Integers.

1. Integers

Positive and negative numbers in everyday life • 15–20 minutes

Speaker notes: Integers include positive numbers, negative numbers, and zero. Today’s examples use temperature, money, addition, and subtraction.

2. Positive and Negative Integers

• Positive integers are greater than zero: 1, 2, 3
• Negative integers are less than zero: -1, -2, -3
• Zero is neither positive nor negative
• Temperature: 4°C is above zero; -4°C is below zero
• Money: RM5 means you have RM5; -RM5 can show owing RM5

Speaker notes: A number line helps show that positive numbers are to the right of zero and negative numbers are to the left. Ask what a temperature of -2°C tells us about the temperature compared with zero.

3. Adding Integers

• Same signs: add the numbers and keep the sign
• Example: 3 + 2 = 5
• Example: -3 + (-2) = -5
• Different signs: subtract; keep the sign of the number farther from zero
• Example: -6 + 4 = -2

Speaker notes: For different signs, compare how far each number is from zero: 6 is farther than 4, so the answer to -6 + 4 is negative. Check the examples on a number line if the signs feel confusing.

4. Subtracting Integers

• Change subtraction to adding the opposite number
• Keep the first number; change − to +; change the second number’s sign
• Example: 5 − 2 = 5 + (−2) = 3
• Example: 3 − 7 = 3 + (−7) = −4
• Example: −2 − (−5) = −2 + 5 = 3

Speaker notes: The key step is to rewrite subtraction as addition of the opposite. In the last example, subtracting negative 5 becomes adding positive 5.

5. Choose the Correct Answer

1. Which is a negative integer? A) 6 B) 0 C) −3 D) 2
2. The temperature is −2°C and rises by 5°C. What is it now? A) −7°C B) −3°C C) 3°C D) 7°C
3. What is −4 + (−3)? A) −7 B) −1 C) 1 D) 7
4. What is 6 + (−9)? A) −15 B) −3 C) 3 D) 15
5. What is 4 − (−2)? A) 2 B) −2 C) 6 D) −6

Speaker notes: Each question has one correct answer. Encourage students to show the calculation, especially when deciding whether to add or subtract the numbers.

6. Answers and Summary

• Answers: 1 C, 2 C, 3 A, 4 B, 5 C
• Positive integers are greater than zero; negative integers are less than zero
• For addition, use the signs to decide whether to add or subtract
• For subtraction, add the opposite
• Goal: answer at least 4 of the 5 questions correctly

Speaker notes: Review any question that was difficult by writing the calculation step by step. Remember: subtracting a number is the same as adding its opposite.

1. Which number is a negative integer?

   • a) 0
   • b) 7
   • c) 4
   • d) -3 ✓ (correct answer) Explanation: -3 is less than zero, so it is a negative integer. Zero is neither positive nor negative.

2. What is -4 + (-2)?

   • a) 6
   • b) 2
   • c) -2
   • d) -6 ✓ (correct answer) Explanation: Both integers are negative, so add 4 and 2 and keep the negative sign. The answer is -6.

3. What is 5 - (-3)?

   • a) -2
   • b) 8 ✓ (correct answer)
   • c) -8
   • d) 2 Explanation: Subtracting a negative is the same as adding its opposite: 5 - (-3) = 5 + 3 = 8.

4. Put the steps for solving -2 - (-5) in the correct order.

   • Correct order: Keep the first number: -2. → Change subtraction to addition. → Change -5 to its opposite, +5. → Calculate: -2 + 5 = 3. Explanation: Rewrite subtraction as addition of the opposite. Then calculate -2 + 5, which equals 3.

5. Match each integer calculation to its answer.

   • 4 + (-2) — 2
   • -3 + (-2) — -5
   • 5 - 7 — -2 Explanation: Calculate each expression using integer addition and subtraction rules. For example, -2 - (-4) = -2 + 4 = 2.

6. Complete the sentence about integers.

   • Integers greater than zero are called positive integers / positive numbers. Explanation: Positive integers are the whole numbers greater than zero, such as 1, 2, and 3.

7. Choose the correct answer to complete the sentence.

   • The temperature is -2°C and rises by 5°C. The new temperature is (3°C / -7°C / -3°C). Explanation: A rise of 5°C means add 5: -2 + 5 = 3°C.

8. Sort each number into the correct group.

   • Positive integers: 1, 6, 12
   • Negative integers: -2, -5, -9
   • Zero: 0 Explanation: Positive integers are greater than zero, negative integers are less than zero, and zero belongs in its own group.

9. Decide whether each statement is true or false.

   • A negative integer is less than zero. (true)
   • Zero is a positive integer. (false)
   • -6 + 2 = -4. (true)
   • 3 - 5 = 2. (false) Explanation: Negative integers are below zero, and zero is neither positive nor negative. Also, -6 + 2 = -4, while 3 - 5 = -2.

10. Calculate: -6 + 9

• Answer: 3 Explanation: The signs are different, so subtract 6 from 9 and keep the positive sign. The answer is 3.