Struggling with positive and negative integers?

When children learn about positive and negative integers in Grade 5 or 6, they often struggle with this abstract idea of numbers being negative. At school, they are often taught rules without the children really “getting” them. Here are some simple, practical, and visual ways to help a child understand these concepts.

1. Build the Basics First

Start by explaining what negative numbers mean. Use real-life ideas:

• Elevator analogy: Positive = going up, Negative = going down.

• Bank account: Positive = money you have, Negative = money you owe.

• Temperature: Above zero and below zero.

2. Use a Number Line with Positive and Negative Integers

I cannot stress the importance of using a number line enough.

Draw a number line on a sheet from -20 to +20. Have the child trace his fingers or pen using this number line while doing sums. You can also draw a line on a whiteboard, and for the various additions and subtractions, use a finger or magnetic peg to move along the number line to the right or the left according to the operation.

Examples:

• -7 - 7 Start at -7, move 7 steps left → ends at -14.

• -8 + 15 Start at -8, move 15 steps right → ends at +7.

• 8 - 15 Start at 8, move 15 steps left → ends at -7.

Physically drawing or tracing a line on a board with fingers helps.

3. Tips for Signs (Addition/Subtraction)

Same signs? Add and keep the sign.

Different signs? Subtract and take the sign of the bigger number.

Examples:

• -7 - 7 = -14 → same signs → add and keep the negative.

• -8 + 15 = +7 → different signs → 15 - 8 = 7 → sign of bigger number = positive.

You can also teach this verbally like a chant. Kids remember through rhythm.

4. Multiplication/Division with Signs

This is just sign rules. Don’t worry about the numbers for now.

Same signs = Positive

Different signs = Negative

Examples:

• -4 × -4 = +16 → same signs → positive.

• -6 × 6 = -36 → different signs → negative.

👉 You can create a cheat card like this:

+ × + = + 
- × - = + 
+ × - = - 
- × + = -

And the same for division.

5. Practice with Patterns

Show them patterns like this:

3 - 1 = 2 
3 - 2 = 1 
3 - 3 = 0 
3 - 4 = -1 
3 - 5 = -2
3 - 6 = -3

This helps build intuition and an internal sense of what we mean when we go in either direction on the number line.

6. Use Real-Life Contexts

• Money: You owe ₹4 and borrow ₹3 more. Now you owe ₹7. (–4 – 3 = –7)

• Temperature: It’s –2°C in the morning and drops 5 degrees. Where are you now? (–2 – 5 = –7). I found it especially useful to use temperature to teach negative integers. It also helps a lot to always refer to a number line while doing these sums, as it creates an internal imagination of the number line and the movement of the final value along the line according to the operation they are doing.

7. Online Tools and Games

If your child is responsive to app based learning on online learning, you could try tools like:

• https://www.mathplayground.com

• https://www.khanacademy.org

• Worksheets from https://www.math-aids.com/

• Use apps with number lines, integer tiles, or gamified quizzes.

8. Practice in Short, Fun Bursts

Don’t do too many problems in one sitting. Do 3-4 a day, orally, like a quiz show. You can make it a timed quiz, and don't react negatively, just keep doing every day. Within a few days, the child will get better.

9. Summary Reminder Card (To Pin on Wall)

Integer Sign Rules
➕➖ Rules: 
Same signs = Add, keep the sign   
Different signs = Subtract, sign of bigger number 

✖️➗ Rules: 
Same signs = Positive   
Different signs = Negative

Let the child write it themselves, color and decorate it—ownership helps memory.

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I hope that these small tips will help your child to develop a foundational understanding of how to change signs when performing operations on positive and negative integers. Do share your tips and feedback in our Facebook Group!

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