Negative numbers are one of the first topics in Year 7 that genuinely feels new to students. Until now, almost everything your child has done in Maths has involved positive numbers. Suddenly they are being asked to add and subtract values below zero, compare numbers like −2 and −8 and work out why subtracting a negative makes something look bigger rather than smaller.
The good news is that your child has almost certainly encountered negative numbers at least at some point in their lives already. Temperatures below zero, a bank account below zero or basement floors in a lift. The challenge in Year 7 is not understanding that negative numbers exist but rather how to work with them accurately and consistently in other areas of the Year 7 Maths syllabus.
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KEY ARTICLE INSIGHTS:
Integers include all whole numbers: positive, negative and zero. Fractions and decimals are not integers
The number line is the most useful tool for helping your child understand and check integer calculations
The most common mistakes come from memorising rules without understanding why they work
A solid understanding of integers in Year 7 Maths is essential for algebra, which is also introduced in Year 7
Understanding negative numbers and how they link to algebra will be important for high school Maths and ATAR Maths subjects such as Maths Methods
What Are Integers?
An integer is any whole number: positive, negative or zero.
✅ Integers: ..., −3, −2, −1, 0, 1, 2, 3, ...
❌ Not integers: 0.5, 3/4, −1.2, 2.7
Zero sits at the centre and is neither positive nor negative. This catches students out occasionally in worded questions so it is worth being clear about.
The Number Line: Your Child's Most Important Tool
Before anything else, make sure your child is comfortable visualising integers on a number line. This is the foundation for everything that follows.
Numbers increase as you move right.
Numbers decrease as you move left.
This means:
−2 is greater than −8 because it sits further to the right
−10 is less than −1 even though 10 looks bigger than 1
Any negative number is always less than any positive number
A very common mistake is assuming that −8 is greater than −2 because 8 is greater than 2. The negative sign completely changes the comparison. Encourage your child to sketch a quick number line and place 0 in the middle of the line whenever they are unsure which number is larger.
Real-life connections that help:
Situation | Negative means... | Positive means... |
🌡️ Temperature | Below zero (freezing) | Above zero (warm) |
💳 Bank account | Money owed (debt) | Money in the account |
🏢 Lift floors | Basement levels | Floors above ground |
🏔️ Elevation | Below sea level | Above sea level |
🎮 Game score | Points lost or penalty | Points earned |
Integer Rules for Each Operation
This is the part most parents want to feel confident about before helping at home. Here is a summary of all four operations with examples on what to do with positive and negative numbers:
Operation | Rule | Example |
➕ Adding a positive | Move right on the number line | −3 + 5 = 2 |
➕ Adding a negative | Move left on the number line | 4 + (−6) = −2 |
➖ Subtracting a positive | Move left on the number line | 2 − 7 = −5 |
➖ Subtracting a negative | Rewrite as addition, move right | 3 − (−4) = 3 + 4 = 7 |
✖️ Same signs multiplied | Answer is positive | −3 × −4 = 12 |
✖️ Different signs multiplied | Answer is negative | 3 × −4 = −12 |
➗ Same signs divided | Answer is positive | −12 ÷ −3 = 4 |
➗ Different signs divided | Answer is negative | 12 ÷ −3 = −4 |
HELPFUL HINT: The double negative rule — subtracting a negative becomes addition — is the one that confuses students most. Think of it this way: if someone takes away a debt you owe, you are better off. Removing something negative has a positive effect.
Why Understanding Integers Beats Memorising Integer Rules
While it is tempting to teach your child the shortcut: "two negatives make a positive", the problem is that this phrase only applies in certain situations and students often apply it where it does not belong.
For example: −3 + (−4) = −7, not positive 7. Two negatives are being added here. However, the rule "two negatives make a positive" doesn't actually mean just having two negative numbers, it refers to two negative signs in the middle of the operation or when you're being asked to take away a negative number (e.g. 3 - (-4) = 7).
In our Year 7 Maths tutoring lessons, integers come up constantly in algebra. We find that a student who understands how negative numbers actually work on a number line will handle equations like 2x − 5 = −11 far more confidently than one who has just memorised positive and negative number rules. We always start with the number line in our tutoring lessons to build up familiarity with integers before moving onto harder applications such as algebra or integer worded problems.
Practice Year 7 Integer Questions with Solutions
Try these with your child before looking at the solutions at the bottom of the page.
Question 1: −4 + 9
Question 2: 6 − 10
Question 3: −3 + (−5)
Question 4: 2 − (−7)
Question 5: −4 × 3
Question 6: −6 × −5
Question 7: −20 ÷ 4
Question 8: −15 ÷ −3
Question 9: The temperature in Brisbane is 18°C. Overnight it drops 23 degrees. What is the temperature in the morning?
