Unit 1 · Number Foundations
Understanding Positive and Negative Numbers
Learn how integers describe direction and position, compare them accurately, and use opposites and absolute value.
0–3 minutes
Learning Objectives
- ✓Recognize positive numbers, negative numbers, and zero.
- ✓Place integers correctly on a number line.
- ✓Compare integers using <, >, and =.
- ✓Interpret negative numbers in real-world situations.
3–10 minutes
Warm-up
A city is 4°C in the afternoon and −3°C at night. Which temperature is colder?
Reveal explanation
−3°C is colder because it lies farther left on a number line.
10–23 minutes
Core Teaching
1. What do negative numbers represent?
Positive numbers describe quantities above a reference point. Negative numbers describe quantities below that reference point. Zero is the reference point itself.
Temperature, elevation, money owed, and movement in opposite directions are common situations in which negative numbers are useful.
2. Reading a number line
Numbers increase as you move to the right and decrease as you move to the left.
Every positive integer has an opposite negative integer. For example, 5 and −5 are both five units from zero.
3. Comparing integers
A number farther to the right is always greater. Therefore, 2 > −4 and −3 > −7.
Among negative numbers, the number closer to zero is greater. Use a number line whenever the comparison feels unfamiliar.
4. Opposites and absolute value
Opposites have equal distance from zero but different signs. The opposite of 6 is −6, and the opposite of −9 is 9.
Absolute value ignores direction and measures distance from zero. We write |−7| = 7 and |7| = 7.
23–33 minutes
Guided Practice
1.Which is greater: −2 or −5?
Hint: Locate both numbers on a number line.
Answer: −2, because it is farther to the right.
2.What is the opposite of −11?
Hint: Move the same distance to the other side of zero.
Answer: 11
3.What is |−14|?
Hint: Absolute value is distance from zero.
Answer: 14
33–40 minutes
Independent Practice
- 1.Order these numbers from least to greatest: 3, −4, 0, −1, 6.
- 2.Write an integer representing 12 metres below sea level.
- 3.Insert <, >, or =: −8 ___ −3.
- 4.Find the opposite and absolute value of −21.
Check independent-practice answers
- 1. −4, −1, 0, 3, 6
- 2. −12
- 3. −8 < −3
- 4. Opposite: 21; absolute value: 21
40–45 minutes
Lesson Check
Answer every question. A score of 80% or higher marks this lesson complete.
Lesson Summary
- •Positive numbers are greater than zero; negative numbers are less than zero.
- •Numbers increase to the right on a number line.
- •A negative number closer to zero is greater than one farther from zero.
- •Opposites have equal distance from zero, and absolute value measures that distance.