order various integers.

Learning Objectives

• Classify numbers as positive integers, negative integers, or zero.
• Compare and order integers on a number line.
• Analyze the use of negative integers in real-world scenarios like temperature and financial transactions.
• Construct a number line to represent a given set of integers.

Before You Start

Counting Numbers and Zero

Why: Students need to be familiar with counting numbers (1, 2, 3...) and the concept of zero before they can understand numbers that are less than zero.

Basic Addition and Subtraction

Why: Understanding how to add and subtract small whole numbers helps in grasping the concept of moving left or right on a number line, which is fundamental to ordering integers.

Key Vocabulary

Integer	A whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.
Positive Integer	A whole number greater than zero. These are also known as natural numbers. Examples include 1, 2, and 10.
Negative Integer	A whole number less than zero. These are represented with a minus sign. Examples include -1, -2, and -15.
Zero	The number that represents neither a positive nor a negative value. It is the point of origin on a number line.
Number Line	A straight line with numbers placed at equal intervals along its length. It is used to visualize and order numbers, including integers.

Watch Out for These Misconceptions

Common Misconception

Negative numbers are always smaller than positive numbers regardless of value.

What to Teach Instead

On a number line, compare magnitudes and signs. For example, -5 is less than 3, but -2 is greater than -5.

Common Misconception

Zero is not an integer.

What to Teach Instead

Zero is the integer at the centre of the number line, neither positive nor negative.

Common Misconception

Natural numbers include negatives.

What to Teach Instead

Natural numbers are positive integers starting from 1; negatives are part of integers only.

Active Learning Ideas

Number Line Walk

Mark a long number line on the floor with tape and numbers from -10 to 10. Students stand on numbers representing temperatures or heights. They move left for negatives and right for positives, discussing orders. This reinforces positioning.

15 min·Whole Class

Temperature Tracker

Provide thermometers or charts showing Shimla winters. Students plot daily temperatures as integers on personal number lines. They compare and order from hottest to coldest. Relate to real weather data.

20 min·Individual

Debt and Credit Game

Use play money. Students start with zero, add credits (positive) or debts (negative). In pairs, they simulate shop transactions and check balances on mini number lines. Discuss outcomes.

15 min·Pairs

Integer Ordering Cards

Distribute cards with integers like -5, 3, -2, 0. Students arrange in order on desks or walls. Explain reasons using number lines drawn nearby.

10 min·Small Groups

Real-World Connections

• Meteorologists use negative integers to report temperatures below freezing point in places like Leh or Shimla during winter. For example, a temperature of -5°C means 5 degrees below zero.
• Accountants track financial balances using integers. A positive balance means money in the bank, while a negative balance indicates debt or money owed, such as a shopkeeper's ledger showing a customer owes ₹200.

Assessment Ideas

Exit Ticket

Give students a card with three numbers, e.g., 5, -2, 0. Ask them to write one sentence explaining what each number represents in a real-world context (e.g., temperature, bank balance). Then, ask them to arrange these numbers from smallest to largest.

Quick Check

Draw a number line on the board from -5 to 5. Ask students to come up and place specific integers on the line. Ask follow-up questions like, 'Which is greater, -3 or -1?' or 'How many steps is -4 from zero?'

Discussion Prompt

Pose a scenario: 'Imagine you are playing a game where you gain 3 points for a correct answer and lose 2 points for an incorrect answer. If you start with 0 points, what is your score after one correct and one incorrect answer?' Discuss how positive and negative numbers are used to represent gains and losses.

Frequently Asked Questions

What are the differences between natural numbers, whole numbers, and integers?

Natural numbers begin at 1 and count positives like 1, 2, 3. Whole numbers add zero, so 0, 1, 2, 3. Integers include negatives, zero, and positives: ..., -2, -1, 0, 1, 2. Use a number line to visualise: negatives left, positives right. This helps in Class 7 CBSE to extend counting skills logically.

How can we represent integers on a number line?

Draw a straight line with zero in the middle. Mark positives to the right increasing: 1, 2, 3. Mark negatives to the left decreasing: -1, -2, -3. Plot any integer by counting steps from zero. Practice with temperatures or elevations for better understanding in Indian contexts like Himalayan regions.

What are real-world examples of negative integers?

Negative integers appear in temperatures below zero during winters in North India, like -4°C in Delhi fog. Bank overdrafts show debt as -500 rupees. Sea level below ground in mines or basements in multi-storey buildings use -1, -2. These connect maths to daily life effectively.

How does active learning help in understanding integers?

Active learning engages students through hands-on number line walks or games with debt-credit scenarios. They physically move or manipulate objects, making abstract negatives concrete. This builds deeper intuition, reduces fear of negatives, and improves retention. In CBSE Class 7, it aligns with NCERT's emphasis on experiential learning for better problem-solving.