Study case: adding and subtracting negative numbers with a number line In this Year 7 Negative Numbers Problem Tutor, I use one simple study case to help students understand integers rather than memorise confusing rules. The problem is: calculate -3 + 8 - 10. The answer is -5. I like this example because it includes moving in both directions on a number line and it can also be explained using temperature or money. Before solving, I ask the student to imagine a number line. Negative numbers are to the left of zero and positive numbers are to the right. Starting at -3 means we begin three places below zero. Adding 8 means move 8 steps to the right. From -3, moving 8 steps right lands on 5. Then subtracting 10 means move 10 steps to the left. From 5, moving 10 steps left lands on -5. Method 1 is the number line method. I draw the number line and show each movement. Start at -3. Add 8 to reach 5. Subtract 10 to reach -5. This method is helpful because students can see the direction of movement. It also reduces the fear of negative signs because each operation becomes a movement. Method 2 is the temperature method. I explain the problem as a temperature question. If the temperature starts at -3 degrees, rises by 8 degrees, it becomes 5 degrees. If it then falls by 10 degrees, it becomes -5 degrees. Many Year 7 students understand temperature changes before they fully understand integer rules, so this context can make the calculation feel natural. Method 3 is grouping positives and negatives. The expression -3 + 8 - 10 can be seen as positive 8 and negative parts -3 and -10. The negative parts total -13. Then -13 + 8 = -5. This method is useful once the student is more confident because it prepares them for simplifying longer expressions with positive and negative terms. After the methods, I compare them. The number line method is best for understanding. The temperature method gives a real-life context. Grouping positives and negatives is efficient for longer calculations. I want students to have all three routes because different questions require different levels of confidence and speed. Common mistakes include thinking that every minus sign means the answer must be negative, moving the wrong way on the number line, confusing subtracting 10 with adding 10, and losing track of the starting point. I use these mistakes gently. If a student moves in the wrong direction, we return to the meaning of add and subtract. If they confuse signs, we use a context such as temperature or debt. This topic is important for KS3 because negative numbers appear in algebra, coordinates, directed numbers, equations and graphs. A student who becomes confident with negative numbers in Year 7 will find later topics much easier. I also connect this work to coordinates, where negative x-values move left and negative y-values move down. A useful extension is to calculate -4 - 7 + 12, then explain the steps using both a number line and a temperature story. Another extension is to compare two negative numbers, such as -6 and -2, and explain why -2 is greater. These exercises build number sense, not just calculation skill. In one-to-one tutoring, I would finish by asking the student to create their own negative number question and solve it using two methods. When a student can create and explain a problem, it shows deeper understanding. My aim is to make negative numbers feel normal, visual and manageable. For support with this topic, students can book one-to-one tutor services: https://www.mastermathstutoring.co.uk/services. For the wider course page, visit KS3 Maths tutoring: https://www.mastermathstutoring.co.uk/ks3. To ask about lessons or availability, use contact MasterMaths Tutoring: https://www.mastermathstutoring.co.uk/contact-me.