Grade 7 Integers: Understand Negative Numbers Step by Step

By Future Kids Academy

Negative numbers can make familiar arithmetic feel unfamiliar. For Grade 7 integers, a number line gives every number a place and makes the direction of a calculation visible. Begin with what the signs mean, then practise a few movements before introducing a list of rules.

What are integers?

Integers include negative whole numbers, zero and positive whole numbers: for example, −3, −2, −1, 0, 1, 2, 3. Fractions such as one half are not integers. Zero is neither positive nor negative.

On a number line, values increase as you move right and decrease as you move left. This means −2 is greater than −5: it lies farther right. The digit five is larger than two, but the signed numbers describe positions on opposite sides of a different comparison.

Begin with the lesson’s number-line method

The worked maths example begins with 21 − 2. Start at 21 and move two unit steps left: first to 20, then to 19. Check by adding two back: 19 + 2 = 21. This simple example establishes the movement before a calculation crosses zero.

Now extend the example across zero

Imagine a temperature of 3°C that falls by 5°C. The calculation is 3 − 5.

1. Locate the starting value. Mark 3 on a number line.
2. Choose the direction. Subtracting positive five means moving five steps left.
3. Count the steps. Move to 2, 1, 0, −1, then −2. Each move counts once.
4. Interpret the result. The final temperature is −2°C, which is two degrees below zero.
5. Check with the reverse change. Add five to −2. You return to 3.

Adding to a negative number

For −4 + 7, start at −4 and move seven places right. Four moves reach zero; three more reach 3. So −4 + 7 = 3. Ask your child to split the movement at zero if counting seven steps at once is difficult.

What about subtracting a negative?

Subtraction undoes addition. In 3 − (−2), we undo adding negative two. Adding negative two would move left by two, so undoing it moves right by two: 3 − (−2) = 5. Write the brackets clearly to distinguish the subtraction operation from the sign of the number being subtracted.

Avoid a confusing shortcut

“Two negatives make a positive” is not a general rule for every calculation. For example, −3 + (−2) = −5: starting at −3 and adding negative two moves two places left. Keep addition, subtraction and multiplication rules separate, and ask what the operation means.

For homework, ask your child to name the starting point, direction and distance before calculating. Those three decisions often reveal exactly where an error begins.

More practice with answers

Write your working first, then open each answer to check your method.

Why is −2 greater than −5?

−2 is farther right on the number line. A temperature of −2°C is warmer than −5°C, which gives a useful everyday comparison.