Question 10: Mia has $12 in her bank account. She spends $20. What is her account balance?
Common Negative Number Mistakes to Watch For
1) Comparing negative numbers incorrectly
Your child assumes −9 > −2 because 9 > 2. Remind them to picture the number line. −2 is closer to zero and therefore greater.
2) Confusing the negative sign with a subtraction sign
In the expression 5 + (−3), the minus sign belongs to the number −3, not to the operation between 5 and 3. Writing it in brackets helps separate the two.
3) Applying the double negative rule incorrectly
The double negative shortcut only applies when there are two negative signs in the middle of the operation (e.g. 3 - (-4) = 7) or you are multiplying (-3 x -2 = 6) or dividing (-6 / -2 = 3).
4) Not showing working for multi-step problems
Encourage your child to write each step separately, especially when combining negative numbers with brackets and order of operations. Errors made mentally are hard to find and correct.
How This Connects to the Rest of Year 7 Maths Syllabus
Positive and negative integers do not stay in their own topic in high school Maths. They appear immediately in algebra, which your child is also learning in Year 7. Equations like 3x + (−5) = 10 or finding the value of −2x when x = 4 both require a solid understanding of how negative numbers work. Students who are not confident with integers tend to find algebra significantly harder as a result.
Negative number questions also appear in Year 7 NAPLAN Numeracy, often found inside multi-step worded problems involving temperature changes, bank balances or elevation. Practising integers in real-life contexts is one of the most effective ways to prepare your child for both classroom assessments and the Year 7 NAPLAN.
Understanding negative numbers is foundational for Year 7 and beyond. It feeds directly into algebra, measurement and statistics as the year progresses. When students understand the rules conceptually rather than just as phrases to recall, they make far fewer errors and adapt much better when the questions look unfamiliar.
How to Help at Home
You do not need to remember all the negative number rules yourself to help your child.
A few guiding questions are often more useful than showing them the answer:
Which direction are you moving on the number line?
Should the answer be bigger or smaller than what you started with?
Is the answer positive or negative and does that make sense in context?
Can you sketch a number line to check?
When to Get Extra Year 7 Maths Tutoring Support
If your child consistently reverses the order of negative numbers, applies the wrong rule or relies on memorised phrases that they cannot explain, those are signs the underlying concept has not clicked yet. More practice alone will not fix this. What helps is working through the number line model with someone who can explain why each rule works, not just what it is.
At Cloud Tuition, our Maths tutoring sessions for Year 7 students address integer gaps directly and connect them to algebra so your child builds understanding in line with the Year 7 Maths curriculum. Your child's first lesson is completely free with no payment details required. Book a free lesson with a Year 7 Maths tutor
Frequently Asked Questions
What are integers in Year 7?
Integers are all whole numbers including positive numbers, negative numbers and zero. They do not include fractions or decimals. In Year 7, your child learns to compare, order, add and subtract integers and is often introduced to multiplication and division of integers as well.
How do you explain negative numbers to a child?
Start with real-life examples your child already understands: temperatures below zero, owing money, basement floors below ground level. Once they can picture what a negative number represents, move to the number line to show how operations work by moving left or right. Understanding the concept first makes the rules much easier to apply correctly.
Why does subtracting a negative give a bigger answer?
Because subtracting something negative is the same as adding its positive. Think of it as removing a debt: if you owe someone $5 and that debt is cancelled, you are $5 better off. Mathematically, 3 − (−5) = 3 + 5 = 8. The two negatives combine to become a positive operation, not a positive number.
Do integers appear in Year 7 NAPLAN?
Yes. Integer questions appear in Year 7 NAPLAN Numeracy, often within multi-step worded problems involving temperature changes, financial contexts or elevation. Practising integers in real-life settings helps your child recognise them in unfamiliar question formats and apply the right approach under time pressure.
What if my child keeps making the same integer mistakes?
If the same errors are recurring despite practice, the issue is usually conceptual rather than effort-related. Drilling more questions will reinforce the mistake rather than correct it. Working through the number line model with a Year 7 Maths tutor who can identify exactly where the understanding breaks down is the most effective way to fix it.
Solutions
Q1: Start at −4, move 9 right → 5
Q2: Start at 6, move 10 left → −4
Q3: Start at −3, move 5 left → −8
Q4: Rewrite as 2 + 7 → 9
Q5: Different signs → −12
Q6: Same signs → 30
Q7: Different signs → −5
Q8: Same signs → 5
Q9: 18 − 23 = −5°C
Q10: 12 − 20 = −$8
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