Integers and Negative Numbers Explained for Parents

Negative numbers show up in sixth grade and quickly become part of almost everything in middle school math. Integers are the whole numbers, their opposites, and zero: ... negative 3, negative 2, negative 1, 0, 1, 2, 3 and so on. For many kids, the rules for adding, subtracting, multiplying, and dividing them feel like a list of random facts. The trick is to connect them to things your child already understands.

Where negative numbers show up in real life

• Temperature: 5 degrees below zero is negative 5.
• Money: owing a friend 10 dollars is like having negative 10.
• Elevation: a place below sea level has a negative elevation.
• Sports: yards lost in football, or golf scores below par.
• Floors: basement levels in a building are often labeled with negatives.

Start conversations with these examples before touching rules. If it is 3 degrees and the temperature drops 5 degrees, what is it now? Most kids can answer negative 2 by thinking about a thermometer.

The number line is your best friend

Draw a horizontal number line with zero in the middle, positives to the right, and negatives to the left. Numbers get bigger as you move right. This helps with a common confusion: negative 8 is less than negative 2, because it is farther to the left. Think of temperature: negative 8 degrees is colder than negative 2 degrees.

Absolute value is simply the distance from zero. Both 5 and negative 5 are 5 steps from zero, so both have an absolute value of 5.

Adding and subtracting

1. Adding a positive number means moving right on the number line. Negative 3 plus 5 lands on 2.
2. Adding a negative number means moving left. 4 plus negative 6 lands on negative 2.
3. Subtracting is adding the opposite. 3 minus 7 is the same as 3 plus negative 7, which is negative 4.
4. Subtracting a negative is adding a positive. 5 minus negative 2 is the same as 5 plus 2, which is 7.

That last one confuses nearly everyone. A helpful story: if someone takes away a debt you owe, you are better off. Removing a negative makes the total go up.

Two-color counters make this concrete. Use one color for positives and another for negatives. A positive and a negative together make zero, so they cancel out. Kids can physically see why negative 3 plus 5 is 2.

Multiplying and dividing

The rules here are simpler to state:

• Positive times positive is positive.
• Positive times negative, or negative times positive, is negative.
• Negative times negative is positive.
• Division follows the same sign rules.

A pattern helps explain why negative times negative is positive. Write 3 times negative 2 is negative 6, 2 times negative 2 is negative 4, 1 times negative 2 is negative 2, 0 times negative 2 is 0. Each answer goes up by 2. Continue the pattern: negative 1 times negative 2 must be 2, and negative 2 times negative 2 must be 4. The rule is not arbitrary; it keeps the pattern going.

Common mistakes

• Mixing up the rules for adding and multiplying. Two negatives make a positive only when multiplying or dividing, not when adding. Negative 3 plus negative 4 is negative 7.
• Thinking a bigger digit means a bigger number. Negative 10 is less than negative 1.
• Losing the negative sign while working. Encourage your child to write the sign clearly and circle it if needed.
• Confusing the minus sign with a negative sign. In 5 minus negative 3, there are two different symbols doing two different jobs. Parentheses help: 5 minus (negative 3).

A 10-minute activity: integer card game

Use a deck of cards where black cards are positive and red cards are negative. Remove face cards. Each player draws two cards and adds them; the highest sum wins the round. Later, switch to multiplying, or have each player draw three cards. Keep a number line on the table so your child can check answers when needed. It is a quick way to practice many problems without it feeling like homework.

Build fluency slowly

Integer rules take time to become automatic. Short, regular practice with mixed problems helps more than long sessions on one rule at a time. Ask your child to explain their thinking aloud; if they can describe why an answer makes sense, the rules are becoming real understanding.

Practice for the exact rule that trips them up

Some students have trouble only with subtracting negatives; others mix up adding and multiplying rules. Study Tutor's AI tutor pinpoints the specific difficulty and builds printable practice on that rule, with just enough mixed review.