Unit 1 · Number Foundations
Comparing and Ordering Integers
Use number-line position, inequality symbols, and absolute value to compare and order integers reliably.
Recommended prerequisites
0–3 minutes
Learning Objectives
- ✓Compare any two integers using <, >, or =.
- ✓Order a set of integers from least to greatest or greatest to least.
- ✓Explain why a negative number closer to zero is greater.
- ✓Apply integer comparisons to temperature, elevation, and account balances.
3–10 minutes
Warm-up
Which location is higher: a cave at −35 m or a tunnel at −18 m?
Reveal explanation
The tunnel at −18 m is higher because −18 is greater than −35.
10–23 minutes
Core Teaching
1. Compare by position
On a number line, the value farther right is greater. This single rule works for positive numbers, negative numbers, and zero.
For example, −4 is to the right of −9, so −4 > −9.
2. Use inequality symbols
The open side of < or > faces the greater value, while the pointed side faces the smaller value.
Read −7 < 2 as ‘negative seven is less than two’ and 5 > −1 as ‘five is greater than negative one.’
3. Order several integers
To arrange integers from least to greatest, imagine moving from left to right on a number line.
Separate negative numbers, zero, and positive numbers. Among negatives, the number with the larger absolute value is smaller.
4. Apply comparisons in context
A higher temperature has the greater integer. A deeper elevation has the smaller integer. A larger debt is represented by a more negative balance.
Always identify what zero represents before comparing values in a real situation.
23–33 minutes
Guided Practice
1.Insert < or >: −6 ___ −10
Hint: Which value is farther right?
Answer: −6 > −10
2.Order 4, −3, −8, 0, 2 from least to greatest.
Hint: Begin with the value farthest left.
Answer: −8, −3, 0, 2, 4
3.Which balance is better: −$12 or −$40?
Hint: The greater number represents less debt.
Answer: −$12
33–40 minutes
Independent Practice
- 1.Insert <, >, or =: −15 ___ −9.
- 2.Order −1, 7, −6, 3, 0 from greatest to least.
- 3.The morning temperature was −4°C and the afternoon temperature was 2°C. Which was warmer?
- 4.Write the least and greatest values in this set: −20, 5, −2, 0, 11.
Check independent-practice answers
- 1. −15 < −9
- 2. 7, 3, 0, −1, −6
- 3. 2°C
- 4. Least: −20; greatest: 11
40–45 minutes
Lesson Check
Answer every question. A score of 80% or higher marks this lesson complete.
Lesson Summary
- •The integer farther right on a number line is greater.
- •Use < for less than and > for greater than.
- •Ascending order goes from least to greatest; descending order reverses it.
- •Context does not change integer order, but it helps explain what the comparison means.