NSW Maths (Years 7 to 10)
Ordering and Comparing Integers: Number Lines, Negatives and Everyday Contexts
Negative numbers trip up a surprising number of students, and the reason is almost always the same: they judge integers by their digits alone and ignore the sign. That habit works fine for whole numbers, but the moment negatives appear, it leads to backwards answers. Maths teachers see this constantly in school assessments, and the good news is that one simple habit, always using a number line, fixes the problem almost immediately.
What the syllabus asks
The NSW Mathematics 7–10 curriculum expects you to order and compare integers, including negative numbers that appear in everyday contexts such as temperature and money. You need to be able to place integers correctly on a number line and use that placement to decide which number is larger or smaller.
The idea, explained
The number line rule
The single most important fact in this concept is this: on a number line, the number further to the right is always the larger number. This is true whether you are comparing two positive numbers, two negative numbers, or a mix.
For whole numbers you already know this from primary school. Ordering 5, 12, and 30 is straightforward because 30 sits furthest to the right, then 12, then 5.
Negative numbers extend the number line to the left of zero. Every negative number sits to the left of zero, which means every negative number is smaller than zero. Numbers like -1 or -2 sit just to the left of zero, while numbers like -8 or -15 sit much further to the left.
Worked example: which is larger, -3 or -8?
Step 1. Locate -8 on the number line. It is eight steps to the left of zero.
Step 2. Locate -3 on the number line. It is three steps to the left of zero.
Step 3. Compare positions. -3 sits to the right of -8 on the number line.
Step 4. State the answer: -3 > -8.
This surprises many students because the digit 8 is larger than the digit 3. But for negative numbers, a bigger digit means the number is further from zero in the negative direction, which actually makes it smaller. Think of it like a bank account: owing $8 is a worse situation than owing $3.
Everyday context: ordering temperatures
Imagine four overnight temperatures: -4 degrees, 2 degrees, -9 degrees, and 0 degrees. To order them from coldest to warmest, plot each on a number line and read from left to right.
Reading left to right gives: -9, -4, 0, 2.
Written with inequality signs: -9 < -4 < 0 < 2.
The coldest temperature is -9 degrees because it sits furthest to the left.
Practice variations to try
- Compare -9 and -2 using < or >. (Answer: -9 < -2, because -2 is closer to zero and sits further right.)
- Order 7, -3, 0 from smallest to largest. (Answer: -3, 0, 7.)
- Order -15, -6, -20 from smallest to largest. (Answer: -20, -15, -6.)
- Stretch question: four nights had lows of -2 degrees, -11 degrees, 4 degrees, and -6 degrees. List them coldest to warmest. (Answer: -11, -6, -2, 4.)
What the exam asks
School assessment questions on this concept typically ask you to:
- Place a set of integers in order from smallest to largest, or largest to smallest.
- Insert a < or > symbol between two integers.
- Interpret a real-world scenario (temperatures, floors in a building, bank balances) and order the values.
The key habit that earns marks is showing your reasoning. Sketch a number line, mark the values, and read off the order. Maths teachers can award method marks even if you make a small arithmetic slip, provided your working shows the correct approach.
Common mistakes
- Judging negative numbers by digit size alone. Writing -8 > -3 because "8 is bigger than 3" is the most common error. Always plot on a number line first; -3 sits to the right of -8, so -3 > -8.
- Placing zero after negative numbers. Some students order -3, 0, 2 as 0, -3, 2, treating zero as the starting point. On the number line, zero sits to the right of every negative number, so all negatives come before zero.
- Skipping the number line and guessing. Without a number line, it is easy to mix up the order of several negatives such as -15, -6, and -20. Plotting first removes the guesswork.
- Forgetting the sign when copying an answer. After correctly ordering on a number line, some students drop the minus sign when writing the final list. Check each value includes its sign.
- Assuming a negative number is always smaller than a positive one, but not checking between two negatives. Students who understand that -5 < 3 sometimes still write -5 > -20 incorrectly. The number line rule applies to all comparisons, not just negative-versus-positive ones.
If you want step-by-step practice with instant feedback, Avocado's AI-native tutoring service walks you through each of these ideas at your own pace. Try the Ordering and Comparing Integers lesson to build confidence before your next school assessment.